<%BANNER%>

First Observation and Measurements of Chi_cj Decays into Two Charged and Two Neutral Hadrons

Permanent Link: http://ufdc.ufl.edu/UFE0019819/00001

Material Information

Title: First Observation and Measurements of Chi_cj Decays into Two Charged and Two Neutral Hadrons
Physical Description: 1 online resource (160 p.)
Language: english
Creator: Patel, Rukshana Alli
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: cesr, charm, charmonium, chicj, cleo, psi2s
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We measure exclusive hadronic decays of the P-wave spin-triplet charmonium states chicJ, where J = 0, 1, 2, into 4-hadron final states with two charged and two neutral mesons. The chicJ are produced in radiative decays of 3.08 million psi (2S) observed in the CLEO III 1 and CLEO-c 2 detectors. We report first measurements of the branching fractions of the chicJ for the modes pi+ pi- pi0 pi0, K+ K- pi0 pi0, pi+ pi- eta pi0, K+ K- eta pi0, K+- pi-+ K0 pi0 for J = 0,1,2, and p pbar pi0 pi0 for J = 0,2; and present upper limits at 90% C.L. for the mode p pbar pi0 pi0 for J = 1 and p pbar eta pi0 for J = 0, 1, 2. We also measure for the first time the branching fractions via intermediate resonances for the 4-body final states: rho+- pi-+ pi0, K*0 K0 pi0, and rho+- K-+ K0 for J = 0, 1, 2; K*0 K+- pi-+ for J = 2; K*+- pi-+ K0 and K*+- K-+ pi0 for J = 0, 2. The results presented will serve as useful phenomenological inputs to perturbative QCD based calculations trying to understand the decay dynamics of these charmonium states.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Rukshana Alli Patel.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Yelton, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0019819:00001

Permanent Link: http://ufdc.ufl.edu/UFE0019819/00001

Material Information

Title: First Observation and Measurements of Chi_cj Decays into Two Charged and Two Neutral Hadrons
Physical Description: 1 online resource (160 p.)
Language: english
Creator: Patel, Rukshana Alli
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: cesr, charm, charmonium, chicj, cleo, psi2s
Physics -- Dissertations, Academic -- UF
Genre: Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: We measure exclusive hadronic decays of the P-wave spin-triplet charmonium states chicJ, where J = 0, 1, 2, into 4-hadron final states with two charged and two neutral mesons. The chicJ are produced in radiative decays of 3.08 million psi (2S) observed in the CLEO III 1 and CLEO-c 2 detectors. We report first measurements of the branching fractions of the chicJ for the modes pi+ pi- pi0 pi0, K+ K- pi0 pi0, pi+ pi- eta pi0, K+ K- eta pi0, K+- pi-+ K0 pi0 for J = 0,1,2, and p pbar pi0 pi0 for J = 0,2; and present upper limits at 90% C.L. for the mode p pbar pi0 pi0 for J = 1 and p pbar eta pi0 for J = 0, 1, 2. We also measure for the first time the branching fractions via intermediate resonances for the 4-body final states: rho+- pi-+ pi0, K*0 K0 pi0, and rho+- K-+ K0 for J = 0, 1, 2; K*0 K+- pi-+ for J = 2; K*+- pi-+ K0 and K*+- K-+ pi0 for J = 0, 2. The results presented will serve as useful phenomenological inputs to perturbative QCD based calculations trying to understand the decay dynamics of these charmonium states.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Rukshana Alli Patel.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Yelton, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0019819:00001


This item has the following downloads:


Full Text





FIRST OBSERVATION AND MEASUREMENTS OF XcJ DECAYS INTO
TWO CHARGED AND TWO NEUTRAL HADRONS


















By
RUK(SHANA PATEL


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FITLFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007


































S2007 Rukshana Patel



































To my family and to all my teachers









ACKENOWLED GMENTS

I, the author of this dissertation owe my heartfelt gratitude to all those who phI i-- d a

role in making this a piece of work.

I begin by thanking the Almighty God for showering his mercy over me at all times,

especially during the twists and turns of graduate life.

The one person I can't thank enough is my advisor Dr. Yelton, who stood by me like

a fortress in all the hardships that came my way. Where shall I begin with, the d or when

he put his faith in me and introduced me to a new world of analysis by teaching me in

small steps, or the d .va Of his endless patience when he let me grow at my own pace while

guiding me in many subtle and unique r- .vs~. He is truly a great mentor and I truly admire

him, as in spite of his busy faculty schedule he manages to actually do analysis himself

from scratch, because of which he remained aware of every problem that I was faced

with in my research and provided means for me to tackle them. He is a great facilitator,

providing me with many opportunities to present my work at external meetings.

I would like to thank my committee members Dr. Paul Avery, Dr. Andrew K~orytov,

Dr. David Reitze, Dr. John Schueller, and Dr. Richard Woodard for their interest, time

and expertise, and for their inputs in this dissertation.

I owe many thanks to all my teachers particularly Dr. Dufty, Dr. Fry and Dr.

Ingersent for the core courses. I also thank Dr. Dufty and Dr. Meisel for motivating me

during the difficult initial two semesters at graduate school. Many thanks are due to Dr.

Woodard for teaching me to struggle hard and for boosting my confidence during his

rigorous field theory class and for being a teacher of his kind. I thank Dr. K~orytov and

Dr. Mitselmakher for their wonderful and enriching particle physics courses which I sat

through over and over more than once for the thrill and excitement they carried.

