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SEARCH FOR RADIATIVE DECAYS OF UPSILON(IS) INTO ETA AND ETAPRIME 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 MahlkeKrueger 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 GParity ................... .. 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+ rt . ... 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 REFITTING OF 7"  .7 ...... 115 REFERENCES ................... ............. 119 BIOGRAPHICAL SKETCH .................. ......... .. 121 LIST OF TABLES Table page 11 Basic fermions and some of their properties ... . ... 3 12 Gauge bosons and some of their properties ..... . . 3 13 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 14 Theoretical branching fractions as predicted by various authors for radiative decays of T(1S) into 7r and r' .................. ..... 17 15 Product branching ratios for decay modes of r and . .... 18 31 Liiir.ili numbers for various data sets used in the analysis . 39 32 Efficiency (in %) of basic cuts for rl modes ................ ..42 33 Efficiency (in %) of basic cuts for rl' modes ................ ..42 34 Efficiency of selection criteria for the mode T(1S) 7rq; ] 7+rr7 47 35 Efficiency table for the mode T(1S)  7yr; r] 7r 7. . . 55 36 Final efficiency table for the mode T(1S) q 7r; 7 . . 66 37 Final efficiency table for the mode r]' rl+r and then 77 . 73 38 Final efficiency table for the mode r]' rl+t and then r] 7000 78 39 Final efficiency table for the mode T(1S)  7rq'; r  7r+77 . 82 310 Efficiency table for the mode T(1S)  7r'; r' 7p . . 89 41 Systematics' table for T(1S) 7rq'; r' p 7 ..... . . 101 42 Systematics uncertainties for various decay modes of . . 105 43 Systematics uncertainties for various decay modes of . ... 105 44 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 11 Simple gluonexchange diagram .................. ...... 4 12 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 electromagnetic decay through a virtual photon that in turn decays electromagnetically into a pair of charged fundamental particles, such as quarks or charged leptons (the charged leptons are represented by the symbol ). . . 15 21 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 22 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 23 The CLEO III detector. .................. ..... 25 24 View of the SVD III along the beampipe. ..... . . ...... 28 25 The RICH detector i,i, I, 1 .. ................. . 32 26 Two kinds of RICH LiF radiators. For normal incidence particles (z 0) a sawtooth radiator is necessary to avoid internal reflection. ...... .. 33 31 Candidate rl  7r+7r7 reconstructed invariant mass distribution from signal Monte Carlo for the mode T(1S)  7q; r  7+770. The reconstruction efficiency is 32.8 0.4% after all the cuts. ............... .. 49 32 Distribution from signal Monte Carlo: For the mode T(1S) 7'r; r  7+77 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 33 Invariant mass of distribution of the tr candidate for the mode T(1S)  7y; ty  7+77 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 34 Reconstructed rl candidate invariant mass distribution in real data for the mode T(1S)  7rq; r  7+77o0. No events are observed in the signal mass window denoted by the region in between blue arrows (inset), and a clear ac  7 +77770 peak is visible from the QED process e+e  52 35 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 36 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 37 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 38 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 39 '/1 vs AE distribution plot(a) for signal MC for T(1S)  7r; r] 77 and plot(b) for e+e 777 MC. .................. .... 59 310 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 eventtype have not been rejected yet . .. 60 311 Distribution of AO vs AO in real data for events in the 7r mass window passing our basic cuts. .................. ...... 62 312 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 overtraining is not exhibited at all. The learning process saturates however, and training is stopped after 10K iterations. . 65 313 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. . . ... 66 314 77 invariant mass distribution from signal Monte Carlo for the mode T(IS) q 7 r; .r . 77 .................. ..... .... 67 315 77 invariant mass distribution in real data. All cuts except neural net cut are in place. .................. .............. ..68 316 77 invariant mass distribution in real data after all cuts. . ... 69 317 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. .................. .......... ..70 318 Normalized probability distribution for different signal area for the mode T(1S) 7; 7 ' 77. The shaded area spans 90% of the probability. 71 319 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. 72 320 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. .................. .... 74 321 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. ................ ..... 75 322 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). . ... 76 323 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). ................ ..... 77 324 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. ............... .. 79 325 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. ..... . . 80 326 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.. .81 327 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 .................. .. .... .. .. 82 328 Reconstructed candidate r' invariant mass distribution from signal Monte Carlo for the mode T(1S)  7r'; r 7i+f770: The reconstruction efficiency is 24.5 0.5% after all the cuts. ............... .. 83 329 Distribution from signal Monte Carlo: For the mode T(1S)  7r'; r 7+77 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. 84 330 Invariant mass of r]' candidate for the mode T(1S)  7r'; r]  7+770: 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. .. . . ...... 