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- Permanent Link:
- https://ufdc.ufl.edu/UFE0013823/00001
## Material Information- Title:
- Search for Radiative Decays of Upsilon(IS) into Eta and Eta-Prime
- Creator:
- POTLIA, VIJAY SINGH (
*Author, Primary*) - Copyright Date:
- 2008
## Subjects- Subjects / Keywords:
- Asymmetry ( jstor )
Barrels ( jstor ) Electrons ( jstor ) Gluons ( jstor ) Mass distribution ( jstor ) Mesons ( jstor ) Photons ( jstor ) Quarks ( jstor ) Radiation counters ( jstor ) Signals ( jstor )
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- Copyright Vijay Singh Potlia. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Embargo Date:
- 7/24/2006
- Resource Identifier:
- 496626238 ( OCLC )
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SEARCH FOR RADIATIVE DECAYS OF UPSILON(IS) INTO ETA AND ETA-PRIME By VIJAY SINGH POTLIA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006 Copyright 2006 by Vijay Singh Potlia To my parents ACKNOWLEDGMENTS I would like to thank all those people who helped me at different stages during the course of this dissertation work. I would, first and foremost like to thank my advisor Dr. Yelton for his invaluable guidance and expertise in the conducted research, and for giving me the freedom to develop and put to test my own ideas in many different aspects. Besides being an excellent mentor, he has always been very patient and is a very understanding person which helped immensely during the -iip. and d ,1-" phases of the analysis. I also thank my Physics teachers Dr. Thorn and Dr. Woodard, and Committee members Dr. Avery and Dr. Tanner at the University of Florida, for inculcating the lessons of 1ir, -i. and for being a source of inspiration. I would like to extend my thanks to the entire CLEO collaboration for setting up the pl.1v.'round for this research. I particularly would like to thank my internal analysis committee members David Besson, Helmut Vogel, Jianchun Wang and especially Rich Galik for all their help and -II.-.i -lions to improve this work. Many thanks to Hanna Mahlke-Krueger and Basit Athar for their help. I also thank my fellow colleagues Luis Breva, Valentin Necula, G. Suhas, and many others for fruitful phli -i -, discussions. I also thank the computer staff at the University of Florida, especially David Hansen for his computing help. Rukhsana Patel, Sanjay Siwach, Sunil Bhardwaj, and Lakhan Gusain have been extremely supportive friends during this long journey. I can not thank them enough. I owe many thanks to my parents Ranbir and Premlata, and my cousin Fateh. Last but not the least, the most important person without whose support and endurance this dissertation would not have been completed is my wife Nisha. I thank her for being by my side in all odds and for her love and patience which served as my guiding torch. TABLE OF CONTENTS page ACKNOWLEDGMENTS ................... ...... iv LIST OF TABLES ........ ...... ............... viii LIST OF FIGURES ........ ....................... ix ABSTRACT .. .. ........................... xv CHAPTER 1 THEORY ............. .... ........... .... 1 1.1 Particle Physics and the Standard Model ....... ..... ... 1 1.1.1 The Standard Model: Inputs and Interactions ....... 1 1.1.2 Quantum Chromodynamics ...... ............. 4 1.1.3 Sym m etries . . . . . . 6 1.1.3.1 Isospin ........... ...... ....... 7 1.1.3.2 Parity . . . . . . 7 1.1.3.3 Charge conjugation ......... ........ 9 1.1.3.4 G-Parity ................... .. 10 1.1.4 Mesons ....... ....... ....... .. ....... 11 1.2 Quarkonia ...... ....... ..... ... ... 13 1.2.1 Decay Mechanisms of T(1S) ... . . 13 1.2.2 Radiative Decays of T(1S) into rl and . . ... 15 2 EXPERIMENTAL APPARATUS ................. .. .. 19 2.1 Cornell Electron Storage Ring ................... ... .. 19 2.1.1 Linear Accelerator .................. .... .. 19 2.1.2 Synchrotron .................. ........ .. 21 2.1.3 Storage Ring .................. ...... .. .. 21 2.1.4 Interaction Region ...... ....... .. .. .. 22 2.2 T Resonances .................. ........... .. 23 2.3 CLEO III Detector .................. ........ .. 24 2.3.1 Superconducting Coil ................. . .. 26 2.3.2 Charged Particle Tracking System . . ..... 26 2.3.2.1 Silicon Vertex Detector . . ...... 27 2.3.2.2 The Central Drift Chamber . . 28 2.3.3 Ring Imaging Cherenkov Detector . . ..... 30 2.3.4 Crystal Calorimeter ................ .... .. 32 2.3.5 Muon Chambers .................. ..... .. 34 2.3.6 CLEO III Trigger . .. . . . 35 3 DATA ANALYSIS .. .............. ......... ..38 3.1 Data ....... ......... .. ...... ...... 38 3.2 Skim and Trigger Efficiency ................ .. .. 39 3.3 Reconstruction ........... . . ... 43 3.3.1 Reconstruction of T(1S) 7q; r 7+ r-t . ... 47 3.3.2 Reconstruction of T(IS) qy7 ; 7 Tr0 . . 54 3.3.3 Reconstruction of T(IS) .qy ; r . . 59 3.3.3.1 Possible Background e+e- 7( e+e-) . 61 3.3.3.2 Handling e+e- yyy background . ... 61 3.3.3.3 Final Selection and Comparison of Neural Net vs Asymmetry ........ .... ....... 64 3.3.3.4 Data Plots and Upper Limit . . ... 67 3.3.4 Reconstruction of T(IS) 7y'; . . 73 3.3.5 Reconstruction of T(1S) 7 ''; .Tr . . 78 3.3.6 Reconstruction of T(IS) 77'; 7+r -"r .... . 81 3.3.7 Reconstruction of T(1S) q '; p . . 87 3.4 Summary .................. ............. .. 97 4 SYSTEMATIC UNCERTAINTIES AND COMBINED UPPER LIMIT 99 4.1 Systematic Uncertainties .................. ... .. 99 4.1.1 Trigger Considerations .............. .. .. .. .. 99 4.1.2 Standard Contributions . . ..... ... 100 4.1.3 Contributions from Event Selection Criteria . ... 101 4.2 Combined Upper Limits ................ .. .. 106 5 SUMMARY AND CONCLUSIONS ............. ... .. 113 APPENDIX EVENT VERTEX AND RE-FITTING OF 7" -- .7 ...... 115 REFERENCES ................... ............. 119 BIOGRAPHICAL SKETCH .................. ......... .. 121 LIST OF TABLES Table page 1-1 Basic fermions and some of their properties ... . ... 3 1-2 Gauge bosons and some of their properties ..... . . 3 1-3 Symbol, name, quark composition, mass in units of MeV/c2, angular momentum (L), internal spin (S), parity (P), and charge conjugation eigenvalues (C) for a few of the particles used in this analysis. . 12 1-4 Theoretical branching fractions as predicted by various authors for radiative decays of T(1S) into 7r and r' .................. ..... 17 1-5 Product branching ratios for decay modes of r and . .... 18 3-1 Liiir.-ili numbers for various data sets used in the analysis . 39 3-2 Efficiency (in %) of basic cuts for rl modes ................ ..42 3-3 Efficiency (in %) of basic cuts for rl' modes ................ ..42 3-4 Efficiency of selection criteria for the mode T(1S) 7rq; ] 7+rr-7 47 3-5 Efficiency table for the mode T(1S) -- 7yr; r] 7r 7. . . 55 3-6 Final efficiency table for the mode T(1S) q 7r; 7 . . 66 3-7 Final efficiency table for the mode r]' rl+r- and then 77 . 73 3-8 Final efficiency table for the mode r]' rl+t- and then r] 7000 78 3-9 Final efficiency table for the mode T(1S) -- 7rq'; r -- 7r+7-7 . 82 3-10 Efficiency table for the mode T(1S) -- 7r'; r' 7p . . 89 4-1 Systematics' table for T(1S) 7rq'; r' p 7 ..... . . 101 4-2 Systematics uncertainties for various decay modes of . . 105 4-3 Systematics uncertainties for various decay modes of . ... 105 4-4 Results of the search for T(1S) 77r' and T(1S) 77r. Results include statistical and systematic uncertainties, as described in the text. The combined limit is obtained after including the systematic uncertainties. 108 LIST OF FIGURES Figure page 1-1 Simple gluon-exchange diagram .................. ...... 4 1-2 Lowest order decays of the T(1S) allowed by color conservation, charge conjugation symmetry, and parity. (a) Shows the decay into three gluons, (b) shows a radiative decay, and (c) shows the electro-magnetic decay through a virtual photon that in turn decays electro-magnetically into a pair of charged fundamental particles, such as quarks or charged leptons (the charged leptons are represented by the symbol ). . . 15 2-1 Wilson Laboratory accelerator facility located about 40 feet beneath Cornell University's Alumni Fields. Both the CESR and the synchrotron are engineered in the same tunnel. .............. .... 20 2-2 Visible cross section in e+e- collisions as a function of center of mass energy. Plot (a) on the left shows peaks for T(nS) for n = 1,2,3, and 4. Plot (b) on the left shows T(5S) and T(6S) as well as a blow up for T(4S) resonance. .................. ................ ..23 2-3 The CLEO III detector. .................. ..... 25 2-4 View of the SVD III along the beampipe. ..... . . ...... 28 2-5 The RICH detector -i,-i, -I, 1- .. ................. . 32 2-6 Two kinds of RICH LiF radiators. For normal incidence particles (z 0) a sawtooth radiator is necessary to avoid internal reflection. ...... .. 33 3-1 Candidate rl -- 7r+7r-7 reconstructed invariant mass distribution from signal Monte Carlo for the mode T(1S) -- 7q; r -- 7+7-70. The reconstruction efficiency is 32.8 0.4% after all the cuts. ............... .. 49 3-2 Distribution from signal Monte Carlo: For the mode T(1S) 7'r; r - 7+7-7 variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) o(T of the 7r candidate, plot(b) for S dx, plot(c) for 4, and plot(d) is a scatter plot of the pion hypothesis SdEldx for the charged tracks. . . ...... 50 3-3 Invariant mass of distribution of the tr candidate for the mode T(1S) -- 7y; ty -- 7+7-7 0: Plot(a) with no cuts, plot(b) with a cut on x4 only, plot(c) after cutting on o,< of the 7 candidate only, plot(d) after cutting on S2 n SdE/dx alone. The red overlay on plot(d) is obtained after imposing all the cuts. No candidate event was observed in signal region ........ 51 3-4 Reconstructed rl candidate invariant mass distribution in real data for the mode T(1S) -- 7rq; r -- 7+7-7o0. No events are observed in the signal mass window denoted by the region in between blue arrows (inset), and a clear ac -- 7 +77-770 peak is visible from the QED process e+e- -- 52 3-5 Scatter plot of eop distribution for track 2 vs track 1 for the events rejected by SdE/dx > 16.0 cut. Most of the rejected events are clearly electron like. 53 3-6 Reconstructed invariant mass distribution for the candidate tr -- o 707070 from signal Monte Carlo for the mode T(1S) -- 7rq; p -- 707070. The reconstruction efficiency is 11.8 0.2% after all the cuts. . ... 56 3-7 Distributions from T(1S) -- 7qy; ] -- 707070 signal Monte Carlo, showing the variables we cut on. The yellow (shaded) area in these plots represents the acceptance. Plot (a) S of the 7i candidates, plot (b) for x4, and plot (c) # of showers in the event. The dashed (red) line in plot (a) shows the h e e 1..-'-' .1 7r candidates. As can be seen, majority of good events are confined within /5 < 10.0, giving us a reason to select our acceptance region. Plot (d) shows the shower multiplicity from the signal MC for the process e+e- -- 7y. Although plot (d) is not normalized to plot (c), we can clearly see that if Monte Carlo be trusted, a cut on the number of showers help reject ~ 50% of this background. . ... 57 3-8 Invariant mass of rl candidate for the mode T(1S) -- 7qr; r -- 70i0o0: Plot (a) allowing multiple candidates per event, plot (b) after selecting best candidate, plot (c) selecting best candidates with x 4 < 200.0, plot (d) best candidate with # of showers cut. The red ov,-l.'iv on plot (d) is obtained after imposing all the cuts. There are no events in the acceptance mass window (denoted by blue arrows) after all the cuts. . ... 58 3-9 '/1 vs AE distribution plot(a) for signal MC for T(1S) -- 7r; r] 77 and plot(b) for e+e- --777 MC. .................. .... 59 3-10 Asymmetry distribution for r candidate. Plot (a) from Monte Carlo data for e+e- -- 777 (black) and signal MC T(1S) -- 7r; r Y77 (red) and plot (b) for datal8 and datal9. For asymmetry < 0.75, the events in plot (b) are overshadowed by the events beyond asymmetry > 0.75. The huge pile at the higher in end in plot (b) is because in this plot, the events classified as gamGam event-type have not been rejected yet . .. 60 3-11 Distribution of AO vs AO in real data for events in the 7r mass window passing our basic cuts. .................. ...... 62 3-12 Training the Neural Net: During the course of ti.iiii. red denotes the training error and black denotes the testing error (shifted by 0.02 for clarity) from an independent sample. The testing error follows the training errors closely and over-training is not exhibited at all. The learning process saturates however, and training is stopped after 10K iterations. . 65 3-13 Comparison of background rejection vs efficiency: The lower curve in red shows the performance of asymmetry cut and upper curve in black is from neural net. For any chosen value of efficiency, neural net gives a higher background rejection as compared to asymmetry cut. Inset is S/ B plotted for various values of neural net cut. . . ... 66 3-14 77 invariant mass distribution from signal Monte Carlo for the mode T(IS) q 7 -r; .r .- 77 .................. ..... .... 67 3-15 77 invariant mass distribution in real data. All cuts except neural net cut are in place. .................. .............. ..68 3-16 77 invariant mass distribution in real data after all cuts. . ... 69 3-17 Fit to 77 invariant mass distribution for the mode T(1S) -- 7q; 7 -- 77. Leaving the area floating while keeping the mean, width and other parameters fixed to MC fit parameters, we obtain -2.3 8.7 events, which is consistent with 0. .................. .......... ..70 3-18 Normalized probability distribution for different signal area for the mode T(1S) 7; 7 -' 77. The shaded area spans 90% of the probability. 71 3-19 The fit to reconstructed 77 invariant mass distribution from real data for the mode T(1S) -- 7'y; -- 77. The area is fixed to the number of events obtained from 90% confidence level upper limit. The mean, width and other parameters are fixed to the ones obtained from Monte Carlo. 72 3-20 Reconstructed candidate iq' invariant mass distribution from signal Monte Carlo for the mode T(1S) -- 7y'; -- Y77. The reconstruction efficiency is 40.6 0.4% after all the cuts. .................. .... 74 3-21 Distribution from signal Monte Carlo: For the mode T(1S) -- 7'y'; q -- 77, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) 2 distribution, plot(b) for , plot(c) for /x4, and plot(d) is a scatter plot of the dE/dx aT for pion hypothesis for the charged tracks. ................ ..... 75 3-22 Invariant mass of l' candidate for the mode T(1S) -- 7l'; r -- 77: Plot(a) without any cuts, plot(b) after selecting candidates with X2 < 200, plot(c) after dE/dx cut, plot(d) requiring xP4 < 100. The red overlay on plot(d) is obtained after imposing all the cuts. No candidate signal event is observed in our acceptance mass window (denoted by blue arrows). . ... 76 3-23 Extended range of invariant mass distribution of r' candidate for the mode T(1S) -- 7l';r -- 77. No candidate signal event is observed in our acceptance mass window (inset). ................ ..... 77 3-24 Reconstructed invariant mass distribution of the candidate r' from signal Monte Carlo for the mode T(1S) -- 7r'; rl rr0ir0 0: The reconstruction efficiency is 16.6 0.4% after all the cuts. ............... .. 79 3-25 Distributions from signal Monte Carlo: For the mode T(1S) 7rl'; rl r00r0, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) for IX, Plot(b) /x for two tracks, plot(c) for xU4, and plot(d) /- of the 7r candidates. The dashed (red) line in plot(d) shows the V5 of the t.-'-, d 70 candidates. As can be seen, majority of good events are confined within S < 10.0 giving us a reason to select our acceptance region. ..... . . 80 3-26 Invariant mass of r]' candidate for the mode T(1S) -- 7r'; r] -> 7000: We found two events when no cuts are in place. None of the two events in the q' invariant mass histogram survive the /x4 < 200 requirement.. .81 3-27 Extended range of invariant mass distribution of r' candidate for the mode T(1S) 7r'i; pr -- r0700. No candidate signal event is observed in our acceptance mass window .................. .. .... .. .. 82 3-28 Reconstructed candidate r' invariant mass distribution from signal Monte Carlo for the mode T(1S) -- 7r'; r 7i+f7-70: The reconstruction efficiency is 24.5 0.5% after all the cuts. ............... .. 83 3-29 Distribution from signal Monte Carlo: For the mode T(1S) -- 7r'; r- 7+7-7 0, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) for /x4, plot(b) for a, of 7r candidate plot(c) for ,,, and Plot(d) SdE/dx for all four tracks. 84 3-30 Invariant mass of r]' candidate for the mode T(1S) -- 7r'; r] -- 7+7-70: Plot(a) with no cuts, plot(b) with the requirement 4 < 100, plot(c) with pion hypothesis consistency in the form dE/dx < 4.0, and plot(d) with all the cuts. We find two candidate events. .. . . ...... 85 3-31 Extended range of invariant mass distribution of r' candidate for the mode T(1S) 7rl';rl r+r7-70. Two good candidate signal events are observed in our acceptance mass window (inset). . .... 86 3-32 Reconstructed 7p candidate invariant mass distribution from signal MC for r -Y7p: The kinematic fitting improves the invariant mass resolution by w 30% and reconstruction efficiency by w 5 .......... ..89 3-33 Reconstructed invariant mass distribution from signal Monte Carlo for the mode T(1S) -- 7q'; r' -- 7'p: The reconstruction efficiency is 40.1 0.4% after all the cuts. ... .. .. .. ... .. .. .. ........... .. 90 3-34 Reconstructed invariant mass distribution in real data for the mode T(1S) -- yrl'; rl -7p: In top plot, black histogram shows the distribution from IS data and overlaid in red is the scaled distribution from 4S data. The bottom plot after subtracting the continuum. We assume the same reconstruction efficiency at 4S energy. .................. .... 91 3-35 Without continuum subtraction, the fit to data plot for the mode T(1S) -- 7yrl; rl -7p: Leaving the area floating while keeping the mean, width and other parameters fixed to MC fit parameters, we obtain -3.1 5.3 events. 92 3-36 The fit to the continuum subtracted data plot for the mode T(1S) -- '; r/ -- 7-p: Leaving the area floating while keeping the mean, width and other parameters fixed to MC fit parameters, we obtain -3.5 6.3 events. The underlying continuum has been subtracted using the distribution from 4S data .................. ................. .. 93 3-37 The normalized probability distribution for different signal area for the mode T(1S) -- 7ql'; rl -7p: The shaded area spans 90% of the probability. 94 3-38 The 90% upper limit fit to the invariant mass distribution without continuum subtraction . . . . . . . ... .. 95 3-39 After subtracting the underlying continuum, the 90% upper limit fit to the invariant mass distribution .................. ...... 96 4-1 Amount of background rejected for various values of ..-mm.,,, I, ry and neural net cut having the same efficiency. The TI iT i y" is obtained from signal Monte Carlo. "Background rjei,, I, i is obtained either from QED Monte Carlo sample (red pluses) or from real data (black crosses). . ... 103 4-2 Energy of the hard photon in MC samples after all our selection criteria for respective modes .................. .......... .. 104 4-3 Probability distribution as function of branching ratio for the decay mode T(1S) -- -l: Black curve denotes the combined distribution. The distributions have been normalized to the same area. ..... . ... 109 4-4 Plotted on log-scale, the likelihood distribution as function of branching ratio for the decay mode T(1S) -- yl: Black curve denotes the combined distribution. All distributions have been normalize to the same area. 110 4-5 Probability distribution as function of branching ratio for the decay mode T(1S) -- yr': Black curve denotes the combined distribution. All distributions have been normalize to the same area. .... . .. 111 4-6 Plotted on log-scale, the likelihood distribution as function of branching ratio for the decay mode T(1S) -- 7y': Black curve denotes the combined distribution. All distributions have been normalized to the same area. 112 1 Reconstructed invariant mass distribution of 7+7r-7r candidate from signal Monte Carlo for the mode T(1S) -- 7; r -- 7r+7-70: After all cuts in place, solid black histogram represents the rl -- 7r+7r- candidate invariant mass distribution when 7r candidate is re-fit from the event vertex. Overlay in dotted, red histogram is obtained using default 7r candidates. .. ... .. .. .. .. ... .. ... . .. .... .. .. 117 2 Reconstructed invariant mass distribution of qrl+- candidate from signal Monte Carlo from signal Monte Carlo for the mode T(1S) -- 7'; l 77: After all cuts in place, solid, black histogram represents the rl'; l Y77 candidate invariant mass distribution when l y77 candidate is re-fit from the event vertex. Overlay in dotted, red histogram is obtained using default l y77 candidates. .................. ..... 118 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SEARCH FOR RADIATIVE DECAYS OF UPSILON(IS) INTO ETA AND ETA-PRIME By Vijay Singh Potlia \.,.r 2006 Chair: John M. Yelton AI.., ir Department: Physics We conducted a new search for the radiative decay of T(1S) to the pseudoscalar mesons r] and r' in (21.2 0.2) x 106 T(1S) decays collected with the CLEO III detector operation at the Cornell Electron Strorage Ring (CESR). The r] meson was reconstructed in the three modes r] yy, r] 7r+7r-7 or r] -- 7r0A00. The q' meson was reconstructed in the mode r]' 7+-rq with r] decaying through any of the above three modes; and also rq' 7po, where po -_ 7r+t-. The first six of these decay chains were searched for in the previous CLEO II analysis on this subject, which used a data sample 14.6 times smaller. Five of the seven submodes were virtually background free. We found no signal events in four of them. The only exception was T(1S) 7'r'; -r t 7r+7-70 where we observed two good signal candidates. The other two submodes (r -- 77 and rq -7p) are background limited, and showed no excess of events in the signal region. We combined the results from different channels and obtained 90% confidence level (C.L.) upper limits B(T(1S) -- 7r) < 9.3 x 10-7 and B(T(1S) 7) < 1.77 x 10-6 Our limits challenge theoretical models. CHAPTER 1 THEORY 1.1 Particle Physics and the Standard Model Humankind has always been intrigued by questions like "What is matter made of?" and "How do the constituents of matter interact with each other?" In their quest for fundamental building blocks of matter, l',--i- i- -1 found even more compositeness. The existence of more than 100 elements showing periodically recurring properties was a clear indication that atoms (once thought indestructible and fundamental building blocks) have an internal structure. At the start of the 20th century, the internal structure of the atom was revealed through a series of experiments. The core of an atom (the nucleus) was found to be made of protons and neutrons (collectively called nucleons), surrounded by an electron cloud. This picture of the atom was right; however, the observation of radioactive /-decay and the stability of the nucleus prompted 1.r, -i, i-i to take the reductionist approach farther and a new branch of 'll -i -, was born called as particle ]li, -i. - Modern particle 1.li-,-i -, research represents the most ambitious and most organized effort of humankind to answer the questions of fundamental building blocks and their interactions. Over the last half century, our understanding of particle p11, -i -, advanced tremendously and we now have a theoretical structure (the Standard Model) firmly grounded in experiment that splendidly describes the fundamental constituents of matter and their interactions. 1.1.1 The Standard Model: Inputs and Interactions The Standard Model (1\I) of elementary particle 11r, -i -, comprises the unified theory of all the known forces except gravity. These forces are the electro-magnetic force (well known to us in everyday life), the weak force, and the strong force. In the Standard Model, the fundamental constituents of the matter are quarks and leptons. These constituents are spin-} particles fermionss) obeying Fermi-Dirac statistics. The quarks and leptons come in three generations: * up and down quarks (u, d), and electronic neutrino and electron (V e) * charm and strange quarks (c, s), and muonic neutrino and muon (V p) * top and bottom quarks (t, b), and tauonic neutrino and tauon (V,, T) Each generation has a doublet of particles arranged according to the electric charge. The leptons fall into two classes, the neutral neutrinos v P,, v,, and negatively charged e-, t-, and r-. The quarks u, c, and t have electric charge +2e/3 and the d, s, and b quarks have electric charge -e/3. Each quark is said to constitute a separate flavor (six quark flavors exist in nature). The generations are arranged in the mass hierarchy and the masses fit no evident pattern. The neutrinos are considered as massless. The Standard Model does not attempt to explain the variety and the number of quarks and leptons or to compute any of their properties; the fundamental fermions are taken as truly elementary at the I\! level. Each of the fundamental fermions has an anti-fermion of equal mass and spin, and opposite charge. Other than the electric charge, the basic fermions have two more charges S"color charge" coupling to strong force, an attribute of quarks only (but not leptons), and "weak charge" or "weak i-. -pini" coupling to weak force, carried by all fundamental fermions. The properties of these fermions (Table 1-1) recur in each generation. In the paradigm of Standard Model, the three different types of interactions existing among the elementary particles arise as a natural and automatic consequence of enforcing local gauge symmetry. Each force is mediated by a force carrier, a gauge boson which couples to the charge on the particle. The bosons are spin-1 particles. The guage bosons of '\! are shown in Table 1-2. Table 1-1. Basic fermions and some of their properties Quarks Leptons Flavor Mass Electric Weak Flavor Mass Electric Weak (MeV/c2) charge charge (MeV/c2) charge charge u 2-8 +2e/3 +1/2 v, < 0.000015 0 +1/2 d 5-15 -e/3 -1/2 e 0.511 -e -1/2 c 1000-1600 +2e/3 +1/2 uv < 0.19 0 +1/2 s 100-300 -e/3 -1/2 It 105.7 -e -1/2 t w 175000 +2e/3 +1/2 v, < 18.2 0 +1/2 b 4100-4500 -e/3 -1/2 7 1777.0 -e -1/2 The familiar electro-magnetic force (also called as Quantum Electrodynamics, or QED) is mediated by the exchange of a photon. Only particles with electric charge can interact electro-magnetically. The strong force is mediated by gluons and couples to particles that have color charge. This force is responsible for holding quarks together inside the hadrons (neutron and proton are two example of hadrons). Leptons have no color and thus do not experience strong force. This is one of the primary differences between leptons and quarks. The weak force is mediated by the W' and Z bosons. Particles with weak charge, or weak isospin, can interact via the weak force. The mediators of weak force are different from the photons and gluons in the sense that these mediating particles (W' and Z0) are massive. The weak force thus is a short range force as opposed to electro-magnetic and strong forces which are long-range in nature due to masslessness of photon and gluons. Table 1-2. Gauge bosons and some of their properties Particle Symbol Force Mediated Charge Mass (GeV/c2) jV Photon 7 Electromagnetic 0 0 1- Gluon g Strong 8 colors 0 1- Z Z Weak 0 91.187 1 W W Weak e 80.40 1 1.1.2 Quantum Chromodynamics Strong interactions in the Standard Model are described by the theory of Quantum Chromodynamics (QCD). The quarks come in three primary colors:1 r (red), g (green), and b (blue) and the anti-quarks have complementary colors (or anti-colors) r cyann), g (magenta), and b (yellow). The quarks interact strongly by exchanging color which is mediated by gluon exchange (Figure 1-1). Gluon exchange is possible only if the gluons themselves are colored (carry color charge), and in fact, the gluons carry the color and anti-color simultaneously. The strength of strong interaction is flavor independent. b r g (rb) b r Figure 1-1. Simple gluon-exchange diagram Since there are three possible colors and three possible anti-colors for gluons, one might guess that the gluons come in as many as nine different color combinations. However, one linear combination of color anti-color states has no net color and therefore can not mediate among color charges. Thus only eight linearly independent color combinations are possible. The way in which these eight states are constructed from colors and anti-colors is a matter of convention. One possible choice is shown in Equation 1-1 for the octet, and the color singlet is represented in Equation 1-2, 'rg, rb, gb, gr, br, bg, /2(rr gg), //6(rr + gg 2bb) (1 1) V/3(r+ g + bb) (1-2) 1 The "c(l1,[" in QCD is a degree of freedom describing the underlying 1]l',-i -. and should not be misinterpreted with ordinary colors we see in life. 5 This situation is analogous to the perhaps more familiar example of two spin 1/2 particles. Each particle can have its spin up (1) or down (1) along the z axis corresponding to four possible combinations represented by each giving a total spin S = 0 or 1 represented by IS Sz >. The S = 1 states form a triplet, 1 +1 > TT> |10 > (|I > +1 I>) (1-3) 1 -1>= | > and there is a singlet state with S = 0, 1 |0 0 >- (I T> -I>). (1-4) V2 The proliferation of gluons in QCD contrasts with QED where there is only a single photon. Another striking difference between QED and QCD is that the force carriers in QED, the photons, do not carry any charge. The photons therefore, do not have self-interactions. On the other hand, the gluons in QCD have color charge and thus they undergo self-interactions. In field-theoretic language, theories in which field quanta may interact directly are called -i' .i-Abelian." The gluon self-interaction leads to two very important characteristics of QCD: "color confinement" and I ,-, Iitic freedom." Color confinement means that the observed states in nature have no net color charge: i.e., the observed states are color singlets. An implication of color confinement is that free quarks and free gluons can not be observed in nature. Bound states of two or more gluons having overall zero color charge can be found in principle. Such bound states are referred to as "glueballs." Many experimental searches for such states have been made, without conclusive results, for example [1]. Asymptotic freedom means that the interaction gets weaker at shorter inter-quark distances and the quarks are relatively free in that limit. The phenomenon of color confinement constrains the way quarks combine to form observed particle states. The only combinations allowed (and observed for that matter) are qq forming mesons, and qqq forming '.., .11,- Group-theoretically, it is possible to decompose 3 x 3 (qq) to obtain an octet and a singlet. The color singlet for qq is simply the state shown in Equation 1-2. The color singlet for qqq can be obtained from decomposition 3 0 3 3 = 10( 8 ( 81 and is shown in Equation 1-5, 1 |qqq >color singlet (rgb grb r+brg bgr + gbr rbg). (1-5) V6 The existence of particles with fractional charges, as for example made from bound state qq, is ruled out as it is not possible to obtain a color singlet qq configuration. Group theory quickly tells us that 303 decomposition is 6 ( 3 (a sextet and a triplet, but no singlet). 1.1.3 Symmetries Symmetries are of great importance in pl'i-i. A symmetry arises in nature whenever some change in the variables of the system leaves the essential ]li,--i. - unchanged. The symmetry thus leads to conservation laws -universal laws of nature valid for all interactions, for example, the conservation of linear momentum and angular momentum arise from translational invariance and rotational invariance, respectively. Enforcing local gauge symmetry gives rise to interactions in field theory. Isospin symmetry is responsible for attractive force between nucleons on an equal footing. In particle 1lir, -i. -. the discrete symmetry operations parity and charge conjugation play a special role in particle production and decay. Certain reactions are forbidden due to the constraints imposed by these symmetries -the symmetries thus become dynamics. In the next few sections we review some of these symmetry operations, the details of which can be found in Griffiths [2], Perkins [3], and Halzen and Martin [4]. 1.1.3.1 Isospin The nuclear force between nucleons is the same irrespective of the charge on the nucleon. The proton and neutron are thus treated as two states of a nucleon which form an 'i-.-piii" doublet (I = 1/2), ) (16) with Is, the third component of I, being +1/2 for proton and -1/2 for neutron. The origin of isospin lies in the near i iii.,li iv of the u and d quark masses, so, the idea of isospin can be taken to a more fundamental level where u and d quarks form a doublet which can be transformed into each other in the isospin space. The 13 for an u quark is +1/2 and that for a d quark is -1/2 and based upon this assignment, 13 speaks for the quark flavor. The 13 for anti-quarks is the negative of that of quarks. The treatment of isospin goes very much like quantum mechanical angular momentum. Since strong and electro-magnetic interactions conserve the quark flavor, the third component of isospin is a good quantum number for these interactions. However, total isospin I is not conserved under electro-magnetic interactions as the isotropy of isospin is broken due to different electric charge on the u and d quarks. Only strong interactions conserve both I and Is. 1.1.3.2 Parity The parity operator, P, reverses the sign of an object's spatial coordinates. Consider a particle |a > with a wave function 1a(5, t). By the definition of the parity operator, PT(Y, t) Pa4a(- t) (1-7) where Pa is a constant phase factor. If we consider an eigenfunction of momentum (1-8) ^p(f, t) = e"PY-Et) then PI( ), t) =Papl(-, t) Pa_(, 0), (1 9) so that any particle at rest, with = 0, remains unchanged up to a multiplicative number, Pa, under the parity operator. States with this property are called eigenstates with eigenvalue Pa. The quantity Pa is also called the intrinsic parity of particle a, or more usually just the parity of particle a. Since two successive parity transformations leave the system unchanged, Pa = 1, implying that the possible values for the parity eigenvalue are Pa = 1. In addition to a particle at rest, a particle with definite orbital angular momentum is also an eigenstate of parity. The wave function for such a particle in spherical coordinates is nim(, t) = (r) (0, ), (1 10) where (r, 0, ) are spherical polar coordinates, R,~(r) is a function of the radial variable r only, and the Y"(0, 9) is a spherical harmonic. The spherical harmonics are well known functions which have the following property, yn(o, ) = (-1)ly ( 7 + >). (111) Hence P'nlm(5, 1t) Pa lnlm(-5, t) Fa P )(-I)'nn(Y, t) (1-12) proving that a particle with a definite orbital angular momentum I is indeed an eigenstate of the parity operator with eigenvalue Pa(-1)'. The parity of the fundamental fermions cannot be measured or derived. All that Nature requires is that the parity of a fermion be opposite to that of an anti-fermion. As a matter of convention fermions are assigned P = +1 and anti-fermions are assigned P =-1. In contrast, the parities of the photon and gluon can be derived by applying P to the field equations resulting in P, -1 and Pg 1. The parity of T(1S), a spin 1 bb bound state (described in Section 1.2) with L 0 is P = PbPb(1)L -1. Parity is a good quantum number because it is a symmetry of the strong and electro-magnetic force. This means that in any reaction involving these forces, parity must be conserved. 1.1.3.3 Charge conjugation The operation that replaces all particles by their anti-particles is known as charge conjugation. In quantum mechanics the charge conjugation operator is represented by C. For any particle la > we can write Cla > Cala > (1 13) where Ca is a phase factor. If we let the C operator act twice to recover the original state |a >, Ia >= C2la >= (cala >) = Ca a >= CaCala > (114) which shows that CaCa = 1. If (and only if) a is its own anti-particle, it is an eigenstate of C. The possible eigenvalues are limited to C = ca = ca = 1. All systems composed of the same fermion and an anti-fermion pair are eigenstates of C with eigenvalue C = (-)(L+S). This factor can be understood because of the need to exchange both particles' position and spin to recover the original state after the charge conjugation operator is applied. Exchanging the particles' position gives a factor of (-1)L as shown in the previous section. Exchanging the particles' spin gives a factor of (-I)s+1 as can be verified by inspecting Equations 1-3 and 1-4, and a factor of (-1) which arises in quantum field theory whenever fermions and anti-fermions are interchanged. With this result we can calculate the charge conjugation eigenvalue for the T(1S) and obtain C = -1 since L + S = 1. The photon is an eigenstate of C since it is its own anti-particle. The C eigenvalue for the photon can be derived by inserting C into the field equations and is C = -1. 1.1.3.4 G-Parity We just learned from the charge conjugation operation that only neutral particles can be eigenstates of charge conjugation operator. A useful conservation law for the strong interactions can be set up by combining the charge conjugation operation with a 1800 rotation about a chosen axis in the isospin space. This combined operation of rotation in the isospin space, followed by charge conjugation, is called as G-parity G Cexp(-T ) (1 15) As noted earlier, the isospin has the same algebraic properties that of quantum mechanical angular momentum operator, the rotation of an isospin state I, 13 > in isospin space about y-axis by an angle F can be carried out as: R2(7) 1, 13 > exp(-irT27)I, 13 >_ (-1)-13 I, -13 > (1 16) Thus, for a rotation F about the 2 axis (y axis) in isospin space we have R2(7)I+ > = > R2(7)I- > I+ > (1-17) R2(7)17 > -(-1)|7 > In this way, we find that the G-parity for neutral pion is unambiguously fixed to -1. Since the strong interactions conserve isospin and are invariant under charge conjugation, one might expect that the G-parity of F' is same as that of 7. Thus, under G-parity transformation, we have GI'" >= (-1)1"' > (1-18) G-parity is a multiplicative quantum number, therefore, the G-parity of a system of n pions is (-1)". G-parity is a good quantum number of non-strange mesons and is conserved in strong interactions. 