I would like to thank the entire CLEO collaboration for their support and sometimes

rigorous -II_0----- -Gas which are a key towards making this work of publication quality. I

thank my CLEO internal committee, Matt Shepherd, David K~reinick and Hector Mendez










for serving on this analysis and for their excellent and thought-full questions as well as

detailed discussions which guided this through. I especially thank the CLEO an~ lli-;-

co-ordinator Hanna Mahlke-K~rueger for her ever extended support and constant guidance,

and for preparing the stage for all our analyses. Words are not enough to thank Basit

Athar, for ? wing 3. to any kind of help that I have ever asked of him during the past 6

years in all kinds of situations, and for serving as a great mentor too. Rich Galik, Hajime

Muramatsu and Gary Adams deserve a special thanks for their constant inputs to this

work. I also thank Guangshun Huang, Werner Sun, and Pete Zweber for some of the most

valuable physics discussions.

I would like to thank my teachers in India particularly Dr. Anuradha Mishra, Dr.

Abbas Rangfwala, Dr. Sridhar, Dr. S.B Patel, Prof. Jivan Seshan, Prof. Shroff, and Prof.

Mistry for motivating me to pursue my doctoral studies in physics.

I would also like to thank my senior colleagues Luis Breva and Vijay Potlia for the

many discussions that we had in our office. Luis was pivotal in my initial learning of the

CLEO software and he helped me understand the basics of doing analyses while Vijay

being a software expert was akr- .va there to answer those special queries as well as many

more .

I also thank Gary Varner from the University of Hawaii for providing me with his

thesis, which served as a useful source of guidance for this work.

I thank my other colleagues, Aparna Baskaran, K~arthik Shankar, Ethan Siegel for the

many late night homework sessions and especially Anand Balaraman who has been my

best buddy through many ups and downs of graduate course work. I must remember to

thank Vidya Ramanathan for all her help in making me feel comfortable during my initial

stay in Gainesville.

I cannot forget to thank my friends that I made outside of the physics department

who comforted me during my stay in Gainesville and served as my family.










I thank the administrative staff especially Darlene Latimer, Nathan Williams, Dianna

Carver (Dee Dee) and Irina Maslova for their help with the mandatory non-technical

aspects of graduate paper-work. I thank the computer Czars Brent Nelson, Bryan, Craig

Prescott and David Hansen for computing support.

I thank my yoga and pilates instructors at the University of Florida (UF) recreation

and sports facility for their relaxing and energizing sessions which made me healthier and

kept me calm.

The most important person in my life without whose love and affection, I could not

have made it this far is my husband Shadab. Being under similar boundary conditions

of doctoral studies away from homeland, we found each other, and became best friends

sharing all the colors of life together. I truly believe that it was his relentless prodding and

high expectations of me, which brought the best out of me.

I now take pleasure in thanking my family: mummy, pappa and younger sister Ansu.

It was hard for my family to send me to a distant land so far away from home for the very

first time, to study an unknown world of particles. I thank them for everything from start

to end, all of which is simply inexplicable.

I thank Pat Bartlett, Srivatsan, and K~en Booth of the UF Editorial and technical

support staff for their efforts in guiding me with the formatting of this document.

I gratefully acknowledge the effort of the CESR staff in providing us with excellent

luminosity and running conditions. This work was supported by the A.P. Sloan Foundation,

the National Science Foundation, and the U.S. Department of Energy.

I thank the Department of Energy for supporting this work.











TABLE OF CONTENTS

page

ACK(NOWLEDGMENTS ......... ... .. 4

LIST OF TABLES ......... ..... .. 9

LIST OF FIGURES ......... .... .. 10

ABSTRACT ......... ...... 14

CHAPTER



1 THEORY ... ......... ............. 15

1.1 Introduction ......... . . .. 15
1.2 Relevant Particle Physics Literature . .... .. 15
1.2.1 The Standard Model ......... .. 16
1.2.2 Symmetries ......... .. .. 21
1.2.3 Mesons and Resonances ....... .. .. 23
1.2.4 C'll1~iinualistill! . . .. . 23
1.2.5 Quantum ('ll.Ine~!! dynamics in the ('I!. In..~~!Instin Energy Regime 26
1.3 Motivation for Exclusive ('1.. In..~~! Insti Decays ... .. .. 26

2 EXPERIMENTAL APPARATUS ........ .. 32

2.1 The Cornell Electron-Positron Storage Ring .... ... .. 33
2.2 The Interaction ......... . .. .. 35
2.3 The CLEO Detector ......... . 37
2.3.1 The CLEO III detector ....... .. .. 37
2.3.1.1 Tracking system . ...... .. 38
2.3.1.2 Silicon vertex detector ...... .. 39
2.3.1.3 The central drift chamber .... .. .. 40
2.3.1.4 Super-conducting coil .... .... . 41
2.3.1.5 dE/dx particle identification system ... .. . .. 41
2.3.1.6 Ring imaging cherenkov detector ... .. . .. 42
2.3.1.7 Crystal calorimeter .... .. .. 44
2.3.1.8 Muon detectors . .... .. .. 45
2.3.1.9 The trigger system ..... .. .. 45
2.3.2 The CLEO-c detector ...... ... .. 46
2.3.2.1 ZD ........_._. ......... 47
2.4 Monte Carlo Simulation ........ ... .. 47

3 ANALYSIS TECHNOLOGY ....._ ._. ... .. 64

3.1 Dataset and MC Samples ....... ... .. 64
3.2 Final State Selection ........ .. .. 65











3.2.1 C'!I. .ved Particle Reconstruction .... .. . 65
3.2.2 Neutral Particle Reconstruction ..... .. . 68
3.2.3 K~inematic Constraint Fittingf ...... .... 70
3.3 Fittingf Procedure ......... . 71
3.4 Efficiencies and Yields ......... .. 72