85 331 Extended range of invariant mass distribution of r' candidate for the mode T(1S) 7rl';rl r+r770. Two good candidate signal events are observed in our acceptance mass window (inset). . .... 86 332 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 .......... ..89 333 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. ... .. .. .. ... .. .. .. ........... .. 90 334 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. .................. .... 91 335 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. 92 336 The fit to the continuum subtracted data plot for the mode T(1S)  '; r/  7p: 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 .................. ................. .. 93 337 The normalized probability distribution for different signal area for the mode T(1S)  7ql'; rl 7p: The shaded area spans 90% of the probability. 94 338 The 90% upper limit fit to the invariant mass distribution without continuum subtraction . . . . . . . ... .. 95 339 After subtracting the underlying continuum, the 90% upper limit fit to the invariant mass distribution .................. ...... 96 41 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 42 Energy of the hard photon in MC samples after all our selection criteria for respective modes .................. .......... .. 104 43 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 44 Plotted on logscale, 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 45 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 46 Plotted on logscale, 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+7r7r candidate from signal Monte Carlo for the mode T(1S)  7; r  7r+770: After all cuts in place, solid black histogram represents the rl  7r+7r candidate invariant mass distribution when 7r candidate is refit 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 refit 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 ETAPRIME 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+7r7 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+770 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 107 and B(T(1S) 7) < 1.77 x 106 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, ii 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 electromagnetic 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 FermiDirac 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 antifermion 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 11) 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 spin1 particles. The guage bosons of '\! are shown in Table 12. Table 11. 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 28 +2e/3 +1/2 v, < 0.000015 0 +1/2 d 515 e/3 1/2 e 0.511 e 1/2 c 10001600 +2e/3 +1/2 uv < 0.19 0 +1/2 s 100300 e/3 1/2 It 105.7 e 1/2 t w 175000 +2e/3 +1/2 v, < 18.2 0 +1/2 b 41004500 e/3 1/2 7 1777.0 e 1/2 The familiar electromagnetic force (also called as Quantum Electrodynamics, or QED) is mediated by the exchange of a photon. Only particles with electric charge can interact electromagnetically. 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 electromagnetic and strong forces which are longrange in nature due to masslessness of photon and gluons. Table 12. 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 antiquarks have complementary colors (or anticolors) r cyann), g (magenta), and b (yellow). The quarks interact strongly by exchanging color which is mediated by gluon exchange (Figure 11). Gluon exchange is possible only if the gluons themselves are colored (carry color charge), and in fact, the gluons carry the color and anticolor simultaneously. The strength of strong interaction is flavor independent. b r g (rb) b r Figure 11. Simple gluonexchange diagram Since there are three possible colors and three possible anticolors for gluons, one might guess that the gluons come in as many as nine different color combinations. However, one linear combination of color anticolor 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 anticolors is a matter of convention. One possible choice is shown in Equation 11 for the octet, and the color singlet is represented in Equation 12, 'rg, rb, gb, gr, br, bg, /2(rr gg), //6(rr + gg 2bb) (1 1) V/3(r+ g + bb) (12) 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>) (13) 1 1>=  > and there is a singlet state with S = 0, 1 0 0 > (I T> I>). (14) 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 selfinteractions. On the other hand, the gluons in QCD have color charge and thus they undergo selfinteractions. In fieldtheoretic language, theories in which field quanta may interact directly are called i' .iAbelian." The gluon selfinteraction 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 interquark 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, Grouptheoretically, 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 12. The color singlet for qqq can be obtained from decomposition 3 0 3 3 = 10( 8 ( 81 and is shown in Equation 15, 1 qqq >color singlet (rgb grb r+brg bgr + gbr rbg). (15) 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'ii. 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 antiquarks is the negative of that of quarks. The treatment of isospin goes very much like quantum mechanical angular momentum. Since strong and electromagnetic 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 electromagnetic 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) (17) where Pa is a constant phase factor. If we consider an eigenfunction of momentum (18) ^p(f, t) = e"PYEt) 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) (112) 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 antifermion. As a matter of convention fermions are assigned P = +1 and antifermions 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 electromagnetic 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 antiparticles 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 antiparticle, 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 antifermion 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 13 and 14, and a factor of (1) which arises in quantum field theory whenever fermions and antifermions 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 antiparticle. The C eigenvalue for the photon can be derived by inserting C into the field equations and is C = 1. 