1.1.4 Mesons At this point, we can introduce the lowest lying mesonic states. From the light2 quarks u, d, and s we expect nine possible qq combinations, thus nine mesons, which break into an octet and a singlet as per 303 = 8 1. For lowest lying states, it is safe to assume that the relative angular momentum quantum number L is 0. The parity for such states then is P = (-1)L+1 = -1. Since the relative angular momentum is 0, the total angular momentum is same as the spin of the qq combination. The two spin-1/2 quarks can be combined either to get total spin 1 (leading to JP = 1-) or spin 0. States with S = 0 (and therefore J = 0) are pseudoscalar mesons (JP = 0-), some of which are the subject of interest of this study. The normalized, orthogonal set of octet is I7+ > = ud 7K- > 0r > IK+ > |K- > IKo > IKo > I|> Iqs > du 1 I(dd uu) us su ds sd 1 (dd+ uu 2ss) VI6- (1-19) and the flavor symmetric singlet is I|' > I |qo > 1 v(dd + uu + ss) v'3- (1-20) 2 The quarks u, d, and s are considered as light on the scale of QCD parameter A. The quarks c, b, and t are considered as heavy quarks. Table 1-3. Symbol, name, quark composition, mass in units of MeV/c2, angular momentum (L), internal spin (S), parity (P), and charge conjugation eigenvalues (C) for a few of the particles used in this analysis. Symbol Name Quark Composition Mass I G L S P C T(1S) Upsilon(1S) bb 9460.30 0 -1 0 1 -1 -1 7+ Pion ud 139.57 1 -1 0 0 -1 x 7- Pion du 139.57 1 -1 0 0 -1 x 7r Pi0 (dd uu) 134.98 1 -1 0 0 -1 +1 r Eta 6(dd+ uu- 2ss) 547.75 0 +1 0 0 -1 +1 r9 Eta-prime -(dd + uu+ ss) 957.78 0 +1 0 0 -1 +1 po RhoO I(uu- dd) 775.8 1 +1 0 1 -1 -1 7 Photon x 0 0,1 x x 1 -1 -1 In the real world, the r] and r' states are a mixture of rls and 7ro, with r] being 11.-1 iy octet" rls and rj' being -ii .-1 iy singlet" ro. The mixing angle between rls- ro is a -200, the consequence of which is that ss content is decreased for r] and increased for ri [5]. Various properties of pseudoscalar mesons pr, r' along with pion triplet are shown in Table 1-3. If we assume that the masses of quarks u, d, and s is zero, then these particles exhibit SU(3)L x SU(3)R chiral3 symmetry. The Goldstone theorem [6] -.i,- that a massless particle (called Goldstone boson) is generated for each generator of the broken symmetry. The SU(3) chiral symmetry is spontaneously broken to vector SU(3), giving rise to eight massless Goldstone bosons which are identified with the octet part of the lowest lying meson nonet. These Goldstone bosons acquire mass due to explicit breaking of the symmetry where quarks have unequal masses. The singlet r' is very massive compared to the members of octet. This happens because the rl' is not a Goldstone boson and acquires mass due to a different mechanism [5]. 3 When the particle mass is zero, the left-handed and right-handed particles are treated differently. This is what we understand by chiral symmetry. 1.2 Quarkonia Quarkonia are flavor-less mesons made up from a heavy4 quark and its own anti-quark. Charmonium (cc) and bottomonium (bb) are the only examples of quarkonia which can be produced. The bound state tt is not expected to be formed as the top quark has a fleeting lifetime owing to its large mass. In spectroscopic notation, the quantum numbers of quarkonia are expressed as n2S+1Lj where n, L, S and J represent the principal quantum number, orbital angular momentum, spin, and total angular momentum respectively. In literature, the n 3S charmonium and bottomonium states are called as T(nS) and T(nS) respectively. The combined spin of qq in the above mentioned systems is 1. The qq relative angular momentum in these mesons is L = 0, i.e., an "S" wave and hence the symbol "S" in the notation. The n3S1 quarkonia have JPC 1-- which is same as that of photon, therefore these mesons can be produced in the decay of virtual photon5 generated in e+e- annihilation carried out at the right center-of-mass energy. The lowest such state is (1lS) (commonly called J/y), a cc state produced at center-of-mass energy 3.09GeV. The corresponding state for bb is T(1S), produced at 9.46GeV. 1.2.1 Decay Mechanisms of T(1S) Armed with all the basic information, we are now ready to understand the possible ways in which T(1S) can decay. Strong and electro-magnetic interactions conserve color, parity and charge conjugation. These constraints leave very few 4 qq states from light quarks u, d, s are rather mixtures of the light quarks than well defined states in terms of quark-antiquark of the same flavor. Even 0 is also not a pure ss state. 5 Such a photon is called virtual because it cannot conserve the 4-momentum of the initial system (e+e- here) and is unstable, existing only for a brief period of time, as allowed by the uncertainty principle, after which it decays to a pair of charged fermion-antifermion. decay routes open, for example T(1S) decay to an even number of photons or an even number of gluons is forbidden by charge conjugation. The easiest route would have been T(1S) decaying into a pair of B mesons, but this is not allowed kinematically. A possible simple decay mechanism is that bb pair first interact electro-magnetically and annihilate into a virtual photon. This process is allowed as it does not violate any of the fundamental principals. The virtual photon then readily decays either into a pair of leptons or it decays into a pair of quark-antiquark which further hadronize. On the other hand, the decay of T(1S) into a single gluon is forbidden because it violates color conservation. When T(1S) decays via intermediate gluons, the minimum number of gluons it should decay to is three so that all the constraints including color conservation are satisfied. In principle, T(1S) decay proceeding via three photons is also possible, but this mechanism is highly suppressed as compared to the one proceeding through a virtual photon, just because three successive electro-magnetic interactions are much less likely to occur than a single one. A very important decay mechanism which has not been introduced so far is the ,.,.1i.w ive decay." The decay in this case proceeds through a photon and two gluons. The two gluons can form a color singlet state and the presence of a photon in team with two gluons ensures that parity and charge conjugation are not violated. Naively, the p n.i.llr for this replacement of one of the gluons with a photon is of the order of the ratio of coupling constants, a : as. Despite this suppression, the radiative decays of T(1S) are important because emission of a high energy photon leaves behind a glue-rich environment from which we can learn about the formation of resonances from gluons or potentially discover fundamental new forms of matter allowed by QCD like "glueballs" and qgq "hybrids." This dissertation concentrates on one class of radiative decays. The three different possible T(1S) decays with least amount of interactions (also called lowest order decays) are shown in Figure 1-2. b9 (a) g g b (b) g (c) Figure 1-2. Lowest order decays of the T(1S) allowed by color conservation, charge conjugation symmetry, and parity. (a) Shows the decay into three gluons, (b) shows a radiative decay, and (c) shows the electro-magnetic decay through a virtual photon that in turn decays electro-magnetically into a pair of charged fundamental particles, such as quarks or charged leptons (the charged leptons are represented by the symbol 1). 1.2.2 Radiative Decays of T(1S) into rl and rl' The radiative decays of heavy quarkonia into a single hadron provide a particularly clean environment to study the conversion of gluons into hadrons, and thus their study is a direct test of QCD. T(1S) 7rl' is one such channel, involving only single light hadron. This decay channel has been observed in the J/y system, as have the decays into other pseudoscalar states, for example the rl and re(1S). Naive scaling predicts a ratio of partial decay widths F(T(lS) 7ri')/F(J/y 7r') of (qbmc/qcmrb)2 1/40. This naive factor of 1/40 is in the decay rates; to find the expected ratio of branching fractions, we have to multiply by the ratio of the total widths, 1.71, which gives a suppression factor of a 0.04. However, the search for the decay T(1S) -> 7r' by CLEO in 61.3 pb-1 of data taken with the CLEO II detector [7] found no signal in this mode, and resulted in an upper limit of 1.6 x10-5 for the branching fraction T(1S) -- 7r', which is an order of magnitude less than the naive expectation. Furthermore, the two-body decay T(1S) -- 7f2(1270) has been observed in the old CLEO II T(1S) data [8], and this observation has been confirmed with much greater statistics in the CLEO III data [1]. In radiative J/y) decays the ratio of rl' to f2(1270) production is 3.10.4. If the same ratio held in T(1S), and as the decay diagram is identical, this would be expected, then the ql' channel would be clearly visible. Another interesting channel we study in this analysis is T(1S) -- 7l. This channel has been observed in J/y decays, albeit with the modest branching fraction of (8.6 0.8) x 10-4. The previous analysis [9] of T(1S) decays produced an upper limit for this mode of 2.1 x 10-5. Several authors have tried to explain the lack of signals in radiative T(1S) decays into pseudoscalar mesons using a variety of models which produce branching ratio predictions of the order 10-6 to 10-4. Korner and colleagues' [10] approach -ii.'-.I -1 j''" dependence for rl' and f2(1270) production in the radiative decays of heavy vector mesons of mass Mv. Using the mixing mechanism of rl, ql' with the as yet unobserved pseudoscalar resonance qib, Chao [11] calculates the B(T(1S) 7y') ) 6 x 10-5, B(T(1S) rI) 1 x 10-5. The process V -- y P, where V is the heavy vector meson T(1S), T(2S) and P is a light pseudoscalar meson (Tr, r, r0) was also studied by Intemann [12] using the Vector Meson Dominance Model (VDM). In the VDM paradigm, the decay is assumed to proceed via an intermediate vector meson state, that is V -- V' P -- P where the virtual V' is a T(1S) or T(2S). The predicted branching ratios for T(1S) 7y, T(1S) 7r' are ~ 10-7 to 10-6. There is an ambiguity regarding the signs of various amplitudes (and thus whether the amplitudes add constructively or destructively to the intermediate virtual vector meson V') that contribute to the partial decay width F(V -- P). The author notes that the amplitudes, if added constructively, give answers which are in agreement with the experiment for the J/y :-,-I, II, Making a note that VDM has no direct relation to QCD as the fundamental theory of strong interactions, and referring to [7], Ma tries to address the problem in Non-Relativistic QCD (NRQCD) [13] paradigm along with twist-2 operators and predicts B(T(1S) -- r') 1.7x 10-6, and B(T(1S) -- 7r) x 3.3x 10-7, which are almost half the respective ratios predicted using constructive interference VDM approach (Table 1-4). Table 1-4. Theoretical branching fractions as predicted by various authors for radiative decays of T(1S) into r] and r]' Author/_\Idel/Approach Chronology B(T(1S) 7r') B(T(1S) -- 7r) QCD inspired models: Korner et al. [10] 1982 20 x 10-5 3.6 x 10-5 6 Vector Meson Dominance: 5.3 x 10-' 1.3 x 10-7 Intemann [12] 1983 to to 2.5 x 10-6 6.3 x 10-7 Mixing of tr, r' with rib: Chao [11] 1990 6 x 10-5 1 x 10-5 NRQCD with twist-2 operators: Ma [13] 2002 m 1.7 x 10-6 3.3 x 10-7 In this study, we search for the processes T(1S) -- 7r' and T(1S) 7yr. We reconstruct 7r mesons in the three modes r y77, r -+ 7+r-, and 7 7r0. The rl' mesons are reconstructed in the modes rl7+7- with pr decaying through any of the above decay modes. These six decay chains were investigated in the previous 6 Constructed from table 4 of Ref. [10] as: B(T(1S) r)/) 0.10x 1( x B(T - 0.24 13( --4-f2) %f2). CLEO analysis on this subject. In addition, we have also added the decay mode rq]' yp, where pO -- 7+-. We should also note that we know that five of the seven submodes under investigation are going to be largely background free, and so to get the most sensitivity we must carefully choose our cuts7 in these submodes to retain the most possible efficiency. The two exceptions are r] 7y and r]' ?p. These two have high branching fractions, but large backgrounds, and so our analysis strategy will aim to decrease these backgrounds even if this necessitates a decrease in the efficiency. For later reference and final calculations, the product branching fractions for the decays modes of r] and r]' are listed in Table 1-5 where the values have been compiled from PDG[14]. Table 1-5. Product branching ratios for decay modes of p] and q]' Decay Mode B(rl -- 77+rr) B(q -0) 1(rq' -+ 7r q) B(ri +r-rl ; rl O) 3B(qr -- 7+7-r ; rl 77+-70) B(rl' -- 7+7-rl; rl -- 7O7070) Product branching fraction 39.43 0.26 22.6 0.4 32.51 0.29 44.3 1.5 17.5 0.6 10.0 0.4 14.4 0.5 29.5 1.0 7 In parlance of High Energy Experimental studies, "( I is a synonym for selection criterion. An event must satisfy a set of cuts to be considered as an event of interest. Cuts are carefully chosen to reject the background events. CHAPTER 2 EXPERIMENTAL APPARATUS The first steps towards the study of radiative decays of T(1S) resonance is to be able to produce the T(1S) resonance, and then to be able to observe the decay daughters of this readily decaying resonance. The T resonances are produced only in a high energy collision, the decay daughters of which fly off at relativistic speeds. To detect these daughter particles, a detector is required to be set up around the production point (of the T(1S) resonance) which covers as much as possible of the total 47 solid angle. For this analysis, we need a multipurpose detector permitting us to trace the charged tracks back to the production point, identify the particles and detect neutral particles as well. CLEO III detector has been designed to perform the studies of T resonances produced by the Cornell Electron Storage Ring. 2.1 Cornell Electron Storage Ring Located at the Wilson Laboratory's accelerator facility in Cornell University, Ithaca, NY, the Cornell Electron Storage Ring (CESR) is a circular electron-positron collider with a circumference of 768 meters. Since its inception in 1979, it has provided e+e- collisions and synchrotron radiation to several experiments. Various components of CESR as shown in the schematic picture (Figure 2-1) are discussed in the next few sections. The components are discussed in the order in which they are rnpl-v-d to create e+e- collisions. 2.1.1 Linear Accelerator The electrons and positrons used in the collision to produce T resonance are produced in a 30 meter long vacuum pipe called the Linear Accelerator (LINAC). The electrons are first created by evaporating them off a hot filament wire at the back of LINAC. In technical parlance, it is the electron gun which produces the electrons, SLINAC e- / CLEO C 8 BUNCH OF POSITRONS O BUNCH OF ELECTRONS Figure 2-1. Wilson Laboratory accelerator facility located about 40 feet beneath Cornell University's Alumni Fields. Both the CESR and the synchrotron are engineered in the same tunnel. which is very similar to the procedure inside the picture tube of a television. The electrons thus created are accelerated by a series of Radio Frequency Acceleration Cavities (RF Cavities) to bombard a tungsten target located at about the center of LINAC. The result of the impact of high speed electrons with energy about 140 MeV on the tungsten target is a spray of electrons, positrons and photons. The electrons are cleared away with magnetic field leaving us with a sample of positrons which are further accelerated down the remaining length of LINAC. In case of electrons, the electrons as obtained from the electron gun are simply accelerated down the length of LINAC without having to bombard the tungsten wire. These accelerated bunch of electrons and positrons are introduced into the synchrotron. This is the process of "filling" a run which normally takes ten minutes. 2.1.2 Synchrotron The electrons and positrons as filled in the synchrotron are accelerated to the operating energy which is 9.46 GeV in our case, the mass of T(1S). The synchrotron is a circular accelerator where the electrons and positrons are made to travel in opposite directions in circular orbits inside a vacuum pipe. The guiding of traveling particles is accomplished via magnetic field, and the acceleration is carried out by radio frequency electro-magnetic field. In principle, the charged particles can stay in an orbit of a particular radius for a particular velocity for a particular strength of magnetic field. As the particles are accelerated, the value of the magnetic field must be adjusted in synchronism with the velocity to keep the particles in the orbit of constant radius. 2.1.3 Storage Ring After the electron and positron bunches have reached the operating energy the highly energetic particles are injected into the storage ring. The process of transferring the electron and positron beams into the storage ring (CESR) is called "injection." The beam is guided along a circular path inside the ring by magnetic field and coasts there for roughly an hour, a typical duration of a run. To prevent the electrons and positrons scattering off the gas molecules in the beam pipe, a high quality of vacuum has to be maintained inside the beam pipe. While the particles coast in the storage ring, they radiate a beam of X-rays thus leading to energy loss. This radiation is called "synchrotron radiation" and is a used for experiments in the CHESS area. The synchrotron radiation is rather a useful by-product used as a research instrument in surface p, l-i. -. chemistry, biology, and medicine. The energy lost by the beam in the form of synchrotron radiation is replenished by RF cavities similar to those in the synchrotron. To avoid the beam collisions .i1,-,- h. i- besides the interaction region, the electrostatic separators hold the electron and positron beams slightly apart from each other. The orbit thus is not a perfect circle, it rather assumes the shape of a pretzel. 2.1.4 Interaction Region The interaction region (IR) is a small region of space located at the very center of the CLEO III detector where the electron and positron beams are made to collide. The rate at which collisions happen directly point to the performance of the accelerator. The ability to obtain a high collision rate is crucial for the success of the accelerator and the experiment it serves. The figure of merit then is the number of possible collisions per second per unit area; this is called the luminosity, which is given as L = fn (2-1) A where f is the frequency of revolution for each train. n is the number of populated cars in each train for each particle species, A is the cross-sectional area of the cars, and Ne+ and N- are the numbers of positrons and electrons per car, respectively. In order to maximize the Iliii.- il'i, the beams are focused as narrow as possible in the IR. To this end, several magnetic quadrupole magnets were added to CESR during CLEO III installation. A standard practice of measuring the integrated lli'iin. -il Ii over a period of time in high energy experiments is to count how many times a well understood reference process occurs during a certain time interval at the IR. The two reference processes that are used at CLEO III detector are, one e+e- interacting to produce a new e+e- pair, and second e+e- annihilating to produce a pair of photons. Using the well known cross-section for each process, the number of events is converted to a lilii. ."-ili called the Bhabha integrated l'uiiii "-ili for the first process, and the 77 (GamGam) integrated luminosity for the second one. 2.2 T Resonances The family of T resonances was discovered in 1977 in Fermilab. The experiment conducted at Fermilab was unable to resolve the members of this family, however, it was certain that a bound state of a new flavor, bottom, was discovered. Soon, CLEO detector operating at CESR was able to resolve the states T(1S), T(2S), and T(3S). These resonances are shown in Figure 2-2 on top of hadronic "background." The fourth state discovered in 1980, namely T(4S) is much wider compared to low-lying T states as T(4S) has more decay channels open to it. 0250187-012 ST(1S) (a ) (b) :20 3.5- T(4S) 0 t16 12 T (2S) 3.0- T(5S) U 8 T(3S) T(6S) .) ) 2.5- 9.45 10.00 10.40 10.50 10.60 10.5 10.8 11.1 9.50 10.05 W, Center of Mass Energy (GeV) Figure 2-2. Visible cross section in e+e- collisions as a function of center of mass energy. Plot (a) on the left shows peaks for T(nS) for n = 1,2,3, and 4. Plot (b) on the left shows T(5S) and T(6S) as well as a blow up for T(4S) resonance. The composition of hadronic background is primarily from the "( ,nl wilIii " process e+e -- qq, where q is a light quark (u, d, s, as well as c at this energy). The process is referred to continuum as this process happens for a range of operating energy high enough to produce the light quarks. Some contribution to the hadronic continuum also comes from the process e+e- -- 7T -, where one or both T leptons decay to hadronic daughters. To study the decay processes of T resonances, we not only need the data collected at the operating energy equal to the mass of resonance under study, but we also need a sample of pure continuum at operating energy just below' the resonance to understand the background. 2.3 CLEO III Detector The colliding e+e- annihilate electro-magnetically into a virtual photon 7*, a highly unstable "off mass shell" particle decaying readily into "on shell" daughters. Even at the operating energy equal to the mass of T(1S) resonance, the virtual photon may either produce the resonance T(1S), or produce the continuum background. We really do not have any means of directly knowing what happens at the interaction point. But the long lived on-shell daughters flying off at relativistic speeds possess the information post-collision process as to what Nature decided to do with the energy. It is at this point we enter the world of particle detectors. Like any other probe, to measure a certain quantity, the probe should be able to interact with the quantity. The underlying principles of particle detectors are based upon the electro-magnetic interactions of particle with matter (the detector here). The particle detectors are sensitive to such interactions and are equipped with instruments to record the information about interaction, which is used by experimenter to infer the properties of the interacting particle, such as its energy, momentum, mass and charge. In this analysis, we are interested in the process where a 7* first decays into T(1S) resonance which further decays radiatively into a rp and pr' mesons. The light, pseudoscalar mesons pr and r' themselves are highly unstable and readily decay into 1 The reason for collecting the continuum sample at an energy below and not above the resonance energy is that at an energy above the resonance, the colliding particles may radiate photon(s), thereby losing energy and possibly forming the resonance. 2230402-005 SC Quadrupole Pylon 4 Magnet Barrel Muon Iron Chambers Figure 2-3. The CLEO III detector. lighter particles long lived enough to survive the volume of detector. It is these particles that we detect using the CLEO III detector [15], a major upgrade to CLEO II.V [16] having an improved particle identification capability along with a new drift chamber and a new silicon vertex detector. As the suffix III to the name CLEO -II.. -1 -. there have been many generations of CLEO detectors evolved from the original CLEO detector. As can be seen in Figure 2-3, the CLEO III detector is a composite of many sub-detector elements. Typically arranged as concentric cylinders around the beam pipe, the sub-detectors are generally specialized for one particular task. The entire detector is approximately cube shaped, with one side measuring about 6 meters, and weighs over 1000 tons. CLEO III operated in this configuration from 2000 to 2003. The CLEO III detector is a versatile, multi-purpose detector with excellent charged particle and photon detection capabilities. In the following sections, we discuss some of the particle detection schemes and techniques implemented in the CLEO detectors, and how raw detector data is transformed into measurements of particle energy, moment, trajectories. A thorough description of the detector can be found elsewhere [17]. 2.3.1 Superconducting Coil All the CLEO III detector -Iii-' -1. m-, except the muon chambers are located inside a superconducting coil. The superconducting coil is a key element, providing a uniform magnetic field of 1.5 Tesla to bend the paths of charged particles in the detector, thus allowing the experimenter to measure the momentum of the passing particle. The magnetic field due to the coil points in -z direction (east) and is uniform up to 0.2'. The 3.5 meter long coil has an inner diameter of 2.90 meter with a radial thickness of 0.10 meter. The winding around the coil is carried from a 5 mm x 16 mm superconducting cable made from aluminum stabilized Cu-NbTi alloy kept in superconducting state by the liquid helium reservoir as shown in Figure 2-3. The coil is wound in 2 layers, each having 650 turns, on an aluminum shell. When in operation, a current of 3300 amps flows through the coil. 2.3.2 Charged Particle Tracking System The particles created at the interaction point pass the low-mass beam pipe before they begin to encounter the active elements of detector tracking system. The CLEO III tracking system is responsible for tracking a charged particle's trajectory and thus giving the experimenter a measure of the particle momentum. The tracking - -1.'I, of CLEO III detector is composed of two sub-detectors to accomplish the tracking of curved path of charged particles. The first sub-detector is silicon vertex detector measuring z and the cotangent of polar angle 0, surrounded by the central drift chamber measuring the curvature. Both devices measure the azimuthal angle 9 and the impact parameter. The typical momentum resolution is 0.35% (1%) for 1 GeV (5 GeV) tracks. The tracking system also measures the ionization energy loss due to charged particles a measurement useful in distinguishing between various mass hypotheses of charged particles. The energy loss due to ionization is measured with an accuracy of about 6% for hadrons (pion, kaon, and proton), and 5% for electrons. The tracking system is not sensitive to neutral particles. 2.3.2.1 Silicon Vertex Detector The silicon vertex detector in CLEO III [18], also called SVD III is a silicon strip detector "barrel-only" design without endcaps or tapers, consisting of four silicon layers concentric with the IR beam pipe. The silicon tracker provides four 0 and four z measurements covering 93% of the solid angle. The average radius of inner surface of the four layers is 25 mm, 37.5 mm, 72 mm and 102 mm. Each of the four barrels is constructed from independent chains (called ladders) which are made by connecting individual silicon wafers (sensors) together. There are a total of 447 identical double-sided silicon wafers, each 27.0 mm in 0, 52.6 mm in z and 0.3 mm thick used in constructing the four barrels. The four layers have respectively 7, 10, 18, and 26 ladders, and the four ladder design consists of respectively 3, 4, 7, and 10 silicon wafers daisy chained longitudinally (Figure 2-4). The bottom side of each silicon wafer has n-type strips implanted perpendicular to the beam line. The top side of the wafer has p-type implants parallel to the beam line. The wafers are instrumented and read out on both sides. Each wafer has 512 strips on either side. The instrumentation on each side consists of aluminized traces atop the doped strips. The so formed aluminum strips are connected to preamplifiers stationed at the end of the detector and move the collected charge from the wafers. The entire wafer forms a p-n junction. When reverse bias is applied across the wafer, a sensitive region depleted of mobile charge is formed. 1 cm Iu Figure 2-4. View of the SVD III along the beampipe. As in any other material, charged particles traversing the wafer lose energy. In the sensitive region of the wafer, this lost energy is used to create electron-hole pairs. Approximately 3.6 eV is required to create a single electron-hole pair. The liberated electrons and holes then travel (in opposite directions) in the electric field applied by the bias to the surfaces of the wafers until they end up on the aluminum strips, and then the detector registers a "hit." When combined together, the hit on the inner side of a wafer and the hit on the outer side give a measurement of (z, 0). The wafer position itself determines r. 2.3.2.2 The Central Drift Chamber The CLEO III central drift chamber (DR III) is full of drift gas with 60:40 helium-propane mixture held at about 270 K and at a pressure slightly above one atmosphere. The drift chamber is strung with an array of anode (sense) wires of gold-plated tungsten of 20 pm diameter and cathode (field) wires of gold-plated aluminum tubes of 110 Pm diameter. All wires are held at sufficient tension to have only a 50 pm gravitational sag at the center (z 0). The anodes are kept at a positive potential (about 2000 V), which provides an electric field throughout the volume of the drift chamber. The cathodes are kept grounded, and shape the electric field so that the fields from neighboring anode wires do not interfere with each other. During its passage through the DR III, the charged particle interacts electro-magnetically with the gas molecules inside the chamber. The energy is transferred from the high energy particle to the gas molecule thereby ionizing the gas by liberating the outer shell electrons. The liberated electrons "drift" in the electric field towards the closest sense wire. The thin sense wire maintained at a high potential produces a very strong electric field in its vicinity. As the electron approaches the sense wire, it gains energy enough to become an ionizing electron itself thereby kicking more electrons out of the surrounding gas molecules. An avalanche of electrons is created this way which collapses on the sense wire in a very short amount of time (less than a nanosecond) and the sense wire registers a "hit." The current on the anode wire from the avalanche is amplified and collected at the end of the anode wire. Both the amount of charge and the time it takes it to move to the end of the detector are measured. A calibration of the drift chamber is used to convert the amount of charge to a specific ionization measurement of the incident particle. A calibrated drift chamber can also convert the time to roughly measure the position along the sense wire where the charge was deposited. The CLEO III DR has 47 layers of wires, the first 16 of which form the inner stepped section ( '-, i i i i cake" end-plates) where in the wires are strung along the z-direction. These wires are called axial wires. The remaining outer 31 layers are small angle stereo layers. The stereo wires are strung in with a slight angle (about 25 milliradians) with respect to the z-direction to help with the z measurement. There are 1696 axial sense wires and 8100 stereo sense wires, 9796 total. For stereo ti. iij- . the tracker divides the 31 stereo layers into eight super layers, the first seven of which have four layers of stereo wires each, and the last super layer has only three layers of wires. The odd and even numbered super layers have a positive and negative phi tilt with respect to the z, respectively. The odd(even) super layers are called as U(V) super layers in short. There are 3 field wires per sense wire and the 9796 drift cells thus formed are approximately 1.4 cm side square. The drift position resolution is around 150 ftm in r and about 6 mm in z. 2.3.3 Ring Imaging Cherenkov Detector Cherenkov radiation detectors belong to the set of tools to discriminate between two particles of same momentum and different masses. This goal is accomplished by measuring the velocity of the charged particle and match it against the momentum measured by the tracking chamber. This goal is termed as 1.. Iticle identification." The CLEO III detector received its major upgrade for the purpose of particle identification by replacing the existing time of flight system of CLEO II.V detector by Ring Imaging Cherenkov Detector (RICH). Both ;-'v-I ii -. the old time of flight detector and the new RICH sub-detector provide the measurement of particle velocity. The underlying principle behind the RICH is the phenomenon of Cherenkov radiation. The Cherenkov radiation occurs when a particle travels faster than the speed of light in a certain medium, v > c/n. (2-2) where v is the velocity of the particle, c is the speed of light in free space and n is the index of refraction of the medium the particle is traveling in. The charged particle, as it travels through medium, polarizes the molecules of the medium. The polarized molecules relax to their ground state in no time, emitting photons. Because the charged particle is traveling faster than the speed of light in the medium, it tri. .- -i a cascade of photons which are in phase with each other and can constructively interfere to form a coherent wavefront. The Cherenkov light wavefront forms the surface of a cone about the axis of charged particle trajectory, where the half-angle 0 of the cone is given by cos(0) 1 P > (2-3) vn fpn n The measurement of 0 is thus a measurement of particle's speed which when related to the measured momentum of the particle gives a measurement of the particle mass, and is useful in particle identification. As can be noted from the conditions under which Cherenkov radiation is emitted, the charged particle has to have a threshold velocity vmin = c/n before the radiation can be emitted. At threshold, the cone has a very small half-angle 0 w 0. The maximum emission angle occurs when vTma = c and is given by cos(Oax) (2-4) The RICH (see Figure 2-5) starts at a radius of 0.80 m and extends to 0.90 m has a 30-fold azimuthal symmetry geometry formed from 30 modules, each of which is 0.192 m wide and 2.5 m long. Each module has 14 tiles of solid crystal LiF radiator at approximately 0.82 m radius. Each tile measures 19.2 cm in width, 17 cm in length and a mean thickness of 10 mm. Inner separation between radiators is typically 50 ftm. The LiF index of refraction is n = 1.5. The radiators closest to z = 0 in each module have a 45 degree sawtooth outer face to reduce total internal reflection of the Cherenkov light for normal incident particles (see Figure 2-6). The radiators are followed by a 15.7 cm radial drift space filled with pure N2, an un-instrumented volume allowing the expansion of Cherenkov cone. The drift space is followed by the photo-detector, a thin-gap multi-wire photosensitive proportional chamber filled with a photon conversion gas of triethylamine and methane where the Cherenkov cone is intercepted. SGlO Box Rib Photon Detector -G / 1 / 6 article 20 rm wires CH. F Pur N-' e lass e\ N7 Poton/1 CaF, Wmdow S rall LIF Radiato 192 mm Figure 2-5. The RICH detector -1 i,- v-I i- With this index, particles in the LiF radiator with = 1 produce Cherenkov cones of half-angle cos-l(1/n) = 0.84 radians. With a drift space 16 cm in length, this produces a circle of radius 13 cm. The RICH is capable of measuring the Cherenkov angle with a resolution of a few milliradians. This great resolution allows for good separation between pions and kaons up to about 3 GeV. 2.3.4 Crystal Calorimeter Calorimeters perform energy measurements based upon total absorption methods. The absorption process is characterized by the interaction of the incident particle in a detector mass, generating a cascade of secondary, tertiary particles and so on, so that all (or most) of the incident energy appears as ionization or excitation in the medium. A calorimeter, is thus an instrument measuring the deposited energy. The calorimeter can detect neutral as well as charged particles. The fractional energy resolution of calorimeters is generally proportional to E-1/2, which makes them even more indispensable in yet higher energy experiments. The CLEO III Crystal Calorimeter (CC) is an electro-magnetic-shower calorimeter which absorb incoming electrons or photons which cascade into a series of electro-magnetic track A 10mm t / Y T 170 mm track 10 mm I Figure 2-6. Two kinds of RICH LiF radiators. For normal incidence particles (z 0) a sawtooth radiator is necessary to avoid internal reflection. showers. It is vital sub-detector for the analysis presented in this dissertation, as all our events contain at least two, mostly three, and often more, photons. The calorimeter is constructed from 7784 thallium-doped CsI crystals with 6144 of them arranged to form the barrel portion and the remaining 1640 are evenly used to construct two endcaps, together covering 95% of the solid angle. The (I -l.1-, in the endcap are rectangular in shape and are aligned parallel to the z axis whereas the crystals in the barrel are tapered towards the front face and aligned to point towards the interaction point so that the photons originating from the interaction point strike the barrel crystals at near normal incidence. The CC barrel inner radius is 1.02 m, outer radius is 1.32 m, and length in z at the inner radius is 3.26 m. It covers the polar angle range from 32 to 148 degrees. The endcap extends from 0.434 m to 0.958 m in radius. The front faces are z = 1.308 m from the interaction point (IP); the back faces are z = 1.748 m from the IP. It covers the polar angle region from 18 to 34 degrees in +z, and 146 to 162 in -z. The electronic system composed of 4 photodiodes present at the back of each of the crystals are calibrated to measure the energy deposited by the incoming particles. Incoming particles other than photons and electrons are partially, and sometimes fully, absorbed by the (I '.-1.,-' giving an energy reading. Each of the ( ',-1.,-' is 30 cm long which is equivalent to 16.2 radiation lengths. On the front face, the crystals measure 5 cm x 5 cm, providing an angular resolution of 2 milliradians. The photon energy resolution in the barrel (endcap) is 1.5% (2.5%) for 5 GeV photons, and deteriorates to 3.8% (5.0%) for 100 MeV photons. 