4 SYSTEMATIC UNCERTAINTY STUDIES ..... .. . 102

5 SEARCH FOR INTERMEDIATE STATES (SUBSTRUCTURE) .. .. .. 107

5.1 Introduction and Scope ......... .. .. 107
5.2 Substructure Analysis ......... .. .. 107

6 MEASUREMENT RESULTS ......... ... .. 144

7 CONCLUSION AND SUMMARY . ...... .. 149

APPENDIX

A ISOSPIN ANALYSES ......... . .. 150

REFERENCES ......... . .. . 156

BIOGRAPHICAL SK(ETCH ....._._. .. .. 160










LIST OF TABLES


Table page

1-1 Standard Model fermions. ......... . 29

1-2 Standard Model forces and gauge bosons. . .... .. 29

3-1 CLEO-c MC efficiencies (in .~) for each mode. ..... .. 74

3-2 CLEO-3 MC efficiencies (in .~) for each mode. ..... .. 74

3-3 Yields and combined CLEO-c and CLEO III efficiencies ( .) of 4-hadron final
states. ......... ..... . 75

4-1 Systematic uncertainties (in .~) are shown. .... ... . 105

4-2 MC efficiencieS E (in .~) for all modes are shown. ... .... .. 106

5-1 Yields and efficiencies (in .~) for substructure modes. .. .. . .. 110

6-1 Branching fractions (B.F.) with statistical and systematic uncertainties. .. .. 147

6-2 Comparison of results. ......... . .. 148

6-3 Results related by isospin are shown. . ..... .. 148










LIST OF FIGURES


Figure page

1-1 Figure shows the charmonium system of resonances. ... .. .. .. :30

1-2 Figure shows the cn annihilation of #(2S) ...... .. .. :31

2-1 A schematic of the CESR apparatus is shown. ..... .. 50

2-2 Definition of crossing angle ac., at CLEO. ...... .. 51

2-3 C'!I. .! in nI I n! cross section in an exploratory energy scan at CLEO. .. .. .. 52

2-4 Figure shows a cut-open front view of the CLEO III detector. .. .. .. 5:3

2-5 Figure shows the CLEO detector side view (quarter) cross-section. .. .. .. 54

2-6 The CLEO co-ordinate system is shown. ...... .. 55

2-7 End view cross section of the CLEO III silicon vertex detector is shown. .. 56

2-8 Figure illustrates the principle of working of the DR. .. .. .. 57

2-9 Figure shows a plot of the dE/dx as a function of particle momentum. .. .. 58

2-10 Figure shows the RICH detector. ......... .. 59

2-11 Figure shows the RICH particle separation. ..... .. . 60

2-12 Figure shows the CC energy resolution as a function of photon energy. .. .. 61

2-1:3 Figure shows a cut-open front view of the CLEO-c detector. .. .. .. .. 62

2-14 Figure shows an isometric view of the ZD detector. ... .. .. .. 6:3

:3-1 Reconstructed invariant mass distribution of the Kro qq candidate. .. .. 76

:3-2 Effect of the~ KS flight significance cut in data for the mode K~~r KrO..o 77

:3-3 Profile of the kinematic constraint cut of X2 < 25. .... .. 78

:3-4 Improvements in the signal to noise ratio, and the ke. mass resolution due to
the X2 < 25 cut. ......... . . 79

:3-5 The unconstrained (constrained) ye. candidate invariant mass distributions. .. 80

:3-6 The transition photon energy distributions before (after) the kinematic fitting
procedure. ......... ... . 81

:3-7 The effect of multiple candidate rejection criteria. ... ... .. 82

:3-8 The double Gaussian functional representation of the detector resolution. .. 8:3










3-9 Double Gaussian convoluted with B-W functional representation of the signal
variable .

3-10 Double Gaussian convoluted with B-W functional representation of the signal
variable .


aussian convoluted with B-W functional representation of the signal
.. 86

fan anticipated background from J/th. .... .. .. 87

Signal variable for the x ~-xrozro mode. .... .. .. 88

Signal variable for the K K-wro a mode. ... .. .. .. 89

Signal variable for the pproro mode. .... .... .. 90

Signal variable for the x x~-rlxo mode. .... .. .. 91

Signal variable for the K K-rlxo mode. ... ... .. .. 92

Signal variable for the ppyro mode. ... .. .. 93

Signal variable for the K~~r K~ro mode. ... .. .. .. 94

ds for the x ~-xrozro mode. . ...... .. .. 95

ds for the K K-wro a mode. . ..... .. .. 96

ds for the pro a0 mode. ........ ... .. 97

ds for the x x~-rlxo mode. . ...... .. 98

ds for the K K-rlxo mode. . ...... .. .. 99

ds for the pprl~o mode. ......... ... .. 100

ds for the K~~r K~r o mode. ...... ... . 101

Icidates signal and sideband regions for the Xc states. .. .. .. .. 111

ows data for the decay Xno xx xr~r~o a mode. .. .. .. 112

ows data for the decay Xco xx xr~r~o a mode. .. .. .. 113

ows data for the decay Xno xx xr~r~o a mode. .. .. .. 114

ows data for the decay Xco xx xr~r~o a mode. .. .. .. 115

ows data for the decay Xct xx xr~r~o a mode. .. .. .. 116

ows data for the decay X,1 xx xr~r~o a mode. .. .. .. 117


3-11 Double G
variable .