1.1.3.4 GParity 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 Gparity 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 yaxis 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+ > (117) R2(7)17 > (1)7 > In this way, we find that the Gparity 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 Gparity of F' is same as that of 7. Thus, under Gparity transformation, we have GI'" >= (1)1"' > (118) Gparity is a multiplicative quantum number, therefore, the Gparity of a system of n pions is (1)". Gparity is a good quantum number of nonstrange 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 spin1/2 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 (119) and the flavor symmetric singlet is I' > I qo > 1 v(dd + uu + ss) v'3 (120) 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 13. 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 Etaprime (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 13. 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 lefthanded and righthanded particles are treated differently. This is what we understand by chiral symmetry. 1.2 Quarkonia Quarkonia are flavorless mesons made up from a heavy4 quark and its own antiquark. 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 centerofmass energy. The lowest such state is (1lS) (commonly called J/y), a cc state produced at centerofmass 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 electromagnetic 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 quarkantiquark 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 4momentum 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 fermionantifermion. 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 electromagnetically 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 quarkantiquark 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 electromagnetic 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 gluerich 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 12. b9 (a) g g b (b) g (c) Figure 12. 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 electromagnetic decay through a virtual photon that in turn decays electromagnetically 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 pb1 of data taken with the CLEO II detector [7] found no signal in this mode, and resulted in an upper limit of 1.6 x105 for the branching fraction T(1S)  7r', which is an order of magnitude less than the naive expectation. Furthermore, the twobody 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 104. The previous analysis [9] of T(1S) decays produced an upper limit for this mode of 2.1 x 105. 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 106 to 104. 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 105, B(T(1S) rI) 1 x 105. 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 ~ 107 to 106. 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 NonRelativistic QCD (NRQCD) [13] paradigm along with twist2 operators and predicts B(T(1S)  r') 1.7x 106, and B(T(1S)  7r) x 3.3x 107, which are almost half the respective ratios predicted using constructive interference VDM approach (Table 14). Table 14. 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 105 3.6 x 105 6 Vector Meson Dominance: 5.3 x 10' 1.3 x 107 Intemann [12] 1983 to to 2.5 x 106 6.3 x 107 Mixing of tr, r' with rib: Chao [11] 1990 6 x 105 1 x 105 NRQCD with twist2 operators: Ma [13] 2002 m 1.7 x 106 3.3 x 107 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( 4f2) %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 15 where the values have been compiled from PDG[14]. Table 15. 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 +rrl ; rl O) 3B(qr  7+7r ; rl 77+70) B(rl'  7+7rl; 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 electronpositron 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 21) are discussed in the next few sections. The components are discussed in the order in which they are rnplvd 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 21. 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 electromagnetic 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 Xrays 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 byproduct used as a research instrument in surface p, li. . 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 (21) 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 crosssectional 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 crosssection 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 22 on top of hadronic "background." The fourth state discovered in 1980, namely T(4S) is much wider compared to lowlying T states as T(4S) has more decay channels open to it. 0250187012 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 22. 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 electromagnetically 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 onshell daughters flying off at relativistic speeds possess the information postcollision 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 electromagnetic 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. 2230402005 SC Quadrupole Pylon 4 Magnet Barrel Muon Iron Chambers Figure 23. 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 23, the CLEO III detector is a composite of many subdetector elements. Typically arranged as concentric cylinders around the beam pipe, the subdetectors 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, multipurpose 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 CuNbTi alloy kept in superconducting state by the liquid helium reservoir as shown in Figure 23. 