2.3.5 Muon Chambers Muons are highly penetrating charged particles which compared to other charged particles, can travel large distances through matter without interacting. For this reason, the sub-detector component Muon Detector used in identifying muons is placed outside the main body of CLEO III detector. The muon detectors are composed of plastic stream counters embedded in several layers of iron. Particles other than muons emanating from the detector are blocked by the iron layers. Like the CC, the muon detector is arranged as a barrel and two endcaps, covering .' .- of the 47 solid angle (roughly 30-150 degrees in polar angle). The barrel region is divided in 8 octants in 9, with three planes of chambers in each octant. The plastic barrel planes lie at depths of 36, 72, and 108 cm of iron (at normal incidence), corresponding to roughly 3, 5, and 7 hadronic interaction lengths (16.8 cm in iron) referred to as DPTHMU. There is one plane of chambers in each of the two endcap regions, arranged in 4 rough quadrants in 9. They lie at z = 2.7 m, roughly covering the region 0.80 < I cos() | < 0.85. The planar tracking chambers use plastic proportional counters at about 2500 V with drift gas of 60% He, 40% propane, identical to (and supplied by the same system as) the drift chamber gas. Individual counters are 5 m long and 8.3 m wide, with a space resolution (along the wire, using charge division) of 2.4 cm. The tracking chambers are made of extruded plastic, 8 cm wide by 1 cm thick by 5 m long, containing eight tubes, coated on 3 sides with graphite to form a cathode, with 50 pm silver-plated Cu-Be anode wires held at 2500 V. The orthogonal coordinate is provided by 8 cm copper strips running perpendicular to the tubes on the side not covered by graphite. When a hit is recorded, the anode wire position provides the 0 coordinate of the hit, and charge division is used to extract the z coordinate. Besides detecting muons, the heavy iron layers also act as magnetic flux return yoke for the superconducting coil. The other important purpose served by iron layers is to protect the inner sub- -i--. i n- of CLEO III detector from cosmic ray background (except for cosmic ray muons of course). 2.3.6 CLEO III Trigger The CLEO III tri.-. -r described fully in [19] is both a tracking and calorimeter based system designed to be highly efficient in collecting events of interest. The tracking based tri.-.-r relies on "axial" and "stereo" tri.-.' -r derived from the hit patterns (pattern recognition performed every 42 ns) on the 16 axial layers and 31 stereo layers of the drift chamber. As there are only 1696 axial wires in the CLEO III drift chamber, the tracker is able to examine all possible valid hit patterns due to tracks having transverse momentum P1 greater than 200 MeV/c. To maintain high track finding efficiency, the hit patterns due to tracks as far as 5 mm away from the axis of beam pipe are included, and upto two hits (one each from the inner and outer set of eight wires) are allowed to be missing. The output from axial tri-.' -r is the number of tracks, the event time and a 48-bit array representing event topology. Since the number (8100) of stereo wires is relatively large, not all wires are examined for hit pattern, rather the wires are grouped in 4x4 arrays (for super layer 8, it uses 4x3 .iii.,-). The U and V super layers (defined in Section 2.3.2.2) are examined separately (as they tilt in opposite directions) and to satisfy a block pattern, at least 3 out of the 4 layers in a super layer must record hits from tracks -.,l i-fvi-ir the momentum cut PI > 250 MeV/c. This is designed to maintain high efficiency; however, missing blocks are not allowed. The stereo track output is projected in azimuth on to the axial layer 9 (to match with the axial tracks) and the CC on the other end. A more detailed discussion is beyond the scope of this dissertation; suffice it is to say that the information from axial and stereo parts of tracker is combined to deduce tracking correlation. The tracks matched in both regions are t...-.' .1 as "long," carrying more weight in tri-. r decision compare to the axial only -I-h.r t" tracks. The calorimeter-based tri.-. r is designed to be more efficient in CLEO III than its predecessors. The energy deposited in overlapping 2x2 .i.,.- of 4x4 crystal tiles (altogether 64 (i .--1.,]) is summed and compared against three thresholds, low (150 MeV), medium (750 MeV), and high (1.5 GeV). The scheme of overlapping tiles (also called tile sharing) did not exist in CLEO II.V and CLEO II detectors, so the calorimeter-based tri..- r was not as efficient, because a shower shared by (, v--.l1, spanning a boundary of tiles could be below threshold in both regions, thus failing the tri-- -r condition. Some decay modes studied in this dissertation rely purely on the calorimeter-based tri.-. -r decision, and the redesigned CLEO III calorimeter tri.-.-r is an added advantage. Based upon tracking and calorimetry tri2.- -r bits, many different tri.-. -r lines (or conditions) are checked and an event is recorded if at least one line is set. The calorimeter based tri.-. -r lines are important for the "all neutral" modes T(1S) - 7r; ] 77 and T(1S) 7rq; r 7r00r0 studied in this dissertation. The two tri-i -r lines which help collect events for the above modes are * BARRELBHABHA, demanding there are two, back-to-back high energy shower clusters in the barrel region. For being classified as back-to-back, the showers should be in opposite halves of the barrel and the 0 angle should be such that if one shower is in octant 1 (0 to 45 degrees in 0), then the other shower should be in octants 4,5, or 6 (135 to 270 degrees in 0), for example. * ENDCAPBHABHA, requiring there are two high energy shower clusters, one in each of the two endcaps. For the modes with charged tracks, the tri.- -r lines have again very relaxed criteria ensuring high efficiency. The important tri:.- r lines are 37 * ELTRACK, demanding a medium energy shower cluster in the barrel region accompanied by at least one axial track. It is very easy to see that this line would be highly efficient if the radiative photon hits the barrel region. * RADTAU, demanding two stereo tracks accompanied with either a medium energy shower cluster in the barrel region, or two low energy shower clusters in the barrel region. * 2TRACK, demanding two axial tracks. This tri.-- r line is pre-scaled by a factor of 20. CHAPTER 3 DATA ANALYSIS 3.1 Data This study is based upon the data sets 18 and 19 collected with CLEO III detector during the running period January 2002 through April 2002 at center-of-mass energy 9.46GeV. The acquired luminosity was 1.13 0.03 fb-1 with the beam energy range 4.727-4.734 GeV. This T(1S) on-resonance data contains both resonant e+e -- T(1S) and continuum events. The number of resonant events available to us, NT(Is) 21.2 0.2 x 106 [20], is roughly 14 times the 1.45 x 106 T(1S) mesons used in the previous search [7, 9] using data collected with CLEO II detector. In order to understand the continuum background present in the T(1S) on-resonance data, a pure continuum data sample is available to us collected at the center-of-mass energy below the T(1S) energy (Ebeam = 4.717-4.724 GeV) with an integrated luminosity of 0.192 0.005 fb-1. Unfortunately, if we use this data to represent our background, we first have to scale it by the large factor of 5.84, which leads to large statistical uncertainties. However, in this analysis, we can also use the large data sample taken on and near the T(4S) as a good source of pure continuum events. Many of these events are of the form T(4S) -- BB decays, but these will not satisfy our selection criteria leaving only continuum events. Thus, we use T(4S) datasets 9, 10, 12, 13, and 14 as a model of our continuum background, with integrated 3.490.09 fb-1 in the beam energy range 5.270-5.300 GeV. We note that in this analysis, we use the "GamGam" liiiii,,,il' rather than using the more commonly used (and more statistically precise) "BhaBha" measure of the luminosity. This is because the measured Bhabha luminosity at T(1S) energy is increased by ~ 3% owing to the resonant process T(1S) -- e+e-, and this must be accounted for while doing the continuum subtraction. By using GamGam luminosity, we avoid this complication and its associated uncert.,iilr v. Statistical details of the data used are listed in Table 3-1. Table 3-1. iliiii .-ili numbers for various data sets used in the analysis T(1S) T(4S) T(1S)-off Dataset 18, 19 9, 10, 12, 13, 14 18, 19 Average Ebeam(GeV) 4.730 5.286 4.717 Range of Ebeam(GeV) 4.727 4.734 5.270 5.300 4.714 4.724 c(e+e-)( fb-1) 1.20 0.02 3.56 0.07 0.200 0.004 (7)( fb-1) 1.13 0.03 3.49 0.09 0.192 0.005 T(1S) continuum scale factor 1 0.404 5.84 3.2 Skim and Trigger Efficiency After the e+e- collision happens, the tri.- .red events are collected by the CLEO III detector. In CLEO terminology this procedure is called as -1...--1." The raw data as collected by the detector is processed and stored in convenient data structures so that an average collaborator can use the data seamlessly in her analysis. This data processing phase is called 1..i-- 2 At this stage, the events are classified into various event-types and stored into different groups called sub-collections, depending upon the characteristics of the event. In a typical analysis, not all collected events are useful, so the first step is to make skim of the events of interest. As our signal events are low multiplicity, we need to ensure that we have tri-.''r-d on the events reasonably efficiently, and furthermore, having collected the events online, we need to know which pass2 sub-collection the events are to be found so that we can skim the events off at Cornell. Using the event generator QQ [21], we generated signal Monte Carlo (\IC) events for the processes e+e- -- -- l' and e+e- -+ 7r using -'i .del 1" with the (1+ cos2 0) angular distribution expected for decays T(1S) -7 + pseudoscalar for each mode, at a center-of-mass energy 9.46 GeV. The MC predicted that ELTRACK (tri-.- -r lines described in Section 2.3.6) was the most significant tri.- -r line for our events that have charged tracks. On the other hand, for "all neutral" modes T(1S) -- r; rl 77 and T(1S) -- qr; r -- 7Tr000, the tri.---r lines BARRELBHABHA or ENDCAPBHABHA were satisfied efficiently. For modes with charged tracks, hardGam event-type was by far the most important. For an event to be classified as hardGam, all the criteria listed below must be satisfied: * eGaml > 0.5, the highest isolated shower energy relative to the beam energy. * I SlI2 < 0.7, second most energetic shower energy relative to the beam energy. * eOverP1 < 0.85, the matched calorimeter energy for the most energetic track divided by the measured track momentum. If the event has no reconstructed tracks, the eOverP1 qi(.i,,l il'v is assigned a default value of zero. * eVis > 0.4, assuming pion hypothesis, the total measured energy relative to the center-of-mass energy. The energy matched to the charged tracks is excluded while summing up total energy. * aCosTh < 0.95, absolute value of z-component of unit net momentum vector. For all-neutral modes, the significant event-types are gamGam, radGam and hardGam, the significance not necessarily in this order. The gamGam event-type has to pass the fairly simple tests nTk the number of reconstructed charged tracks < 2, and i Sl12 > 0.4 (see hardGam). A radGam event-type is necessarily gamGam event-type with the additional requirement that I SI. ;, the energy of third most energetic shower relative to the beam energy should be > 0.08 and eCC, the total energy deposited in the calorimeter be less than 75% of the center-of-massenergy. Due to the softer SIl2 criterion for hardGam, events for the all neutral mode rl 7Tr00 are classified as hardGam more frequently than gamGam or radGam. For the mode T(1S) -- 7r; l Y77, however, the decay of high energy rl into two photons always satisfied SlI 2 > 0.4 thus gamGam is the most efficient followed by radGam. However, during the course of analysis, it was learnt that a cut on the energy .'.,111..... I ry (defined later in Section 3.3.3) of the two photons helps us reduce the background by a large proportion. This cut was conveniently chosen to be < 0.8, which throws away all the events of type gamGam which have not been classified as radGam as well. We thus can select only radGam event-types for ] 77y skim. In addition to the sub-collection/event-type cuts, the following topological cuts were required during the skimming process: * The topology of radiative T(1S) decays is very distinctive. They have a high momentum photon, of energy similar to the beam energy, and a series of particles on the away side of the event. Thus, we require the existence of a shower with measured energy > 4.0 GeV having the shower profile consistent with a photon. To such a shower, we refer as hard photon. * We require the NTracks cut to be satisfied. This term means differently for different modes. For modes with no charged tracks in them, we require NTracks, the number of reconstructed tracks (good or bad) be 0 For modes with charged tracks, we require NTracks to have at least 1 or 2 pairs of oppositely charged, ;uud tl., 1.;- for 2, 4 tracks modes respectively. A "good track" should have: 1. |d01, the distance of closest approach of the charged track to the origin of CLEO coordinate system should be less than 5 mm. 2. z0, the z measurement of the track position at the point of closest approach to the CLEO coordinate system should be less than 10 cm. 3. The momentum '/1 of charged track should be such that 200 MeV < '/K < 5.3 GeV. Selection criteria used in the skimming process are referred to as "basic cuts." Tables 3-2 and 3-3 quantify the basic cuts' efficiencies for decay modes of p] and p]' respectively. Please note that most of the tables from now on have columns bearing two labels, iili" and "cmb" whenever we talk about the efficiency of a selection criterion listed in a particular row. The column labeled with -iiil" stands for the efficiency of the individual cut under consideration and "cmb" stands for the combined efficiency of all the selection criteria which have been used so far, including the current cut under consideration. With this legend, we would read the l y77 column in Table 3-2 as 73.5% efficiency for tri.-i.-r alone (and also 73.5% in the "cmb" column as this is the first cut). Next level cut is applied which has individual efficiency as 93."' .; but the efficiency is 73.5% after applying both the tri'.':r and level cuts, and so on. Table 3-2. Efficiency (in %) Mode --- Events Generated Cut Trigger Level4 Event Type Hard Photon NTracks r -' 77 25000 ind cmb 73.5 73.5 93.2 73.5 68.4 56.0 85.2 54.3 89.1 53.4 of basic cuts for r modes ---7+7-7 r0 --- 70700 25000 25000 ind cmb ind cmb 85.1 85.1 70.6 70.6 93.5 84.7 93.0 70.6 76.3 71.1 71.2 54.6 83.3 68.6 83.2 52.5 92.9 68.1 78.2 44.6 Table 3-3. Efficiency (in %) of basic cuts for ]' modes Mode --- Events Generated Cut Trigger Level4 Event Type Hard Photon NTracks r]' ; r] -- 7 24967 ind cmb 87.6 87.6 94.0 87.3 67.5 64.5 83.2 61.6 92.0 61.0 r1 ; r] + 7 7+ 7r0 25000 ind cmb 89.4 89.4 94.5 88.8 74.1 71.9 83.3 69.2 80.5 60.9 17 ; r 0- 7 FT oF 25000 ind cmb 85.9 85.9 93.7 85.6 73.0 69.1 82.5 66.2 92.0 65.6 To further reduce the skim size, we carried the skimming procedure through another iteration. For each of the modes, complete decay chain was reconstructed with very loose cuts. The 7r 77 and r 77y candidates were constrained to their nominal masses, and restricted in the invariant mass window 50-230 MeV/c2 and 350-900 MeV/c2 respectively. The photon candidates used in reconstructing above meson candidates were not required to pass the standard quality criteria (discussed in next section). Other intermediate meson candidates were formed by simply adding the 4-momenta of daughter particles by making sure that none of the constituent rq7' -7 25000 ind cmb 85.5 85.5 93.8 84.8 75.2 70.8 82.9 67.9 90.6 66.7 tracks or showers have been used more than once in the decay chain. Candidate ] -- 7r+7T-70 and ] -- 7r000 decays (collectively referred to as p] -- 37 from now on) were required to have a reconstructed invariant mass of 400-700 MeV/c2. No invariant mass cut was imposed on the ]q' candidate. To complete the decay chain, a hard photon was added and the energy of the reconstructed event was compared to the center-of-mass energy. The event was selected if |AE| the magnitude of difference between the energy of reconstructed event and the center-of-mass energy was less than 2.5 GeV. Data skim for mode T(1S) -- 7y'; i' 7p was made by requiring an event to have a pair of oppositely charged good tracks accompanied by a hard photon. Since most of the reconstructed energy is measured in CsI, |AE| criterion had been kept generous in anticipation of shower energy leakage. The kinematic fitting we will use in the final analysis will allow effectively tighter cuts on |AE| and p, the magnitude of net momentum vector. 3.3 Reconstruction In our refined version of reconstructing the decay chain, our track selection criteria remained the same, the "good track" as explained in Section 3.2. To reject the background from spurious photons on the other hand, we used some photon selection criteria. Before we list the photon selection criteria used in reconstructing 7r and r] 77 candidates, we introduce the term E90VEREC-". E90VERE25. E9OVERE-'", is a selection criterion used to decide whether the shower has a lateral profile consistent with being a photon. The decision is made based upon the energy deposited by the shower in inner 3x3 block of nine CC (I ,--1 .,1- around the highest energy ( i --I 1 and the energy deposited in 5x5 block of 25 crystals around the highest energy crystal. The energy deposited in inner 9 crystals divided by the energy deposited in 25 ( --1 .1-, is commonly called E90VERE25. A true photon is expected to deposit almost all of its energy in the inner 3x3 block. This ratio is then expected to be equal to one for true photons. For isolated photons, this criterion is highly efficient. However, to maintain high efficiency for photons lying in proximity to each other, a modified version, called E90VERE25Unf(olded), where the energy in the overlapping ( 1--I .1,- is shared. The photon candidates used in reconstructing candidates r 77 and 7r had to satisfy the following quality criteria: * At least one of the showers must have lateral profile consistent with being a photon, which is achieved by 99% efficiency E90VERE-',Unf cut. * None of the showers could be associated to shower fragments from the interaction of charged tracks in the CC. Since the 7r and pl mesons are the decay daughters of highly energetic pl and fl' mesons, the decay daughters fly off in a collimated jet and some efficiency loss is expected due to this requirement. However, this cut is necessary to reduce the background from false showers. * eMin, the minimum shower energy be 30 MeV for 7r candidates and 50 MeV for pl candidates. Further, the default requirement for 7r and rl 77 candidates, that the constituent showers should be reconstructed either in the fiducial barrel or the fiducial endcap calorimeter region was relaxed' for 7r candidates (see Section 3.3.2). It may be noteworthy that this requirement was also relaxed during the data skimming process. In order to get the maximum information out of the detector, for those decay modes involving charged tracks, an event vertex was calculated using the charged tracks, and the 4-momenta of the photons were calculated using this event vertex as the origin. The algorithm for event vertex is discussed in Appendix 5. The 7r and 1 The fiducial regions of the barrel and endcap are defined by I cos(O) < 0.78 and 0.85 < Icos(0)| < 0.95, respectively; the region between the barrel fiducial region and the endcap fiducial region is not used due to its relatively poor resolution. For this study, we relaxed this requirement (which we call fiducial region cut) for 7r candidates as there is a significant chance that at least one of the six photons from the r] o 7070o0 decay may be detected in the non-fiducial regions. intermediate rp states were mass constrained using these recalculated photons2 to their nominal masses. This produces an improvement in the resolution ({ 10%) of the candidate r and iq' invariant mass (see Appendix 5). This corresponds to a slight improvement in the sensitivity of the measurement. Our general analysis strategy is to reconstruct the complete decay chain to build the T(1S) candidate, ensuring that none of the constituent tracks or showers have been used more than once, and kinematically constrain the intermediate 7r and pq meson candidates to their nominal masses [14]. The mode T(1S) -- 7yr; r --- was an exception where no mass constraining was done to the l -- 77 candidate. The candidate rl -- 7+i -7-0 was built by first constraining a pair of oppositely charged good tracks to originate from a common vertex. Then, a 7r candidate was added to complete the reconstruction of rl + 7+7-7rr chain. The candidate rl -- 7rr0r00 was reconstructed by simply adding the four moment of three different 7 candidates, making sure that no constituent photon candidate contributed more than once in the reconstruction. The reconstruction of f' -- rp+r- where rl decays to all neutrals (y7 or 37r) is similar to rl -- 7r+7r-7 candidate reconstruction where we first vertexed a pair of oppositely charged good tracks and then added the rl candidate constrained to its nominal mass. In the reconstruction of tiq; l -- 7r+7-70, the rl candidate had position information, so we constrained all three, the pair of oppositely charged good tracks and the mass-constrained rl + 7+7-7rr candidate, to originate from a common vertex. Once the final state rl or r' candidates were reconstructed, we added a hard photon to build the T(1S) candidate. The reconstruction of T(1S) y 7r'; r--' - was slightly different and is not discussed in this section. 2 Only in the absence of event vertex, 7r and rl candidates are used as provided by the standard CLEO III software called PhotonDecaysProd producer. The T candidate was further constrained to the four momentum of the e+e -,-1-i i, The idea behind 4-constraint is two fold: firstly, substituting the traditional |AE|, p cuts used towards judging the completeness of event by a single more powerful quantity, the X4 which is capable of taking the correlation |AE| and p and secondly, X4, along with other handles will be exploited in discarding the multiple counting leading to combinatoric background, a problem of varied severity from mode to mode. We took into account the crossing angle of the beams when performing 4-momentum constraint and calculating xU4. Multiply reconstructed T candidates in one event give an artificially higher reconstruction yield, and also increase the overall width of the signal. The problem of multiple counting is dealt with by selecting the combination with lowest XTotal, the sum of chi-squared of the 4-momentum constraint (KU4) and chi-squared values of all the mass-constraints involved in a particular decay chain. For example, there are four mass-constraints involved in the decay chain T(1S) -- 7 rl; rq o 7r00oo0, three 7r mass-constraints and one pr mass-constraint. The mode T(1S) 7yr; r0 -- r000 is an exception in which we preferred to accept the r - o00oo0 candidate having the lowest S ET Si,, with S,i ((my mro)/cr) of the ith r candidate. The quantity a, is the momentum dependent invariant mass resolution of 7r candidate. To estimate the reconstruction efficiency, we counted the r' or rl candidates contributing towards reconstructing an T candidate3 within our acceptance mass window defined as the invariant mass region centered around the mean value and providing 'I' signal coverage as determined from signal Monte Carlo. In addition, the event was required to pass trin.- -r and event-type cuts as listed in Tables 3-2 and 3-3. The method outlined above was common to all modes. Mode specific details are explained below. 3 An alternative scheme is to count the number of T candidates reconstructed from good rl or r' candidates. 3.3.1 Reconstruction of T(1S) --- 7y; ,q +-- wo r Although multiple counting was not a severe problem for this mode as there are only two tracks and two photons (in principle at least) on the other side of the hard photon, we still had some events in which there were more than one reconstructed T(1S) candidates. The T(1S) candidate with the lowest value of (X 4 + Xo) was selected. Candidate 7r mesons within 7 aT. (i.e., a very loose cut) were used in reconstructing the q 7r+7r-7 candidate. A fairly loose particle identification criterion using dE/dx information was employed by requiring the charged tracks to be consistent with being pions. We added the pion hypothesis SdE/dx in quadrature for two tracks (SdEl/dx =- Z S dE dz(i)), where SdE/dx for the ith track is defined as SdE/dx(i) = (dE/dx(measured) dE/dx(expected))/adE/dx and ddE/dx is the dE/dx resolution for pion hypothesis. We then required SdE/dx to be less than 16. Finally, to judge the completeness of the event, a cut of XP4 < 100 was applied. The efficiencies of these cuts are listed in Table 3-4. Table 3-4. Efficiency of selection criteria for the mode T(1S) -+ 7q; r 7+7- Cut Ind Eff (%) Cmb Eff (%) 7r reconstruction 38.2 34.6 ary < 7 96.5 34.7 S /dx< 16 100.0 34.7 XP4 < 100 93.4 32.8 all cuts 32.8 0.4 The invariant mass distribution for the rl + 7r-7or candidate from signal MC after all the cuts is shown in Figure 3-1. Figure 3-2 shows the distribution for various variable we cut on. With this highly efficient reconstruction scheme, we found no event within our invariant mass acceptance window (Figures 3-3(d), 3-4). In Figure 3-3(d), it does appear that dE/dx cut rejects a lot of (background) events. We notice that the rejected background is mostly electrons (see Figure 3-5), which can alternatively be rejected using eop (the energy deposited in the CsI by a track divided by its measured momentum) cut. However, using SE/dx as a selection criterion gave us better background rejecti-on compared to eop cut, with basically the same efficiency. The efficiency for SdE/dx cut was checked using the ca peak (from the continuum process e+e- 7yw) by plotting the sideband subtracted signal and was found to be 'I.'*,; which is lower than the signal MC prediction of 99.9'. We believe the discrepancy is largely accounted for by the fact that background to the cc peak ramps up under the peak, rather than imperfections of the detector response simulation. Thus we will continue to use the 99.9% number as our efficiency, but will give it a suitable systematic uncert.,iini v. The high efficiency and good background rejection of this cut is because the 7 and e dE/dx lines are well separated in the momentum range of interest. Likelihood = 128.3 x= 117.5 for 100 8d.o.f., Errors Parabolic Function 1: Two Gaussians (sigma) AREA 8201.0 93.94 MEAN 0.54727 + 6.9177E-05 SIGMA1 1.16237E-02 + 4.1875E-04 AR2/AREA 0.64843 2.3090E-02 * DELM 0.00000E+00 + 0.0000E+00 SIG2/SIG1 0.37259 + 1.0042E-02 Function 2: Chebyshev Polynomial of Order 2 NORM 1452.9 + 148.8 CHEB01 0.21470 + 0.1355 CHEB02 -0.82008 + 1.7189E-05 1200 1000 800 600 400 200 0.47 0.51 0.55 0.59 m(7T+[ 0 ) (GeV/c2) Figure 3-1. Candidate rq -- 7r+7-7r signal Monte Carlo for reconstruction efficiency reconstructed invariant mass distribution from the mode T(1S) -- 7q; 7+7 -O0. The is 32.8 0.4% after all the cuts. Minos -0.0000E+00 7.1628E-05 3.7866E-04 - .000OE+00 0.000OE+00 0.000OE+00 0.000OE+00 0.000OE+00 0.000OE+00 C.L.= 3.8% 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.0187E-02 0.0000E+00 0.0000E+00 0.0000E+00 0.63 50 800 I I I (a) (b) a 400 > 400 - w w 0 I . 0 0 --L 0 4 8 12 0 4 8 S(Sd E/dx) 8 '" ) 1600 (C) (d) 0 WU 800 0 -8 0 200 400 -8 0 8 X2 SdEdftrackl) P4 Figure 3-2. Distribution from signal Monte Carlo: For the mode T(1S) 7; -- 7 +7-7, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) c7 of the 7r candidate, plot(b) for S ,dx, plot(c) for 4, and plot(d) is a scatter plot of the pion hypothesis SdE/dx for the charged tracks. 0. m^+ 9.55 2 m(n n ) (GeV/c) + q.55 m(+: i-t ) (GeV/c) 2.5 " m 9+ 9 55 2 m(n n ) (GeV/c) 0.63 0.47 Q.55 2 m(+ n-i ) (GeV/c) Figure 3-3. Invariant mass of distribution of the rq candidate for the mode T(1S) 7 -; 7 r +-o: Plot(a) with no cuts, plot(b) with a cut on X24 only, plot(c) after cutting on oa of the 7r candidate only, plot(d) after cutting on SdE/dx alone. The red overlay on plot(d) is obtained after imposing all the cuts. No candidate event was observed in signal region. I I I I (a) I .* I 1 -I 0.47 0.63 8 -- C 4 - ILl 0 0.47 (d) 0.63 63 0.47 "'H H 1 2 0 I I 1 1 1 1 1 1 I 3 '' I '' I I ' 100 -2 1 C S80 S - 0 0.47 0.51 0.55 0.59 0.63 S60 4 40- 20 0 ,1, I ,-,L In,-, r r, r i, 1 I 0.40 0.50 0.60 0.70 0.80 0.90 m( + r ) (GeV/c2) Figure 3-4. Reconstructed r candidate invariant mass distribution in real data for the mode T(1S) -- 7; l -- 7r+r7-70. No events are observed in the signal mass window denoted by the region in between blue arrows (inset), and a clear ac -- 7++7T-70 peak is visible from the QED process e+e- --w. 53 1.2 I + I I I + ++ 1.0 + + + ++ + + + + 1. O + + + + +^4 - + + +++++ -1+ ++ + + * 0.8- ++ 0.6- + + + 0.4- + 0.2 0.0 I I I I i I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 eop(trackl) Figure 3-5. Scatter plot of eop distribution for track 2 vs track 1 for the events rejected by SE/d > 16.0 cut. Most of the rejected events are clearly electron like. 3.3.2 Reconstruction of T(1S) -- 7qr; r -- 7Tr Tr0 The kinematics involved in this decay mode are largely responsible for a comparatively low efficiency and reconstruction quality. The decay of high energy p into three 7r mesons does not cause them to spread out a lot, as a result the showers from different 7r mesons frequently lie on top of each other. Just one overlap of two showers often makes it impossible to reconstruct two of the 7r mesons. By seeking the help of tag- ger4 we figure that more than 50% of the events suffer from this pathology. In total MC this leaves us with only a 22.7% (5675 out of 25000) events where the showers from the p have proper tags We define an MC p having proper tag when all six photons from r decay are t.-'-.' d to six different reconstructed showers. Roughly 20% of the events with proper tags were filtered out by the fiducial region cut (discussed in Section 3.3) alone, which is why this cut was relaxed so that a more reasonable reconstruction efficiency could be obtained. To address the problem of multiple (' li1liin:. we select the T(1S) candidate in the event having the lowest S2 (defined in Section 3.3). From now on, we will refer to such a candidate as the best candidate. Using It.-.-' .1 Monte Carlo, we find that we pick up the correct combination (i.e., each of the three 7r candidates is reconstructed from the photons candidates which have been t..-.-' .1 to the actual generated ones) approximately 72% of the time5 Having selected the best T(15) candidate, we require the following two selection criteria to be satisfied: 4 The It.-.-' r is a software part of the CLEO III software library. The ..-'-' r is capable of performing hit-level t..-.-in,, and therefore, can tell us which reconstructed track or shower is due to which generated charged particle or photon. By hit-level 1.,.-.- i i ,-: it is understood that the 1. .-. i ,.-; software keeps track of the cause of simulated hits (i.e., which hit is from which track, etc.), and so it is very reliable. 5 An alternative scheme based upon X otal gives statistically same answer, though any two schemes may disagree on an event by event basis. * 5 < 10.0. primarily to select good q(i.lilv 7r candidates and reduce possible background in real data. * X 4 < 200.0 to ensure that the reconstructed event conserves the 4-momentum. In addition, we notice that requiring the number of reconstructed showers in event to be < 13 is 99.9% efficient in signal MC and helps us reduce some background. The reason that this cut is useful is that one source of background is the process e+e- 7 where q -- KsKL. The decays chain ends with Ks -- 7rr0 and a possible KL -- 7Tr 000 giving rise to an event with a hard photon along with at least 2 7r mesons with some extra showers. Even if the KL does not decay within the volume of the detector, its interaction in the CC is not well understood and it can possibly leave a bunch of showers. Such a background can easily be rejected by a requirement on the number of showers. From respective Monte Carlo samples, the shower multiplicity for processes T(1S) -- 7yq; p 70Tr00 and e+e- -- 7yp is shown in Figures 3-7 (c) and (d) respectively. As per the Monte Carlo, roughly 50% of the type e+e- 79 are rejected by the cut restricting number of showers to be < 13 whereas only this requirement is almost 100% efficient in signal MC. Thus, we require the reconstructed event to pass this highly efficient test as well. Table 3-5 lists the selection criteria used in the reconstruction. Figure 3-6 shows the invariant mass distribution from signal MC for the mode T(1S) -- 7q; -- 7rT00. Figure 3-7 shows the distribution of the quantities we cut on. With this reconstruction scheme, we find no candidate events from real IS data as the Figure 3-8 shows. Table 3-5. Efficiency table for the mode T(1S) 7q; r 7TrTr Cut Ind Eff (%) Cmb Eff (%) /S of 7rs < 10 94.9 12.3 X <4 < 200 95.4 11.8 # Showers < 13 99.9 11.8 all cuts 11.8 0.2 Likelihood = 102.8 = 110.4 for 100- 6d.o.f., Errors Parabolic Function 1 :Two Gaussians (sigma) AREA 2947.2 + 55.26 MEAN 0.54531 + 3.3034E-04 SIGMA1 1.08638E-02 4.8996E-04 AR2/AREA 0.45522 2.7350E-02 * DELM 0.00000E+00 0.0000E+00 SIG2/SIG1 3.2527 + 0.1286 Function 2: Chebyshev Polynomial of Order 0 NORM 42.718 + 36.38 300 Minos - 54.96 - 3.3059E-04 - 4.8200E-04 -2.7294E-02 -0.0000E+00 - 0.1268 31.49 C.L.= 11.9% 55.57 3.3022E-04 4.9938E-04 2.7435E-02 0.0000E+00 0.1306 + 41.11 200 100 0.0 0.40 0.50 0.60 m(xt xo) (GeV/c2) 0.70 Figure 3-6. Reconstructed invariant mass distribution for the candidate 1r -i 7U7TU7 from signal Monte Carlo for the mode T(1S) 7r; rl -i 0rr0. The reconstruction efficiency is 11.8 0.2% after all the cuts. 57 150 o, 500 '. (a) 250 I - 0 0 > > 250 W W 50 .... ", O -- lB 0 1500 1000 500 0) 3 5 10 1 2 i i i ,_ (c) , 5 0 200 400 2 P4 60 . I (d) 40 U, W 20 0 iL 5 10 15 20 5 10 15 21 # Showers # Showers Figure 3-7. Distributions from T(1S) -0 7; -- 7 %x 700 signal Monte Carlo, showing the variables we cut on. The yellow (shaded) area in these plots represents the acceptance. Plot (a) S of the 7r candidates, plot (b) for X(4, and plot (c) # of showers in the event. The dashed (red) line in plot (a) shows the S of the 1.'' .-.1 7r candidates. As can be seen, majority of good events are confined within N < 10.0, giving us a reason to select our acceptance region. Plot (d) shows the shower multiplicity from the signal MC for the process e e- 7y. Although plot (d) is not normalized to plot (c), we can clearly see that if Monte Carlo be trusted, a cut on the number of showers help reject ~ 50% of this background. 0 (b) 8 . ,, a 4 I " (a) (b) 0 0 3 . 0 j "gL 0 ... IAU 0.40 0.50 0.60 0.70 0.40 0.50 0.60 0.70 m(no no) (GeV/c2) m( 10~n0) (GeV/c2) Figure 3-8. Invariant mass of q candidate for the mode T(1S) --+ ; q --+o 7000: Plot () allowing multiple candidates per event, plot (b) after selecting "o -o 0 - best candidate, plot (c) selecting best candidates with 24 < 200.0, plot (d) best candidate with # of showers cut. The red o,. on plot (d) is obtained after imposing all the cuts. There are no events in the acceptance mass window (denoted by blue arrows) after all the cuts. 0.40 0.50 0.60 0.70 0.40 0.50 0.60 0.70 m(nrirt) (GeV/c2) m(nrnrit) (GeV/c2) Figure 3-8. Invariant mass of r] candidate for the mode T(1S) -> 7?y; p -> ir0^00: Plot (a) allowing multiple candidates per event, plot (b) after selecting best candidate, plot (c) selecting best candidates with xU, < 200.0, plot (d) best candidate with # of showers cut. The red o;'il.';v on plot (d) is obtained after imposing all the cuts. There are no events in the acceptance mass window (denoted by blue arrows) after all the cuts. 59 3.3.3 Reconstruction of T(1S) -7; r 77 We first form all possible 77 combinations to build r candidate. Then, the T(1S) candidate is reconstructed by combining a hard photon to the r candidate, which is kinematically constrained to the 4-momentum of e+e --,-1 II We accept an T(1S) candidate if x4 < 200.0. We do not attempt to reject events with more than one T(1S) candidate as only the right combination enters our final r candidate invariant mass plot. Our selection criteria so far, namely using a hard photon and constraining the T(1S) candidate to the 4-momentum of beam, are not sufficient to suppress the QED background from the process e+e -> 777 (See Figure 3-9). The QED MC was generated using Berends-Kliess generator[22]. .UUI .UU I (a) 0.75 0.50 .i. :: . 0.25 0.00 -1.0 -0.5 0.0 0.5 1.0 AE (GeV) I.UU (b)- : ": ". : . 0.50 - o .7 5 i: .: .... ....* . 0.00 -1.0 -0.5 0.0 0.5 1.0 AE (GeV) Figure 3-9. 'j/ vs AE distribution plot(a) for signal MC for T(1S) -- 7l; r 77 and plot(b) for e+e- 777 MC. The QED events, however, have very ..-' iiI. 11 i': distribution of energy Eh and El, for two lower energy photons used in reconstructing rp. The real pq has equal probability of having the decay asymmetry from 0 to 1 (Figure 3-10) where asymmetry (a) 80000 (b) 600 60000 -4 400 t 40000 200 20000 0 0 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 asymmetry asymmetry Figure 3-10. Asymmetry distribution for r candidate. Plot (a) from Monte Carlo data for e+eC -- 777 (black) and signal MC T(1S) -- 7; rl 77 (red) and plot (b) for datal8 and datal9. For asymmetry < 0.75, the events in plot (b) are overshadowed by the events beyond asymmetry > 0.75. The huge pile at the higher in end in plot (b) is because in this plot, the events classified as gamGam event-type have not been rejected yet. is defined as (E E1o)/(Ehi + Eo). We note the signal MC prediction that majority of the signal events are classified as either radGam or gamGam event-types. The events classified as gamGam event-type only, however, have very ..I-. mmetric decays with asymmetry> 0.84. The event-type gamGam is thus automatically ruled out by the asymmetry cut, which is applied at 0.8. The expected efficiency for this cut is .I'i ,; in reality it is more than that as the peak6 asymmetry can not be equal to one. Considering the efficiency and the amount of QED suppression achieved, we add this as one of our basic selection criteria. The QED background, however, is not fully suppressed. 