3-12 Studies of

3-13 The fitted

3-14 The fitted

3-15 The fitted

3-16 The fitted

3-17 The fitted


3-18

3-19

3-20

3-21

3-22

3-23

3-24

3-25

3-26

5-1

5-2

5-3

5-4

5-5

5-6

5-7


The fitted

The fitted

Data yiele

Data yiele

Data yiele

Data yiele

Data yiele

Data yiele

Data yiele

Figure elu

Figure she

Figure she

Figure she

Figure she

Figure she

Figure she





A-1 Feynman diagram and isospin eigen states for XcJ K*oKo 0.


Xc2~~ 0r 0mode. ...
Xc2 0 0T jTde .

Xo K KT~T-iTo aT mode. ..

Xco K K+-wro a mode. ..

Xco K K+-wro a mode. ..

Xco K K+-wro a mode. ..

Xc K K-wro a mode. ..

X,1 K K+-iTo aT mode. ..

Xo K xK-iToiT mode. ..

Xco K x K~~iTo mode. ..

Xco K x K~~iTo mode. ..

Xco K x K~~iTo mode. ..

Xco K x K~~iTo mode. ..

XcO K iT K~iTo mode. ..

Xcl K iT K~iTo mode. ..

Xcl K iT K~iTo mode. ..

Xcl K iT K~iTo mode. ..

Xcl K iT K~iTo mode. ..

Xcl K iT K~iTo mode. ..

Xc2 K x K~~iTo mode. ..

Xc2 K x K~~iTo mode. ..

Xc2 K x K~~iTo mode. ..

Xc2 K x K~~iTo mode. ..

Xc2 K x K~~iTo mode. ..

Xca i KfTpTo mode. ....

Xc i iT~T-lTOo mode. ....


5-8

5-9

5-10

5-11

5-12

5-13

5-14

5-15

5-16

5-17

5-18

5-19

5-20

5-21

5-22

5-23

5-24

5-25

5-26

5-27

5-28

5-29

5-30

5-31

5-32

5-33


Figfure

Figure

Figure

Figure

Figfure

Figfure

Figfure

Figure

Figure

Figfure

Figfure

Figfure

Figure

Figure

Figfure

Figfure

Figfure

Figure

Figure

Figure

Figfure

Figfure

Figure

Figure

Figure

Figfure


shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows

shows


data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data

data


for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the

for the


decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay

decay


. . 118

. . 119

. . 120

. . 121

. . 122

. . 123

. . 124

. . 125

. . 126

. . 127

. . 128

. . 129

. . 130

. . 131

. . 132

. . 133

. . 134

. . 135

. . 136

. . 137

. . 138

. . 139

. . 140

. . 141

. . 142

. . 143

. . 150


for the decay










A-2 Feynman diagram and isospin eigen states for XcJ K*oK r-. .. .. .. .. 151

A-3 Feynman diagram and isospin eigen states for XJ K* K-ro. .. .. .. .. 153

A-4 Feynman diagram and isospin eigen states for XcJ K* xr-Ko. .. .. .. .. 154









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

FIRST OBSERVATION AND MEASUREMENTS OF XcJ DECAYS INTO
TWO CHARGED AND TWO NEUTRAL HADRONS

By

Rukshana Patel

December 2007

C'I !.v: John Yelton
Major: Physics

We measure exclusive hadronic decays of the P-wave spin-triplet charmonium

states XJ, where J = 0, 1, 2, into 4-hadron final states with two charged and two

neutral mesons. The XcJ are produced in radiative decays of 3.08 million d(2S) observed

in the CLEO III [1] and CLEO-c [2] detectors. We report first measurements of the

branching fractions of the XJ for the modes xr+xr-xozo, K+K-wror o + r- lo, K+K-rlxo,

I~rKxKo aO for J = 0, 1, 2, and pporo afor J = 0, 2; and present upper limits at CI' .~

C.L. for the mode ppiro a for J = 1 and ppy~ro for J = 0, 1, 2. We also measure for the

first time the branching fractions via intermediate resonances for the 4-body final states:

p~~r wo, K*oKozro, and p*K Ko for J = 0, 1, 2; K*oK~~r for J = 2; K**x ~Ko and

K**K xro for J = 0, 2. The results presented will serve as useful phenomenological inputs

to perturbative QCD based calculations trying to understand the decay dynamics of these

charmonium states.










CHAPTER 1
THEORY

1.1 Introduction

Particle Physics is a fundamental branch of modern science on a complex mission

to find the answers to the most eternal questions of mankind: What are we made of?

What are the most fundamental constituents of nature and how do they interact? The

attempt to explain the intriguing complexity and diversity of the universe in terms of a

terse mathematical framework has captivated scientists for ages.

Particle physicists study the elementary constituents of matter, and their interactions

by producing and studying elementary particles at high energies in the laboratory.

Although the experimental triumphs of elementary particle physics can he traced

to the year 1897 with the discovery of the electron [3, 4]; the era of the mid twentieth

century was marked hv the discoveries of Nobel dreams [5]. The seemingly large

chaotic jungle of new particles yelled out to the physicists their need for an organized

classification of some kind to explain their roles and existence in nature. It all came to

some rest with the invention of a model that was able to explain the medley in terms

of few fundamental particles. A new theory emerged during the last three decades, and

succeeded in describing all of the known elementary particle interactions except gravity.

This chapter does a literature review of some of the fundamental concepts useful for

understanding the work conducted in this dissertation, and concludes with the motivation

for this work.