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 lowmass 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 subdetectors to accomplish the tracking of curved path of charged particles. The first subdetector 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 "barrelonly" 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 doublesided 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 24). The bottom side of each silicon wafer has ntype strips implanted perpendicular to the beam line. The top side of the wafer has ptype 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 pn junction. When reverse bias is applied across the wafer, a sensitive region depleted of mobile charge is formed. 1 cm Iu Figure 24. 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 electronhole pairs. Approximately 3.6 eV is required to create a single electronhole 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 heliumpropane 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 goldplated tungsten of 20 pm diameter and cathode (field) wires of goldplated 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 electromagnetically 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" endplates) where in the wires are strung along the zdirection. 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 zdirection 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 ;'vI ii . the old time of flight detector and the new RICH subdetector 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. (22) 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 halfangle 0 of the cone is given by cos(0) 1 P > (23) 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 halfangle 0 w 0. The maximum emission angle occurs when vTma = c and is given by cos(Oax) (24) The RICH (see Figure 25) starts at a radius of 0.80 m and extends to 0.90 m has a 30fold 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 26). The radiators are followed by a 15.7 cm radial drift space filled with pure N2, an uninstrumented volume allowing the expansion of Cherenkov cone. The drift space is followed by the photodetector, a thingap multiwire 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 25. The RICH detector 1 i, vI i With this index, particles in the LiF radiator with = 1 produce Cherenkov cones of halfangle cosl(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 E1/2, which makes them even more indispensable in yet higher energy experiments. The CLEO III Crystal Calorimeter (CC) is an electromagneticshower calorimeter which absorb incoming electrons or photons which cascade into a series of electromagnetic track A 10mm t / Y T 170 mm track 10 mm I Figure 26. 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 subdetector 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 thalliumdoped 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 subdetector 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 30150 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 silverplated CuBe 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 48bit 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 ifviir 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 Ih.r t" tracks. The calorimeterbased 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 calorimeterbased 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 calorimeterbased 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 trii r lines which help collect events for the above modes are * BARRELBHABHA, demanding there are two, backtoback high energy shower clusters in the barrel region. For being classified as backtoback, 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 prescaled 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 centerofmass energy 9.46GeV. The acquired luminosity was 1.13 0.03 fb1 with the beam energy range 4.7274.734 GeV. This T(1S) onresonance 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) onresonance data, a pure continuum data sample is available to us collected at the centerofmass energy below the T(1S) energy (Ebeam = 4.7174.724 GeV) with an integrated luminosity of 0.192 0.005 fb1. 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 fb1 in the beam energy range 5.2705.300 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 31. Table 31. 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)( fb1) 1.20 0.02 3.56 0.07 0.200 0.004 (7)( fb1) 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 eventtypes and stored into different groups called subcollections, 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.''rd on the events reasonably efficiently, and furthermore, having collected the events online, we need to know which pass2 subcollection 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 centerofmass 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 eventtype 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 centerofmass energy. The energy matched to the charged tracks is excluded while summing up total energy. * aCosTh < 0.95, absolute value of zcomponent of unit net momentum vector. For allneutral modes, the significant eventtypes are gamGam, radGam and hardGam, the significance not necessarily in this order. The gamGam eventtype has to pass the fairly simple tests nTk the number of reconstructed charged tracks < 2, and i Sl12 > 0.4 (see hardGam). A radGam eventtype is necessarily gamGam eventtype 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 centerofmassenergy. 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 eventtypes for ] 77y skim. In addition to the subcollection/eventtype 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 32 and 33 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 32 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 32. 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+77 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 33. 