6 Asymmetry equal to one means one of the photons has measured energy equal to 0 3.3.3.1 Possible Background e+e- 77(- e+e-) We make a brief digression to another possible background which was reported in the previous analysis [9]. This background arises from e+e- y77 where one of the photons converts into an e+e- pair sufficiently far into the drift chamber that no tracks are reconstructed. This e+e- pair separates in 9 under the influence of magnetic field, and mimics two showers. Such a -, ," event might satisfy our selection criteria. A distinct geometric characteristic of such a shower pair is that AO, the difference in polar angle 0 of two showers, is close to 0, whereas |A0|, the magnitude of difference in azimuthal angle 0 of two showers, is not. In [9] a geometric cut requiring |A01 > 3 was used in reducing this background which was otherwise a substantial fraction of the entries in the final r 77 invariant mass distribution. Motivated by this, we looked for the presence of such background in our analysis. However, we did not find any obvious signature in real data as Figure 3-11 shows. A further investigation was done by generating a dedicated Monte Carlo sample comprising 115K events for the process e+e -- 77 without any ISR (initial state radiation) effects. We did not find any background event of this type surviving our cuts in e+e- 7 Monte Carlo sample either. 3.3.3.2 Handling ee- yy7 background To study our main QED background process, e+e- yy7, we generated a dedicated MC sample for this process, using a stringent ISELECT function (a piece of code primarily meant to accept the events of interest before computing intensive, full detector simulation is carried out) demanding * Only 3 photons generated, all with | cos(0) I < 0.95 * At least one photon with generated energy of at least 4.0 GeV * Remaining two photons have y7 invariant mass in the range 0.2-1.0 GeV/c2 and asymmetry < 0.8 .. I ....:I A * -] [].*' : : M: *a .. .*: . iv; .. S .... *. D ...* * . ],, s : s : : .. .. *. ... . I ,': I " "" : S ": ,,-, e l B ; ,:" B 0 -20 -10 0 AO * :. . ..... :.* : : - i i.: B R I .'" :" ,"- ." r': ,: : - I. *8 Hi . B. ...[].. .:D... * !.. .. : .. ;.: .'.* . : ": ., .i :.* . S... .." B ". :I * : : ". .. - ** .: ** ".:" "" "- *HB * 'B^'^^";:'^ 10 20 30 Figure 3-11. Distribution of AO vs AO in real data for events in the p mass window passing our basic cuts. We analyze the two MC data samples (signal MC and QED) in detail, but except for asymmetry we do not find any distinct feature which can help us help us discriminate between them. There should be, however, some minor differences in distributions of some variables, which may be harnessed collectively to achieve further signal to background separation. Thus we wrote a neural network program in an attempt to combine the information in an optimal way. Artificial Neural Net. An Artificial Neural Net (ANN) is a mathematical structure inspired from our understanding of biological nervous system and their capability to learn through exposure to external stimuli and to generalize. ANNs have proved their usefulness in diverse areas of science, industry, and business. In the field of experimental high energy plr, -i' -. ANNs have been exploited in performing tri .rV operations, pattern recognition and classification of events into different categories, -10 -20 -30 -3 -.,v signal and background. Generally, the goal is to do a multivariate analysis to carve out a decision surface, a method superior to a series of cuts. ANNs have already made their impact on discovery (top quark). An ANN consists of ar'.:l, .:,, neurons or nodes which exchange information. Each node receives input signal from other nodes, and the weighted sum of these inputs is transformed by an activation function g(x), the result of which is the output from the node. This output multiplied by the weight of the node serves as an input to some other node. Without discussing the gory details of the functioning of an ANN, we mention of feed-forward neural network where the information flow is in one direction only. The neural network used in this analysis is a multi-layer perception [23] which is essentially a feed-forward ANN having an input layer accepting a vector of input variables, a few hidden layers and an output layer with single output. To be able to use a neutral network in solving a problem, it needs to be trained over a set of training patterns, which is done iteratively. During the course of t.iiii, :. the weights of individual nodes adapt according to the patterns fed to the neural network. The difference between the desired output (1 for signal and -1 background in our case) and the actual output from the neural net is used to modify the weights and the discrepancy (or error) is minimized as the training progresses. The architecture of the neural net used is [ 9 14 5 ], a three layered neural net having tanh(x) as the activation function, with single output in the range [-1,1]. The output from the trained neural net is expected to peak at 1 for signal events and at -1 for background events. The input to the neural net is a vector of six variables, namely the measured energy and polar angle 0 of the three showers used in reconstruction. The isotropy in azimuthal angle 9 renders it powerless in making any discrimination in separating the signal from background. The choice of input vector as well as the training data sample is very important. The general tendency of neural nets is to figure out the easily identifiable differences in the two samples first invariant mass of the ,q candidate being the easy catch between signal MC and QED background here, as with this choice of input vector, the neural net can easily work out the invariant mass of the 17 candidate. For this reason, we generate a signal MC having a "wide" 17 and select the data for training where invariant mass of i7 is in the range 0.4-0.7 GeV/c2. The background data sample is comprised of the e+e -- 777 Monte Carlo generated at center-of-mass energy 9.46GeV, having di-photon invariant mass in the range 0.4-0.7 GeV/c2, a 300 MeV/c2 window around the nominal i7 mass. With this sample, the bias due to invariant mass is eliminated. To avoid the well known "over-fitting" problem where the neural-net starts remembering the data too specifically and hence losing its ability to generalize, we build a large training sample of 10,000 events of each type (signal and background). As the training progresses, we monitor (see Figure 3-12) the performance of the neural-net over a similar, independent testing sample comprised of signal and background Monte Carlo data. 3.3.3.3 Final Selection and Comparison of Neural Net vs Asymmetry Using independent samples of signal and e+e -- 777 Monte Carlo, we compare the performance of neural net cut with asymmetry cut. The neural net outperforms the asymmetry cut only marginally as is clear from Figure 3-13. For any chosen efficiency, neural net gives a higher background rejection as compared with asym- metry. For our final selection, we choose net-value > 0.4 with 51% efficiency while rejecting i.' of the background. To choose the value for this cut, we optimize S/\B which was found to be fairly flat in the range 0.15-0.40 . The efficiency of the cuts used is listed in Table 3-6. Figure 3-14 shows the signal MC events' 77 invariant mass distribution for iq candidates surviving our final cuts. The final reconstruction efficiency for this mode is 23.8 0.3% . Figure 312. Figure 3-12. 0.351 I I I I I 0 2.5 5 7.5 10 log(epoch) Training the Neural Net: During the course of ti.iiniii. red denotes the training error and black denotes the testing error (shifted by 0.02 for clarity) from an independent sample. The testing error follows the training errors closely and over-training is not exhibited at all. The learning process saturates however, and training is stopped after 10K iterations. 2 0 *z . * * * ) 25 50 75 100 nII I I II I I I I If -.-..- I % efficiency Figure 3-13. Comparison of background rejection vs efficiency: The lower curve in red shows the performance of asymmetry cut and upper curve in black is from neural net. For any chosen value of efficiency, neural net gives a higher background rejection as compared to asymmetry cut. Inset is S/lB plotted for various values of neural net cut. Table 3-6. Final efficiency table for the mode T(1S) q; q 7 Cut XP4 < 2000 .-1.IIIII.... I ry < 0.8 net > 0.4 all cuts Ind Eff (%) Cmb Eff (%) 100.0 55.6 83.9 46.7 51.1 23.8 23.8 0.3 Likelihood= 118.7 2= 123.3 for 100 6 d.o.f., Errors Parabolic Function 1: Two Gaussians (sigma) AREA 5961.0 77.32 MEAN 0.54209 + 2.2597E-04 SIGMA1 1.51605E-02 4.2932E-04 AR2/AREA 0.15594 4.3434E-02 * DELM 0.00000E+00 + 0.0000E+00 SIG2/SIG1 1.9340 0.1251 Function 2: Chebyshev Polynomial of Order 0 NORM 1.92566E-05 + 14.05 800 I 600 S 400 ^ -- LU 200 Minos -0.0000E+00 2.2175E-04 -0.0000E+00 -0.0000E+00 0.0000E+00 -0.0000E+00 0.0000E+00 C.L.= 2.3% + 77.54 + 2.2560E-04 + 0.0000E+00 + 3.9938E-02 + 0.0000E+00 + 0.0000E+00 + 2.304 0.30 0.40 0.50 0.60 0.70 m(y y) (GeV/c2) 0.80 Figure 3-14. y7 invariant mass distribution from signal Monte Carlo for the mode T(1S) 7; -; 77 3.3.3.4 Data Plots and Upper Limit Requiring all cuts except the neural net, Figure 3-15 shows the yy invariant mass distribution in real data. After imposing neural net cut as well, the y7 invariant mass distribution is shown in Figure 3-16. We fit the y7 invariant mass distribution to a Gaussian of fixed mean and width as obtained from signal MC convoluted with a background function. If we let the 68 area float, we obtain -2.3 8.7 events (Figure 3-17), consistent with 0. To obtain the upper limit for this mode, we fix the parameters to the ones obtained from Monte Carlo and do likelihood fits for different, fixed signal yields and record the X2 of fit. We assign a probability P of obtaining this yield as: 2 P oce which we normalize to 1.0 and numerically integrate up to 90% of the area to obtain the yield at 90% confidence level as shown in Figure 3-18. Figure 3-19 shows the upper limit area, which is the result of summing up the probability distribution in Figure 3-18 upto 90% . O1 0.30 0.40 0.50 0.60 0.70 m(y y) (GeV/c2) 0.80 Figure 3-15. 77 invariant mass distribution in real data. All cuts except neural net cut are in place. 69 16 12 C2 q M l 8 [ [ [ 4 IF III 0.30 0.40 0.50 0.60 0.70 0.80 m(y y) (GeV/c2) Figure 3-16. 77 invariant mass distribution in real data after all cuts. Likelihood = 91.3 S= 85.2 for 100- 4 d.o.f., Errors Function 1 :Two Gaussians (sigma) Parabolic AREA -2.2984 8.698 * MEAN 0.54209 + 0.000OE+00 * SIGMAl 1.51605E-02 0.0000E+00 * AR2/AREA 0.15594 0.0000E+00 * DELM 0.00000E+00 0.0000E+00 * SIG2/SIG1 1.9340 + 0.0000E+00 Function 2: Chebyshev Polynomial of Order 2 NORM 962.16 + 50.63 CHEB01 0.58156 + 7.1844E-02 CHEB02 4.85822E-02 + 8.0037E-02 Minos - 8.363 - 0.0000E+00 - 0.0000E+00 -0.0000E+00 -0.0000E+00 - 0.0000E+00 - 49.61 - 7.3095E-02 - 8.0679E-02 C.L.= 77.6% 9.047 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 51.66 7.0503E-02 7.9255E-02 0.30 0.40 0.50 0.60 0.70 0.80 m(y y) (GeV/c) Figure 3-17. Fit to 77 invariant mass distribution for the mode T(1S) -- 7; + - 77. Leaving the area floating while keeping the mean, width and other parameters fixed to MC fit parameters, we obtain -2.3 8.7 events, which is consistent with 0. 71 0.0030 I 0.0020 0 0 0.0010 : 0.0000 e, ,,I 0 25 50 75 100 # Events Figure 3-18. N.. i,,.li : '1 probability distribution for different signal area for the mode T(1S) 7p7; ] 77. The shaded area spans 90% of the probability. Likelihood = 94.6 2 X = 87.9 for 100 3 d.o.f., Errors Function 1:Two Gaussians (sigma) Parabolic * AREA 14.460 + 0.0000E+00 * MEAN 0.54209 + 0.000OE+00 * SIGMAl 1.51605E-02 0.0000E+00 * AR2/AREA 0.15594 0.0000E+00 * DELM 0.00000E+00 0.0000E+00 * SIG2/SIG1 1.9340 + 0.000OE+00 Function 2: Chebyshev Polynomial of Order 2 NORM 951.63 + 50.50 CHEB01 0.58880 + 7.2552E-02 CHEB02 0.10505 + 7.3963E-02 Minos - 0.0000E+00 - 0.000OE+00 - 0.0000E+00 -0.0000E+00 -0.0000E+00 - 0.000OE+00 - 49.47 - 7.3821 E-02 - 7.5016E-02 C.L.= 73.5% 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 51.55 7.1176E-02 7.2802E-02 0.30 0.40 0.50 0.60 0.70 0.80 m(y y) (GeV/c) Figure 3-19. The fit to reconstructed y7 invariant mass distribution from real data for the mode T(1S) -+ ; l -- 7. The area is fixed to the number of events obtained from 90% confidence level upper limit. The mean, width and other parameters are fixed to the ones obtained from Monte Carlo. 3.3.4 Reconstruction of T(1S) -> 7r; r -- 77 By selecting the T(1S) candidate with lowest value for X?4 + X, we take care of multiple (o'liil.-. a problem which is not so serious for this mode. Good quality rl candidates are selected by requiring the ), < 200 where X, is the 2 of constraining the pr candidate to its nominal mass. To select the pion tracks and to reject the background from electron tracks, we require the SdE/dx to be less than 16.0 (this was also a requirement for the mode T(1S) -- 7rq; r -- 7r+7-7). To ensure that the event is fully reconstructed, i.e., balanced in momentum and adds up to the centre-of-mass energy of the e+e- system, we require the /x4 < 100. The efficiency of the cuts used is listed in Table 3-7 . Table 3-7. Final efficiency table for the mode r]' rlrr- and then r] 77 Cut Ind Eff (%) Cmb Eff (%) 2 < 200 99.6 41.9 SE/dx < 16 99.7 41.8 XP4 < 100 97.1 40.6 all cuts 40.6 0.4 The invariant mass distribution for the reconstructed r' candidate after above mentioned selection criteria from signal MC is shown in Figure 3-20. The invariant mass distribution for r' candidate from real data is shown in Figures 3-22 and 3-23. We find no candidate signal event within our acceptance mass window. Likelihood = 107.1 = 99.8 for 100 6 d.o.f., Errors Parabolic Function 1:Two Gaussians (sigma) AREA 10140. + 103.3 MEAN 0.95752 + 4.4356E-05 SIGMA1 7.84061E-03 + 3.7000E-04 AR2/AREA 0.71651 3.0577E-02 * DELM 0.00000E+00 0.0000E+00 SIG2/SIG1 0.43387 + 1.3547E-02 Function 2: Chebyshev Polynomial of Order 0 NORM 2311.6 + 333.2 1000 1 Minos - 102.9 - 4.4347E-05 -3.5620E-04 - 3.2012E-02 - 0.0000E+00 - 1.3629E-02 - 324.0 C.L.= 32.2% 103.6 4.4368E-05 3.8556E-04 2.9224E-02 0.0000E+00 1.3521E-02 + 342.6 750 500 250 0.920 0.940 0.960 0.980 m(ript ) (GeV/c2) 1.000 Figure 3-20. Reconstructed candidate r1' invariant mass distribution from signal Monte Carlo for the mode T(1S) -+ r'; r -- 7 The reconstruction efficiency is 40.6 0.4% after all the cuts. 8000 1 1 1 1 1.. . (a) (b) | 400 >4000 wU wU S I 0 I 0 0 0 100 200 0 4 8 22 X2 1(SdE/dx) 1500 1 I I I I 8 (c) (d) 1000 - 0 500 - 0 -8 0 100 200 -8 0 8 X2 SdEd(trackl) P4 Figure 3-21. Distribution from signal Monte Carlo: For the mode T(1S) 7'; rl 77, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) x2 distribution, plot(b) for \/SE/dx, plot(c) for X34, and plot(d) is a scatter plot of the dE/dx a for pion hypothesis for the charged tracks. (a) - II I II 0.960 m(lt +7i-) (GeV/c2) 1.C 3 Co 2 O a 1 0 LL )00 0.920 II I i 0 L.'-' 1.000 0.920 Figure 3-22. Invariant mass of r' candidate for the mode T(1S) 7'r'; r 7: Plot(a) without any cuts, plot(b) after selecting candidates with X2 < 200, plot(c) after dE/dx cut, plot(d) requiring x 4 < 100. The red overlay on plot(d) is obtained after imposing all the cuts. No candidate signal event is observed in our acceptance mass window (denoted by blue arrows). (b) ,I S.9 920 0.960 2 m(il+7-) (GeV/c2) 1.000 0 0.920 0.960 m(lt i+7-) (GeV/c2) 0.960 2 m(+ijn-) (GeV/c2) 1.000 ' ' ' ' ) 77 m 6 3 I I < I ' 2 - co CD,, , 4 0.920 0.940 0.960 0.980 1.000 C 00 C,) -D > LU 2- 0.82 1.02 1.22 1.42 1.62 m(97ci-) (GeV/c2) Figure 3-23. Extended range of invariant mass distribution of r' candidate for the mode T(1S) -- 7r; r-- 77. No candidate signal event is observed in our acceptance mass window (inset). 3.3.5 Reconstruction of T(1S) -- 7qr; r -- 70Tr00 This is one of the three modes studied in this analysis where multiple counting poses a serious problem. The origin of the problem, like in the mode T(1S) -- 7'y; -- 700Tr0, lies in the decay of high energy p into 3 7r mesons where the showers from different 7r mesons lie so close to each other in the CC and are so close in energy that an overwhelming number of p candidates are reconstructed. Such r candidates have invariant mass close to the nominal p mass, leading to poor resolution and an artificially high efficiency. From the whole raff of T(1S) candidates, we select the one having lowest X)otal where ot X + Xo + Xo+ Xo + X 4. The 7o candidates are selected by requiring V < 10. Good quality p] candidates are selected by requiring the x2 < 200. To be consistent with other modes, we require fE/d to be less than 4. Fill [I -'-i.i. iii nliii conservation is enforced by requiring X 4 to be less than 200. The efficiency for all these cuts is listed in Table 3-8 and the distribution for cut variables is shown in Figure 3-25. Table 3-8. Final efficiency table for the mode r' rr7+7r- and then r] 70o0o0 Cut Ind Eff (%) Cmb Eff (%) 2 < 200 98.3 22.8 SdEdx< 4 99.9 22.7 X4 < 200 96.3 21.9 /2 of 7r0 < 10 73.7 16.6 all cuts 16.6 0.4 Using the above reconstruction scheme, the invariant mass for reconstructed r' candidate is shown in Figure 3-24. We find no candidate event in real data as the Figures 3-26 and 3-27 show. Likelihood = 104.0 = 99.9 for 100 8 d.o.f., Errors Function 1:Two Gaussians (sigma) AREA 4138.0 MEAN 0.95706 SIGMA1 8.95188E-03 AR2/AREA 0.52764 * DELM 0.00000E+00 SIG2/SIG1 0.39751 Function 2: Chebyshev Polynomial NORM 6300.3 CHEB01 -5.29920E-02 CHEB02 -0.90488 Parabolic + 108.8 + 9.4093E-05 7.1537E-04 4.8912E-02 0.000OE+00 2.1951E-02 of Order 2 + 822.1 5.5787E-02 + 7.4757E-02 Minos - 105.1 - 9.4181E-05 -6.6378E-04 - 5.0541E-02 - 0.0000E+00 - 2.1682E-02 879.7 5.7735E-02 6.4937E-02 C.L.= 27.0% 114.2 9.4031E-05 7.8420E-04 4.7314E-02 0.0000E+00 2.2505E-02 788.0 5.6000E-02 8.8170E-02 300 200 100 0.0 0.920 0.940 0.960 0.980 m(rp-t ) (GeV/c2) Figure 3-24. Reconstructed invariant mass distribution of the candidate ir' signal Monte Carlo for the mode T(1S) 7r';l --i 7OTr0 0: reconstruction efficiency is 16.6 0.4% after all the cuts. 1.000 from The I I I I I I I (a) L 1000 U, I 500 =Wt 400 200 (b) 0 12.5 2E <(SdE/dx I I I I . I ..( (C) . I . I. 1I -,' - Figure 3-25. Distributions from signal Monte Carlo: For the mode T(1S) --'- 7; A _ 7Tr000, variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) for X, Plot(b) Edx for two tracks, plot(c) for XU4, and plot(d) /S of the 7r candidates. The dashed (red) line in plot(d) shows the \S of the l..-.-' 1 7r candidates. As can be seen, majority of good events are confined within / < 10.0 giving us a reason to select our acceptance region. 3000 | 2000 1000 0 600 (I (c) --~4nruLlk~n "S" 2 0920 0940 0960 0980 1000 Figure 3-26. Invariant mass of q' candidate for the mode T(1S) 7y; ] 7Tr00r0: We found two events when no cuts are in place. None of the two events in the q' invariant mass histogram survive the XP4 < 200 requirement. 3.3.6 Reconstruction of T(1S) --> 7'; T -- 7+r7-7t We first constrain a pair of oppositely charged tracks to originate from a common vertex. Next, we add a 7r candidate and build the T] candidate. The T] candidate is mass-constrained to its nominal mass and then vertexed to another pair of oppositely charged tracks to make q'. The kinematics of the charged tracks involved in this mode is such that using wrong tracks at the p] reconstruction level results in ]q' having invariant mass within the acceptance region very often. This leads to multiple counting and poor resolution. To handle this situation, the T(1S) candidate with lowest )Xota, is selected where 2 2 2 XTotal means X.o + XY + X4. The selected T(1S) candidate is required to pass the consistency checks listed in Table 3-9. Figure 3-28 shows the invariant mass distribution for q' candidates passing our selection criteria. Figure 3-29 shows the distribution of cut variables used in this 1 22 m(Tl i ) (GeV/c2) 1 62 Figure 3-27. Extended range of invariant mass distribution of iq' candidate for the mode T(1S) -- 7'; --- 7r0rT00. No candidate signal event is observed in our acceptance mass window mode. In real data, we find two candidate events passing our selection cuts, as shown in Figure 3-30. These two events have been looked at in detail and show no signs of not being good signal events. Table 3-9. Final efficiency table for the mode T(1S) y7-'; r 7 + -7F0 Cut Ind Eff (%) Cmb Eff (%) XK4 < 200 96.6 25.4 a7 of 7o < 10 97.9 24.8 X < 100 99.1 24.7 dx < 4 98.9 24.5 all cuts 24.5 0.4 Likelihood = 111.0 = 112.5 for 100 8 d.o.f., Errors Function 1: Two Gaussians (sigma) AREA MEAN SIGMA1 AR2/AREA * DELM SIG2/SIG1 Function 2 NORM CHEB01 CHEB02 600 6125.0 0.95752 7.00002E-03 0.56394 0.00000E+00 0.36746 Parabolic 107.5 5.4365E-05 4.1859E-04 3.4331 E-02 0.0000E+00 1.5146E-02 :Chebyshev Polynomial of Order 2 12188. 717.1 -0.17360 + 4.6555E-02 -0.68293 7.0060E-02 Minos 106.1 5.4391 E-05 3.9725E-04 3.5332E-02 0.000OE+00 1.4990E-02 726.8 4.6885E-02 6.5904E-02 C.L.= 7.2% 109.1 5.4347E-05 4.4388E-04 3.3364E-02 0.0000E+00 1.5392E-02 711.2 4.6422E-02 7.4719E-02 400 200 0.0 0.920 0.940 0.960 0.980 m(pr+0 (GeV/c2) Figure 3-28. Reconstructed candidate r' invariant mass distribution from signal Monte Carlo for the mode T(1S) -- 7r'; -- 7+rr -7: The reconstruction efficiency is 24.5 0.5% after all the cuts. 1.000 1500 i i ,i 800 i I I i (a) (b) 1000 S- 400 IU IU 500 0 0 0 200 400 0 5 10 15 2 XP4 (yy 5000 I I 600 i I (c) (d) 400 r- t- 02500 -- w w 200 0 I 0 - 0 40 80 120 0 4 8 22 2 1(SdE/dx Figure 3-29. Distribution from signal Monte Carlo: For the mode T(1S) 7'; rl 7T+T7-7 variables we cut on are plotted. The yellow (shaded) area in these plots represents the acceptance. Plot(a) for XP4, plot(b) for oT of 7r candidate plot(c) for X., and Plot(d) SEdx for all four tracks. (a) - ]I I 1 [ I 0.920 0 UL 0.920 0.960 m(lt +7-) (GeV/c2) 0.960 m(lt +7i-) (GeV/c2) 1 . 3 C4 0 > 2 a0 )00 0.920 1.000 0.920 1.000 0.920 Figure 3-30. Invariant mass of r' candidate for the mode T(1S) 7r'; 7 +7r-Tr0: Plot(a) with no cuts, plot(b) with the requirement P 4 < 100, plot(c) with pion hypothesis consistency in the form \V "E/dx < 4.0, and plot(d) with all the cuts. We find two candidate events. (b) I II I I I 1n1 (d) ' " 0.960 2 m(iln+7i-) (GeV/c2) 0.960 2 m(iji)+7-) (GeV/c2) 1.000 1.000 I I I I I I I |

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PAGE 1 SEAR CH F OR RADIA TIVE DECA YS OF UPSILON(1S) INTO ET A AND ET A-PRIME By VIJA Y SINGH POTLIA A DISSER T A TION PRESENTED TO THE GRADUA TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQUIREMENTS F OR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORID A 2006 PAGE 2 Cop yrigh t 2006 b y Vija y Singh P otlia PAGE 3 T o m y paren ts PAGE 4 A CKNO WLEDGMENTS I w ould lik e to thank all those p eople who help ed me at dieren t stages during the course of this dissertation w ork. I w ould, rst and foremost lik e to thank m y advisor Dr. Y elton for his in v aluable guidance and exp ertise in the conducted researc h, and for giving me the freedom to dev elop and put to test m y o wn ideas in man y dieren t asp ects. Besides b eing an excellen t men tor, he has alw a ys b een v ery patien t and is a v ery understanding p erson whic h help ed immensely during the \ups and do wns" phases of the analysis. I also thank m y Ph ysics teac hers Dr. Thorn and Dr. W o o dard, and Committee mem b ers Dr. Av ery and Dr. T anner at the Univ ersit y of Florida, for inculcating the lessons of ph ysics and for b eing a source of inspiration. I w ould lik e to extend m y thanks to the en tire CLEO collab oration for setting up the pla yground for this researc h. I particularly w ould lik e to thank m y in ternal analysis committee mem b ers Da vid Besson, Helm ut V ogel, Jianc h un W ang and esp ecially Ric h Galik for all their help and suggestions to impro v e this w ork. Man y thanks to Hanna Mahlk e-Krueger and Basit A thar for their help. I also thank m y fello w colleages Luis Brev a, V alen tin Necula, G. Suhas, and man y others for fruitful ph ysics discussions. I also thank the computer sta at the Univ ersit y of Florida, esp ecially Da vid Hansen for his computing help. Rukhsana P atel, Sanja y Siw ac h, Sunil Bhardw a j, and Lakhan Gusain ha v e b een extremely supp ortiv e friends during this long journey I can not thank them enough. I o w e man y thanks to m y paren ts Ran bir and Premlata, and m y cousin F ateh. Last but not the least, the most imp ortan t p erson without whose supp ort and endurance this dissertation w ould not ha v e b een completed is m y wife Nisha. I thank her for iv PAGE 5 b eing b y m y side in all o dds and for her lo v e and patience whic h serv ed as m y guiding torc h. v PAGE 6 T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . iv LIST OF T ABLES . . . . . . . . . . . . . . . . viii LIST OF FIGURES . . . . . . . . . . . . . . . . ix ABSTRA CT . . . . . . . . . . . . . . . . . . xv CHAPTER1 THEOR Y . . . . . . . . . . . . . . . . . 1 1.1 P article Ph ysics and the Standard Mo del . . . . . . . 1 1.1.1 The Standard Mo del: Inputs and In teractions . . . . 1 1.1.2 Quan tum Chromo dynamics . . . . . . . . . 4 1.1.3 Symmetries . . . . . . . . . . . . . 6 1.1.3.1 Isospin . . . . . . . . . . . . 7 1.1.3.2 P arit y . . . . . . . . . . . . 7 1.1.3.3 Charge conjugation . . . . . . . . . 9 1.1.3.4 G-P arit y . . . . . . . . . . . . 10 1.1.4 Mesons . . . . . . . . . . . . . . . 11 1.2 Quark onia . . . . . . . . . . . . . . . . 13 1.2.1 Deca y Mec hanisms of (1S) . . . . . . . . . 13 1.2.2 Radiativ e Deca ys of (1S) in to and 0 . . . . . . 15 2 EXPERIMENT AL APP ARA TUS . . . . . . . . . . . 19 2.1 Cornell Electron Storage Ring . . . . . . . . . . 19 2.1.1 Linear Accelerator . . . . . . . . . . . . 19 2.1.2 Sync hrotron . . . . . . . . . . . . . 21 2.1.3 Storage Ring . . . . . . . . . . . . . 21 2.1.4 In teraction Region . . . . . . . . . . . . 22 2.2 Resonances . . . . . . . . . . . . . . . 23 2.3 CLEO I I I Detector . . . . . . . . . . . . . 24 2.3.1 Sup erconducting Coil . . . . . . . . . . . 26 2.3.2 Charged P article T rac king System . . . . . . . 26 2.3.2.1 Silicon V ertex Detector . . . . . . . . 27 2.3.2.2 The Cen tral Drift Cham b er . . . . . . 28 2.3.3 Ring Imaging Cherenk o v Detector . . . . . . . 30 2.3.4 Crystal Calorimeter . . . . . . . . . . . 32 vi PAGE 7 2.3.5 Muon Cham b ers . . . . . . . . . . . . 34 2.3.6 CLEO I I I T rigger . . . . . . . . . . . . 35 3 D A T A ANAL YSIS . . . . . . . . . . . . . . . 38 3.1 Data . . . . . . . . . . . . . . . . . 38 3.2 Skim and T rigger Eciency . . . . . . . . . . . 39 3.3 Reconstruction . . . . . . . . . . . . . . 43 3.3.1 Reconstruction of (1S) r ; + 0 . . . . 47 3.3.2 Reconstruction of (1S) r ; 0 0 0 . . . . . 54 3.3.3 Reconstruction of (1S) r ; r r . . . . . . 59 3.3.3.1 P ossible Bac kground e + e r r ( e + e ) . . 61 3.3.3.2 Handling e + e r r r bac kground . . . . 61 3.3.3.3 Final Selection and Comparison of Neural Net vs Asymmetry . . . . . . . . . . . 64 3.3.3.4 Data Plots and Upp er Limit . . . . . . 67 3.3.4 Reconstruction of (1S) r 0 ; r r . . . . . . 73 3.3.5 Reconstruction of (1S) r 0 ; 0 0 0 . . . . . 78 3.3.6 Reconstruction of (1S) r 0 ; + 0 . . . . 81 3.3.7 Reconstruction of (1S) r 0 ; 0 r . . . . . 87 3.4 Summary . . . . . . . . . . . . . . . . 97 4 SYSTEMA TIC UNCER T AINTIES AND COMBINED UPPER LIMIT 99 4.1 Systematic Uncertain ties . . . . . . . . . . . . 99 4.1.1 T rigger Considerations . . . . . . . . . . 99 4.1.2 Standard Con tributions . . . . . . . . . . 100 4.1.3 Con tributions from Ev en t Selection Criteria . . . . 101 4.2 Com bined Upp er Limits . . . . . . . . . . . . 106 5 SUMMAR Y AND CONCLUSIONS . . . . . . . . . . 113 APPENDIX EVENT VER TEX AND RE-FITTING OF 0 r r . . . 115 REFERENCES . . . . . . . . . . . . . . . . . 119 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . 121 vii PAGE 8 LIST OF T ABLES T able page 1{1 Basic fermions and some of their prop erties . . . . . . . . 3 1{2 Gauge b osons and some of their prop erties . . . . . . . . 3 1{3 Sym b ol, name, quark comp osition, mass in units of MeV = c 2 angular momen tum (L), in ternal spin (S), parit y (P), and c harge conjugation eigen v alues (C) for a few of the particles used in this analysis. . . . 12 1{4 Theoretical branc hing fractions as predicted b y v arious authors for radiativ e deca ys of (1S) in to and 0 . . . . . . . . . . . . 17 1{5 Pro duct branc hing ratios for deca y mo des of and 0 . . . . . 18 3{1 Luminosit y n um b ers for v arious data sets used in the analysis . . . 39 3{2 Eciency (in %) of basic cuts for mo des . . . . . . . . 42 3{3 Eciency (in %) of basic cuts for 0 mo des . . . . . . . . 42 3{4 Eciency of selection criteria for the mo de (1S) r ; + 0 . 47 3{5 Eciency table for the mo de (1S) r ; 0 0 0 . . . . . 55 3{6 Final eciency table for the mo de (1S) r ; r r . . . . . 66 3{7 Final eciency table for the mo de 0 + and then r r . . 73 3{8 Final eciency table for the mo de 0 + and then 0 0 0 . 78 3{9 Final eciency table for the mo de (1S) r 0 ; + 0 . . . 82 3{10 Eciency table for the mo de (1S) r 0 ; 0 r . . . . . . 89 4{1 Systematics' table for (1S) r 0 ; 0 r . . . . . . . . 101 4{2 Systematics uncertain ties for v arious deca y mo des of . . . . . 105 4{3 Systematics uncertain ties for v arious deca y mo des of 0 . . . . . 105 4{4 Results of the searc h for (1S) r 0 and (1S ) r Results include statistical and systematic uncertain ties, as describ ed in the text. The com bined limit is obtained after including the systematic uncertain ties. 108 viii PAGE 9 LIST OF FIGURES Figure page 1{1 Simple gluon-exc hange diagram . . . . . . . . . . . 4 1{2 Lo w est order deca ys of the (1S) allo w ed b y color conserv ation, c harge conjugation symmetry and parit y (a) Sho ws the deca y in to three gluons, (b) sho ws a radiativ e deca y and (c) sho ws the electro-magnetic deca y through a virtual photon that in turn deca ys electro-magnetically in to a pair of c harged fundamen tal particles, suc h as quarks or c harged leptons (the c harged leptons are represen ted b y the sym b ol l ). . . . . . 15 2{1 Wilson Lab oratory accelerator facilit y lo cated ab out 40 feet b eneath Cornell Univ ersit y's Alumni Fields. Both the CESR and the sync hrotron are engineered in the same tunnel. . . . . . . . . . . . . 20 2{2 Visible cross section in e + e collisions as a function of cen ter of mass energy Plot (a) on the left sho ws p eaks for ( n S ) for n = 1,2,3, and 4. Plot (b) on the left sho ws (5S) and (6S) as w ell as a blo w up for (4S) resonance. . . . . . . . . . . . . . . . . . 23 2{3 The CLEO I I I detector. . . . . . . . . . . . . . 25 2{4 View of the SVD I I I along the b eampip e. . . . . . . . . . 28 2{5 The RICH detector subsystem. . . . . . . . . . . . 32 2{6 Tw o kinds of RICH LiF radiators. F or normal incidence particles ( z 0) a sa wto oth radiator is necessary to a v oid in ternal rerection. . . . 33 3{1 Candidate + 0 reconstructed in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r ; + 0 The reconstruction eciency is 32 : 8 0 : 4% after all the cuts. . . . . . . . . 49 3{2 Distribution from signal Mon te Carlo: F or the mo de (1S) r ; + 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) r r of the 0 candidate, plot(b) for q S 2dE =dx plot(c) for 2P 4 and plot(d) is a scatter plot of the pion h yp othesis S dE =dx for the c harged trac ks. . . . . . . . 50 ix PAGE 10 3{3 In v arian t mass of distribution of the candidate for the mo de (1S) r ; + 0 : Plot(a) with no cuts, plot(b) with a cut on 2P4 only plot(c) after cutting on r r of the 0 candidate only plot(d) after cutting on S 2dE =dx alone. The red o v erla y on plot(d) is obtained after imp osing all the cuts. No candidate ev en t w as observ ed in signal region. . . . . 51 3{4 Reconstructed candidate in v arian t mass distribution in real data for the mo de (1S) r ; + 0 No ev en ts are observ ed in the signal mass windo w denoted b y the region in b et w een blue arro ws (inset), and a clear ! + 0 p eak is visible from the QED pro cess e + e r . 52 3{5 Scatter plot of e op distribution for trac k 2 vs trac k 1 for the ev en ts rejected b y S 2dE =dx > 16 : 0 cut. Most of the rejected ev en ts are clearly electron lik e. 53 3{6 Reconstructed in v arian t mass distribution for the candidate 0 0 0 from signal Mon te Carlo for the mo de (1S) r ; 0 0 0 The reconstruction eciency is 11 : 8 0 : 2% after all the cuts. . . . . 56 3{7 Distributions from (1S ) r ; 0 0 0 signal Mon te Carlo, sho wing the v ariables w e cut on. The y ello w (shaded) area in these plots represen ts the acceptance. Plot (a) p S 2 of the 0 candidates, plot (b) for 2P4 and plot (c) # of sho w ers in the ev en t. The dashed (red) line in plot (a) sho ws the p S 2 of the tagged 0 candidates. As can b e seen, ma jorit y of go o d ev en ts are conned within p S 2 < 10 : 0, giving us a reason to select our acceptance region. Plot (d) sho ws the sho w er m ultiplicit y from the signal MC for the pro cess e + e r Although plot (d) is not normalized to plot (c), w e can clearly see that if Mon te Carlo b e trusted, a cut on the n um b er of sho w ers help reject 50% of this bac kground. . . . . 57 3{8 In v arian t mass of candidate for the mo de (1S ) r ; 0 0 0 : Plot (a) allo wing m ultiple candidates p er ev en t, plot (b) after selecting b est c andidate plot (c) selecting b est c andidates with 2P4 < 200.0, plot (d) b est c andidate with # of sho w ers cut. The red o v erla y on plot (d) is obtained after imp osing all the cuts. There are no ev en ts in the acceptance mass windo w (denoted b y blue arro ws) after all the cuts. . . . . 58 3{9 j ~ p j vs E distribution plot(a) for signal MC for (1S) r ; r r and plot(b) for e + e r r r MC. . . . . . . . . . . . . 59 3{10 Asymmetry distribution for candidate. Plot (a) from Mon te Carlo data for e + e r r r (blac k) and signal MC (1S) r ; r r (red) and plot (b) for data18 and data19. F or asymmetry < 0 : 75, the ev en ts in plot (b) are o v ershado w ed b y the ev en ts b ey ond asymmetry > 0 : 75. The h uge pile at the higher in end in plot (b) is b ecause in this plot, the ev en ts classied as gamGam ev en t-t yp e ha v e not b een rejected y et. . . . 60 x PAGE 11 3{11 Distribution of vs in real data for ev en ts in the mass windo w passing our basic cuts. . . . . . . . . . . . . . . 62 3{12 T raining the Neural Net: During the course of training, red denotes the training error and blac k denotes the testing error (shifted b y 0.02 for clarit y) from an indep enden t sample. The testing error follo ws the training errors closely and o v er-training is not exhibited at all. The learning pro cess saturates ho w ev er, and training is stopp ed after 10K iterations. . . 65 3{13 Comparison of bac kground rejection vs eciency: The lo w er curv e in red sho ws the p erformance of asymmetry cut and upp er curv e in blac k is from neural net. F or an y c hosen v alue of eciency neural net giv es a higher bac kground rejection as compared to asymmetry cut. Inset is S= p B plotted for v arious v alues of neural net cut. . . . . . . 66 3{14 r r in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r ; r r . . . . . . . . . . . . . . 67 3{15 r r in v arian t mass distribution in real data. All cuts except neural net cut are in place. . . . . . . . . . . . . . . . . 68 3{16 r r in v arian t mass distribution in real data after all cuts. . . . . 69 3{17 Fit to r r in v arian t mass distribution for the mo de (1S) r ; r r Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 2 : 3 8 : 7 ev en ts, whic h is consisten t with 0. . . . . . . . . . . . . . . 70 3{18 Normalized probabilit y distribution for dieren t signal area for the mo de (1S) r ; r r The shaded area spans 90% of the probabilit y . 71 3{19 The t to reconstructed r r in v arian t mass distribution from real data for the mo de (1S) r ; r r The area is xed to the n um b er of ev en ts obtained from 90% condence lev el upp er limit. The mean, width and other parameters are xed to the ones obtained from Mon te Carlo. . 72 3{20 Reconstructed candidate 0 in v arian t mass distribution from signal Mon te Carlo for the mo de (1S ) r 0 ; r r The reconstruction eciency is 40 : 6 0 : 4% after all the cuts. . . . . . . . . . . . 74 3{21 Distribution from signal Mon te Carlo: F or the mo de (1S) r 0 ; r r v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) 2 distribution, plot(b) for q S 2dE =dx plot(c) for 2P4 and plot(d) is a scatter plot of the dE =dx for pion h yp othesis for the c harged trac ks. . . . . . . . . . . . 75 xi PAGE 12 3{22 In v arian t mass of 0 candidate for the mo de (1S) r 0 ; r r : Plot(a) without an y cuts, plot(b) after selecting candidates with 2 < 200, plot(c) after dE =dx cut, plot(d) requiring 2P4 < 100. The red o v erla y on plot(d) is obtained after imp osing all the cuts. No candidate signal ev en t is observ ed in our acceptance mass windo w (denoted b y blue arro ws). . . . . 76 3{23 Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; r r No candidate signal ev en t is observ ed in our acceptance mass windo w (inset). . . . . . . . . . . . 77 3{24 Reconstructed in v arian t mass distribution of the candidate 0 from signal Mon te Carlo for the mo de (1S) r 0 ; 0 0 0 : The reconstruction eciency is 16 : 6 0 : 4% after all the cuts. . . . . . . . . 79 3{25 Distributions from signal Mon te Carlo: F or the mo de (1S) r 0 ; 0 0 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) for 2 Plot(b) q S 2dE =dx for t w o trac ks, plot(c) for 2P4 and plot(d) p S 2 of the 0 candidates. The dashed (red) line in plot(d) sho ws the p S 2 of the tagged 0 candidates. As can b e seen, ma jorit y of go o d ev en ts are conned within p S 2 < 10 : 0 giving us a reason to select our acceptance region. . . . . . . . . 80 3{26 In v arian t mass of 0 candidate for the mo de (1S) r 0 ; 0 0 0 : W e found t w o ev en ts when no cuts are in place. None of the t w o ev en ts in the 0 in v arian t mass histogram surviv e the 2P4 < 200 requiremen t. . 81 3{27 Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; 0 0 0 No candidate signal ev en t is observ ed in our acceptance mass windo w . . . . . . . . . . . . . 