1.2 Relevant Particle Physics Literature

In this section, the fundamental particle physics concepts relevant to the subject

in this dissertation are reviewed. A logical starting point can he a brief tour of the




1 This period was marked by many experimental findings of unexpected particles (so
much so that in one particular instance of the discovery of the muon, Rabi exclaimed,
l--heordered that?" [3]).










Standard Model a theory that has survived all experimental challenges to date [6] in

spite of the fact that it uses nineteen underived numerical parameter inputs and does not

answer some questions, rendering the theory incomplete [7]. This Particle Physics review

section concludes with a discussion of the Charmonium system which is the heart of this

dissertation.

1.2.1 The Standard Model

The Standard Model (SM) [8] of Particle Physics is the modern theory that attempts

to explain all the phenomena of particle physics in terms of the properties and interactions

of a small number of point-line (elementary) particles which possess intrinsic properties.

This theory emerged by the 1980's, and all of the known elementary particle interactions

and their governing forces, except gravity can he derived from the SM.

In the SM, the dynamics of all the matter in the universe can he explained using few

fundamental elements (matter particles, and force mediating particles) which are classified

into two broad categories: fermions and hosons. The SM fermionS2 are Spill~ particles,

while the SM hosons (which are the force mediators) have an intrinsic spin value of 13

The fermions can he further separated into two families of elementary particles: leptons

and quarks. An organized classification of the SM particles is enumerated below:

1. Leptons:

There are six leptons which come in three generations or flavors; the electron (e) and

its neutrino (v,), the muon (p) and an associated muon neutrino (&,,), and the tau

(-r) and its neutrino (v,).



2 Ill general fermions have half odd integer spins, while hosons have zero or integer
spmns.

SAccording to the SM, there is one hoson (known as Higgs) with an intrinsic spin of 0,
but it has not been observed experimentally to date.











charge 0 ve upv
charge -e e p 7I

Each generation is made up of a particle doublet, and one partner in each generation

carries a charge of -e (second row), while the other partner carries no charge (first

row).

2. Quarks:

There are six types or flavors of quarks, arranged in three generations; up (u) and

down (d), charm (c) and strange (s), top (t) and bottom (b).


charge +e c t

charge e a b

Each generation has two quarks, and the quarks inside every generation carry a

charge of either + e (first row) or -_e(scnro)
3. Mediators:

These are spin-1 bosons which are also known as the force carriers: a charge-less

photon (y), three gauge bosonS4 COnSISting of two charged W*, and a neutral Zo,

and eight charge-less gluons (g).

In the SM theory there also exists a Higgs boson [9] with spin-0, however there

is no direct evidence experimentally [10] for its existence yet5 This particle is a

critical element in the SM and is postulated to impart particles with their masses. A

discussion of the Higgs is beyond the scope of this dissertation.



4 These are spin-1 bosons that act as carries of the fundamental interactions between
particles.

s The Large Hadron Collider experiments scheduled to operate in 2008, we hope will
resolve this mystery.










Table 1-1 lists the properties of the SM fermions. In addition to carrying a fractional

electric charge, each quark member also possesses a color" charge (red, green or blue),

intrinsic property analogous to the familiar electric charge. On the other hand, leptons do

not carry any color charge.

Furthermore, all the twelve fermions (leptons and quarks) have an associated

anti-particle which has the same mass and spin, but opposite electric charge (in fact,

all the additive quantum numbers undergo a change in sign as we move from particle

to anti-particle). The anti-particles of the charged leptons are represented hv the same

symbol as the particles themselves, but with an opposite charge sign (the anti-particle of

an electron is the positron and is represented as e+). The charge-less anti-neutrinos and

all anti-quarks are represented by an overhead har symbol (for example, an anti-electron

neutrino is written as v,, and a charm anti-quark is written as c).

According to the SM, there are three types of fundamental' interaction forces that

exists between particles (the SM ignores the effects of the gravitational force). These

forces are the electro-magnetic force between electrically charged particles, the strong force

between particles with color charge, and the weak force between particles possessing the

weak charge [3]. Table 1-2 lists some of the properties of the SM forces.

Among these, the strong force is the strongest pll ri~i and operates over a short

interaction range and is described by a theory known as Quantum Chromodynamics

(QCD) [12]. This strong force holds quarks together inside protons and neutrons The

theory of QCD predicts that a relatively weak interaction between quarks and gluons




6 The quarks are not literally colored, color is merely a quantum number or a special
property of a quark.

SA fundamental interaction is an interaction or mechanism which is irreducible in
nature, that is it cannot he explained in terms of another interaction.

SProtons and neutrons are not elementary particles, but are manifestations of quark
combinations. They are also members of the family of particles known as hadrons.










comes into pili rendering them to behave as almost free particles at short distances

between quarks or at very high energies (> 10 GeV) and momentum transfers (this is

referred to as .I-i-misind ilc freedom [13] discovered by Gross, Wilczek and Politzer who were

awarded the Nobel Prize in Physics in 2004 for this work). However at the other end of

.I-i-misind ilc freedom, is the phenomenon of quark confinement [14]. At low energies, the

strength of the interaction increases with decreasing energy, and becomes strong enough to

"confine" the quarks and gluons together inside hadrons.

The electro-magnetic force is a long range force obeying an inverse square 1i.\--' and

is described by the familiar Quantum Electro-dynamics (QED) [15] theory. An example of

the electro-magfnetic force is the force of attraction between nuclei and electrons inside an

atom. The electro-weak [16, 17] theory describes the electro-magnetic and weak forces as

two manifestations of one underlying force. The weak force is effective only over extremely

short distances, is weaker in strength than both electro-magnetic and strong forces, and is

responsible for the p decay of heavy nuclei.