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 50230 MeV/c2 and 350900 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 4momenta 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+7T70 and ]  7r000 decays (collectively referred to as p]  37 from now on) were required to have a reconstructed invariant mass of 400700 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 centerofmass energy. The event was selected if AE the magnitude of difference between the energy of reconstructed event and the centerofmass 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 ( 1I .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 4momenta 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 nonfiducial 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 70 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+77rr 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+7r7 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+770, the rl candidate had position information, so we constrained all three, the pair of oppositely charged good tracks and the massconstrained rl + 7+77rr 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 ,1i i, The idea behind 4constraint 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 4momentum 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 chisquared of the 4momentum constraint (KU4) and chisquared values of all the massconstraints involved in a particular decay chain. For example, there are four massconstraints involved in the decay chain T(1S)  7 rl; rq o 7r00oo0, three 7r massconstraints and one pr massconstraint. 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 eventtype cuts as listed in Tables 32 and 33. 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+7r7 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 34. Table 34. 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 + 7r7or candidate from signal MC after all the cuts is shown in Figure 31. Figure 32 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 33(d), 34). In Figure 33(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 35), 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 rejection 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 + 6.9177E05 SIGMA1 1.16237E02 + 4.1875E04 AR2/AREA 0.64843 2.3090E02 * DELM 0.00000E+00 + 0.0000E+00 SIG2/SIG1 0.37259 + 1.0042E02 Function 2: Chebyshev Polynomial of Order 2 NORM 1452.9 + 148.8 CHEB01 0.21470 + 0.1355 CHEB02 0.82008 + 1.7189E05 1200 1000 800 600 400 200 0.47 0.51 0.55 0.59 m(7T+[ 0 ) (GeV/c2) Figure 31. Candidate rq  7r+77r 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 7.1628E05 3.7866E04  .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 1.0187E02 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 32. Distribution from signal Monte Carlo: For the mode T(1S) 7;  7 +77, 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(+: it ) (GeV/c) 2.5 " m 9+ 9 55 2 m(n n ) (GeV/c) 0.63 0.47 Q.55 2 m(+ ni ) (GeV/c) Figure 33. 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 34. Reconstructed r candidate invariant mass distribution in real data for the mode T(1S)  7; l  7r+r770. No events are observed in the signal mass window denoted by the region in between blue arrows (inset), and a clear ac  7++7T70 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 35. 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 hitlevel t...in,, and therefore, can tell us which reconstructed track or shower is due to which generated charged particle or photon. By hitlevel 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 4momentum. 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 37 (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 35 lists the selection criteria used in the reconstruction. Figure 36 shows the invariant mass distribution from signal MC for the mode T(1S)  7q;  7rT00. Figure 37 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 38 shows. Table 35. 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 + 3.3034E04 SIGMA1 1.08638E02 4.8996E04 AR2/AREA 0.45522 2.7350E02 * 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  3.3059E04  4.8200E04 2.7294E02 0.0000E+00  0.1268 31.49 C.L.= 11.9% 55.57 3.3022E04 4.9938E04 2.7435E02 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 36. 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 37. 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 38. 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 38. 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 4momentum 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 4momentum of beam, are not sufficient to suppress the QED background from the process e+e > 777 (See Figure 39). The QED MC was generated using BerendsKliess 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 39. '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 310) 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 310. 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 eventtype 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 eventtypes. The events classified as gamGam eventtype only, however, have very ..I. mmetric decays with asymmetry> 0.84. The eventtype 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 311 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 0.21.0 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 311. 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 feedforward neural network where the information flow is in one direction only. The neural network used in this analysis is a multilayer perception [23] which is essentially a feedforward 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 0.40.7 GeV/c2. The background data sample is comprised of the e+e  777 Monte Carlo generated at centerofmass energy 9.46GeV, having diphoton invariant mass in the range 0.40.7 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 "overfitting" problem where the neuralnet 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 312) the performance of the neuralnet 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 313. For any chosen efficiency, neural net gives a higher background rejection as compared with asym metry. For our final selection, we choose netvalue > 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 0.150.40 . The efficiency of the cuts used is listed in Table 36. Figure 314 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 312. 