82 3{28 Reconstructed candidate 0 in v arian t mass distribution from signal Mon te Carlo for the mo de (1S ) r 0 ; + 0 : The reconstruction eciency is 24 : 5 0 : 5% after all the cuts. . . . . . . . . 83 3{29 Distribution from signal Mon te Carlo: F or the mo de (1S) r 0 ; + 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) for 2P4 plot(b) for r r of 0 candidate plot(c) for 2 and Plot(d) q S 2dE =dx for all four trac ks. . 84 3{30 In v arian t mass of 0 candidate for the mo de (1S ) r 0 ; + 0 : Plot(a) with no cuts, plot(b) with the requiremen t 2P4 < 100, plot(c) with pion h yp othesis consistency in the form q S 2dE =dx < 4 : 0, and plot(d) with all the cuts. W e nd t w o candidate ev en ts. . . . . . . . . 85 xii PAGE 13 3{31 Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; + 0 Tw o go o d candidate signal ev en ts are observ ed in our acceptance mass windo w (inset). . . . . . 86 3{32 Reconstructed r candidate in v arian t mass distribution from signal MC for 0 r : The kinematic tting impro v es the in v arian t mass resolution b y 30% and reconstruction eciency b y 5%. . . . . . . 89 3{33 Reconstructed in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r 0 ; 0 r : The reconstruction eciency is 40 : 1 0 : 4% after all the cuts. . . . . . . . . . . . . . . . 90 3{34 Reconstructed in v arian t mass distribution in real data for the mo de (1S) r 0 ; 0 r : In top plot, blac k histogram sho ws the distribution from 1S data and o v erlaid in red is the scaled distribution from 4S data. The b ottom plot after subtracting the con tin uum. W e assume the same reconstruction eciency at 4S energy . . . . . . . . . . . . . . 91 3{35 Without con tin uum subtraction, the t to data plot for the mo de (1S) r 0 ; 0 r : Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 3 : 1 5 : 3 ev en ts. 92 3{36 The t to the con tin uum subtracted data plot for the mo de (1S) r 0 ; 0 r : Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 3 : 5 6 : 3 ev en ts. The underlying con tin uum has b een subtracted using the distribution from 4S data. . . . . . . . . . . . . . . . . . . 93 3{37 The normalized probabilit y distribution for dieren t signal area for the mo de (1S) r 0 ; 0 r : The shaded area spans 90% of the probabilit y 94 3{38 The 90% upp er limit t to the in v arian t mass distribution without con tin uum subtraction . . . . . . . . . . . . . . . . . 95 3{39 After subtracting the underlying con tin uum, the 90% upp er limit t to the in v arian t mass distribution . . . . . . . . . . . 96 4{1 Amoun t of bac kground rejected for v arious v alues of asymmetry and neural net cut ha ving the same eciency The \eciency" is obtained from signal Mon te Carlo. \Bac kground rejection" is obtained either from QED Mon te Carlo sample (red pluses) or from real data (blac k crosses). . . . . 103 4{2 Energy of the hard photon in MC samples after all our selection criteria for resp ectiv e mo des . . . . . . . . . . . . . . 104 4{3 Probabilit y distribution as function of branc hing ratio for the deca y mo de (1S) r : Blac k curv e denotes the com bined distribution. The distributions ha v e b een normalized to the same area. . . . . . . . . . 109 xiii PAGE 14 4{4 Plotted on log-scale, the lik eliho o d distribution as function of branc hing ratio for the deca y mo de (1S) r : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalize to the same area. . 110 4{5 Probabilit y distribution as function of branc hing ratio for the deca y mo de (1S) r 0 : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalize to the same area. . . . . . . . . . 111 4{6 Plotted on log-scale, the lik eliho o d distribution as function of branc hing ratio for the deca y mo de (1S ) r 0 : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalized to the same area. . 112 1 Reconstructed in v arian t mass distribution of + 0 candidate from signal Mon te Carlo for the mo de (1S) r ; + 0 : After all cuts in place, solid blac k histogram represen ts the + 0 candidate in v arian t mass distribution when 0 candidate is re-t from the ev en t v ertex. Ov erla y in dotted, red histogram is obtained using default 0 candidates. . . . . . . . . . . . . . . . . . 117 2 Reconstructed in v arian t mass distribution of + candidate from signal Mon te Carlo from signal Mon te Carlo for the mo de (1S) r 0 ; r r : After all cuts in place, solid, blac k histogram represen ts the 0 ; r r candidate in v arian t mass distribution when r r candidate is re-t from the ev en t v ertex. Ov erla y in dotted, red histogram is obtained using default r r candidates. . . . . . . . . . . . . . 118 xiv PAGE 15 Abstract of Dissertation Presen ted to the Graduate Sc ho ol of the Univ ersit y of Florida in P artial F ulllmen t of the Requiremen ts for the Degree of Do ctor of Philosoph y SEAR CH F OR RADIA TIVE DECA YS OF UPSILON(1S) INTO ET A AND ET A-PRIME By Vija y Singh P otlia Ma y 2006 Chair: John M. Y elton Ma jor Departmen t: Ph ysics W e conducted a new searc h for the radiativ e deca y of (1S ) to the pseudoscalar mesons and 0 in (21 : 2 0 : 2) 10 6 (1S) deca ys collected with the CLEO I I I detector op eration at the Cornell Electron Strorage Ring (CESR). The meson w as reconstructed in the three mo des r r + 0 or 0 0 0 The 0 meson w as reconstructed in the mo de 0 + with deca ying through an y of the ab o v e three mo des; and also 0 r 0 where 0 + The rst six of these deca y c hains w ere searc hed for in the previous CLEO I I analysis on this sub ject, whic h used a data sample 14.6 times smaller. Fiv e of the sev en submo des w ere virtually bac kground free. W e found no signal ev en ts in four of them. The only exception w as (1S) r 0 ; + 0 where w e observ ed t w o go o d signal candidates. The other t w o submo des ( r r and 0 r ) are bac kground limited, and sho w ed no excess of ev en ts in the signal region. W e com bined the results from dieren t c hannels and obtained 90% condence lev el (C.L.) upp er limits B ((1S) r ) < 9 : 3 10 7 and B ((1S) r 0 ) < 1 : 77 10 6 Our limits c hallenge theoretical mo dels. xv PAGE 16 CHAPTER 1 THEOR Y 1.1 P article Ph ysics and the Standard Mo del Humankind has alw a ys b een in trigued b y questions lik e \What is matter made of ?" and \Ho w do the constituen ts of matter in teract with eac h other?" In their quest for fundamen tal building blo c ks of matter, ph ysicists found ev en more comp ositeness. The existence of more than 100 elemen ts sho wing p erio dically recurring prop erties w as a clear indication that atoms (once though t indestructible and fundamen tal building blo c ks) ha v e an in ternal structure. A t the start of the 20th cen tury the in ternal structure of the atom w as rev ealed through a series of exp erimen ts. The core of an atom (the n ucleus) w as found to b e made of protons and neutrons (collectiv ely called n ucleons), surrounded b y an electron cloud. This picture of the atom w as righ t; ho w ev er, the observ ation of radioactiv e -deca y and the stabilit y of the n ucleus prompted ph ysicists to tak e the reductionist approac h farther and a new branc h of ph ysics w as b orn called as particle ph ysics. Mo dern particle ph ysics researc h represen ts the most am bitious and most organized eort of h umankind to answ er the questions of fundamen tal building blo c ks and their in teractions. Ov er the last half cen tury our understanding of particle ph ysics adv anced tremendously and w e no w ha v e a theoretical structure (the Standard Mo del) rmly grounded in exp erimen t that splendidly describ es the fundamen tal constituen ts of matter and their in teractions. 1.1.1 The Standard Mo del: Inputs and In teractions The Standard Mo del (SM) of elemen tary particle ph ysics comprises the unied theory of all the kno wn forces except gra vit y These forces are the electro-magnetic force (w ell kno wn to us in ev eryda y life), the w eak force, and the strong force. In the 1 PAGE 17 2 Standard Mo del, the fundamen tal constituen ts of the matter are quarks and leptons. These constituen ts are spin1 2 particles (fermions) ob eying F ermi-Dirac statistics. The quarks and leptons come in three generations: up and do wn quarks ( u d ), and electronic neutrino and electron ( e ; e ) c harm and strange quarks ( c s ), and m uonic neutrino and m uon ( ; ) top and b ottom quarks ( t b ), and tauonic neutrino and tauon ( ; ) Eac h generation has a doublet of particles arranged according to the electric c harge. The leptons fall in to t w o classes, the neutral neutrinos e , and negativ ely c harged e , and The quarks u c and t ha v e electric c harge +2e = 3 and the d s and b quarks ha v e electric c harge e = 3. Eac h quark is said to constitute a separate ra v or (six quark ra v ors exist in nature). The generations are arranged in the mass hierarc h y and the masses t no eviden t pattern. The neutrinos are considered as massless. The Standard Mo del do es not attempt to explain the v ariet y and the n um b er of quarks and leptons or to compute an y of their prop erties; the fundamen tal fermions are tak en as truly elemen tary at the SM lev el. Eac h of the fundamen tal fermions has an an ti-fermion of equal mass and spin, and opp osite c harge. Other than the electric c harge, the basic fermions ha v e t w o more c harges | \color c harge" coupling to strong force, an attribute of quarks only (but not leptons), and \w eak c harge" or \w eak isospin" coupling to w eak force, carried b y all fundamen tal fermions. The prop erties of these fermions (T able 1{1 ) recur in eac h generation. In the paradigm of Standard Mo del, the three dieren t t yp es of in teractions existing among the elemen tary particles arise as a natural and automatic consequence of enforcing lo cal gauge symmetry Eac h force is mediated b y a force carrier, a gauge b oson whic h couples to the c harge on the particle. The b osons are spin-1 particles. The guage b osons of SM are sho wn in T able 1{2 PAGE 18 3 T able 1{1. Basic fermions and some of their prop erties Quarks Leptons Fla v or Mass Electric W eak Fla v or Mass Electric W eak ( MeV = c 2 ) c harge c harge ( MeV = c 2 ) c harge c harge u 2-8 +2e/3 +1/2 e < 0 : 000015 0 +1/2 d 5-15 -e/3 -1/2 e 0.511 -e -1/2 c 1000-1600 +2e/3 +1/2 < 0 : 19 0 +1/2 s 100-300 -e/3 -1/2 105.7 -e -1/2 t 175000 +2e/3 +1/2 < 18 : 2 0 +1/2 b 4100-4500 -e/3 -1/2 1777.0 -e -1/2 The familiar electro-magnetic force (also called as Quan tum Electro dynamics, or QED) is mediated b y the exc hange of a photon. Only particles with electric c harge can in teract electro-magnetically The strong force is mediated b y gluons and couples to particles that ha v e color c harge. This force is resp onsible for holding quarks together inside the hadrons (neutron and proton are t w o example of hadrons). Leptons ha v e no color and th us do not exp erience strong force. This is one of the primary dierences b et w een leptons and quarks. The w eak force is mediated b y the W and Z 0 b osons. P articles with w eak c harge, or w eak isospin, can in teract via the w eak force. The mediators of w eak force are dieren t from the photons and gluons in the sense that these mediating particles ( W and Z 0 ) are massiv e. The w eak force th us is a short range force as opp osed to electro-magnetic and strong forces whic h are long-range in nature due to masslessness of photon and gluons. T able 1{2. Gauge b osons and some of their prop erties P article Sym b ol F orce Mediated Charge Mass (GeV = c 2 ) J P Photon r Electromagnetic 0 0 1 Gluon g Strong 8 colors 0 1 Z 0 Z 0 W eak 0 91.187 1 W W W eak e 80.40 1 PAGE 19 4 1.1.2 Quan tum Chromo dynamics Strong in teractions in the Standard Mo del are describ ed b y the theory of Quan tum Chromo dynamics (QCD). The quarks come in three primary colors: 1 r (red), g (green), and b (blue) and the an ti-quarks ha v e complemen tary colors (or an ti-colors) r (cy an), g (magen ta), and b (y ello w). The quarks in teract strongly b y exc hanging color whic h is mediated b y gluon exc hange (Figure 1{1 ). Gluon exc hange is p ossible only if the gluons themselv es are colored (carry color c harge), and in fact, the gluons carry the color and an ti-color sim ultaneously The strength of strong in teraction is ra v or indep enden t. g ( r b ) b b r r Figure 1{1. Simple gluon-exc hange diagram Since there are three p ossible colors and three p ossible an ti-colors for gluons, one migh t guess that the gluons come in as man y as nine dieren t color com binations. Ho w ev er, one linear com bination of color an ti-color states has no net color and therefore can not mediate among color c harges. Th us only eigh t linearly indep enden t color com binations are p ossible. The w a y in whic h these eigh t states are constructed from colors and an ti-colors is a matter of con v en tion. One p ossible c hoice is sho wn in Equation 1{1 for the o ctet, and the color singlet is represen ted in Equation 1{2 r g ; r b; g b; g r ; b r ; b g ; p 1 = 2 ( r r g g ) ; p 1 = 6( r r + g g 2 b b ) (1{1) p 1 = 3( r r + g g + b b ) (1{2) 1 The \color" in QCD is a degree of freedom describing the underlying ph ysics, and should not b e misin terpreted with ordinary colors w e see in life. PAGE 20 5 This situation is analogous to the p erhaps more familiar example of t w o spin 1/2 particles. Eac h particle can ha v e its spin up ( ) or do wn ( # ) along the z axis corresp onding to four p ossible com binations represen ted b y eac h giving a total spin S = 0 or 1 represen ted b y j S S z > The S = 1 states form a triplet, j 1 + 1 > = j "" > j 1 0 > = 1 p 2 ( j "# > + j #" > ) j 1 1 > = j ## > (1{3) and there is a singlet state with S = 0, j 0 0 > = 1 p 2 ( j "# > j #" > ) : (1{4) The proliferation of gluons in QCD con trasts with QED where there is only a single photon. Another striking dierence b et w een QED and QCD is that the force carriers in QED, the photons, do not carry an y c harge. The photons therefore, do not ha v e self-in teractions. On the other hand, the gluons in QCD ha v e color c harge and th us they undergo self-in teractions. In eld-theoretic language, theories in whic h eld quan ta ma y in teract directly are called \non-Ab elian." The gluon self-in teraction leads to t w o v ery imp ortan t c haracteristics of QCD: \color connemen t" and \asymptotic freedom." Color connemen t means that the observ ed states in nature ha v e no net color c harge: i.e., the observ ed states are color singlets. An implication of color connemen t is that free quarks and free gluons can not b e observ ed in nature. Bound states of t w o or more gluons ha ving o v erall zero color c harge can b e found in principle. Suc h b ound states are referred to as \glueballs." Man y exp erimen tal searc hes for suc h states ha v e b een made, without conclusiv e results, for example [ 1 ]. Asymptotic freedom means that the in teraction gets w eak er at shorter in ter-quark distances and the quarks are relativ ely free in that limit. PAGE 21 6 The phenomenon of color connemen t constrains the w a y quarks com bine to form observ ed particle states. The only com binations allo w ed (and observ ed for that matter) are q q forming mesons, and q q q forming bary ons. Group-theoretically it is p ossible to decomp ose 3 3 ( q q ) to obtain an o ctet and a singlet. The color singlet for q q is simply the state sho wn in Equation 1{2 The color singlet for q q q can b e obtained from decomp osition 3 n 3 n 3 = 10 8 8 1 and is sho wn in Equation 1{5 j q q q > col or sing l et = 1 p 6 ( r g b g r b + br g bg r + g br r bg ) : (1{5) The existence of particles with fractional c harges, as for example made from b ound state q q is ruled out as it is not p ossible to obtain a color singlet q q conguration. Group theory quic kly tells us that 3 n 3 decomp osition is 6 3 (a sextet and a triplet, but no singlet). 1.1.3 Symmetries Symmetries are of great imp ortance in ph ysics. A symmetry arises in nature whenev er some c hange in the v ariables of the system lea v es the essen tial ph ysics unc hanged. The symmetry th us leads to conserv ation la ws | univ ersal la ws of nature v alid for all in teractions, for example, the conserv ation of linear momen tum and angular momen tum arise from translational in v ariance and rotational in v ariance, resp ectiv ely Enforcing lo cal gauge symmetry giv es rise to in teractions in eld theory Isospin symmetry is resp onsible for attractiv e force b et w een n ucleons on an equal fo oting. In particle ph ysics, the discrete symmetry op erations parit y and c harge conjugation pla y a sp ecial role in particle pro duction and deca y Certain reactions are forbidden due to the constrain ts imp osed b y these symmetries | the symmetries th us b ecome dynamics. In the next few sections w e review some of these symmetry op erations, the details of whic h can b e found in Griths [ 2 ], P erkins [ 3 ], and Halzen and Martin [ 4 ]. PAGE 22 7 1.1.3.1 Isospin The n uclear force b et w een n ucleons is the same irresp ectiv e of the c harge on the n ucleon. The proton and neutron are th us treated as t w o states of a n ucleon whic h form an \isospin" doublet (I = 1/2), = p n (1{6) with I 3 the third comp onen t of I, b eing +1 = 2 for proton and 1 = 2 for neutron. The origin of isospin lies in the near equalit y of the u and d quark masses, so, the idea of isospin can b e tak en to a more fundamen tal lev el where u and d quarks form a doublet whic h can b e transformed in to eac h other in the isospin space. The I 3 for an u quark is +1 = 2 and that for a d quark is 1 = 2 and based up on this assignmen t, I 3 sp eaks for the quark ra v or. The I 3 for an ti-quarks is the negativ e of that of quarks. The treatmen t of isospin go es v ery m uc h lik e quan tum mec hanical angular momen tum. Since strong and electro-magnetic in teractions conserv e the quark ra v or, the third comp onen t of isospin is a go o d quan tum n um b er for these in teractions. Ho w ev er, total isospin I is not conserv ed under electro-magnetic in teractions as the isotrop y of isospin is brok en due to dieren t electric c harge on the u and d quarks. Only strong in teractions conserv e b oth I and I 3 1.1.3.2 P arit y The parit y op erator, ^ P rev erses the sign of an ob ject's spatial co ordinates. Consider a particle j a > with a w a v e function a ( ~ x ; t ). By the denition of the parit y op erator, ^ P ( ~ x; t ) = P a a ( ~ x ; t ) (1{7) where P a is a constan t phase factor. If w e consider an eigenfunction of momen tum ~ p ( ~ x; t ) = e i ( ~ p ~ x E t ) (1{8) PAGE 23 8 then ^ P ~ p ( ~ x; t ) = P a ~ p ( ~ x ; t ) = P a ~ p ( ~ x ; t ) ; (1{9) so that an y particle at rest, with ~ p = 0, remains unc hanged up to a m ultiplicativ e n um b er, P a under the parit y op erator. States with this prop ert y are called eigenstates with eigen v alue P a The quan tit y P a is also called the in trinsic parit y of particle a or more usually just the parit y of particle a Since t w o successiv e parit y transformations lea v e the system unc hanged, P 2 a = 1, implying that the p ossible v alues for the parit y eigen v alue are P a = 1. In addition to a particle at rest, a particle with denite orbital angular momen tum is also an eigenstate of parit y The w a v e function for suc h a particle in spherical co ordinates is nl m ( ~ x; t ) = R nl ( r ) Y m l ( ; ) ; (1{10) where ( r ; ; ) are spherical p olar co ordinates, R nl ( r ) is a function of the radial v ariable r only and the Y m l ( ; ) is a spherical harmonic. The spherical harmonics are w ell kno wn functions whic h ha v e the follo wing prop ert y Y m l ( ; ) = ( 1) l Y m l ( ; + ) : (1{11) Hence ^ P nl m ( ~ x; t ) = P a nl m ( ~ x ; t ) = P a ( 1) l nl m ( ~ x; t ) (1{12) pro ving that a particle with a denite orbital angular momen tum l is indeed an eigenstate of the parit y op erator with eigen v alue P a ( 1) l The parit y of the fundamen tal fermions cannot b e measured or deriv ed. All that Nature requires is that the parit y of a fermion b e opp osite to that of an an ti-fermion. As a matter of con v en tion fermions are assigned P = +1 and an ti-fermions are assigned P = 1. In con trast, the parities of the photon and gluon can b e deriv ed b y applying ^ P to the eld equations resulting in P r = 1 and P g = 1. PAGE 24 9 The parit y of (1S ), a spin 1 b b b ound state (describ ed in Section 1.2 ) with L = 0 is P = P b P b ( 1) L = 1. P arit y is a go o d quan tum n um b er b ecause it is a symmetry of the strong and electro-magnetic force. This means that in an y reaction in v olving these forces, parit y m ust b e conserv ed. 1.1.3.3 Charge conjugation The op eration that replaces all particles b y their an ti-particles is kno wn as c harge conjugation. In quan tum mec hanics the c harge conjugation op erator is represen ted b y ^ C F or an y particle j a > w e can write ^ C j a > = c a j a > (1{13) where c a is a phase factor. If w e let the ^ C op erator act t wice to reco v er the original state j a > j a > = ^ C 2 j a > = ^ C ( c a j a > ) = c a ^ C j a > = c a c a j a > (1{14) whic h sho ws that c a c a = 1. If (and only if ) a is its o wn an ti-particle, it is an eigenstate of ^ C The p ossible eigen v alues are limited to C = c a = c a = 1. All systems comp osed of the same fermion and an an ti-fermion pair are eigenstates of ^ C with eigen v alue C = ( 1) ( L + S ) This factor can b e understo o d b ecause of the need to exc hange b oth particles' p osition and spin to reco v er the original state after the c harge conjugation op erator is applied. Exc hanging the particles' p osition giv es a factor of ( 1) L as sho wn in the previous section. Exc hanging the particles' spin giv es a factor of ( 1) S +1 as can b e v eried b y insp ecting Equations 1{3 and 1{4 and a factor of ( 1) whic h arises in quan tum eld theory whenev er fermions and an ti-fermions are in terc hanged. With this result w e can calculate the c harge conjugation eigen v alue for the (1S) and obtain C = 1 since L + S = 1. The photon is an eigenstate of ^ C since it is its o wn an ti-particle. The C eigen v alue for the photon can b e deriv ed b y inserting ^ C in to the eld equations and is C r = 1. PAGE 25 10 1.1.3.4 G-P arit y W e just learned from the c harge conjugation op eration that only neutral particles can b e eigenstates of c harge conjugation op erator. A useful conserv ation la w for the strong in teractions can b e set up b y com bining the c harge conjugation op eration with a 180 rotation ab out a c hosen axis in the isospin space. This com bined op eration of rotation in the isospin space, follo w ed b y c harge conjugation, is called as G-parit y G = ^ C exp ( i 2 ) (1{15) As noted earlier, the isospin has the same algebraic prop erties that of quan tum mec hanical angular momen tum op erator, the rotation of an isospin state j I ; I 3 > in isospin space ab out y-axis b y an angle can b e carried out as: R 2 ( ) j I ; I 3 > = exp ( i 2 ) j I ; I 3 > = ( 1) I I 3 j I ; I 3 > (1{16) Th us, for a rotation ab out the 2 axis (y axis) in isospin space w e ha v e R 2 ( ) j + > = j > R 2 ( ) j > = j + > R 2 ( ) j 0 > = ( 1) j 0 > (1{17) In this w a y w e nd that the G-parit y for neutral pion is unam biguously xed to 1. Since the strong in teractions conserv e isospin and are in v arian t under c harge conjugation, one migh t exp ect that the G-parit y of is same as that of 0 Th us, under G-parit y transformation, w e ha v e G j ; 0 > = ( 1) j ; 0 > (1{18) G-parit y is a m ultiplicativ e quan tum n um b er, therefore, the G-parit y of a system of n pions is ( 1) n G-parit y is a go o d quan tum n um b er of non-strange mesons and is conserv ed in strong in teractions. PAGE 26 11 1.1.4 Mesons A t this p oin t, w e can in tro duce the lo w est lying mesonic states. F rom the ligh t 2 quarks u d and s w e exp ect nine p ossible q q com binations, th us nine mesons, whic h break in to an o ctet and a singlet as p er 3 n 3 = 8 1. F or lo w est lying states, it is safe to assume that the relativ e angular momen tum quan tum n um b er L is 0. The parit y for suc h states then is P = ( 1) L+1 = 1. Since the relativ e angular momen tum is 0, the total angular momen tum is same as the spin of the q q com bination. The t w o spin-1/2 quarks can b e com bined either to get total spin 1 (leading to J P = 1 ) or spin 0. States with S = 0 (and therefore J = 0) are pseudoscalar mesons (J P = 0 ), some of whic h are the sub ject of in terest of this study The normalized, orthogonal set of o ctet is j + > = u d j > = d u j 0 > = 1 p 2 ( d d u u ) j K + > = u s j K > = s u j K 0 > = d s j K 0 > = s d j > j 8 > = 1 p 6 ( d d + u u 2 s s ) (1{19) and the ra v or symmetric singlet is j 0 > j 0 > = 1 p 3 ( d d + u u + s s ) (1{20) 2 The quarks u d and s are considered as ligh t on the scale of QCD parameter The quarks c b and t are considered as hea vy quarks. PAGE 27 12 T able 1{3. Sym b ol, name, quark comp osition, mass in units of MeV = c 2 angular momen tum (L), in ternal spin (S), parit y (P), and c harge conjugation eigen v alues (C) for a few of the particles used in this analysis. Sym b ol Name Quark Comp osition Mass I G L S P C (1S) Upsilon(1S) b b 9460.30 0 1 0 1 1 1 + Pion u d 139.57 1 1 0 0 1 x Pion d u 139.57 1 1 0 0 1 x 0 Pi0 1 p 2 ( d d u u ) 134.98 1 1 0 0 1 +1 Eta 1 p 6 ( d d + u u 2 s s ) 547.75 0 +1 0 0 1 +1 0 Eta-prime 1 p 3 ( d d + u u + s s ) 957.78 0 +1 0 0 1 +1 0 Rho0 1 p 2 ( u u d d ) 775.8 1 +1 0 1 1 1 r Photon x 0 0,1 x x 1 1 1 In the real w orld, the and 0 states are a mixture of 8 and 0 with b eing \mostly o ctet" 8 and 0 b eing \mostly singlet" 0 The mixing angle b et w een 8 0 is 20 the consequence of whic h is that s s con ten t is decreased for and increased for 0 [ 5 ]. V arious prop erties of pseudoscalar mesons 0 along with pion triplet are sho wn in T able 1{3 If w e assume that the masses of quarks u d and s is zero, then these particles exhibit SU(3) L SU(3) R c hiral 3 symmetry The Goldstone theorem [ 6 ] sa ys that a massless particle (called Goldstone b oson) is generated for eac h generator of the brok en symmetry The SU(3) c hiral symmetry is sp on taneously brok en to v ector SU(3), giving rise to eigh t massless Goldstone b osons whic h are iden tied with the o ctet part of the lo w est lying meson nonet. These Goldstone b osons acquire mass due to explicit breaking of the symmetry where quarks ha v e unequal masses. The singlet 0 is v ery massiv e compared to the mem b ers of o ctet. This happ ens b ecause the 0 is not a Goldstone b oson and acquires mass due to a dieren t mec hanism [ 5 ]. 3 When the particle mass is zero, the left-handed and righ t-handed particles are treated dieren tly This is what w e understand b y c hiral symmetry PAGE 28 13 1.2 Quark onia Quark onia are ra v or-less mesons made up from a hea vy 4 quark and its o wn an ti-quark. Charmonium ( c c ) and b ottomonium ( b b ) are the only examples of quark onia whic h can b e pro duced. The b ound state t t is not exp ected to b e formed as the top quark has a reeting lifetime o wing to its large mass. In sp ectroscopic notation, the quan tum n um b ers of quark onia are expressed as n 2S +1 L J where n L, S and J represen t the principal quan tum n um b er, orbital angular momen tum, spin, and total angular momen tum resp ectiv ely In literature, the n 3 S 1 c harmonium and b ottomonium states are called as ( n S ) and ( n S) resp ectiv ely The com bined spin of q q in the ab o v e men tioned systems is 1. The q q relativ e angular momen tum in these mesons is L = 0, i.e., an \S" w a v e and hence the sym b ol \S" in the notation. The n 3 S 1 quark onia ha v e J PC = 1 whic h is same as that of photon, therefore these mesons can b e pro duced in the deca y of virtual photon 5 generated in e + e annihilation carried out at the righ t cen ter-of-mass energy The lo w est suc h state is (1S) (commonly called J/ ), a c c state pro duced at cen ter-of-mass energy 3.09 GeV. The corresp onding state for b b is (1S), pro duced at 9.46 GeV. 1.2.1 Deca y Mec hanisms of (1 S ) Armed with all the basic information, w e are no w ready to understand the p ossible w a ys in whic h (1S) can deca y Strong and electro-magnetic in teractions conserv e color, parit y and c harge conjugation. These constrain ts lea v e v ery few 4 q q states from ligh t quarks u d s are rather mixtures of the ligh t quarks than w ell dened states in terms of quark-an tiquark of the same ra v or. Ev en is also not a pure s s state. 5 Suc h a photon is called virtual b ecause it cannot conserv e the 4-momen tum of the initial system ( e + e here) and is unstable, existing only for a brief p erio d of time, as allo w ed b y the uncertain t y principle, after whic h it deca ys to a pair of c harged fermion-an tifermion. PAGE 29 14 deca y routes op en, for example (1S) deca y to an ev en n um b er of photons or an ev en n um b er of gluons is forbidden b y c harge conjugation. The easiest route w ould ha v e b een (1S ) deca ying in to a pair of B mesons, but this is not allo w ed kinematically A p ossible simple deca y mec hanism is that b b pair rst in teract electro-magnetically and annihilate in to a virtual photon. This pro cess is allo w ed as it do es not violate an y of the fundamen tal principals. The virtual photon then readily deca ys either in to a pair of leptons or it deca ys in to a pair of quark-an tiquark whic h further hadronize. On the other hand, the deca y of (1S ) in to a single gluon is forbidden b ecause it violates color conserv ation. When (1S ) deca ys via in termediate gluons, the minim um n um b er of gluons it should deca y to is three so that all the constrain ts including color conserv ation are satised. In principle, (1S) deca y pro ceeding via three photons is also p ossible, but this mec hanism is highly suppressed as compared to the one pro ceeding through a virtual photon, just b ecause three successiv e electro-magnetic in teractions are m uc h less lik ely to o ccur than a single one. A v ery imp ortan t deca y mec hanism whic h has not b een in tro duced so far is the \radiativ e deca y ." The deca y in this case pro ceeds through a photon and t w o gluons. The t w o gluons can form a color singlet state and the presence of a photon in team with t w o gluons ensures that parit y and c harge conjugation are not violated. Naiv ely the p enalt y for this replacemen t of one of the gluons with a photon is of the order of the ratio of coupling constan ts, : s Despite this suppression, the radiativ e deca ys of (1S) are imp ortan t b ecause emission of a high energy photon lea v es b ehind a glue-ric h en vironmen t from whic h w e can learn ab out the formation of resonances from gluons or p oten tially disco v er fundamen tal new forms of matter allo w ed b y QCD lik e \glueballs" and q g q \h ybrids." This dissertation concen trates on one class of radiativ e deca ys. PAGE 30 15 The three dieren t p ossible (1S) deca ys with least amoun t of in teractions (also called lo w est order deca ys) are sho wn in Figure 1{2 g g g g g bb b bbb b b bb q q q q (a)(b)(c)(d) Figure 1{2. Lo w est order deca ys of the (1S) allo w ed b y color conserv ation, c harge conjugation symmetry and parit y (a) Sho ws the deca y in to three gluons, (b) sho ws a radiativ e deca y and (c) sho ws the electro-magnetic deca y through a virtual photon that in turn deca ys electro-magnetically in to a pair of c harged fundamen tal particles, suc h as quarks or c harged leptons (the c harged leptons are represen ted b y the sym b ol l ). 1.2.2 Radiativ e Deca ys of (1 S ) in to and 0 The radiativ e deca ys of hea vy quark onia in to a single hadron pro vide a particularly clean en vironmen t to study the con v ersion of gluons in to hadrons, and th us their study is a direct test of QCD. (1S) r 0 is one suc h c hannel, in v olving only single ligh t hadron. This deca y c hannel has b een observ ed in the J/ system, as ha v e the deca ys in to other pseudoscalar states, for example the and c (1S). Naiv e scaling predicts a ratio of partial deca y widths ((1S) r 0 ) = ( J = r 0 ) of ( q b m c =q c m b ) 2 1/40. This naiv e factor of 1/40 is in the deca y rates; to nd the exp ected ratio of branc hing fractions, w e ha v e to m ultiply b y the ratio of the total widths, 1.71, whic h giv es a suppression factor of 0 : 04. Ho w ev er, the searc h for the deca y (1S) r 0 b y CLEO in 61 : 3 pb 1 of data tak en with the CLEO I I detector [ 7 ] found no signal PAGE 31 16 in this mo de, and resulted in an upp er limit of 1.6 10 5 for the branc hing fraction (1S) r 0 whic h is an order of magnitude less than the naiv e exp ectation. F urthermore, the t w o-b o dy deca y (1S ) r f 2 (1270) has b een observ ed in the old CLEO I I (1S) data [ 8 ], and this observ ation has b een conrmed with m uc h greater statistics in the CLEO I I I data [ 1 ]. In radiativ e J/ deca ys the ratio of 0 to f 2 (1270) pro duction is 3.1 0.4. If the same ratio held in (1S), and as the deca y diagram is iden tical, this w ould b e exp ected, then the 0 c hannel w ould b e clearly visible. Another in teresting c hannel w e study in this analysis is (1S) r This c hannel has b een observ ed in J = deca ys, alb eit with the mo dest branc hing fraction of (8 : 6 0 : 8) 10 4 The previous analysis [ 9 ] of (1S ) deca ys pro duced an upp er limit for this mo de of 2 : 1 10 5 Sev eral authors ha v e tried to explain the lac k of signals in radiativ e (1S) deca ys in to pseudoscalar mesons using a v ariet y of mo dels whic h pro duce branc hing ratio predictions of the order 10 6 to 10 4 K orner and colleagues' [ 10 ] approac h suggests M 6 V dep endence for 0 and f 2 (1270) pro duction in the radiativ e deca ys of hea vy v ector mesons of mass M V Using the mixing mec hanism of 0 with the as y et unobserv ed pseudoscalar resonance b Chao [ 11 ] calculates the B ((1S) r 0 ) 6 10 5 B ((1S) r ) 1 10 5 The pro cess V r P where V is the hea vy v ector meson (1S) ; (2S) and P is a ligh t pseudoscalar meson ( 0 ; ; 0 ) w as also studied b y In temann [ 12 ] using the V ector Meson Dominance Mo del (VDM). In the VDM paradigm, the deca y is assumed to pro ceed via an in termediate v ector meson state, that is V V 0 P r P where the virtual V 0 is a (1S) or (2S). The predicted branc hing ratios for (1S) r (1S) r 0 are 10 7 to 10 6 There is an am biguit y regarding the signs of v arious amplitudes (and th us whether the amplitudes add constructiv ely or destructiv ely to the in termediate virtual v ector meson V 0 ) that con tribute to the partial deca y width (V r P). The author notes that the amplitudes, if added PAGE 32 17 constructiv ely giv e answ ers whic h are in agreemen t with the exp erimen t for the J/ system. Making a note that VDM has no direct relation to QCD as the fundamen tal theory of strong in teractions, and referring to [ 7 ], Ma tries to address the problem in Non-Relativistic QCD (NR QCD) [ 13 ] paradigm along with t wist-2 op erators and predicts B ((1S) r 0 ) 1.7 10 6 and B ((1S) r ) 3.3 10 7 whic h are almost half the resp ectiv e ratios predicted using constructiv e in terference VDM approac h (T able 1{4 ). T able 1{4. Theoretical branc hing fractions as predicted b y v arious authors for radiativ e deca ys of (1S) in to and 0 Author/Mo del/Approac h Chronology B ((1S) r 0 ) B ((1S) r ) QCD inspired mo dels: K orner et al. [ 10 ] 1982 20 10 5 3 : 6 10 5 6 V ector Meson Dominance: 5 : 3 10 7 1 : 3 10 7 In temann [ 12 ] 1983 to to 2 : 5 10 6 6 : 3 10 7 Mixing of 0 with b : Chao [ 11 ] 1990 6 10 5 1 10 5 NR QCD with t wist-2 op erators: Ma [ 13 ] 2002 1 : 7 10 6 3 : 3 10 7 In this study w e searc h for the pro cesses (1S) r 0 and (1S) r W e reconstruct mesons in the three mo des r r + 0 and 0 0 0 The 0 mesons are reconstructed in the mo des + with deca ying through an y of the ab o v e deca y mo des. These six deca y c hains w ere in v estigated in the previous 6 Constructed from table 4 of Ref. [ 10 ] as: B ((1S) r ) = 0 : 10 0 : 24 B ( r ) B ( r f 2 ) B ( r f 2 ). PAGE 33 18 CLEO analysis on this sub ject. In addition, w e ha v e also added the deca y mo de 0 r 0 where 0 + W e should also note that w e kno w that v e of the sev en submo des under in v estigation are going to b e largely bac kground free, and so to get the most sensitivit y w e m ust carefully c ho ose our cuts 7 in these submo des to retain the most p ossible eciency The t w o exceptions are r r and 0 r These t w o ha v e high branc hing fractions, but large bac kgrounds, and so our analysis strategy will aim to decrease these bac kgrounds ev en if this necessitates a decrease in the eciency F or later reference and nal calculations, the pro duct branc hing fractions for the deca ys mo des of and 0 are listed in T able 1{5 where the v alues ha v e b een compiled from PDG[ 14 ]. T able 1{5. Pro duct branc hing ratios for deca y mo des of and 0 Deca y Mo de Pro duct branc hing fraction B ( r r ) 39 : 43 0 : 26 B ( + 0 ) 22 : 6 0 : 4 B ( 0 0 0 ) 32 : 51 0 : 29 B ( 0 + ) 44 : 3 1 : 5 B ( 0 + ; r r ) 17 : 5 0 : 6 B ( 0 + ; + 0 ) 10 : 0 0 : 4 B ( 0 + ; 0 0 0 ) 14 : 4 0 : 5 B ( 0 r ) 29 : 5 1 : 0 7 In parlance of High Energy Exp erimen tal studies, \cut" is a synon ym for selection criterion. An ev en t m ust satisfy a set of cuts to b e considered as an ev en t of in terest. Cuts are carefully c hosen to reject the bac kground ev en ts. PAGE 34 CHAPTER 2 EXPERIMENT AL APP ARA TUS The rst steps to w ards the study of radiativ e deca ys of (1S) resonance is to b e able to pro duce the (1S) resonance, and then to b e able to observ e the deca y daugh ters of this readily deca ying resonance. The resonances are pro duced only in a high energy collision, the deca y daugh ters of whic h ry o at relativistic sp eeds. T o detect these daugh ter particles, a detector is required to b e set up around the pro duction p oin t (of the (1S) resonance) whic h co v ers as m uc h as p ossible of the total 4 solid angle. F or this analysis, w e need a m ultipurp ose detector p ermitting us to trace the c harged trac ks bac k to the pro duction p oin t, iden tify the particles and detect neutral particles as w ell. CLEO I I I detector has b een designed to p erform the studies of resonances pro duced b y the Cornell Electron Storage Ring. 2.1 Cornell Electron Storage Ring Lo cated at the Wilson Lab oratory's accelerator facilit y in Cornell Univ ersit y Ithaca, NY, the Cornell Electron Storage Ring (CESR) is a circular electron-p ositron collider with a circumference of 768 meters. Since its inception in 1979, it has pro vided e + e collisions and sync hrotron radiation to sev eral exp erimen ts. V arious comp onen ts of CESR as sho wn in the sc hematic picture (Figure 2{1 ) are discussed in the next few sections. The comp onen ts are discussed in the order in whic h they are emplo y ed to create e + e collisions. 