The fermions in the SM interact with each other in various v- .--s determined by their

properties. The charged leptons participate in electro-magfnetic and weak interactions,

while their neutral counterparts (the neutrinos) interact only weakly. The quarks being all

charged and colored, interact both electro-magnetically and strongly, and also v-- .:!'

Table 1-2 lists some of the properties of the force mediators in the SM. The massless

photons mediate the electro-magnetic force between particles possessing electric charge.

The massless gluons act as mediators between strongly interacting particles. The eight




9 if the distance between the charges particles is doubled, the strength of this force is
reduced by a factor of four.

1o All fermions participate in weak nuclear interactions because they possess i.-* II:
!!i a coupling to the weak force.










gluons themselves possess color. Each gluon carries combinations of color and anti-color"l

charge, rendering them color neutral, yet not colorless. Due to their "(c lu s..li character,

in addition to mediating the strong force the gluons themselves interact strongly [3]. The

massive gauge bosons are responsible for mediating the weak force between particles of

different flavors (all quarks and leptons). In addition to mediating the weak force, being

charged themselves, the W* bosons participate in electro-magfnetic interactions.

A parameter of interest indicating the relative strength of a force is called a coupling

constant [18] a dimensionless quantity. Table 1-2 summarizes these for the three SM

forces. Ironically, none of these coupling "(c ix-I .11 are real constants. Instead, they

vary with the energy scale at which the particular interaction in question occurs, and are

said to "run" with energy. In order to understand this "runningt qualitatively, we must

understand the action of the force field (;?i an electric field due to a charged particle)

on virtual particles carrying the relevant charge. Vacuum polarization effects can explain

this concept. The vacuum consists of virtual electron-positron pairs, and an external

electric charge has the effect of polarizing it. Thus such a medium with virtual electric

dipoles has the effect of screening the actual charge due to a partial cancelation of the

field. Consequently very near the charged particle in question this "screeningt effect is

small leading to an overall increase in the effective strength of the field.

In QCD the same trend is observed with virtual quark-anti-quark pairs which tend

to screen the color charge of the "(c ul .i. particle in question. However, QCD has an

additional complication due to the fact that in addition to the quarks, even the gluons

are "(c lIus.. l and are capable of causing interactions, possibly in a different fashion. The

virtual gluons in the vacuum also polarize it, but this time the effect of the polarization is

called 1.is s--I 1.. i ding,' whereby the effective field strength is escalated. Since the virtual




11 Anti-color is as opposite charge is to charge (electric). Each gluon is "bi-culus ..l i and
is a mixture of two different kinds of color and anti-color charges.









quarks and the virtual gluons contribute opposite effects, the winner in this tugf of war

is ultimately determined by the relative number of flavors (this depends on the number

of quarks in the SM) and colors (this depends on the number of gluons involved in the

interaction). The outcome is that the anti-screening of the gluons overcomes the screening

due to the quarks making QCD essentially .I-i-mptotically free, and as one approaches

the colored particle in question, with decreasing distance of approach the strength of

the interaction decreases. Thus, the QCD coupling (denoted as as,) decreaseS12 at high

energies. Conversely due to the phenomena of confinement discussed previously, the

coupling increases with decreasing energy making as, large at low energies. The energy

cut-off which defines this QCD scale is called XQCD [19]13

1.2.2 Symmetries

A symmetry is a transformation of one or more system variables which leaves the

overall physics of the system unchanged. In nature, symmetries lead to conservation

laws. Here we discuss some of the symmetries which are important in particle physics and

govern the decay of particles. A thorough treatment of these concepts may be found in

standard literature [3, 16], here we present a short summary of the relevant concepts.

A symmetry related to quark flavor is known as !-n'-pII") symmetryl4 and isospin

is a quantum number related to strong interactions. Isospin space is an abstract internal

space, and the proton and neutron are two members of an isospin doublet (with isospin

quantum number, I = ~) within this space. The algebraic operations for isospin are

identical to those used for angular momentals Accordingly, there is a third component of



12 The decrease due to .I-i-mptotic freedom [13] is logarithmic.

13 XQCD M 200 MeV or 1 fm-

14 Although introduced during the nucleon period, it was not until the discovery of
quarks that the cause of isospin symmetry was understood.

1s Vector addition of individual components holds.










isospin (Izl6 ) Which for the proton is + and the neutron is 17 .Another example of an

isospin triplet with I = 1 is the pion system with members xr+, wro, and xr-. The members

in an isospin multiple have a near equality of masses, for instance the u and d quarks
form an isospin doublet (I =\ ),nd son do the c andl a quanrks I = The strong and

the electro-magfnetic interaction forces conserve the third component of isospin, Iz. This

is a consequence of the fact that both strong and electro-magfnetic interactions conserve

quark flavor. On the other hand, the total isospin I is a good symmetry only of strong

interactions. The weak interaction does not conserve isospin. An application of isospin

analysis in this dissertation can be found in Appendix A.

We now discuss two discrete (non-continuous) symmetry operations which phI i- a

special role in the dynamics of the production and decay of particles: Parity (P) and

C'I Iage conjugation (C). The spatial inversion of position coordinates with respect to the

origin is obtained by the P operator.


PF'= P(x, y, z) =(-x, -y, -z) = -r' (1-1)


The physical quantities which change an overall sign under the parity operation have

a parity eigenvalue or intrinsic parity of P = -1. Velocities, acceleration and linear

momentum are examples of such quantities. Those which do not undergo a sign reversal

under P, such an orbital angular momentum (both position and linear momentum undergo

spatial inversion, leaving the overall orbital angular momentum unchanged) have an

intrinsic parity P = +1. Note that two successive parity transformations leave a system

unchanged, thus mimicking an identity operation, with possible eigenvalues of P = +1.