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 overtraining 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 313. 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 36. 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 + 2.2597E04 SIGMA1 1.51605E02 4.2932E04 AR2/AREA 0.15594 4.3434E02 * DELM 0.00000E+00 + 0.0000E+00 SIG2/SIG1 1.9340 0.1251 Function 2: Chebyshev Polynomial of Order 0 NORM 1.92566E05 + 14.05 800 I 600 S 400 ^  LU 200 Minos 0.0000E+00 2.2175E04 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 C.L.= 2.3% + 77.54 + 2.2560E04 + 0.0000E+00 + 3.9938E02 + 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 314. 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 315 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 316. 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 317), 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 318. Figure 319 shows the upper limit area, which is the result of summing up the probability distribution in Figure 318 upto 90% . O1 0.30 0.40 0.50 0.60 0.70 m(y y) (GeV/c2) 0.80 Figure 315. 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 316. 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 1.51605E02 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 + 7.1844E02 CHEB02 4.85822E02 + 8.0037E02 Minos  8.363  0.0000E+00  0.0000E+00 0.0000E+00 0.0000E+00  0.0000E+00  49.61  7.3095E02  8.0679E02 C.L.= 77.6% 9.047 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 51.66 7.0503E02 7.9255E02 0.30 0.40 0.50 0.60 0.70 0.80 m(y y) (GeV/c) Figure 317. 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 318. 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 1.51605E02 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 + 7.2552E02 CHEB02 0.10505 + 7.3963E02 Minos  0.0000E+00  0.000OE+00  0.0000E+00 0.0000E+00 0.0000E+00  0.000OE+00  49.47  7.3821 E02  7.5016E02 C.L.= 73.5% 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 51.55 7.1176E02 7.2802E02 0.30 0.40 0.50 0.60 0.70 0.80 m(y y) (GeV/c) Figure 319. 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+77). To ensure that the event is fully reconstructed, i.e., balanced in momentum and adds up to the centreofmass energy of the e+e system, we require the /x4 < 100. The efficiency of the cuts used is listed in Table 37 . Table 37. 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 320. The invariant mass distribution for r' candidate from real data is shown in Figures 322 and 323. 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 + 4.4356E05 SIGMA1 7.84061E03 + 3.7000E04 AR2/AREA 0.71651 3.0577E02 * DELM 0.00000E+00 0.0000E+00 SIG2/SIG1 0.43387 + 1.3547E02 Function 2: Chebyshev Polynomial of Order 0 NORM 2311.6 + 333.2 1000 1 Minos  102.9  4.4347E05 3.5620E04  3.2012E02  0.0000E+00  1.3629E02  324.0 C.L.= 32.2% 103.6 4.4368E05 3.8556E04 2.9224E02 0.0000E+00 1.3521E02 + 342.6 750 500 250 0.920 0.940 0.960 0.980 m(ript ) (GeV/c2) 1.000 Figure 320. 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 321. 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 322. 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 323. 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 38 and the distribution for cut variables is shown in Figure 325. Table 38. 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 324. We find no candidate event in real data as the Figures 326 and 327 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 8.95188E03 AR2/AREA 0.52764 * DELM 0.00000E+00 SIG2/SIG1 0.39751 Function 2: Chebyshev Polynomial NORM 6300.3 CHEB01 5.29920E02 CHEB02 0.90488 Parabolic + 108.8 + 9.4093E05 7.1537E04 4.8912E02 0.000OE+00 2.1951E02 of Order 2 + 822.1 5.5787E02 + 7.4757E02 Minos  105.1  9.4181E05 6.6378E04  5.0541E02  0.0000E+00  2.1682E02 879.7 5.7735E02 6.4937E02 C.L.= 27.0% 114.2 9.4031E05 7.8420E04 4.7314E02 0.0000E+00 2.2505E02 788.0 5.6000E02 8.8170E02 300 200 100 0.0 0.920 0.940 0.960 0.980 m(rpt ) (GeV/c2) Figure 324. 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 325. 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 326. 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+r77t 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 massconstrained 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 39. Figure 328 shows the invariant mass distribution for q' candidates passing our selection criteria. Figure 329 shows the distribution of cut variables used in this 1 22 m(Tl i ) (GeV/c2) 1 62 Figure 327. 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 330. These two events have been looked at in detail and show no signs of not being good signal events. Table 39. 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 7.00002E03 0.56394 0.00000E+00 0.36746 Parabolic 107.5 5.4365E05 4.1859E04 3.4331 E02 0.0000E+00 1.5146E02 :Chebyshev Polynomial of Order 2 12188. 717.1 0.17360 + 4.6555E02 0.68293 7.0060E02 Minos 106.1 5.4391 E05 3.9725E04 3.5332E02 0.000OE+00 1.4990E02 726.8 4.6885E02 6.5904E02 C.L.= 7.2% 109.1 5.4347E05 4.4388E04 3.3364E02 0.0000E+00 1.5392E02 711.2 4.6422E02 7.4719E02 400 200 0.0 0.920 0.940 0.960 0.980 m(pr+0 (GeV/c2) Figure 328. 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 329. Distribution from signal Monte Carlo: For the mode T(1S) 7'; rl 7T+T77 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 330. Invariant mass of r' candidate for the mode T(1S) 7r'; 7 +7rTr0: 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 