2.1.1 Linear Accelerator The electrons and p ositrons used in the collision to pro duce resonance are pro duced in a 30 meter long v acuum pip e called the Linear Accelerator (LINA C). The electrons are rst created b y ev ap orating them o a hot lamen t wire at the bac k of LINA C. In tec hnical parlance, it is the electron gun whic h pro duces the electrons, 19 PAGE 35 20 LINAC SYNCHROTRON CESRCHESS WESTCLEOCHESS EASTN e e + BUNCH OF POSITRONSBUNCH OF ELECTRONS WEST TRANSFER LINE TRANSFER LINE EAST r Figure 2{1. Wilson Lab oratory accelerator facilit y lo cated ab out 40 feet b eneath Cornell Univ ersit y's Alumni Fields. Both the CESR and the sync hrotron are engineered in the same tunnel. whic h is v ery similar to the pro cedure inside the picture tub e of a television. The electrons th us created are accelerated b y a series of Radio F requency Acceleration Ca vities (RF Ca vities) to b om bard a tungsten target lo cated at ab out the cen ter of LINA C. The result of the impact of high sp eed electrons with energy ab out 140 MeV on the tungsten target is a spra y of electrons, p ositrons and photons. The electrons are cleared a w a y with magnetic eld lea ving us with a sample of p ositrons whic h are further accelerated do wn the remaining length of LINA C. In case of electrons, the electrons as obtained from the electron gun are simply accelerated do wn the length PAGE 36 21 of LINA C without ha ving to b om bard the tungsten wire. These accelerated bunc h of electrons and p ositrons are in tro duced in to the sync hrotron. This is the pro cess of \lling" a run whic h normally tak es ten min utes. 2.1.2 Sync hrotron The electrons and p ositrons as lled in the sync hrotron are accelerated to the op erating energy whic h is 9.46 GeV in our case, the mass of (1S ). The sync hrotron is a circular accelerator where the electrons and p ositrons are made to tra v el in opp osite directions in circular orbits inside a v acuum pip e. The guiding of tra v eling particles is accomplished via magnetic eld, and the acceleration is carried out b y radio frequency electro-magnetic eld. In principle, the c harged particles can sta y in an orbit of a particular radius for a particular v elo cit y for a particular strength of magnetic eld. As the particles are accelerated, the v alue of the magnetic eld m ust b e adjusted in sync hronism with the v elo cit y to k eep the particles in the orbit of constan t radius. 2.1.3 Storage Ring After the electron and p ositron bunc hes ha v e reac hed the op erating energy the highly energetic particles are injected in to the storage ring. The pro cess of transferring the electron and p ositron b eams in to the storage ring (CESR) is called \injection." The b eam is guided along a circular path inside the ring b y magnetic eld and coasts there for roughly an hour, a t ypical duration of a run. T o prev en t the electrons and p ositrons scattering o the gas molecules in the b eam pip e, a high qualit y of v acuum has to b e main tained inside the b eam pip e. While the particles coast in the storage ring, they radiate a b eam of X-ra ys th us leading to energy loss. This radiation is called \sync hrotron radiation" and is a used for exp erimen ts in the CHESS area. The sync hrotron radiation is rather a useful b y-pro duct used as a researc h instrumen t in surface ph ysics, c hemistry biology PAGE 37 22 and medicine. The energy lost b y the b eam in the form of sync hrotron radiation is replenished b y RF ca vities similar to those in the sync hrotron. T o a v oid the b eam collisions an ywhere b esides the in teraction region, the electrostatic separators hold the electron and p ositron b eams sligh tly apart from eac h other. The orbit th us is not a p erfect circle, it rather assumes the shap e of a pretzel. 2.1.4 In teraction Region The in teraction region (IR) is a small region of space lo cated at the v ery cen ter of the CLEO I I I detector where the electron and p ositron b eams are made to collide. The rate at whic h collisions happ en directly p oin t to the p erformance of the accelerator. The abilit y to obtain a high collision rate is crucial for the success of the accelerator and the exp erimen t it serv es. The gure of merit then is the n um b er of p ossible collisions p er second p er unit area; this is called the luminosit y whic h is giv en as L = f n N e + N e A (2{1) where f is the frequency of rev olution for eac h train. n is the n um b er of p opulated cars in eac h train for eac h particle sp ecies, A is the cross-sectional area of the cars, and N e + and N e are the n um b ers of p ositrons and electrons p er car, resp ectiv ely In order to maximize the luminosit y the b eams are fo cussed as narro w as p ossible in the IR. T o this end, sev eral magnetic quadrup ole magnets w ere added to CESR during CLEO I I I installation. A standard practice of measuring the in tegrated luminosit y o v er a p erio d of time in high energy exp erimen ts is to coun t ho w man y times a w ell understo o d reference pro cess o ccurs during a certain time in terv al at the IR. The t w o reference pro cesses that are used at CLEO I I I detector are, one e + e in teracting to pro duce a new e + e pair, and second e + e annihilating to pro duce a pair of photons. Using the w ell kno wn cross-section for eac h pro cess, the n um b er of ev en ts is con v erted to a PAGE 38 23 luminosit y called the Bhabha in tegrated luminosit y for the rst pro cess, and the r r (GamGam) in tegrated luminosit y for the second one. 2.2 Resonances The family of resonances w as disco v ered in 1977 in F ermilab. The exp erimen t conducted at F ermilab w as unable to resolv e the mem b ers of this family ho w ev er, it w as certain that a b ound state of a new ra v or, b ottom, w as disco v ered. So on, CLEO detector op erating at CESR w as able to resolv e the states (1S), (2S), and (3S). These resonances are sho wn in Figure 2{2 on top of hadronic \bac kground." The fourth state disco v ered in 1980, namely (4S) is m uc h wider compared to lo w-lying states as (4S ) has more deca y c hannels op en to it. ible Cross Section (nb)201612 84 3.53.02.5 ( b ) ( a ) 9.45 9.50 10.00 10.05 10.40 10.50 10.60 10.5 10.8 11 .1Center of Mass Energy (GeV) 0250187-012 (1S) (2S) (3S) (4S) (4S) (5S) (6S) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Figure 2{2. Visible cross section in e + e collisions as a function of cen ter of mass energy Plot (a) on the left sho ws p eaks for ( n S) for n = 1,2,3, and 4. Plot (b) on the left sho ws (5S ) and (6S) as w ell as a blo w up for (4S) resonance. The comp osition of hadronic bac kground is primarily from the \con tin uum" pro cess e + e q q where q is a ligh t quark ( u; d; s; as w ell as c at this energy). The pro cess is referred to con tin uum as this pro cess happ ens for a range of op erating energy high enough to pro duce the ligh t quarks. Some con tribution to the hadronic con tin uum also comes from the pro cess e + e + where one or b oth leptons PAGE 39 24 deca y to hadronic daugh ters. T o study the deca y pro cesses of resonances, w e not only need the data collected at the op erating energy equal to the mass of resonance under study but w e also need a sample of pure con tin uum at op erating energy just b elo w 1 the resonance to understand the bac kground. 2.3 CLEO I I I Detector The colliding e + e annihilate electro-magnetically in to a virtual photon r a highly unstable \o mass shell" particle deca ying readily in to \on shell" daugh ters. Ev en at the op erating energy equal to the mass of (1S) resonance, the virtual photon ma y either pro duce the resonance (1S), or pro duce the con tin uum bac kground. W e really do not ha v e an y means of directly kno wing what happ ens at the in teraction p oin t. But the long liv ed on-shell daugh ters rying o at relativistic sp eeds p ossess the information p ost-collision pro cess as to what Nature decided to do with the energy It is at this p oin t w e en ter the w orld of particle detectors. Lik e an y other prob e, to measure a certain quan tit y the prob e should b e able to in teract with the quan tit y The underlying principles of particle detectors are based up on the electro-magnetic in teractions of particle with matter (the detector here). The particle detectors are sensitiv e to suc h in teractions and are equipp ed with instrumen ts to record the information ab out in teraction, whic h is used b y exp erimen ter to infer the prop erties of the in teracting particle, suc h as its energy momen tum, mass and c harge. In this analysis, w e are in terested in the pro cess where a r rst deca ys in to (1S) resonance whic h further deca ys radiativ ely in to a and 0 mesons. The ligh t, pseudoscalar mesons and 0 themselv es are highly unstable and readily deca y in to 1 The reason for collecting the con tin uum sample at an energy b elo w and not ab o v e the resonance energy is that at an energy ab o v e the resonance, the colliding particles ma y radiate photon(s), thereb y losing energy and p ossibly forming the resonance. PAGE 40 25 Solenoid Coil Barr el C a lo r i m e t e r RI C H D r i f t C h am b e r Sili c on / b e am p i p e E nd c a p C a lo r i m e t e r I r on P ole p ie c e Barr el Mu on C h am b e r s M a g ne t I r on R ar e E art h Q u a d r u p ole SC Q u a d r u p ole s SC Q u a d r u p ole P y lon 2230402-005 C L E O III Figure 2{3. The CLEO I I I detector. ligh ter particles long liv ed enough to surviv e the v olume of detector. It is these particles that w e detect using the CLEO I I I detector [ 15 ], a ma jor upgrade to CLEO I I.V [ 16 ] ha ving an impro v ed particle iden tication capabilit y along with a new drift c ham b er and a new silicon v ertex detector. As the sux I I I to the name CLEO suggests, there ha v e b een man y generations of CLEO detectors ev olv ed from the original CLEO detector. As can b e seen in Figure 2{3 the CLEO I I I detector is a comp osite of man y sub-detector elemen ts. T ypically arranged as concen tric cylinders around the b eam pip e, the sub-detectors are generally sp ecialized for one particular task. The en tire detector is appro ximately cub e shap ed, with one side measuring ab out 6 meters, and w eighs o v er 1000 tons. CLEO I I I op erated in this conguration from 2000 to 2003. The CLEO I I I detector is a v ersatile, m ulti-purp ose detector with excellen t c harged particle and photon detection capabilities. In the follo wing sections, w e discuss some of the particle detection sc hemes and tec hniques implemen ted in the PAGE 41 26 CLEO detectors, and ho w ra w detector data is transformed in to measuremen ts of particle energy momen ta, tra jectories. A thorough description of the detector can b e found elsewhere [ 17 ]. 2.3.1 Sup erconducting Coil All the CLEO I I I detector subsystems except the m uon c ham b ers are lo cated inside a sup erconducting coil. The sup erconducting coil is a k ey elemen t, pro viding a uniform magnetic eld of 1.5 T esla to b end the paths of c harged particles in the detector, th us allo wing the exp erimen ter to measure the momen tum of the passing particle. The magnetic eld due to the coil p oin ts in z direction (east) and is uniform up to 0.2%. The 3.5 meter long coil has an inner diameter of 2.90 meter with a radial thic kness of 0.10 meter. The winding around the coil is carried from a 5 mm 16 mm sup erconducting cable made from alumin um stabilized Cu-NbTi allo y k ept in sup erconducting state b y the liquid helium reserv oir as sho wn in Figure 2{3 The coil is w ound in 2 la y ers, eac h ha ving 650 turns, on an alumin um shell. When in op eration, a curren t of 3300 amps ro ws through the coil. 2.3.2 Charged P article T rac king System The particles created at the in teraction p oin t pass the lo w-mass b eam pip e b efore they b egin to encoun ter the activ e elemen ts of detector trac king system. The CLEO I I I trac king system is resp onsible for trac king a c harged particle's tra jectory and th us giving the exp erimen ter a measure of the particle momen tum. The trac king system of CLEO I I I detector is comp osed of t w o sub-detectors to accomplish the trac king of curv ed path of c harged particles. The rst sub-detector is silicon v ertex detector measuring z and the cotangen t of p olar angle surrounded b y the cen tral drift c ham b er measuring the curv ature. Both devices measure the azim uthal angle and the impact parameter. PAGE 42 27 The t ypical momen tum resolution is 0.35% (1%) for 1 GeV (5 GeV) trac ks. The trac king system also measures the ionization energy loss due to c harged particles | a measuremen t useful in distinguishing b et w een v arious mass h yp otheses of c harged particles. The energy loss due to ionization is measured with an accuracy of ab out 6% for hadrons (pion, k aon, and proton), and 5% for electrons. The trac king system is not sensitiv e to neutral particles. 2.3.2.1 Silicon V ertex Detector The silicon v ertex detector in CLEO I I I [ 18 ], also called SVD I I I is a silicon strip detector \barrel-only" design without endcaps or tap ers, consisting of four silicon la y ers concen tric with the IR b eam pip e. The silicon trac k er pro vides four and four z measuremen ts co v ering 93% of the solid angle. The a v erage radius of inner surface of the four la y ers is 25 mm, 37.5 mm, 72 mm and 102 mm. Eac h of the four barrels is constructed from indep enden t c hains (called ladders) whic h are made b y connecting individual silicon w afers (sensors) together. There are a total of 447 iden tical double-sided silicon w afers, eac h 27.0 mm in 52.6 mm in z and 0.3 mm thic k used in constructing the four barrels. The four la y ers ha v e resp ectiv ely 7, 10, 18, and 26 ladders, and the four ladder design consists of resp ectiv ely 3, 4, 7, and 10 silicon w afers daisy c hained longitudinally (Figure 2{4 ). The b ottom side of eac h silicon w afer has n-t yp e strips implan ted p erp endicular to the b eam line. The top side of the w afer has p-t yp e implan ts parallel to the b eam line. The w afers are instrumen ted and read out on b oth sides. Eac h w afer has 512 strips on either side. The instrumen tation on eac h side consists of aluminized traces atop the dop ed strips. The so formed alumin um strips are connected to preampliers stationed at the end of the detector and mo v e the collected c harge from the w afers. The en tire w afer forms a p-n junction. When rev erse bias is applied across the w afer, a sensitiv e region depleted of mobile c harge is formed. PAGE 43 28 3 3 0 m rad r ( c m ) 2 5 0 3 7 5 7 5 0 1 0 7 5 1 c m 1 0 c m Figure 2{4. View of the SVD I I I along the b eampip e. As in an y other material, c harged particles tra v ersing the w afer lose energy In the sensitiv e region of the w afer, this lost energy is used to create electron-hole pairs. Appro ximately 3.6 eV is required to create a single electron-hole pair. The lib erated electrons and holes then tra v el (in opp osite directions) in the electric eld applied b y the bias to the surfaces of the w afers un til they end up on the alumin um strips, and then the detector registers a \hit." When com bined together, the hit on the inner side of a w afer and the hit on the outer side giv e a measuremen t of ( z ; ). The w afer p osition itself determines r 2.3.2.2 The Cen tral Drift Cham b er The CLEO I I I cen tral drift c ham b er (DR I I I) is full of drift gas with 60:40 helium-propane mixture held at ab out 270 K and at a pressure sligh tly ab o v e one atmosphere. The drift c ham b er is strung with an arra y of ano de (sense) wires of gold-plated tungsten of 20 m diameter and catho de (eld) wires of gold-plated PAGE 44 29 alumin um tub es of 110 m diameter. All wires are held at sucien t tension to ha v e only a 50 m gra vitational sag at the cen ter ( z = 0). The ano des are k ept at a p ositiv e p oten tial (ab out 2000 V), whic h pro vides an electric eld throughout the v olume of the drift c ham b er. The catho des are k ept grounded, and shap e the electric eld so that the elds from neigh b ouring ano de wires do not in terfere with eac h other. During its passage through the DR I I I, the c harged particle in teracts electro-magnetically with the gas molecules inside the c ham b er. The energy is transferred from the high energy particle to the gas molecule thereb y ionizing the gas b y lib erating the outer shell electrons. The lib erated electrons \drift" in the electric eld to w ards the closest sense wire. The thin sense wire main tained at a high p oten tial pro duces a v ery strong electric eld in its vicinit y As the electron approac hes the sense wire, it gains energy enough to b ecome an ionizing electron itself thereb y kic king more electrons out of the surrounding gas molecules. An a v alanc he of electrons is created this w a y whic h collapses on the sense wire in a v ery short amoun t of time (less than a nanosecond) and the sense wire registers a \hit." The curren t on the ano de wire from the a v alanc he is amplied and collected at the end of the ano de wire. Both the amoun t of c harge and the time it tak es it to mo v e to the end of the detector are measured. A calibration of the drift c ham b er is used to con v ert the amoun t of c harge to a sp ecic ionization measuremen t of the inciden t particle. A calibrated drift c ham b er can also con v ert the time to roughly measure the p osition along the sense wire where the c harge w as dep osited. The CLEO I I I DR has 47 la y ers of wires, the rst 16 of whic h form the inner stepp ed section (\w edding cak e" end-plates) where in the wires are strung along the z -direction. These wires are called axial wires. The remaining outer 31 la y ers are small angle stereo la y ers. The stereo wires are strung in with a sligh t angle (ab out 25 milliradians) with resp ect to the z -direction to help with the z measuremen t. There are 1696 axial sense wires and 8100 stereo sense wires, 9796 total. F or stereo trac king, PAGE 45 30 the trac k er divides the 31 stereo la y ers in to eigh t sup er la y ers, the rst sev en of whic h ha v e four la y ers of stereo wires eac h, and the last sup er la y er has only three la y ers of wires. The o dd and ev en n um b ered sup er la y ers ha v e a p ositiv e and negativ e phi tilt with resp ect to the z resp ectiv ely The o dd(ev en) sup er la y ers are called as U(V) sup er la y ers in short. There are 3 eld wires p er sense wire and the 9796 drift cells th us formed are appro ximately 1.4 cm side square. The drift p osition resolution is around 150 m in r and ab out 6 mm in z 2.3.3 Ring Imaging Cherenk o v Detector Cherenk o v radiation detectors b elong to the set of to ols to discriminate b et w een t w o particles of same momen tum and dieren t masses. This goal is accomplished b y measuring the v elo cit y of the c harged particle and matc h it against the momen tum measured b y the trac king c ham b er. This goal is termed as \particle iden tication." The CLEO I I I detector receiv ed its ma jor upgrade for the purp ose of particle iden tication b y replacing the existing time of righ t system of CLEO I I.V detector b y Ring Imaging Cherenk o v Detector (RICH). Both systems, the old time of righ t detector and the new RICH sub-detector pro vide the measuremen t of particle v elo cit y The underlying principle b ehind the RICH is the phenomenon of Cherenk o v radiation. The Cherenk o v radiation o ccurs when a particle tra v els faster than the sp eed of ligh t in a certain medium, v > c=n: (2{2) where v is the v elo cit y of the particle, c is the sp eed of ligh t in free space and n is the index of refraction of the medium the particle is tra v eling in. The c harged particle, as it tra v els through medium, p olarizes the molecules of the medium. The p olarized molecules relax to their ground state in no time, emitting photons. Because the c harged particle is tra v eling faster than the sp eed of ligh t in the medium, it triggers a PAGE 46 31 cascade of photons whic h are in phase with eac h other and can constructiv ely in terfere to form a coheren t w a v efron t. The Cherenk o v ligh t w a v efron t forms the surface of a cone ab out the axis of c harged particle tra jectory where the half-angle of the cone is giv en b y cos ( ) = c v n = 1 n ; > 1 n (2{3) The measuremen t of is th us a measuremen t of particle's sp eed whic h when related to the measured momen tum of the particle giv es a measuremen t of the particle mass, and is useful in particle iden tication. As can b e noted from the conditions under whic h Cherenk o v radiation is emitted, the c harged particle has to ha v e a threshold v elo cit y v min = c=n b efore the radiation can b e emitted. A t threshold, the cone has a v ery small half-angle 0. The maxim um emission angle o ccurs when v max = c and is giv en b y cos( max ) = 1 n : (2{4) The RICH (see Figure 2{5 ) starts at a radius of 0.80 m and extends to 0.90 m has a 30-fold azim uthal symmetry geometry formed from 30 mo dules, eac h of whic h is 0.192 m wide and 2.5 m long. Eac h mo dule has 14 tiles of solid crystal LiF radiator at appro ximately 0.82 m radius. Eac h tile measures 19.2 cm in width, 17 cm in length and a mean thic kness of 10 mm. Inner separation b et w een radiators is t ypically 50 m. The LiF index of refraction is n = 1 : 5. The radiators closest to z = 0 in eac h mo dule ha v e a 45 degree sa wto oth outer face to reduce total in ternal rerection of the Cherenk o v ligh t for normal inciden t particles (see Figure 2{6 ). The radiators are follo w ed b y a 15.7 cm radial drift space lled with pure N 2 an un-instrumen ted v olume allo wing the expansion of Cherenk o v cone. The drift space is follo w ed b y the photo-detector, a thin-gap m ulti-wire photosensitiv e prop ortional c ham b er lled with a photon con v ersion gas of trieth ylamine and methane where the Cherenk o v cone is in tercepted. PAGE 47 32 Photon Detector LiF Radiator Charged Particle Cherenkov Photon LiF Radiators Photon Detectors 192 mm CH +TEA 4 CaF Window 2 Fiberglass Siderail Pure N 2 1 6 cm101 cm82 cm 20 m wires r250 cm G10 Box Rib Figure 2{5. The RICH detector subsystem. With this index, particles in the LiF radiator with = 1 pro duce Cherenk o v cones of half-angle cos 1 (1 =n ) = 0.84 radians. With a drift space 16 cm in length, this pro duces a circle of radius 13 cm. The RICH is capable of measuring the Cherenk o v angle with a resolution of a few milliradians. This great resolution allo ws for go o d separation b et w een pions and k aons up to ab out 3 GeV. 2.3.4 Crystal Calorimeter Calorimeters p erform energy measuremen ts based up on total absorption metho ds. The absorption pro cess is c haracterized b y the in teraction of the inciden t particle in a detector mass, generating a cascade of secondary tertiary particles and so on, so that all (or most) of the inciden t energy app ears as ionization or excitation in the medium. A calorimeter, is th us an instrumen t measuring the dep osited energy The calorimeter can detect neutral as w ell as c harged particles. The fractional energy resolution of calorimeters is generally prop ortional to E 1 = 2 whic h mak es them ev en more indisp ensible in y et higher energy exp erimen ts. The CLEO I I I Crystal Calorimeter (CC) is an electro-magnetic-sho w er calorimeter whic h absorb incoming electrons or photons whic h cascade in to a series of electro-magnetic PAGE 48 33 10 mm 1 7 0 mm4 mmtrack track g g 10 mm g g Figure 2{6. Tw o kinds of RICH LiF radiators. F or normal incidence particles ( z 0) a sa wto oth radiator is necessary to a v oid in ternal rerection. sho w ers. It is vital sub-detector for the analysis presen ted in this dissertation, as all our ev en ts con tain at least t w o, mostly three, and often more, photons. The calorimeter is constructed from 7784 thallium-dop ed CsI crystals with 6144 of them arranged to form the barrel p ortion and the remaining 1640 are ev enly used to construct t w o endcaps, together co v ering 95% of the solid angle. The crystals in the endcap are rectangular in shap e and are aligned parallel to the z axis whereas the crystals in the barrel are tap ered to w ards the fron t face and aligned to p oin t to w ards the in teraction p oin t so that the photons originating from the in teraction p oin t strik e the barrel crystals at near normal incidence. The CC barrel inner radius is 1.02 m, outer radius is 1.32 m, and length in z at the inner radius is 3.26 m. It co v ers the p olar angle range from 32 to 148 degrees. The endcap extends from 0.434 m to 0.958 m in radius. The fron t faces are z = 1 : 308 m from the in teraction p oin t (IP); the bac k faces are z = 1 : 748 m from the IP It co v ers the p olar angle region from 18 to 34 degrees in + z and 146 to 162 in z The electronic system comp osed of 4 photo dio des presen t at the bac k of eac h of the crystals are calibrated to measure the energy dep osited b y the incoming particles. Incoming particles other than photons and electrons are partially and sometimes fully PAGE 49 34 absorb ed b y the crystals giving an energy reading. Eac h of the crystals is 30 cm long whic h is equiv alen t to 16.2 radiation lengths. On the fron t face, the crystals measure 5 cm 5 cm, pro viding an angular resolution of 2 milliradians. The photon energy resolution in the barrel (endcap) is 1.5% (2.5%) for 5 GeV photons, and deteriorates to 3.8% (5.0%) for 100 MeV photons. 2.3.5 Muon Cham b ers Muons are highly p enetrating c harged particles whic h compared to other c harged particles, can tra v el large distances through matter without in teracting. F or this reason, the sub-detector comp onen t Muon Detector used in iden tifying m uons is placed outside the main b o dy of CLEO I I I detector. The m uon detectors are comp osed of plastic stream coun ters em b edded in sev eral la y ers of iron. P articles other than m uons emanating from the detector are blo c k ed b y the iron la y ers. Lik e the CC, the m uon detector is arranged as a barrel and t w o endcaps, co v ering 85% of the 4 solid angle (roughly 30{150 degrees in p olar angle). The barrel region is divided in 8 o ctan ts in with three planes of c ham b ers in eac h o ctan t. The plastic barrel planes lie at depths of 36, 72, and 108 cm of iron (at normal incidence), corresp onding to roughly 3, 5, and 7 hadronic in teraction lengths (16.8 cm in iron) referred to as DPTHMU. There is one plane of c ham b ers in eac h of the t w o endcap regions, arranged in 4 rough quadran ts in They lie at z = 2 : 7 m, roughly co v ering the region 0 : 80 < j cos( ) j < 0 : 85. The planar trac king c ham b ers use plastic prop ortional coun ters at ab out 2500 V with drift gas of 60% He, 40% propane, iden tical to (and supplied b y the same system as) the drift c ham b er gas. Individual coun ters are 5 m long and 8.3 m wide, with a space resolution (along the wire, using c harge division) of 2.4 cm. The trac king c ham b ers are made of extruded plastic, 8 cm wide b y 1 cm thic k b y 5 m long, con taining eigh t tub es, coated on 3 sides with graphite to form a catho de, with 50 m silv er-plated Cu-Be ano de wires held at 2500 V. The orthogonal co ordinate is pro vided b y 8 cm copp er strips running p erp endicular to the PAGE 50 35 tub es on the side not co v ered b y graphite. When a hit is recorded, the ano de wire p osition pro vides the co ordinate of the hit, and c harge division is used to extract the z co ordinate. Besides detecting m uons, the hea vy iron la y ers also act as magnetic rux return y ok e for the sup erconducting coil. The other imp ortan t purp ose serv ed b y iron la y ers is to protect the inner sub-systems of CLEO I I I detector from cosmic ra y bac kground (except for cosmic ra y m uons of course). 2.3.6 CLEO I I I T rigger The CLEO I I I trigger describ ed fully in [ 19 ] is b oth a trac king and calorimeter based system designed to b e highly ecien t in collecting ev en ts of in terest. The trac king based trigger relies on \axial" and \stereo" triggers deriv ed from the hit patterns (pattern recognition p erformed ev ery 42 ns) on the 16 axial la y ers and 31 stereo la y ers of the drift c ham b er. As there are only 1696 axial wires in the CLEO I I I drift c ham b er, the trac k er is able to examine all p ossible v alid hit patterns due to trac ks ha ving transv erse momen tum P ? greater than 200 MeV = c. T o main tain high trac k nding eciency the hit patterns due to trac ks as far as 5 mm a w a y from the axis of b eam pip e are included, and upto t w o hits (one eac h from the inner and outer set of eigh t wires) are allo w ed to b e missing. The output from axial trigger is the n um b er of trac ks, the ev en t time and a 48-bit arra y represen ting ev en t top ology Since the n um b er (8100) of stereo wires is relativ ely large, not all wires are examined for hit pattern, rather the wires are group ed in 4x4 arra ys (for sup er la y er 8, it uses 4x3 arra y). The U and V sup er la y ers (dened in Section 2.3.2.2 ) are examined separately (as they tilt in opp osite directions) and to satisfy a blo c k pattern, at least 3 out of the 4 la y ers in a sup er la y er m ust record hits from trac ks satisfying the momen tum cut P ? > 250 MeV = c. This is designed to main tain high eciency; ho w ev er, missing blo c ks are not allo w ed. The stereo trac k output is pro jected in azim uth on to the axial la y er 9 (to matc h with the axial trac ks) and the CC on the other end. A more PAGE 51 36 detailed discussion is b ey ond the scop e of this dissertation; suce it is to sa y that the information from axial and stereo parts of trac k er is com bined to deduce trac king correlation. The trac ks matc hed in b oth regions are tagged as \long," carrying more w eigh t in trigger decision compare to the axial only \short" trac ks. The calorimeter-based trigger is designed to b e more ecien t in CLEO I I I than its predecessors. The energy dep osited in o v erlapping 2x2 arra y of 4x4 crystal tiles (altogether 64 crystals) is summed and compared against three thresholds, lo w (150 MeV), medium (750 MeV), and high (1.5 GeV). The sc heme of o v erlapping tiles (also called tile sharing) did not exist in CLEO I I.V and CLEO I I detectors, so the calorimeter-based trigger w as not as ecien t, b ecause a sho w er shared b y crystals spanning a b oundary of tiles could b e b elo w threshold in b oth regions, th us failing the trigger condition. Some deca y mo des studied in this dissertation rely purely on the calorimeter-based trigger decision, and the redesigned CLEO I I I calorimeter trigger is an added adv an tage. Based up on trac king and calorimetry trigger bits, man y dieren t trigger lines (or conditions) are c hec k ed and an ev en t is recorded if at least one line is set. The calorimeter based trigger lines are imp ortan t for the \all neutral" mo des (1S) r ; r r and (1S ) r ; 0 0 0 studied in this dissertation. The t w o trigger lines whic h help collect ev en ts for the ab o v e mo des are BARRELBHABHA, demanding there are t w o, bac k-to-bac k high energy sho w er clusters in the barrel region. F or b eing classied as bac k-to-bac k, the sho w ers should b e in opp osite halv es of the barrel and the angle should b e suc h that if one sho w er is in o ctan t 1 (0 to 45 degrees in ), then the other sho w er should b e in o ctan ts 4,5, or 6 (135 to 270 degrees in ), for example. ENDCAPBHABHA, requiring there are t w o high energy sho w er clusters, one in eac h of the t w o endcaps. F or the mo des with c harged trac ks, the trigger lines ha v e again v ery relaxed criteria ensuring high eciency The imp ortan t trigger lines are PAGE 52 37 EL TRA CK, demanding a medium energy sho w er cluster in the barrel region accompanied b y at least one axial trac k. It is v ery easy to see that this line w ould b e highly ecien t if the radiativ e photon hits the barrel region. RADT A U, demanding t w o stereo trac ks accompanied with either a medium energy sho w er cluster in the barrel region, or t w o lo w energy sho w er clusters in the barrel region. 2TRA CK, demanding t w o axial trac ks. This trigger line is pre-scaled b y a factor of 20. PAGE 53 CHAPTER 3 D A T A ANAL YSIS 3.1 Data This study is based up on the data sets 18 and 19 collected with CLEO I I I detector during the running p erio d Jan uary 2002 through April 2002 at cen ter-of-mass energy 9.46 GeV. The acquired luminosit y w as 1 : 13 0 : 03 fb 1 with the b eam energy range 4.727{4.734 GeV. This (1S) on-resonance data con tains b oth resonan t e + e (1S) and con tin uum ev en ts. The n um b er of resonan t ev en ts a v ailable to us, N (1S ) = 21 : 2 0 : 2 10 6 [ 20 ], is roughly 14 times the 1 : 45 10 6 (1S ) mesons used in the previous searc h [ 7 9 ] using data collected with CLEO I I detector. In order to understand the con tin uum bac kground presen t in the (1S) on-resonance data, a pure con tin uum data sample is a v ailable to us collected at the cen ter-of-mass energy b elo w the (1S) energy ( E beam = 4.717{4.724 GeV) with an in tegrated luminosit y of 0 : 192 0 : 005 fb 1 Unfortunately if w e use this data to represen t our bac kground, w e rst ha v e to scale it b y the large factor of 5.84, whic h leads to large statistical uncertain ties. Ho w ev er, in this analysis, w e can also use the large data sample tak en on and near the (4S) as a go o d source of pure con tin uum ev en ts. Man y of these ev en ts are of the form (4S) B B deca ys, but these will not satisfy our selection criteria lea ving only con tin uum ev en ts. Th us, w e use (4S) datasets 9, 10, 12, 13, and 14 as a mo del of our con tin uum bac kground, with in tegrated L = 3 : 49 0 : 09 fb 1 in the b eam energy range 5.270{5.300 GeV. W e note that in this analysis, w e use the \GamGam" luminosit y rather than using the more commonly used (and more statistically precise) \BhaBha" measure of the luminosit y This is b ecause the measured Bhabha luminosit y at (1S) energy is increased b y 3% o wing to the resonan t pro cess (1S ) e + e and this m ust b e 38 PAGE 54 39 accoun ted for while doing the con tin uum subtraction. By using GamGam luminosit y w e a v oid this complication and its asso ciated uncertain t y Statistical details of the data used are listed in T able 3{1 T able 3{1. Luminosit y n um b ers for v arious data sets used in the analysis (1S) (4S) (1S )-o Dataset 18, 19 9, 10, 12, 13, 14 18, 19 Av erage E beam ( GeV) 4.730 5.286 4.717 Range of E beam ( GeV) 4 : 727 4 : 734 5 : 270 5 : 300 4 : 714 4 : 724 L ( e + e )( fb 1 ) 1 : 20 0 : 02 3 : 56 0 : 07 0 : 200 0 : 004 L ( r r )( fb 1 ) 1 : 13 0 : 03 3 : 49 0 : 09 0 : 192 0 : 005 (1S) con tin uum scale factor 1 0 : 404 5 : 84 3.2 Skim and T rigger Eciency After the e + e collision happ ens, the triggered ev en ts are collected b y the CLEO I I I detector. In CLEO terminology this pro cedure is called as \pass1." The ra w data as collected b y the detector is pro cessed and stored in con v enien t data structures so that an a v erage collab orator can use the data seamlessly in her analysis. This data pro cessing phase is called \pass2." A t this stage, the ev en ts are classied in to v arious ev en t-t yp es and stored in to dieren t groups called sub-collections, dep ending up on the c haracteristics of the ev en t. In a t ypical analysis, not all collected ev en ts are useful, so the rst step is to mak e skim of the ev en ts of in terest. As our signal ev en ts are lo w m ultiplicit y w e need to ensure that w e ha v e triggered on the ev en ts reasonably ecien tly and furthermore, ha ving collected the ev en ts online, w e need to kno w whic h pass2 sub-collection the ev en ts are to b e found so that w e can skim the ev en ts o at Cornell. Using the ev en t generator QQ [ 21 ], w e generated signal Mon te Carlo (MC) ev en ts for the pro cesses e + e r r 0 and e + e r r using \mo del 1" with the (1 + cos 2 ) angular distribution exp ected PAGE 55 40 for deca ys (1S) r + pseudoscalar for eac h mo de, at a cen ter-of-mass energy 9.46 GeV. The MC predicted that EL TRA CK (trigger lines describ ed in Section 2.3.6 ) w as the most signican t trigger line for our ev en ts that ha v e c harged trac ks. On the other hand, for \all neutral" mo des (1S) r ; r r and (1S ) r ; 0 0 0 the trigger lines BARRELBHABHA or ENDCAPBHABHA w ere satised ecien tly F or mo des with c harged trac ks, hardGam ev en t-t yp e w as b y far the most imp ortan t. F or an ev en t to b e classied as hardGam, all the criteria listed b elo w m ust b e satised: eGam1 > 0 : 5, the highest isolated sho w er energy relativ e to the b eam energy eSh2 < 0 : 7, second most energetic sho w er energy relativ e to the b eam energy eOv erP1 < 0 : 85, the matc hed calorimeter energy for the most energetic trac k divided b y the measured trac k momen tum. If the ev en t has no reconstructed trac ks, the eOv erP1 quan tit y is assigned a default v alue of zero. eVis > 0 : 4, assuming pion h yp othesis, the total measured energy relativ e to the cen ter-of-mass energy The energy matc hed to the c harged trac ks is excluded while summing up total energy aCosTh < 0 : 95, absolute v alue of z -comp onen t of unit net momen tum v ector. F or all-neutral mo des, the signican t ev en t-t yp es are gamGam, radGam and hardGam, the signicance not necessarily in this order. The gamGam ev en t-t yp e has to pass the fairly simple tests nTk the n um b er of reconstructed c harged trac ks < 2, and eSh2 > 0 : 4 (see hardGam). A radGam ev en t-t yp e is necessarily gamGam ev en t-t yp e with the additional requiremen t that eSh3, the energy of third most energetic sho w er relativ e to the b eam energy should b e > 0 : 08 and eCC, the total energy dep osited in the calorimeter b e less than 75% of the cen ter-of-massenergy Due to the softer eSh2 criterion for hardGam, ev en ts for the all neutral mo de 0 0 0 are classied as hardGam more frequen tly than gamGam or radGam. F or the mo de (1S) r ; r r ho w ev er, the deca y of high energy in to t w o photons alw a ys satised eSh2 > 0 : 4 th us gamGam is the most ecien t follo w ed PAGE 56 41 b y radGam. Ho w ev er, during the course of analysis, it w as learn t that a cut on the energy asymmetry (dened later in Section 3.3.3 ) of the t w o photons helps us reduce the bac kground b y a large prop ortion. This cut w as con v enien tly c hosen to b e < 0 : 8, whic h thro ws a w a y all the ev en ts of t yp e gamGam whic h ha v e not b een classied as radGam as w ell. W e th us can select only radGam ev en t-t yp es for r r skim. In addition to the sub-collection/ev en t-t yp e cuts, the follo wing top ological cuts w ere required during the skimming pro cess: The top ology of radiativ e (1S ) deca ys is v ery distinctiv e. They ha v e a high momen tum photon, of energy similar to the b eam energy and a series of particles on the a w a y side of the ev en t. Th us, w e require the existence of a sho w er with measured energy > 4 : 0 GeV ha ving the sho w er prole consisten t with a photon. T o suc h a sho w er, w e refer as hard photon. W e require the NT rac ks cut to b e satised. This term means dieren tly for dieren t mo des. F or mo des with no c harged trac ks in them, w e require NT rac ks, the n um b er of reconstructed trac ks (go o d or bad) b e 0 F or mo des with c harged trac ks, w e require NT rac ks to ha v e at least 1 or 2 pairs of opp ositely c harged, \go o d trac ks" for 2, 4 trac ks mo des resp ectiv ely A \go o d trac k" should ha v e: 1. j d 0 j the distance of closest approac h of the c harged trac k to the origin of CLEO co ordinate system should b e less than 5 mm. 2. j z 0 j the z measuremen t of the trac k p osition at the p oin t of closest approac h to the CLEO co ordinate system should b e less than 10 cm. 3. The momen tum j ~ p j of c harged trac k should b e suc h that 200 MeV < j ~ p j < 5.3 GeV. Selection criteria used in the skimming pro cess are referred to as \basic cuts." T ables 3{2 and 3{3 quan tify the basic cuts' eciencies for deca y mo des of and 0 resp ectiv ely Please note that most of the tables from no w on ha v e columns b earing t w o lab els, \ind" and \cm b" whenev er w e talk ab out the eciency of a selection criterion listed in a particular ro w. The column lab eled with \ind" stands for the eciency of the individual cut under consideration and \cm b" stands for the com bined eciency of all the selection criteria whic h ha v e b een used so far, including the curren t PAGE 57 42 cut under consideration. With this legend, w e w ould read the r r column in T able 3{2 as 73 : 5% eciency for trigger alone (and also 73 : 5% in the \cm b" column as this is the rst cut). Next lev el4 cut is applied whic h has individual eciency as 93 : 2%, but the eciency is 73 : 5% after applying b oth the trigger and lev el4 cuts, and so on. T able 3{2. Eciency (in %) of basic cuts for mo des Mo de ! r r + 0 0 0 0 Ev en ts Generated 25000 25000 25000 Cut ind cm b ind cm b ind cm b T rigger 73.5 73.5 85.1 85.1 70.6 70.6 Lev el4 93.2 73.5 93.5 84.7 93.0 70.6 Ev en t T yp e 68.4 56.0 76.3 71.1 71.2 54.6 Hard Photon 85.2 54.3 83.3 68.6 83.2 52.5 NT rac ks 89.1 53.4 92.9 68.1 78.2 44.6 T able 3{3. Eciency (in %) of basic cuts for 0 mo des Mo de 0 ; r r 0 ; + 0 0 ; 0 0 0 0 r Ev en ts Generated 24967 25000 25000 25000 Cut ind cm b ind cm b ind cm b ind cm b T rigger 87.6 87.6 89.4 89.4 85.9 85.9 85.5 85.5 Lev el4 94.0 87.3 94.5 88.8 93.7 85.6 93.8 84.8 Ev en t T yp e 67.5 64.5 74.1 71.9 73.0 69.1 75.2 70.8 Hard Photon 83.2 61.6 83.3 69.2 82.5 66.2 82.9 67.9 NT rac ks 92.0 61.0 80.5 60.9 92.0 65.6 90.6 66.7 T o further reduce the skim size, w e carried the skimming pro cedure through another iteration. F or eac h of the mo des, complete deca y c hain w as reconstructed with v ery lo ose cuts. The 0 r r and r r candidates w ere constrained to their nominal masses, and restricted in the in v arian t mass windo w 50{230 MeV = c 2 and 350{900 MeV = c 2 resp ectiv ely The photon candidates used in reconstructing ab o v e meson candidates w ere not required to pass the standard qualit y criteria (discussed in next section). Other in termediate meson candidates w ere formed b y simply adding the 4-momen ta of daugh ter particles b y making sure that none of the constituen t PAGE 58 43 trac ks or sho w ers ha v e b een used more than once in the deca y c hain. Candidate + 0 and 0 0 0 deca ys (collectiv ely referred to as 3 from no w on) w ere required to ha v e a reconstructed in v arian t mass of 400{700 MeV/ c 2 No in v arian t mass cut w as imp osed on the 0 candidate. T o complete the deca y c hain, a hard photon w as added and the energy of the reconstructed ev en t w as compared to the cen ter-of-mass energy The ev en t w as selected if j E j the magnitude of dierence b et w een the energy of reconstructed ev en t and the cen ter-of-mass energy w as less than 2.5 GeV. Data skim for mo de (1S) r 0 ; 0 r w as made b y requiring an ev en t to ha v e a pair of opp ositely c harged go o d trac ks accompanied b y a hard photon. Since most of the reconstructed energy is measured in CsI, j E j criterion had b een k ept generous in an ticipation of sho w er energy leak age. The kinematic tting w e will use in the nal analysis will allo w eectiv ely tigh ter cuts on j E j and p the magnitude of net momen tum v ector. 