States with this property are called eigenstates of the parity operator hadronss are




16 Iz takes values from -I to +I in integer steps.

17 By convention, the particle with the highest charge in an isospin multiple is assigned
the maximum value of Iz.










eigenstates of P) [:3]. The parity of a particle with a definite orbital angular momentum L

is an eigenstate of P with an eigenvalue of (-1)L times its intrinsic parity. The intrinsic

parity of fermions is defined by convention, and cannot he derived. By convention, quarks

(anti-quarks) have P = +1 (P = -1). The parity of a composite system of quarks is the

product of the intrinsic parities of each component quark times a factor of (-1)L, where L

is the orbital angular momentum of the quark system in the hadron. The parities of the

photon and gluon can he derived and give a value of P = -1 for both these mediators.

Parity is a symmetry of strong and electro-magnetic interactions.

Another discrete symmetry of interest is the charge conjugation symmetry (C). The

charge conjugation operator C, reverses the sign of all internal quantum numbers, thus

transforming the particle into its corresponding anti-particle. Thus,


Clparticle >= |anti-particle > (1-2)


Like flavor fermion-anti-fermion systems are eigenstates of C with eigenvalue of C=

(-1)L+s, where L and S denote the orbital and spin angular moment as usual. The

intrinsic value of C for both photons and gluons is -1 [:3, 16].

1.2.3 Mesons and Resonances

We now discuss how quarks manifest themselves. In nature although many particles

carry a net electric charge, none are found to carry a net color, and consequently

experiments have not been able to find isolated quarks [20]. Quarks therefore are found in

colorless combinations of two (mesons) or three baryonss) called hadrons [21]. This is the

phenomenon of confinement [14]. Other color neutral objects are also possible, however

they are rare and exotic and will not he discussed here.
1.2.4 Charmonium

Quarkonium is a bound state of a quark and its anti-quark (qq ). Analogous to

hydrogen (pe-) and positronium (e e- ) hound states in QED [:3], quarkonium is the

QCD counterpart bound by strong interactions. Bound states involving light quarks










(u, d, s) are generally useful for studying weak decays as these systems decay weakly,

however the heavy quarknonia involving c, b quarks are most important for studying strong

interactions. In this dissertation we focus on charmonium bound states of cc which are a

laboratory for testing and understanding the dynamics of the strong interaction.

Cl.I 11!. 1!Instin resonances were discovered experimentallyls during the November

revolution in 1974 [23]. That these charmonium resonances are in fact cc bound states

was interpreted by T. Appelquist and D. Politzer [24], and soon a rich spectrum of these

hidden charml9 StateS WaS confirmed experimentally. Figure 1-1 shows the spectrum of

charmonium states. A spectroscopic notation is used to denote each of these charmonium

states: 2S+1L3 where L = S, P, D... for L = 0, 1, 2... (S = 0, 1 as each quark constituent is a

fermion) .

In addition to this spectroscopic notation, these states are each characterized by

additional quantum numbers of total angular momentum (J20 ), parity (P) and charge

conjugation (C) by the notation JPC. Thus, the ground state with JPC = 0-+ is denoted as

11So (rle(1S)) and the corresponding first excited state is 21So (r1c(2S)). Even though

the lowest level state in this spectrum is the rlc(1S), it was not the first one to be

experimentally observed. The first states to be observed directly were the J/ followed by

~(2S) and were both found in e+e- experiments. In fact, only the states with JPC = 1--

can be produced directly in e+e- collisions because these are the quantum numbers of the

virtual photon formed in such collisions. Other cc states are observed in the transitions of

these JPC = 1-- to lower states, and also in direct pp collisions.



Is Theoretical predictions for the existence of the charm existed before these states were
experimentally found [22].

19 Since the number of net charm quarks in a cc state is zero, we call these hidden charm
in contrast to open charm meson states such as D-mesons.

20 j = + SE in general, and P = (-1)L+1, C = (-1)L+s for fermion-anti-fermion systems.









The decay of the ~(2S) or any other JPC = 1-- state in the charmonium

spectrum can proceed in three possible owsi~, as seen in Figure 1-2. Since the initial

state is colorless, cc annihilation via a single gluon is not allowed as a gluon is colored.

Furthermore, cc annihilation via a single photon is possible (Figure 1-2 c), but is

suppressed relative to a cc annihilation that proceeds through the strong channel. Next,

we consider the annihilation via two gluons, which although a color neutral combination

does not conserve C value. So the only possible dominant gluon channel is the 3-gluon

channel (Figure 1-2 b). Decay via a single photon and 2 gluons is also allowed as this

particular choice conserves C as well as is color neutral (Figure 1-2 a). This latter channel

is also known as a radiative decay and is one of interest in this analysis and is most useful

for observing the states with JPC = ++, from ~(2S).

In fact, the triplet of XcJ(1P) states (J = 0, 1, 2) states in the charmonium spectrum

which are the subject of investigation in this work, were found via such radiative E121

transitions22 from ~(2S) in e+e- experiments using Nal(TI) detectors [25]. These were

later conformed and studied in a series of experiments [26], and the interpretation of the

J/~ and ~(2S) states as non-relativistic bound states of a heavy quark-anti-quark system
was solidified.