3.3 Reconstruction In our rened v ersion of reconstructing the deca y c hain, our trac k selection criteria remained the same, the \go o d trac k" as explained in Section 3.2 T o reject the bac kground from spurious photons on the other hand, w e used some photon selection criteria. Before w e list the photon selection criteria used in reconstructing 0 and r r candidates, w e in tro duce the term E9O VERE25. E9O VERE25 E9O VERE25 is a selection criterion used to decide whether the sho w er has a lateral prole consisten t with b eing a photon. The decision is made based up on the energy dep osited b y the sho w er in inner 3x3 blo c k of nine CC crystals around the highest energy crystal and the energy dep osited in 5x5 blo c k of 25 crystals around the highest energy crystal. The energy dep osited in inner 9 crystals divided b y the energy dep osited in 25 crystals is commonly called E9O VERE25. A true photon is exp ected to dep osit almost all of its energy in the inner 3x3 blo c k. This ratio is PAGE 59 44 then exp ected to b e equal to one for true photons. F or isolated photons, this criterion is highly ecien t. Ho w ev er, to main tain high eciency for photons lying in pro ximit y to eac h other, a mo died v ersion, called E9O VERE25Unf(olded), where the energy in the o v erlapping crystals is shared. The photon candidates used in reconstructing candidates r r and 0 had to satisfy the follo wing qualit y criteria: A t least one of the sho w ers m ust ha v e lateral prole consisten t with b eing a photon, whic h is ac hiev ed b y 99% ecienct E9O VERE25Unf cut. None of the sho w ers could b e asso ciated to sho w er fragmen ts from the in teraction of c harged trac ks in the CC. Since the 0 and mesons are the deca y daugh ters of highly energetic and 0 mesons, the deca y daugh ters ry o in a collimated jet and some eciency loss is exp ected due to this requiremen t. Ho w ev er, this cut is necessary to reduce the bac kground from false sho w ers. eMin, the minim um sho w er energy b e 30 MeV for 0 candidates and 50 MeV for candidates. F urther, the default requiremen t for 0 and r r candidates, that the constituen t sho w ers should b e reconstructed either in the ducial barrel or the ducial endcap calorimeter region w as relaxed 1 for 0 candidates (see Section 3.3.2 ). It ma y b e notew orth y that this requiremen t w as also relaxed during the data skimming pro cess. In order to get the maxim um information out of the detector, for those deca y mo des in v olving c harged trac ks, an ev en t v ertex w as calculated using the c harged trac ks, and the 4-momen ta of the photons w ere calculated using this ev en t v ertex as the origin. The algorithm for ev en t v ertex is discussed in App endix 5 The 0 and 1 The ducial regions of the barrel and endcap are dened b y j cos( ) j < 0 : 78 and 0 : 85 < j cos( ) j < 0 : 95, resp ectiv ely; the region b et w een the barrel ducial region and the endcap ducial region is not used due to its relativ ely p o or resolution. F or this study w e relaxed this requiremen t (whic h w e call ducial region cut) for 0 candidates as there is a signican t c hance that at least one of the six photons from the 0 0 0 deca y ma y b e detected in the non-ducial regions. PAGE 60 45 in termediate states w ere mass constrained using these recalculated photons 2 to their nominal masses. This pro duces an impro v emen t in the resolution ( 10%) of the candidate and 0 in v arian t mass (see App endix 5 ). This corresp onds to a sligh t impro v emen t in the sensitivit y of the measuremen t. Our general analysis strategy is to reconstruct the complete deca y c hain to build the (1S) candidate, ensuring that none of the constituen t trac ks or sho w ers ha v e b een used more than once, and kinematically constrain the in termediate 0 and meson candidates to their nominal masses [ 14 ]. The mo de (1S) r ; r r w as an exception where no mass constraining w as done to the r r candidate. The candidate + 0 w as built b y rst constraining a pair of opp ositely c harged go o d trac ks to originate from a common v ertex. Then, a 0 candidate w as added to complete the reconstruction of + 0 c hain. The candidate 0 0 0 w as reconstructed b y simply adding the four momen ta of three dieren t 0 candidates, making sure that no constituen t photon candidate con tributed more than once in the reconstruction. The reconstruction of 0 + where deca ys to all neutrals ( r r or 3 0 ) is similar to + 0 candidate reconstruction where w e rst v ertexed a pair of opp ositely c harged go o d trac ks and then added the candidate constrained to its nominal mass. In the reconstruction of 0 ; + 0 the candidate had p osition information, so w e constrained all three, the pair of opp ositely c harged go o d trac ks and the mass-constrained + 0 candidate, to originate from a common v ertex. Once the nal state or 0 candidates w ere reconstructed, w e added a hard photon to build the (1S) candidate. The reconstruction of (1S) r 0 ; 0 r w as sligh tly dieren t and is not discussed in this section. 2 Only in the absence of ev en t v ertex, 0 and candidates are used as pro vided b y the standard CLEO I I I soft w are called PhotonDecaysProd pro ducer. PAGE 61 46 The candidate w as further constrained to the four momen tum of the e + e system. The idea b ehind 4-constrain t is t w o fold: rstly substituting the traditional j E j p cuts used to w ards judging the c ompleteness of ev en t b y a single more p o w erful quan tit y the 2P4 whic h is capable of taking the correlation j E j and p and secondly 2P4 along with other handles will b e exploited in discarding the m ultiple coun ting leading to com binatoric bac kground, a problem of v aried sev erit y from mo de to mo de. W e to ok in to accoun t the crossing angle of the b eams when p erforming 4-momen tum constrain t and calculating 2P4 Multiply reconstructed candidates in one ev en t giv e an articially higher reconstruction yield, and also increase the o v erall width of the signal. The problem of m ultiple coun ting is dealt with b y selecting the com bination with lo w est 2T otal the sum of c hi-squared of the 4-momen tum constrain t ( 2P 4 ) and c hi-squared v alues of all the mass-constrain ts in v olv ed in a particular deca y c hain. F or example, there are four mass-constrain ts in v olv ed in the deca y c hain (1S ) r 0 ; 0 0 0 three 0 mass-constrain ts and one mass-constrain t. The mo de (1S) r ; 0 0 0 is an exception in whic h w e preferred to accept the 0 0 0 candidate ha ving the lo w est S 2 P 3i S 2 ;i with S ;i (( m r r m 0 ) = r r ) of the i th 0 candidate. The quan tit y r r is the momen tum dep enden t in v arian t mass resolution of 0 candidate. T o estimate the reconstruction eciency w e coun ted the 0 or candidates con tributing to w ards reconstructing an candidate 3 within our acceptance mass windo w dened as the in v arian t mass region cen tered around the mean v alue and pro viding 98% signal co v erage as determined from signal Mon te Carlo. In addition, the ev en t w as required to pass trigger and ev en t-t yp e cuts as listed in T ables 3{2 and 3{3 The metho d outlined ab o v e w as common to all mo des. Mo de sp ecic details are explained b elo w. 3 An alternativ e sc heme is to coun t the n um b er of candidates reconstructed from go o d or 0 candidates. PAGE 62 47 3.3.1 Reconstruction of (1 S ) r ; + 0 Although m ultiple coun ting w as not a sev ere problem for this mo de as there are only t w o trac ks and t w o photons (in principle at least) on the other side of the hard photon, w e still had some ev en ts in whic h there w ere more than one reconstructed (1S) candidates. The (1S) candidate with the lo w est v alue of ( 2P4 + 2 0 ) w as selected. Candidate 0 mesons within 7 r r (i.e., a v ery lo ose cut) w ere used in reconstructing the + 0 candidate. A fairly lo ose particle iden tication criterion using dE =dx information w as emplo y ed b y requiring the c harged trac ks to b e consisten t with b eing pions. W e added the pion h yp othesis S dE =dx in quadrature for t w o trac ks (S 2dE =dx P 2i =1 S 2dE =dx ( i )), where S dE =dx for the i th trac k is dened as S dE =dx ( i ) = ( dE =dx (measured ) dE =dx (exp ected )) = dE =dx and dE =dx is the dE =dx resolution for pion h yp othesis. W e then required S 2dE =dx to b e less than 16. Finally to judge the completeness of the ev en t, a cut of 2P4 < 100 w as applied. The eciencies of these cuts are listed in T able 3{4 T able 3{4. Eciency of selection criteria for the mo de (1S) r ; + 0 Cut Ind E (%) Cm b E (%) 0 reconstruction 38.2 34.6 r r < 7 96.5 34.7 S 2dE =dx < 16 100.0 34.7 2P4 < 100 93.4 32.8 all cuts 32.8 0.4 The in v arian t mass distribution for the + 0 candidate from signal MC after all the cuts is sho wn in Figure 3{1 Figure 3{2 sho ws the distribution for v arious v ariable w e cut on. With this highly ecien t reconstruction sc heme, w e found no ev en t within our in v arian t mass acceptance windo w (Figures 3{3 (d), 3{4 ). In Figure 3{3 (d), it do es app ear that dE =dx cut rejects a lot of (bac kground) ev en ts. W e notice that the rejected bac kground is mostly electrons (see Figure 3{5 ), whic h can alternativ ely b e rejected using e op (the energy dep osited in the CsI b y a trac k divided PAGE 63 48 b y its measured momen tum) cut. Ho w ev er, using S 2dE =dx as a selection criterion ga v e us b etter bac kground rejection compared to e op cut, with basically the same eciency The eciency for S 2dE =dx cut w as c hec k ed using the p eak (from the con tin uum pro cess e + e r ) b y plotting the sideband subtracted signal and w as found to b e 96%, whic h is lo w er than the signal MC prediction of 99.9%. W e b eliev e the discrepancy is largely accoun ted for b y the fact that bac kground to the p eak ramps up under the p eak, rather than imp erfections of the detector resp onse sim ulation. Th us w e will con tin ue to use the 99.9% n um b er as our eciency but will giv e it a suitable systematic uncertain t y The high eciency and go o d bac kground rejection of this cut is b ecause the and e dE =dx lines are w ell separated in the momen tum range of in terest. PAGE 64 49 Figure 3{1. Candidate + 0 reconstructed in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r ; + 0 The reconstruction eciency is 32 : 8 0 : 4% after all the cuts. PAGE 65 50 0 4 8 12 s g g 0 400 800F Events (a) 0 4 8 R (S dE/dx 2 ) 0 400 F Events (b) 0 200 400 c 2 P4 0 800 1600F Events (c) -8 0 8 S dE/dx (track1) -8 0 8SdE/dx(track2) (d) Figure 3{2. Distribution from signal Mon te Carlo: F or the mo de (1S) r ; + 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) r r of the 0 candidate, plot(b) for q S 2dE =dx plot(c) for 2P 4 and plot(d) is a scatter plot of the pion h yp othesis S dE =dx for the c harged trac ks. PAGE 66 51 0.47 0.55 0.63 m( p + p p 0 ) (GeV/c 2 ) 0 4 8 12Events/1.6 MeV/c2 (a) 0.47 0.55 0.63 m( p + p p 0 ) (GeV/c 2 ) 0 4 8 Events/1.6 MeV/c2 (b) 0.47 0.55 0.63 m( p + p p 0 ) (GeV/c 2 ) 0 4 8Events/1.6 MeV/c2 (c) 0.47 0.55 0.63 m( p + p p 0 ) (GeV/c 2 ) 0 2.5 5Events/1.6 MeV/c2 (d) Figure 3{3. In v arian t mass of distribution of the candidate for the mo de (1S ) r ; + 0 : Plot(a) with no cuts, plot(b) with a cut on 2P4 only plot(c) after cutting on r r of the 0 candidate only plot(d) after cutting on S 2dE =dx alone. The red o v erla y on plot(d) is obtained after imp osing all the cuts. No candidate ev en t w as observ ed in signal region. PAGE 67 52 0.40 0.50 0.60 0.70 0.80 0.90 m( p + p p 0 ) (GeV/c 2 ) 0 20 40 60 80 100 120Events / (5.0 MeV/c2) 0.47 0.51 0.55 0.59 0.63 0 1 2 3 Events/ (1.5 MeV/c2) Figure 3{4. Reconstructed candidate in v arian t mass distribution in real data for the mo de (1S ) r ; + 0 No ev en ts are observ ed in the signal mass windo w denoted b y the region in b et w een blue arro ws (inset), and a clear ! + 0 p eak is visible from the QED pro cess e + e r PAGE 68 53 0.0 0.2 0.4 0.6 0.8 1.0 1.2 eop(track1) 0.0 0.2 0.4 0.6 0.8 1.0 1.2eop(track2) Figure 3{5. Scatter plot of e op distribution for trac k 2 vs trac k 1 for the ev en ts rejected b y S 2dE =dx > 16 : 0 cut. Most of the rejected ev en ts are clearly electron lik e. PAGE 69 54 3.3.2 Reconstruction of (1 S ) r ; 0 0 0 The kinematics in v olv ed in this deca y mo de are largely resp onsible for a comparativ ely lo w eciency and reconstruction qualit y The deca y of high energy in to three 0 mesons do es not cause them to spread out a lot, as a result the sho w ers from dieren t 0 mesons frequen tly lie on top of eac h other. Just one o v erlap of t w o sho w ers often mak es it imp ossible to reconstruct t w o of the 0 mesons. By seeking the help of tagger 4 w e gure that more than 50% of the ev en ts suer from this pathology In total MC this lea v es us with only 22 : 7% (5675 out of 25000) ev en ts where the sho w ers from the ha v e prop er tags W e dene an MC ha ving prop er tag when all six photons from deca y are tagged to six dieren t reconstructed sho w ers. Roughly 20% of the ev en ts with prop er tags w ere ltered out b y the ducial region cut (discussed in Section 3.3 ) alone, whic h is wh y this cut w as relaxed so that a more reasonable reconstruction eciency could b e obtained. T o address the problem of m ultiple coun ting, w e select the (1S) candidate in the ev en t ha ving the lo w est S 2 (dened in Section 3.3 ). F rom no w on, w e will refer to suc h a candidate as the b est c andidate Using tagged Mon te Carlo, w e nd that w e pic k up the correct com bination (i.e., eac h of the three 0 candidates is reconstructed from the photons candidates whic h ha v e b een tagged to the actual generated ones) appro ximately 72% of the time 5 Ha ving selected the b est (1 S ) c andidate w e require the follo wing t w o selection criteria to b e satised: 4 The tagger is a soft w are part of the CLEO I I I soft w are library The tagger is capable of p erforming hit-lev el tagging, and therefore, can tell us whic h reconstructed trac k or sho w er is due to whic h generated c harged particle or photon. By hit-lev el tagging it is understo o d that the tagging soft w are k eeps trac k of the cause of sim ulated hits (i.e., whic h hit is from whic h trac k, etc.), and so it is v ery reliable. 5 An alternativ e sc heme based up on 2T otal giv es statistically same answ er, though an y t w o sc hemes ma y disagree on an ev en t b y ev en t basis. PAGE 70 55 p S 2 < 10 : 0. primarily to select go o d qualit y 0 candidates and reduce p ossible bac kground in real data. 2P4 < 200 : 0 to ensure that the reconstructed ev en t conserv es the 4-momen tum. In addition, w e notice that requiring the n um b er of reconstructed sho w ers in ev en t to b e 13 is 99.9% ecien t in signal MC and helps us reduce some bac kground. The reason that this cut is useful is that one source of bac kground is the pro cess e + e r where K S K L The deca ys c hain ends with K S 0 0 and a p ossible K L 0 0 0 giving rise to an ev en t with a hard photon along with at least 2 0 mesons with some extra sho w ers. Ev en if the K L do es not deca y within the v olume of the detector, its in teraction in the CC is not w ell understo o d and it can p ossibly lea v e a bunc h of sho w ers. Suc h a bac kground can easily b e rejected b y a requiremen t on the n um b er of sho w ers. F rom resp ectiv e Mon te Carlo samples, the sho w er m ultiplicit y for pro cesses (1S ) r ; 0 0 0 and e + e r is sho wn in Figures 3{7 (c) and (d) resp ectiv ely As p er the Mon te Carlo, roughly 50% of the t yp e e + e r are rejected b y the cut restricting n um b er of sho w ers to b e 13 whereas only this requiremen t is almost 100% ecien t in signal MC. Th us, w e require the reconstructed ev en t to pass this highly ecien t test as w ell. T able 3{5 lists the selection criteria used in the reconstruction. Figure 3{6 sho ws the in v arian t mass distribution from signal MC for the mo de (1S) r ; 0 0 0 Figure 3{7 sho ws the distribution of the quan tities w e cut on. With this reconstruction sc heme, w e nd no candidate ev en ts from real 1S data as the Figure 3{8 sho ws. T able 3{5. Eciency table for the mo de (1S ) r ; 0 0 0 Cut Ind E (%) Cm b E (%) p S 2 of 0 s < 10 94.9 12.3 2P4 < 200 95.4 11.8 # Sho w ers 13 99.9 11.8 all cuts 11.8 0.2 PAGE 71 56 Figure 3{6. Reconstructed in v arian t mass distribution for the candidate 0 0 0 from signal Mon te Carlo for the mo de (1S) r ; 0 0 0 The reconstruction eciency is 11 : 8 0 : 2% after all the cuts. PAGE 72 57 0 5 10 15 R S p 2 0 50 100 150F Events (a) 0 200 400 c 2 P4 0 250 500F Events (b) 5 10 15 20 F Showers 0 500 1000 1500F Events (c) 5 10 15 20 F Showers 0 20 40 60F Events (d) Figure 3{7. Distributions from (1S) r ; 0 0 0 signal Mon te Carlo, sho wing the v ariables w e cut on. The y ello w (shaded) area in these plots represen ts the acceptance. Plot (a) p S 2 of the 0 candidates, plot (b) for 2P4 and plot (c) # of sho w ers in the ev en t. The dashed (red) line in plot (a) sho ws the p S 2 of the tagged 0 candidates. As can b e seen, ma jorit y of go o d ev en ts are conned within p S 2 < 10 : 0, giving us a reason to select our acceptance region. Plot (d) sho ws the sho w er m ultiplicit y from the signal MC for the pro cess e + e r Although plot (d) is not normalized to plot (c), w e can clearly see that if Mon te Carlo b e trusted, a cut on the n um b er of sho w ers help reject 50% of this bac kground. PAGE 73 58 0.40 0.50 0.60 0.70 m( p 0 p 0 p 0 ) (GeV/c 2 ) 0 4 8Events/3.0 MeV/c2 (a) 0.40 0.50 0.60 0.70 m( p 0 p 0 p 0 ) (GeV/c 2 ) 0 2 4Events/3.0 MeV/c2 (b) 0.40 0.50 0.60 0.70 m( p 0 p 0 p 0 ) (GeV/c 2 ) 0 1 2 3Events/3.0 MeV/c2 (c) 0.40 0.50 0.60 0.70 m( p 0 p 0 p 0 ) (GeV/c 2 ) 0 1 2 3Events/3.0 MeV/c2 (d) Figure 3{8. In v arian t mass of candidate for the mo de (1S) r ; 0 0 0 : Plot (a) allo wing m ultiple candidates p er ev en t, plot (b) after selecting b est c andidate plot (c) selecting b est c andidates with 2P 4 < 200.0, plot (d) b est c andidate with # of sho w ers cut. The red o v erla y on plot (d) is obtained after imp osing all the cuts. There are no ev en ts in the acceptance mass windo w (denoted b y blue arro ws) after all the cuts. PAGE 74 59 3.3.3 Reconstruction of (1 S ) r ; r r W e rst form all p ossible r r com binations to build candidate. Then, the (1S) candidate is reconstructed b y com bining a hard photon to the candidate, whic h is kinematically constrained to the 4-momen tum of e + e system. W e accept an (1S) candidate if 2P4 < 200 : 0. W e do not attempt to reject ev en ts with more than one (1S) candidate as only the righ t com bination en ters our nal candidate in v arian t mass plot. Our selection criteria so far, namely using a hard photon and constraining the (1S) candidate to the 4-momen tum of b eam, are not sucien t to suppress the QED bac kground from the pro cess e + e r r r (See Figure 3{9 ). The QED MC w as generated using Berends-Kliess generator[ 22 ]. (a) E ( GeV)j ~ p j ( GeV = c) (b) E ( GeV)j ~ p j ( GeV = c)Figure 3{9. j ~ p j vs E distribution plot(a) for signal MC for (1S) r ; r r and plot(b) for e + e r r r MC. The QED ev en ts, ho w ev er, ha v e v ery asymmetric distribution of energy E hi and E l o for t w o lo w er energy photons used in reconstructing The real has equal probabilit y of ha ving the deca y asymmetry from 0 to 1 (Figure 3{10 ) where asymmetry PAGE 75 60 (a) asymmetry# ev en ts (b) asymmetry# ev en tsFigure 3{10. Asymmetry distribution for candidate. Plot (a) from Mon te Carlo data for e + e r r r (blac k) and signal MC (1S) r ; r r (red) and plot (b) for data18 and data19. F or asymmetry < 0 : 75, the ev en ts in plot (b) are o v ershado w ed b y the ev en ts b ey ond asymmetry > 0 : 75. The h uge pile at the higher in end in plot (b) is b ecause in this plot, the ev en ts classied as gamGam ev en t-t yp e ha v e not b een rejected y et. is dened as ( E hi E l o ) = ( E hi + E l o ). W e note the signal MC prediction that ma jorit y of the signal ev en ts are classied as either radGam or gamGam ev en t-t yp es. The ev en ts classied as gamGam ev en t-t yp e only ho w ev er, ha v e v ery asymmetric deca ys with asymmetry > 0 : 84. The ev en t-t yp e gamGam is th us automatically ruled out b y the asymmetry cut, whic h is applied at 0.8. The exp ected eciency for this cut is 80%, in realit y it is more than that as the p eak 6 asymmetry can not b e equal to one. Considering the eciency and the amoun t of QED suppression ac hiev ed, w e add this as one of our basic selection criteria. The QED bac kground, ho w ev er, is not fully suppressed. 6 Asymmetry equal to one means one of the photons has measured energy equal to 0 PAGE 76 61 3.3.3.1 P ossible Bac kground e + e r r ( e + e ) W e mak e a brief digression to another p ossible bac kground whic h w as rep orted in the previous analysis [ 9 ]. This bac kground arises from e + e r r where one of the photons con v erts in to an e + e pair sucien tly far in to the drift c ham b er that no trac ks are reconstructed. This e + e pair separates in under the inruence of magnetic eld, and mimics t w o sho w ers. Suc h a \ r r r ev en t migh t satisfy our selection criteria. A distinct geometric c haracteristic of suc h a sho w er pair is that the dierence in p olar angle of t w o sho w ers, is close to 0 whereas j j the magnitude of dierence in azim uthal angle of t w o sho w ers, is not. In [ 9 ] a ge ometric cut requiring j j > 3 w as used in reducing this bac kground whic h w as otherwise a substan tial fraction of the en tries in the nal r r in v arian t mass distribution. Motiv ated b y this, w e lo ok ed for the presence of suc h bac kground in our analysis. Ho w ev er, w e did not nd an y ob vious signature in real data as Figure 3{11 sho ws. A further in v estigation w as done b y generating a dedicated Mon te Carlo sample comprising 115K ev en ts for the pro cess e + e r r without an y ISR (initial state radiation) eects. W e did not nd an y bac kground ev en t of this t yp e surviving our cuts in e + e r r Mon te Carlo sample either. 3.3.3.2 Handling e + e r r r bac kground T o study our main QED bac kground pro cess, e + e r r r w e generated a dedicated MC sample for this pro cess, using a stringen t ISELECT function (a piece of co de primarily mean t to accept the ev en ts of in terest b efore computing in tensiv e, full detector sim ulation is carried out) demanding Only 3 photons generated, all with j cos( ) j < 0 : 95 A t least one photon with generated energy of at least 4.0 GeV Remaining t w o photons ha v e r r in v arian t mass in the range 0.2{1.0 GeV = c 2 and asymmetry < 0 : 8 PAGE 77 62 Figure 3{11. Distribution of vs in real data for ev en ts in the mass windo w passing our basic cuts. W e analyze the t w o MC data samples (signal MC and QED) in detail, but except for asymmetry w e do not nd an y distinct feature whic h can help us help us discriminate b et w een them. There should b e, ho w ev er, some minor dierences in distributions of some v ariables, whic h ma y b e harnessed collectiv ely to ac hiev e further signal to bac kground separation. Th us w e wrote a neural net w ork program in an attempt to com bine the information in an optimal w a y Articial Neural Net An Articial Neural Net (ANN) is a mathematical structure inspired from our understanding of biological nerv ous system and their capabilit y to learn through exp osure to external stim uli and to generalize. ANNs ha v e pro v ed their usefulness in div erse areas of science, industry and business. In the eld of exp erimen tal high energy ph ysics, ANNs ha v e b een exploited in p erforming trigger op erations, pattern recognition and classication of ev en ts in to dieren t categories, PAGE 78 63 sa y signal and bac kground. Generally the goal is to do a m ultiv ariate analysis to carv e out a decision surface, a metho d sup erior to a series of cuts. ANNs ha v e already made their impact on disco v ery (top quark). An ANN consists of articial neur ons or no des whic h exc hange information. Eac h no de receiv es input signal from other no des, and the w eigh ted sum of these inputs is transformed b y an activation function g ( x ), the result of whic h is the output from the no de. This output m ultiplied b y the w eigh t of the no de serv es as an input to some other no de. Without discussing the gory details of the functioning of an ANN, w e men tion of fe e d-forwar d neural net w ork where the information ro w is in one direction only The neural net w ork used in this analysis is a m ulti-la y er p erceptron [ 23 ] whic h is essen tially a fe e d-forwar d ANN ha ving an input la y er accepting a v ector of input v ariables, a few hidden la y ers and an output la y er with single output. T o b e able to use a neutral net w ork in solving a problem, it needs to b e trained o v er a set of training p atterns whic h is done iterativ ely During the course of training, the w eigh ts of individual no des adapt according to the p atterns fed to the neural net w ork. The dierence b et w een the desired output (1 for signal and -1 bac kground in our case) and the actual output from the neural net is used to mo dify the w eigh ts and the discrepancy (or error) is minimized as the training progresses. The arc hitecture of the neural net used is [ 9 14 5 ], a three la y ered neural net ha ving tanh( x ) as the activation function with single output in the range [-1,1]. The output from the trained neural net is exp ected to p eak at 1 for signal ev en ts and at -1 for bac kground ev en ts. The input to the neural net is a v ector of six v ariables, namely the measured energy and p olar angle of the three sho w ers used in reconstruction. The isotrop y in azim uthal angle renders it p o w erless in making an y discrimination in separating the signal from bac kground. The c hoice of input v ector as w ell as the training data sample is v ery imp ortan t. The general tendency of neural nets is to gure out the easily iden tiable dierences in the t w o samples rst in v arian t mass of PAGE 79 64 the candidate b eing the easy catc h b et w een signal MC and QED bac kground here, as with this c hoice of input v ector, the neural net can easily w ork out the in v arian t mass of the candidate. F or this reason, w e generate a signal MC ha ving a \wide" and select the data for training where in v arian t mass of is in the range 0.4{0.7 GeV = c 2 The bac kground data sample is comprised of the e + e r r r Mon te Carlo generated at cen ter-of-mass energy 9.46 GeV, ha ving di-photon in v arian t mass in the range 0.4{0.7 GeV = c 2 a 300 MeV = c 2 windo w around the nominal mass. With this sample, the bias due to in v arian t mass is eliminated. T o a v oid the w ell kno wn \o v er-tting" problem where the neural-net starts remem b ering the data to o sp ecically and hence losing its abilit y to generalize, w e build a large training sample of 10,000 ev en ts of eac h t yp e (signal and bac kground). As the training progresses, w e monitor (see Figure 3{12 ) the p erformance of the neural-net o v er a similar, indep enden t testing sample comprised of signal and bac kground Mon te Carlo data. 3.3.3.3 Final Selection and Comparison of Neural Net vs Asymmetry Using indep enden t samples of signal and e + e r r r Mon te Carlo, w e compare the p erformance of neural net cut with asymmetry cut. The neural net outp erforms the asymmetry cut only marginally as is clear from Figure 3{13 F or an y c hosen eciency neural net giv es a higher bac kground rejection as compared with asymmetry F or our nal selection, w e c ho ose net-v alue > 0 : 4 with 51% eciency while rejecting 86% of the bac kground. T o c ho ose the v alue for this cut, w e optimize S= p B whic h w as found to b e fairly rat in the range 0.15{0.40 The eciency of the cuts used is listed in T able 3{6 Figure 3{14 sho ws the signal MC ev en ts' r r in v arian t mass distribution for candidates surviving our nal cuts. The nal reconstruction eciency for this mo de is 23 : 8 0 : 3% PAGE 80 65 0 2.5 5 7.5 10 log(epoch) 0.35 0.45 0.55 0.65 0.75 0.85 0.95error Figure 3{12. T raining the Neural Net: During the course of training, red denotes the training error and blac k denotes the testing error (shifted b y 0.02 for clarit y) from an indep enden t sample. The testing error follo ws the training errors closely and o v er-training is not exhibited at all. The learning pro cess saturates ho w ev er, and training is stopp ed after 10K iterations. PAGE 81 66 0 25 50 75 100 Y efficiency 0 25 50 75 100 Y bgd. rejection -0.8 -0.4 0.0 0.4 0.8 netvalue 0 10 20s/ R b Figure 3{13. Comparison of bac kground rejection vs eciency: The lo w er curv e in red sho ws the p erformance of asymmetry cut and upp er curv e in blac k is from neural net. F or an y c hosen v alue of eciency neural net giv es a higher bac kground rejection as compared to asymmetry cut. Inset is S= p B plotted for v arious v alues of neural net cut. T able 3{6. Final eciency table for the mo de (1S ) r ; r r Cut Ind E (%) Cm b E (%) 2P4 < 2000 100.0 55.6 asymmetry < 0.8 83.9 46.7 net > 0.4 51.1 23.8 all cuts 23.8 0.3 PAGE 82 67 Figure 3{14. r r in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r ; r r 3.3.3.4 Data Plots and Upp er Limit Requiring all cuts except the neural net, Figure 3{15 sho ws the r r in v arian t mass distribution in real data. After imp osing neural net cut as w ell, the r r in v arian t mass distribution is sho wn in Figure 3{16 W e t the r r in v arian t mass distribution to a Gaussian of xed mean and width as obtained from signal MC con v oluted with a bac kground function. If w e let the PAGE 83 68 area roat, w e obtain 2 : 3 8 : 7 ev en ts (Figure 3{17 ), consisten t with 0. T o obtain the upp er limit for this mo de, w e x the parameters to the ones obtained from Mon te Carlo and do lik eliho o d ts for dieren t, xed signal yields and record the 2 of t. W e assign a probabilit y P of obtaining this yield as: P / e 2 2 ; whic h w e normalize to 1.0 and n umerically in tegrate up to 90% of the area to obtain the yield at 90% condence lev el as sho wn in Figure 3{18 Figure 3{19 sho ws the upp er limit area, whic h is the result of summing up the probabilit y distribution in Figure 3{18 upto 90% Figure 3{15. r r in v arian t mass distribution in real data. All cuts except neural net cut are in place. PAGE 84 69 Figure 3{16. r r in v arian t mass distribution in real data after all cuts. PAGE 85 70 Figure 3{17. Fit to r r in v arian t mass distribution for the mo de (1S ) r ; r r Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 2 : 3 8 : 7 ev en ts, whic h is consisten t with 0. PAGE 86 71 Figure 3{18. Normalized probabilit y distribution for dieren t signal area for the mo de (1S) r ; r r The shaded area spans 90% of the probabilit y PAGE 87 72 Figure 3{19. The t to reconstructed r r in v arian t mass distribution from real data for the mo de (1S ) r ; r r The area is xed to the n um b er of ev en ts obtained from 90% condence lev el upp er limit. The mean, width and other parameters are xed to the ones obtained from Mon te Carlo. PAGE 88 73 3.3.4 Reconstruction of (1 S ) r 0 ; r r By selecting the (1S ) candidate with lo w est v alue for 2P4 + 2 w e tak e care of m ultiple coun ting, a problem whic h is not so serious for this mo de. Go o d qualit y candidates are selected b y requiring the 2 < 200 where 2 is the 2 of constraining the candidate to its nominal mass. T o select the pion trac ks and to reject the bac kground from electron trac ks, w e require the S 2dE =dx to b e less than 16.0 (this w as also a requiremen t for the mo de (1S) r ; + 0 ). T o ensure that the ev en t is fully reconstructed, i.e., balanced in momen tum and adds up to the cen tre-of-mass energy of the e + e system, w e require the 2P4 < 100. The eciency of the cuts used is listed in T able 3{7 T able 3{7. Final eciency table for the mo de 0 + and then r r Cut Ind E (%) Cm b E (%) 2 < 200 99.6 41.9 S 2dE =dx < 16 99.7 41.8 2P4 < 100 97.1 40.6 all cuts 40.6 0.4 The in v arian t mass distribution for the reconstructed 0 candidate after ab o v e men tioned selection criteria from signal MC is sho wn in Figure 3{20 The in v arian t mass distribution for 0 candidate from real data is sho wn in Figures 3{22 and 3{23 W e nd no candidate signal ev en t within our acceptance mass windo w. PAGE 89 74 Figure 3{20. Reconstructed candidate 0 in v arian t mass distribution from signal Mon te Carlo for the mo de (1S ) r 0 ; r r The reconstruction eciency is 40 : 6 0 : 4% after all the cuts. PAGE 90 75 0 100 200 c 2 h 0 4000 8000F Events (a) 0 4 8 R (S dE/dx 2 ) 0 400 F Events (b) 0 100 200 c 2 P4 0 500 1000 1500F Events (c) -8 0 8 S dE/dx (track1) -8 0 8SdE/dx(track2) (d) Figure 3{21. Distribution from signal Mon te Carlo: F or the mo de (1S) r 0 ; r r v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) 2 distribution, plot(b) for q S 2dE =dx plot(c) for 2P4 and plot(d) is a scatter plot of the dE =dx for pion h yp othesis for the c harged trac ks. PAGE 91 76 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (a) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (b) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (c) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (d) Figure 3{22. In v arian t mass of 0 candidate for the mo de (1S) r 0 ; r r : Plot(a) without an y cuts, plot(b) after selecting candidates with 2 < 200, plot(c) after dE =dx cut, plot(d) requiring 2P 4 < 100. The red o v erla y on plot(d) is obtained after imp osing all the cuts. No candidate signal ev en t is observ ed in our acceptance mass windo w (denoted b y blue arro ws). PAGE 92 77 0.82 1.02 1.22 1.42 1.62 m( h p + p ) (GeV/c 2 ) 0 2 4 6 Events / (8.0 MeV/c2) 0.920 0.940 0.960 0.980 1.000 0 1 2 3 Events / (0.8 MeV/c2) Figure 3{23. Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; r r No candidate signal ev en t is observ ed in our acceptance mass windo w (inset). PAGE 93 78 3.3.5 Reconstruction of (1 S ) r 0 ; 0 0 0 This is one of the three mo des studied in this analysis where m ultiple coun ting p oses a serious problem. The origin of the problem, lik e in the mo de (1S ) r ; 0 0 0 lies in the deca y of high energy in to 3 0 mesons where the sho w ers from dieren t 0 mesons lie so close to eac h other in the CC and are so close in energy that an o v erwhelming n um b er of candidates are reconstructed. Suc h candidates ha v e in v arian t mass close to the nominal mass, leading to p o or resolution and an articially high eciency F rom the whole ra of (1S ) candidates, w e select the one ha ving lo w est 2T otal where 2T otal = 2 0 1 + 2 0 2 + 2 0 3 + 2 + 2P4 The 0 candidates are selected b y requiring p S 2 < 10. Go o d qualit y candidates are selected b y requiring the 2 < 200. T o b e consisten t with other mo des, w e require q S 2dE =dx to b e less than 4. Energy-momen tum conserv ation is enforced b y requiring 2P4 to b e less than 200. The eciency for all these cuts is listed in T able 3{8 and the distribution for cut v ariables is sho wn in Figure 3{25 T able 3{8. Final eciency table for the mo de 0 + and then 0 0 0 Cut Ind E (%) Cm b E (%) 2 < 200 98.3 22.8 q S 2dE =dx < 4 99.9 22.7 2P4 < 200 96.3 21.9 p S 2 of 0 s < 10 73.7 16.6 all cuts 16.6 0.4 Using the ab o v e reconstruction sc heme, the in v arian t mass for reconstructed 0 candidate is sho wn in Figure 3{24 W e nd no candidate ev en t in real data as the Figures 3{26 and 3{27 sho w. PAGE 94 79 Figure 3{24. Reconstructed in v arian t mass distribution of the candidate 0 from signal Mon te Carlo for the mo de (1S) r 0 ; 0 0 0 : The reconstruction eciency is 16 : 6 0 : 4% after all the cuts. PAGE 95 80 0 200 400 c 2 h 0 1000 2000 3000 F Events (a) 0 12.5 25 R (S dE/dx 2 ) 0 500 1000F Events (b) 0 200 400 c 2 P4 0 200 400 600 F Events (c) 0 10 20 30 R S p 2 0 200 400F Events (c) Figure 3{25. Distributions from signal Mon te Carlo: F or the mo de (1S) r 0 ; 0 0 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) for 2 Plot(b) q S 2dE =dx for t w o trac ks, plot(c) for 2P4 and plot(d) p S 2 of the 0 candidates. The dashed (red) line in plot(d) sho ws the p S 2 of the tagged 0 candidates. As can b e seen, ma jorit y of go o d ev en ts are conned within p S 2 < 10 : 0 giving us a reason to select our acceptance region. PAGE 96 81 0.920 0.940 0.960 0.980 1.000 0 1 2 3 Figure 3{26. In v arian t mass of 0 candidate for the mo de (1S) r 0 ; 0 0 0 : W e found t w o ev en ts when no cuts are in place. None of the t w o ev en ts in the 0 in v arian t mass histogram surviv e the 2P4 < 200 requiremen t. 3.3.6 Reconstruction of (1 S ) r 0 ; + 0 W e rst constrain a pair of opp ositely c harged trac ks to originate from a common v ertex. Next, w e add a 0 candidate and build the candidate. The candidate is mass-constrained to its nominal mass and then v ertexed to another pair of opp ositely c harged trac ks to mak e 0 The kinematics of the c harged trac ks in v olv ed in this mo de is suc h that using wrong trac ks at the reconstruction lev el results in 0 ha ving in v arian t mass within the acceptance region v ery often. This leads to m ultiple coun ting and p o or resolution. T o handle this situation, the (1S) candidate with lo w est 2T otal is selected where 2T otal means 2 0 + 2 + 2P4 The selected (1S) candidate is required to pass the consistency c hec ks listed in T able 3{9 Figure 3{28 sho ws the in v arian t mass distribution for 0 candidates passing our selection criteria. Figure 3{29 sho ws the distribution of cut v ariables used in this PAGE 97 82 0.82 1.02 1.22 1.42 1.62 m( h p + p ) (GeV/c 2 ) 0 2 4 6 8Events / (8.0 MeV/c2) Figure 3{27. Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; 0 0 0 No candidate signal ev en t is observ ed in our acceptance mass windo w mo de. In real data, w e nd t w o candidate ev en ts passing our selection cuts, as sho wn in Figure 3{30 These t w o ev en ts ha v e b een lo ok ed at in detail and sho w no signs of not b eing go o d signal ev en ts. T able 3{9. Final eciency table for the mo de (1S ) r 0 ; + 0 Cut Ind E (%) Cm b E (%) 2P4 < 200 96.6 25.4 r r of 0 < 10 97.9 24.8 2 < 100 99.1 24.7 q S 2dE =dx < 4 98.9 24.5 all cuts 24.5 0.4 PAGE 98 83 Figure 3{28. Reconstructed candidate 0 in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r 0 ; + 0 : The reconstruction eciency is 24 : 5 0 : 5% after all the cuts. PAGE 99 84 0 200 400 c 2 P4 0 500 1000 1500F Events (a) 0 5 10 15 s g g 0 400 800F Events (b) 0 40 80 120 c 2 h 0 2500 5000F Events (c) 0 4 8 R (S dE/dx 2 ) 0 200 400 600F Events (d) Figure 3{29. Distribution from signal Mon te Carlo: F or the mo de (1S) r 0 ; + 0 v ariables w e cut on are plotted. The y ello w (shaded) area in these plots represen ts the acceptance. Plot(a) for 2P4 plot(b) for r r of 0 candidate plot(c) for 2 and Plot(d) q S 2dE =dx for all four trac ks. PAGE 100 85 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (a) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (b) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (c) 0.920 0.960 1.000 m( h p + p ) (GeV/c 2 ) 0 1 2 3Events/0.8 MeV/c2 (d) Figure 3{30. In v arian t mass of 0 candidate for the mo de (1S) r 0 ; + 0 : Plot(a) with no cuts, plot(b) with the requiremen t 2P4 < 100, plot(c) with pion h yp othesis consistency in the form q S 2dE =dx < 4 : 0, and plot(d) with all the cuts. W e nd t w o candidate ev en ts. PAGE 101 86 0.82 1.02 1.22 1.42 1.62 m( h p + p ) (GeV/c 2 ) 0 1 2 3 4 5Events / (8.0 MeV/c2) 0.920 0.940 0.960 0.980 1.000 0 1 2 3 Events / (0.8 MeV/c2) Figure 3{31. Extended range of in v arian t mass distribution of 0 candidate for the mo de (1S) r 0 ; + 0 Tw o go o d candidate signal ev en ts are observ ed in our acceptance mass windo w (inset). PAGE 102 87 3.3.7 Reconstruction of (1 S ) r 0 ; 0 r The candidate is reconstructed b y constraining t w o opp ositely c harged go o d trac ks to originate from a common v ertex. W e then select a photon candidate (whic h w e refer to as the \soft photon" ha ving energy E s in con trast with the high energy radiativ e photon) ha ving lateral prole consisten t with b eing a photon and not asso ciated to a c harged trac k. This soft photon is added to the candidate to reconstruct 0 candidate. The (1S) candidate is then reconstructed b y adding 7 a hard photon to the 0 candidate. The (1S ) candidate is constrained to the 4-momen tum of the initial e + e system and during the kinematic tting, w e k eep trac k of the four-momen ta of constituen ts (i.e., soft photon and the hard photon). W e then use the up dated E s and the up dated in v arian t mass of the 0 candidate in our analysis. The kinematic tting impro v es b oth the resolution as w ell as 0 yield (see Figure 3{32 ). T o handle m ultiple coun ting, the com bination ha ving lo w est v alue for t 2P4 w as selected. T o reduce the bac kground from misiden tied c harged trac ks, w e com bine the dE =dx and RICH information for the pair of c harged trac ks in one n um b er, (e.g., 2I D ( K ) to distinguish b et w een pions and k aons) as follo ws: 2I D ( K ) = S 2dE =dx ( + ) S 2dE =dx ( K + ) + S 2dE =dx ( ) S 2dE =dx ( K ) 2 log ( L RI C H ( + )) + 2 log( L RI C H ( K + )) 2 log ( L RI C H ( )) + 2 log( L RI C H ( K )) (3{1) where 2I D ( K ) < 0 implies that the pair is more lik ely to b e + than K + K Our particle iden tication cut \P article Iden tication" as listed in T able 3{10 comprises of the requiremen t 2I D ( K ) < 0 and 2I D ( p ) < 0 sim ultaneously 7 The particles for this mo de are not com bined in the w a y as describ ed in Section 3.3 W e rather build an ob ject where 4-momen ta and the error matrices of individual particles are k ept trac k during the kinematic tting. PAGE 103 88 T o b e able to use the RICH information, w e require that a trac k's momen tum b e ab o v e the Cherenk o v radiation threshold for b oth mass h yp otheses under consideration, and there are at least 3 photons within 3 of the Cherenk o v angle for at least one of the mass h yp otheses. W e also require that b oth the mass h yp otheses under consideration w ere analyzed b y RICH during pass2. If neither dE =dx nor RICH information is a v ailable, w e accept the pair as + b y default. W e also v eto the electrons b y requiring the e op for b oth trac ks b e outside of the range 0.95{1.05 and 2I D ( e ) > 0. Muon trac ks are rejected b y requiring that the DPTHMU (dened in Section 2.3.5 ) for b oth trac ks b e less than 5. T o ensure that the reconstructed deca y c hain mak es the complete ev en t, 2P 4 is required to b e < 100. Finally to reject the complete, bac kground ev en ts of t yp e e + e r r w e require E s the up dated energy (after kinematic tting) of the photon from 0 deca y to b e greater than 100.0 MeV. The eciency of the cuts used is listed in T able 3{10 Figure 3{33 sho ws the 0 r in v arian t mass distribution for signal MC ev en ts passing our selection criteria. In real data, our cuts are not sucien t to suppress the con tin uum bac kground as Figure 3{34 sho ws. There is no visible p eak in the 0 in v arian t mass distribution either. T o subtract the con tin uum bac kground, w e try t w o dieren t approac hes where 1) w e subtract the scaled con tin uum data from 4S data and assume the same eciency at higher energy 2) w e parameterize the bac kground using a smo oth bac kground function (a rat bac kground in this case). W e t the in v arian t mass distribution for 0 candidates using a double Gaussian function (the t parameters are xed from MC) and a p olynomial bac kground function. W e let the area roat and compare the uncertain t y on the nal yield from t and c hose the one whic h giv es us smaller relativ e uncertain t y W e nd that con tin uum subtracted distribution, when tted with yield roating giv es us 3 : 5 6 : 3 ev en ts whereas 3 : 1 5 : 3 ev en ts are obtained without con tin uum subtraction as Figures 3{36 and 3{35 sho w. PAGE 104 89 Since the dierence b et w een relativ e uncertain ties is v ery small and the eciency at the 4S energy is not w ell studied, w e c ho ose not to do a con tin uum subtraction using 4S data. T able 3{10. Eciency table for the mo de (1S ) r 0 ; 0 r Cut Ind E (%) Cm b E (%) P article Iden tication 99.2 45.8 Electron V eto 91.7 42.0 Muon Rejection 99.1 41.6 4-Momen tum Consistency 98.8 41.4 E s 97.0 40.1 all cuts 40.1 0.4 Figure 3{32. Reconstructed r candidate in v arian t mass distribution from signal MC for 0 r : The kinematic tting impro v es the in v arian t mass resolution b y 30% and reconstruction eciency b y 5%. PAGE 105 90 Figure 3{33. Reconstructed in v arian t mass distribution from signal Mon te Carlo for the mo de (1S) r 0 ; 0 r : The reconstruction eciency is 40 : 1 0 : 4% after all the cuts. PAGE 106 91 Figure 3{34. Reconstructed in v arian t mass distribution in real data for the mo de (1S) r 0 ; 0 r : In top plot, blac k histogram sho ws the distribution from 1S data and o v erlaid in red is the scaled distribution from 4S data. The b ottom plot after subtracting the con tin uum. W e assume the same reconstruction eciency at 4S energy PAGE 107 92 Figure 3{35. Without con tin uum subtraction, the t to data plot for the mo de (1S) r 0 ; 0 r : Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 3 : 1 5 : 3 ev en ts. PAGE 108 93 Figure 3{36. The t to the con tin uum subtracted data plot for the mo de (1S) r 0 ; 0 r : Lea ving the area roating while k eeping the mean, width and other parameters xed to MC t parameters, w e obtain 3 : 5 6 : 3 ev en ts. The underlying con tin uum has b een subtracted using the distribution from 4S data. PAGE 109 94 Figure 3{37. The normalized probabilit y distribution for dieren t signal area for the mo de (1S) r 0 ; 0 r : The shaded area spans 90% of the probabilit y Since w e observ e no clear signal, w e calculated the upp er limit yield at 90% C.L. on the lines describ ed in Section 3.3.3.4 W e obtain an upp er limit of 8.59 ev en ts at 90% C.L. from the 1S data and a sligh tly lo w er n um b er from con tin uum subtracted 1S distribution where 8.35 ev en ts is obtained. W e do a 2 t for con tin uum subtracted distribution rather than a lik eliho o d t. The upp er limit plots are sho wn in Figures 3{38 and 3{39 PAGE 110 95 Figure 3{38. The 90% upp er limit t to the in v arian t mass distribution without con tin uum subtraction PAGE 111 96 Figure 3{39. After subtracting the underlying con tin uum, the 90% upp er limit t to the in v arian t mass distribution PAGE 112 97 3.4 Summary In this c hapter, w e discussed the reconstruction of sev en dieren t deca y c hannels (three submo des of and four submo des of 0 ) for the radiativ e deca ys of (1S) in to and 0 The reconstruction eciency for eac h mo de w as obtained from signal Mon te Carlo generated with the (1 + cos 2 ) angular distribution exp ected for deca ys (1S) r + pseudoscalar The selection criteria w ere delib erately minimal to ensure high eciencies. T o increase our sensitivit y w e mass-constrained the in termediate mesons (except for meson in the mo de 0 r ) to their nominal masses. W e also used the ev en t v ertex information (if a v ailable) to impro v e the sho w er 3-momen tum measuremen t, ev en tually impro ving the in v arian t mass resolution of the nal and 0 b y around 10%. W e w ere also able to impro v e the candidate 0 in v arian t mass resolution in the mo de 0 r b y p erforming the 4-momen tum constrain t to the (1S ) candidate in a sp ecial w a y The 3-photon nal state resulting from (1S) r ; r r w as dominated b y the QED bac kground pro cess e + e r r r whic h w e tried to reject b y training a neural net program. The p erformance of neural net w as sligh tly b etter than the alternativ e c hoice of optimizing the asymmetry cut and a large prop ortion of the bac kground w as lo w ered; ho w ev er, some bac kground ev en ts still remained. Similarly in the mo de (1S) r 0 ; 0 r b y tigh tening the E s cut, most of the bac kground w as rejected. No clear signal w as observ ed in either of the t w o bac kground limited mo des, and upp er limits w ere measured (see Sections 3.3.3.4 and 3.3.7 page 94 ) at the 90% C.L. F or the mo des whic h w ere found to b e virtually bac kground free, no signal candidate ev en ts w ere observ ed in our acceptance mass windo w, the exception b eing (1S) r 0 ; + 0 where t w o go o d signal candidates w ere observ ed. Ho w ev er, b oth the reconstruction eciency and the branc hing ratio of 0 daugh ters is higher PAGE 113 98 for the mo de (1S) r 0 ; r r y et no signal ev en t w as observ ed in this mo de c hallenge the claim of signal from the mo de (1S) r 0 ; + 0 Since there is no clear signal, w e can only quote upp er limits on the branc hing ratios. In the next c hapter w e ev aluate the systematic uncertain ties from our ev en t selection criteria, com bine the results from dieren t submo des and quote individual as w ell as com bined upp er limits. PAGE 114 CHAPTER 4 SYSTEMA TIC UNCER T AINTIES AND COMBINED UPPER LIMIT 4.1 Systematic Uncertain ties W e note that w e already kno w that our measuremen t will b e a limit, and that the statistical uncertain ties are going to dominate o v er the systematic uncertain ties. Therefore, although w e do our b est to correctly ev aluate the systematic uncertain ties, it is not necessary to ev aluate them with as great a precision as is necessary for measuremen ts where they are a limiting factor. 4.1.1 T rigger Considerations There are t w o trigger lines whic h are imp ortan t for this analysis. The ev en ts in the mo des in v olving c harged trac ks in them are primarily collected online b y the ring of EL TRA CK trigger line. Mon te Carlo predicts that the in-eciency of trigger cut (after all other selection criteria are met) in the 0 mo des 0 ; 0 0 0 0 ; + 0 and 0 r is 1.1%, 0.9%, and 2%, resp ectiv ely F or the mo de 0 ; r r MC predicts no loss in eciency due to trigger cut. The highest in-eciency due to trigger cut in the mo des with c harged trac ks is found to b e 2.8%, whic h is noted for the mo de (1S) r ; + 0 Although these are predictions of the Mon te Carlo, high eciency of trigger is reassuring and implies a small uncertain t y It is also dicult to do data based c hec ks for this trigger (in-)eciency ho w ev er the small ineciency implies a small systematic uncertain t y W e assign 1% systematic uncertain t y due to p ossible mismo deling of trigger in mo des with c harged trac ks. F or the all neutral mo des where deca ys to r r or 3 0 the imp ortan t trigger lines are BARRELBHABHA or ENDCAPBHABHA, whic h re when t w o high energy sho w ers are registered bac k-to-bac k in CC. Although these lines are w ell understo o d for e + e r r ev en ts, the trigger eciency for higher m ultiplicit y sho w ers, not 99 PAGE 115 100 necessarily bac k-to-bac k and p ossessing energy lo w er than the b eam energy is less w ell studied. F rom the luminosit y (954 : 2 pb 1 ) of our QED Mon te Carlo sample e + e r r r (whic h w e used in our study of the deca y mo de (1S) r ; r r ), w e exp ect 485 ev en ts in our real data sample, whic h is raised to 2942 ev en ts if w e relax the neural-net cut. In real data, w e nd 471 and 2869 ev en ts for cut conguration with and without the neural-net cut, resp ectiv ely Our yield falls short of the exp ectation b y 3%, whic h again is reassuring that our eciencies are rather understo o d. W e therefore assign p 2869 = 2869 + (2942 2869) = 2869 4 : 5% systematic uncertain t y due to trigger sim ulation in \all neutral" mo des. 4.1.2 Standard Con tributions W e use standard n um b ers for systematic uncertain t y con tributions from imp erfect mo deling of trac ks and sho w ers as advised b y the CLEO Systematic Study of Systematics program (SSS) [ 24 ]. SSS is a group eort to determine the systematic uncertain ties of the detector for use b y collab orators in their analyses. The uncertain t y in the photon, 0 and reconstruction eciency arises from p ossible deciencies in the Mon te Carlo sim ulation of photon and hadronic in teractions in the calorimeter. Within the SSS, the systematic errors of the 0 reconstruction w ere determined [ 25 ] to b e less than 5%. W e therefore assign a systematic uncertain t y con tribution from mismo deling of the calorimeter resp onse as 2 : 5% for eac h sho w er, or 5% for 0 r r r r candidates. F or 0 0 0 w e assign a 15% systematic uncertain t y due to calorimetry The trac k nding systematic eciencies ha v e b een studied in detail [ 26 ] using tau-deca ys in the lo w m ultiplicit y ev en ts and found the trac king systematic uncertain t y as ( 0 : 17 0 : 20)%. A conserv ativ e v alue of 0 : 5% has b een used in [ 27 28 ] and 1 : 0% p er trac k in [ 1 29 ]. W e prefer to use the conserv ativ e estimate of 1% in this analysis. Th us, w e assign a systematic uncertain t y of 2% for mo des in v olving t w o c harged trac ks and 4% for the deca y sequence 0 + ; + 0 PAGE 116 101 4.1.3 Con tributions from Ev en t Selection Criteria As discussed in Section 3.3.1 w e study the eciency of pion h yp othesis S dE =dx for t w o trac ks is com bined in quadrature (S 2dE =dx ) in data using the p eak from the pro cess e + e r and nd a 4% systematic dierence in the eciency This cut is also used in the mo des 0 ; r r 0 ; 0 0 0 and 0 ; + 0 w e therefore assign 4%, 4%, and 5.7% systematic uncertain ties, resp ectiv ely T o ev aluate the systematic uncertain ties for the mo de (1S ) r 0 ; 0 r w e exploit the p eak presen t in data o wing to the con tin uum pro cess e + e r r W e measure the signal in data o v er a roating bac kground function with all cuts in place except the one under consideration and with all cuts in place. F rom these n um b ers, w e calculate the eectiv e eciency of the cut. F or MC, w e rep ort the individual cut eciency relativ e to the ev en ts in 0 in v arian t mass plot that surviv e all the cuts. The dierence with MC and data eciency v alues is tak en as the systematic uncertain t y whic h are added in quadrature. T able 4{1. Systematics' table for (1S) r 0 ; 0 r Cut Data E (%) MC E (%) Sys. Err (%) P article Iden tication 97.35 99.08 1.75 Electron V eto 94.94 91.87 -3.35 Muon Rejection 97.93 98.99 1.07 Ov erall Sys Err 3.93 In the reconstruction of deca y c haine (1S) r ; r r w e use only t w o cuts other than the 4-momen tum consistency One of the cuts, namely energy asymmetry of t w o sho w ers from deca y is rather w ell understo o d and can b e tak en on its face v alue. The other cut is netvalue > 0 : 4, the output from the neural net and w arran ts an in v estigation for systematic uncertain t y The uncertain t y in this case, arises not b ecause of the inabilit y of MC to mo del the prescrib ed bac kground pro cess prop erly but with our o wn understanding of bac kground itself. PAGE 117 102 In the absence of a signal, the task of nding the systematic uncertain t y b ecomes dicult as the con v en tional approac h of taking the dierence b et w een data and MC eciencies, as w e did in mo de 0 r is not applicable. Instead, w e test the neural net's eciency on bac kground, b y comparing the eciency of passing ev en ts in QED Mon te Carlo, with the eciency of passing ev en ts in data (whic h is dominated b y QED ev en ts). T o b e conserv ativ e in our estimate of systematic uncertain t y w e calculate the relativ e dierence in eciency for a wide range of p ossible c hoices for the cut (see Figure 4{1 ) and select the maxim um relativ e dierence and th us, the maxim um p ossible uncertain t y as p er our approac h. W e obtain a systematic uncertain t y of 7 : 0% for netvalue > 0 : 6 ha ving an eciency of 97% in signal MC and bac kground rejection ratios as 24 : 7% and 23 : 0% in QED MC and real data, resp ectiv ely It ma y b e recalled that the actual v alue of neural net cut used in ev en t selection is netvalue > 0 : 4 with 51% eciency in signal MC while rejecting 86% of the bac kground from QED MC. W e note that this do es not pro v e that the neural net is incorrectly mo deled in our real analysis, as it is lik ely that the QED Mon te Carlo that w e generated do es not mimic all the t yp es of ev en t in the real data sample. Once again, our c hoices are erring on the side of conserv ativ e estimates of the systematic uncertain t y W e do not attribute an y systematic uncertain t y to nd a 4.0 GeV hard photon. Just from the basic cuts listed in T ables 3{2 and 3{3 w e nd that eciency of nding the hard-photon after all other basic cuts is 96%. Although w e can not study the in-eciency of 4.0 GeV cut b y relaxing it further as this is our \skim-cut," w e plot the energy of hard photon in six of the sev en mo des from resp ectiv e MC samples after all our selection criteria has b een met. W e nd that there is no cut o at 4.0 GeV, but just a small tail as sho wn in Figure 4{2 whic h conrms that the eciency of this cut is close to maximal. The nal systematic uncertain ties for deca y mo des of and 0 are tabulated in T ables 4{2 and 4{3 resp ectiv ely It is w orth while to note that there is no systematic PAGE 118 103 uncertain t y due to analysis cuts in the mo de (1S) r ; 0 0 0 The p ossible ev en t selection uncertain t y in this mo de has already b een tak en care of in the calorimetery mismo deling. W e also ignore an y systematic uncertain t y due to the highly ecien t cuts on 2 (applicable only in the 0 mo des) and 2P4 in all the mo des. 0 25 50 75 100 Y efficiency 0 25 50 75 100 Y bgd. rejection Figure 4{1. Amoun t of bac kground rejected for v arious v alues of asymmetry and neural net cut ha ving the same eciency The \eciency" is obtained from signal Mon te Carlo. \Bac kground rejection" is obtained either from QED Mon te Carlo sample (red pluses) or from real data (blac k crosses). PAGE 119 104 0 250 500 E g (GeV)Events / (10.0 MeV)h 5 p + p p 0 0 80 160 h 5 3 p 0 0 400 h / K h 5 g g 0 250 500 h / K h 5 p + p p 0 0 100 200 300 h / K h 5 3 p 0 0 400 h / 5 g r Figure 4{2. Energy of the hard photon in MC samples after all our selection criteria for resp ectiv e mo des PAGE 120 105 T able 4{2. Systematics uncertain ties for v arious deca y mo des of Source r r + 0 0 0 0 T rigger Mismo deling 4 : 5% 1% 4 : 5% T rac king 2% Calorimetry 5% 5% 15% Analysis Cuts 7% 4% MC ( Stat. Error ) 1 : 3% 1 : 2% 1 : 7% Ov erall 9 : 8% 6 : 9% 16 : 0% T able 4{3. Systematics uncertain ties for v arious deca y mo des of 0 Source 0 ; r r 0 ; + 0 0 ; 0 0 0 0 r T rigger Mismo deling 1% 1% 1% 1% T rac king 2% 4% 2% 2% Calorimetry 5% 5% 15% 2 : 5% Analysis Cuts 4% 5 : 7% 4% 3 : 9% MC ( Stat. Error ) 1 : 0% 1 : 6% 2 : 4% 1 : 0% Ov erall 6 : 9% 8 : 8% 15 : 9% 5 : 2% PAGE 121 106 4.2 Com bined Upp er Limits In order to get nal limits for the t w o mo des under in v estigation, w e need to com bine the results from the submo des. This is not easy b ecause in eac h case w e ha v e one submo de with bac kground, and roughly Gaussian statistics, and other submo des whic h ha v e no data in the signal region and P oisson statistics are applicable. F urthermore, w e wish to include the systematic uncertain ties in to the calculation to calculate our nal limits. W e deriv e the com bined probabilit y distribution for the branc hing fraction as L P = Q i L P ;i with L P ;i b eing the normalized lik eliho o d functions of the i th submo des. All lik eliho o d functions are in terms of the (1S) r P branc hing fraction B ((1S) r P) = N P = ( i B P ;i N (1S ) ) where P = ; 0 and i and B P ;i denote the eciency and branc hing fractions of i th mo de, and N P is the n um b er of signal ev en ts randomly thro wn. The lik eliho o d functions for bac kground limited mo des (1S) r ; r r and (1S) r 0 ; 0 r and (1S ) r ; r r are tak en from Sections 3.3.3.4 and 3.3.7 (page 94 ), resp ectiv ely F or mo des with zero or few observ ed ev en ts, w e generate P oisson-distributed branc hing ratios compatible with exp erimen tal outcome. The systematic uncertain ties are incorp orated [ 30 ] b y smearing the lik eliho o d functions b y Gaussian distributions giv en b y the errors on nal mo de branc hing fractions, eciencies and N (1S ) The constituen t L i 's as w ell as the com bined L are sho wn in Figures 4{3 { 4{6 The com bined upp er limit on the branc hing ratios (1S) r P is obtained b y in tegrating the corresp onding com bined probabilit y distribution L up to 90% area in the ph ysically allo w ed region whic h are B ((1S) r ) < 9 : 3 10 7 B ((1S) r 0 ) < 1 : 77 10 6 : PAGE 122 107 The upp er limit due to individual mo des, excluding and including the systematic errors are listed in T able 4{4 It is notew orth y that the com bined limit for the (1S) r 0 is larger than one of the constituen t mo des ((1S ) r 0 ; r r ). This happ ens as (1S) r 0 ; + 0 actually has a p ositiv e answ er. PAGE 123 108T able 4{4. Results of the searc h for (1S) r 0and (1S) r Results include statistical and systematic uncertain ties, as describ ed in the text. The com bined limit is obtained after including the systematic uncertain ties. 0; r r 0; +00; 0000! r Observ ed ev en ts 0 2 0 3 : 1 5 : 3 B0;i% 17 : 5 0 : 6 10 : 0 0 : 4 14 : 4 0 : 5 29 : 5 1 : 0 Reconstruction eciency (%) 40 : 6 2 : 8 24 : 5 2 : 2 16 : 6 2 : 6 40 : 1 2 : 1 B ((1S) r 0)(90% C.L.) (excluding sys. uncertain ties) < 1 : 53 10 6< 10 : 25 10 6< 4 : 54 10 6< 3 : 42 10 6B ((1S) r 0)(90% C.L.) (including sys. uncertain ties) < 1 : 54 10 6< 10 : 41 10 6< 4 : 69 10 6< 3 : 44 10 6 Com bined limit on B ((1S ) r 0) < 1 : 77 10 6 r r +0 000 Observ ed ev en ts 2 : 3 8 : 7 0 0 B ;i% 39 : 4 0 : 3 22 : 6 0 : 4 32 : 5 0 : 3 Reconstruction eciency (%) 23 : 8 2 : 4 32 : 8 2 : 2 11 : 8 1 : 9 B ((1S) r )(90% C.L.) (excluding sys. uncertain ties) < 7 : 27 10 6< 1 : 47 10 6< 2 : 83 10 6B ((1S) r )(90% C.L.) (including sys. uncertain ties) < 7 : 35 10 6< 1 : 47 10 6< 2 : 91 10 6 Com bined limit on B ((1S ) r ) < 9 : 3 10 7 PAGE 124 109 0 5 10 15 Branching Fraction (10 6 ) 0.00 0.05 0.10 0.15Probability combined h 5 p 0 p 0 p 0 h 5 p + p p 0 h 5 g g Figure 4{3. Probabilit y distribution as function of branc hing ratio for the deca y mo de (1S) r : Blac k curv e denotes the com bined distribution. The distributions ha v e b een normalized to the same area. PAGE 125 110 0 5 10 15 20 Branching Fraction (10 6 ) 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1Likelihood combined h 5 p 0 p 0 p 0 h 5 p + p p 0 h 5 g g Figure 4{4. Plotted on log-scale, the lik eliho o d distribution as function of branc hing ratio for the deca y mo de (1S) r : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalize to the same area. PAGE 126 111 0 5 10 15 Branching Fraction (10 6 ) 0.00 0.05 0.10 0.15Probability combined h , h 5 g g h , h 5 p + p p 0 h , h 5 p 0 p 0 p 0 h 5 g r Figure 4{5. Probabilit y distribution as function of branc hing ratio for the deca y mo de (1S) r 0 : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalize to the same area. PAGE 127 112 0 5 10 15 20 Branching Fraction (10 6 ) 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1Likelihood combined h , h 5 g g h , h 5 p + p p 0 h , h 5 p 0 p 0 p 0 h 5 g r Figure 4{6. Plotted on log-scale, the lik eliho o d distribution as function of branc hing ratio for the deca y mo de (1S ) r 0 : Blac k curv e denotes the com bined distribution. All distributions ha v e b een normalized to the same area. PAGE 128 CHAPTER 5 SUMMAR Y AND CONCLUSIONS W e rep ort on a new searc h for the radiativ e deca y of (1S) to the pseudoscalar mesons and 0 in (21 : 2 0 : 2) 10 6 (1S) deca ys collected with the CLEO I I I detector. The meson w as searc hed for in the three mo des r r + 0 or 0 0 0 The 0 meson w as searc hed for in the mo de 0 r or 0 + with deca ying through an y of the ab o v e three mo des. All these mo des, except 0 r ha v e b een in v estigated in CLEO I I data amoun ting to N (1S ) = (1 : 45 0 : 03) 10 6 (1S) mesons and resulted in upp er limits whic h w ere rep orted as B ((1S) r 0 ) < 1 : 6 10 5 and B ((1S) r ) < 2 : 1 10 5 at the 90% condence lev el. These limits w ere already signican tly smaller than naiv e predictions, and also the mo del of K orner and colleagues[ 10 ], whose p erturbativ e QCD approac h predictions for B ( J = r X ) where X = ; 0 ; f 2 as w ell as B ((1S) r f 2 ) agree with exp erimen tal results. With CLEO I I I data sample 14.6 times as large as the original CLEO I I data sample w e nd no signican t signal in an y of the mo des. Based purely up on the luminosities, w e w ould exp ect the new upp er limits to b e scaled do wn b y a factor of b et w een 14.6 (in bac kground-free mo des) and p 14 : 6 in bac kground dominated mo des. In the searc h for (1S) r w e nd no hin t of a signal, and manage to reduce the limit b y an ev en larger factor than this. In the searc h for (1S) r 0 ho w ev er, w e nd t w o clean candidate ev en ts in the c hannel (1S ) r 0 ; + 0 whic h, though w e cannot claim them as signal, do indicate the p ossibilit y that w e are close to the sensitivit y necessary to obtain a p ositiv e result. Because of these t w o ev en ts, our com bined limit for (1S) r 0 is not reduced b y as large a factor as the luminosit y ratio, and in fact is lo oser than that obtained using one submo de ((1S) r 0 ; r r ) alone. In this analysis w e found upp er limits whic h w e rep ort at 90% condence 113 PAGE 129 114 lev el as B ((1S) r ) < 9 : 3 10 7 ; B ((1S) r 0 ) < 1 : 77 10 6 : Our results are sensitiv e enough to test the appropriateness of pseudoscalar mixing tec hnique as pursued b y Chao [ 11 ] where mixing angles among v arious pseudoscalars including b are calculated. Then using the predicted allo w ed M1 transition r b he predicts B ((1S ) r ) = 1 10 6 and B ((1S ) r 0 ) = 6 10 5 Our limits are signican tly smaller than Chao's predictions and do not fa v or his approac h. The sensitivit y c hallenge p osed b y b oth extended v ector dominance mo del and t wist approac h of Ma are b ey ond our reac h. In extended VDM, In temann predicts 1 : 3 10 7 < B ((1S ) r ) < 6 : 3 10 7 and 5 : 3 10 7 < B ((1S) r 0 ) < 2 : 5 10 6 where the t w o limits determined b y ha ving destructiv e or constructiv e in terference, resp ectiv ely b et w een the terms in v olving (1S) and (2S ). Ev en if it is determined that the amplitudes are added constructiv ely our limit sta ys higher than the VDM prediction for (1S) r In a more realistic approac h, Ma has calculated the leading con tribution to branc hing ratio using the t wist expansion [ 13 ]. Ma's prediction of B ((1S) r 0 ) 1 : 7 10 6 is consisten t with our result. Ho w ev er, his prediction for B ((1S) r ) 3 : 3 10 7 is a factor 3 smaller than our limit. T o conclude, our upp er limits at 90% C.L. suggest that pseudoscalar mixing approac h as pursued b y Chao do es not explain the exceedingly small rate for radiativ e deca ys of (1S) in to pseudoscalar and 0 The approac h adopted b y Ma is encouraging and it is desirable to include the relativistic corrections and other eects in QCD to explain our exp erimen tal results. PAGE 130 APPENDIX EVENT VER TEX AND RE-FITTING OF 0 r r The standard 0 r r and r r candidates as extracted from the frame are reconstructed b y assuming that sho w ers originate from the origin of CLEO co ordinate system. In the absence of ev en t v ertex information, this is the b est course. T o impro v e our 0 r r and r r 4-momen tum resolution, w e mass constrain the r r pair to the nominal mass while assuming that the sho w ers originate from the ev en t v ertex. Although CLEO I I I soft w are pro vides us with ev en t v ertex information b y means of the pac k age EventVertexProd an algorithm based up on kinematic tting [ 31 ], and th us giving us the b est p ossible measuremen t of the ev en t v ertex, w e b eliev e that the pro cedure is a bit to o slo w and our analysis do es not require a v ery precise information of x and y co ordinates of the ev en t v ertex. It is rather the z co ordinate of ev en t v ertex whic h is most critical as far photon momen tum is concerned. So, w e measure the ev en t v ertex using a relativ ely faster alternativ e, a brief sk etc h of whic h follo ws. The ev en t v ertex ( x v y v z v ) calculation is based up on CLEO I I routine V3FIND where the ev en t v ertex is calculated separately in x,y and in z. The z v co ordinate is tak en as the w eigh ted a v erage of z0 of individual trac ks with w eigh ts b eing the in v erse of r.m.s. error on z0. F or x,y part all pairs of trac ks are formed and the w eigh ted a v erage of these pairs is tak en as ( x v y v ) In our implemen tation, w e rst form a list of qualit y trac ks, and start with b eam sp ot as the guess vertex W e swim the trac ks to the guess vertex and calculate the ( x v y v z v ) whic h is tak en as the new guess vertex and the pro cess is iterated un til con v erges. A t eac h iteration, w e calculate the r.m.s error on z v and k eep only the trac ks whic h ha v e z within one standard deviation of z v The mathematical expressions for z v and standard deviation z are in terms of 115 PAGE 131 116 the individual v alues z k and corresp onding w eigh ts w k are: z v = z = X w k z k = X w k (A-1) 2 z = ( X w k ( z k z )) n ef f = ( n ef f 1) (A-2) where n ef f is giv en b y n ef f = ( X w k ) 2 = X w 2 k : (A-3) The ( x v y v ) part is calculated b y rst nding the in tersection p oin ts x,y for all trac k pairs. Then w e tak e the w eigh ted a v erage of these p oin ts to nd ( x v y v ). The equations to this end are: dm = sin ( 1 ) cos ( 2 ) cos ( 1 ) sin ( 2 ) (A-4) ds = q 2 d 0 ; 1 2 d 0 ; 2 (A-5) w k = dm 4 =ds (A-6) x k = ( d 0 ; 1 cos ( 1 ) d 0 ; 2 cos ( 2 )) =dm (A-7) y k = ( d 0 ; 1 sin ( 1 ) d 0 ; 2 sin ( 2 )) =dm (A-8) If the trac ks in tersect, w e calculate ( x v y v ) as: x v = x = X w k x k = X w k (A-9) y v = y = X w k y k = X w k (A-10) 2 x = 2 y = ( n tr k 1) = X w k (A-11) If the trac ks do not in tersect ho w ev er, w e pro ceed as follo ws: w x k = sin 2 ( k ) = 2 d 0 ;k (A-12) w y k = cos 2 ( k ) = 2 d 0 ;k (A-13) d bk = d 0k + sin ( k ) x beamspot cos ( k ) y beamspot (A-14) PAGE 132 117 x v = x = x beamspot X ( d bk sin ( k ) w x k ) = X w x k (A-15) y v = y = y beamspot X ( d bk sin ( k ) w y k ) = X w y k (A-16) 2 x = 9 : 0 = X w x k (A-17) 2 y = 9 : 0 = X w y k (A-18) File J */bohr/user1/potlia/analysis/eta_pmz/eta_pmz_mc_genxang_feb20_2005_final ID IDB Symb Date/Time Area Mean R.M.S. 1 12 1 060421/2244 8497. 0.5476 1.0139E-02 0.47 0.51 0.55 0.59 0.63 0 200 400 600 800 1000 1200 1 29 2 060421/2244 8496. 0.5478 1.1085E-02 Figure 1. Reconstructed in v arian t mass distribution of + 0 candidate from signal Mon te Carlo for the mo de (1S) r ; + 0 : After all cuts in place, solid blac k histogram represen ts the + 0 candidate in v arian t mass distribution when 0 candidate is re-t from the ev en t v ertex. Ov erla y in dotted, red histogram is obtained using default 0 candidates. PAGE 133 118 File J */bohr/user1/potlia/analysis/etap_gg/etap_gg_mc_genxang_feb20_2005_final ID IDB Symb Date/Time Area Mean R.M.S. 1 12 1 060421/2238 1.0325E+04 0.9576 5.8435E-03 0.920 0.940 0.960 0.980 1.000 0 250 500 750 1000 1 29 2 060421/2238 1.0320E+04 0.9577 6.8586E-03 Figure 2. Reconstructed in v arian t mass distribution of + candidate from signal Mon te Carlo from signal Mon te Carlo for the mo de (1S) r 0 ; r r : After all cuts in place, solid, blac k histogram represen ts the 0 ; r r candidate in v arian t mass distribution when r r candidate is re-t from the ev en t v ertex. 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PAGE 136 BIOGRAPHICAL SKETCH Vija y Singh P otlia w as b orn in a small village in the w estern part of the northern state Hary ana in India. After graduating from high sc ho ol, he attended Kuruksh tra Univ ersit y for 3 y ears, earning a Bac helor of Science (B.Sc.) degree. Later on he joined Ja w aharlal Nehru Univ ersit y New Delhi, India, and obtained his Master of Science (M.Sc.) degree. He w as accepted to attend graduate sc ho ol at the Univ ersit y of Florida in 1999. 121 |