Soon after the discovery of these charmonia states, various potential models [27]

were introduced in an attempt to understand the charmonium spectrum as a strongly

interacting analog of positronium (e+e- bound state). Consider the following potential

V(r) motivated by .-i-mptotic freedom for small cc separation (r) and confinement for

large separation,

V(r) = s+ kr (1-3)




21 An El transition is an odd-parity transition.

22 The Xc states were found in the inclusive photon spectrum of ~(2S) via the decay,
~(2S) i we 77JY/4, J/~ e+e-, p1-.+-










Note that the first term is analogous to the Coulomb force in QED, and involves a single

gluon, with the coupling a~s instead of a~. This term is dominant for short distances. The

second term is spring like and represents confinement.

In order to account for fine structure in the charmonium spectrum, for instance the

splitting between the Xc triplet states, the spin-orbit interactions must be taken into

consideration.

Potential models were successful in describing the gross features of the charmonium

spectrum. For a detailed discussion, see [27].

1.2.5 Quantum Chromodynamics in the Charmonium Energy Regime

In subsection 1.2.1, we discussed about the phenomena of .l- imptotic freedom and

quark confinement, and the consequent "runningt of a~s. In the .I-i inphl icl~ freedom

regime of short distances, quarks behave as almost free particles, and therefore in

this regime one can apply perturbation theory [28] for hard processes involving large

momentum transfers. The smallness of a~s at such energies warrants the use of the

perturbative QCD technique. However, in the low energy regime where a~s is no longer

small, the solution diverges and perturbation theory breaks down. Hence below the

scale of XQCD Where one enters the confinement regime, one has to resort to other

non-perturbative methods [29].

Heavy quarkonia, such as charmonia (cc ) and bottomonia (bb) are non-relativistic

systems with low characteristic quark velocities (a~s a 0.3). Thus these systems are very

useful experimental probes for testing non-perturbative QCD calculations.

1.3 Motivation for Exclusive Charmonium Decays

Exclusive us..! 1" 23 decays provide an excellent laboratory for investigating QCD.

C'!I11 .) !Ininiiti (cc ) was the first heavy quarkonium discovered, and is less relativistic

than the light quarkonia. It thus phI i- a special role in probing strong interactions.




23 Onia TefeTS to quarkonia states.










Many resonances of the charmonium system have been observed viz. rlc, J/q', Xc,

4 (2S) '(:3770) etc. These charmonium states are produced and studied at the charm

energy region (:3-5 GeV) in e+e- experiments such as Mark-L, Mark-II, Alark-III, Crystal

Ball, BES etc. Although vector charmonium states have been studied for decades, the

even parity states are less well studied because they are not produced directly in e+e-

collisions. Three years ago, CLEO working at CESR launched the CLEO-c program [2]

which is aimed at providing extremely high precision in the studies of charmed mesons and

the dynamics of charmonium states in this energy range.

The currently available ye. measurements are sparse [:30]; especially when compared

with other S-wave charmonia like J/4. The data taken by CLEO-c at the 4 (2S) resonance

has made available a bounty of Xe,J states which are produced via the radiative decay

( (2S) 7te YJwith branching ratios of each around 9'; [:31].

Hadronic decays of the Xc offer a number of potentially interesting measurements.

Thus, this is an exploratory endeavor. Past research indicates that the Color Octet

Mechanism (COM) is important and governs the decay of these P-wave charmonia

states [:32-36]. QCD predictions of two body exclusive ye. decays with the inclusion of

the COM exist and are tested using the available experimental data. These show support

for the CONT. In this light, new and precise ke. measurements will contribute towards a

better understanding of the COM and nature of P-wave dynamics. Moreover, the sum

of all known Xso two-hody BR's < 2.5' which -II- -- -; that a large portion of the X,

hadronic width may be due to ]ri Iri.--hody decay modes. This study of 4-hody modes

at CLEO is an attempt to discover such "not yet o~ I--- a i.; decays. In order to build a

comprehensive understanding about the P-wave dynamics, both theoretical predictions

with the inclusion of the COM and precise experimental measurements for ye. Tx .Iii -hody

final states are required. All these together will provide a testing for QCD models and

calculations including effect of the CONT. Furthermore, decays of Xey, in particular XcO,2

provide a direct window on gluehall dynamics [:37] which have been a subject of interest










for a long time. The four body exclusive ye. decay modes are being observed here for the

first time.

This analysis follows the general method of our earlier work on if ty' [:38] and

:3-hody [:39] decays of ye., extending it to higher multiplicity states. The four body

exclusive ke. decay modes studied in this article contain two neutral and two charged

hadrons in the final state, and are being measured for the first time. We also take a first

look at the gross features of the rich substructure of the modes.











Symbol Mass Symbol Mass


Note: The mass values listed are not the constituent quark masses.


Table 1-2: Standard Model forces and gauge bosons.
Force Range Relative Coupling Carrier Carrier Carrier
(m) strength constant [11] mass electric
(GeV/c2) charge
Electro- 00 10-2 a~ = 1/137 y 0 0
magnetic
Strong 10-15 1 a~s = 1 g 0 0
Weak 10-ls 10-13 a~w = 10-6 W* 80.4 + e
Zo 91.2 0


Table 1-1: Standard Model fermions.
Leptons


Quarks


0.511 MeV/c2
< 2 eV/c2
105.7 MeV/c2
< 2 eV/c2
1.777 GeV/c2
< 2 eV/c2


m 3 MeV/c2
m 6 MeV/c2
m: 1.3 GeV/c2
m: 100 MeV/c2
171.4 GeV/c2
m 4.2 GeV/c2


Note: The value of the coupling constants listed here are at the scale
transfers.


of low moment
















0140406-002


-


3.8


2 MD -----


3.6




a,

S3.4


E 32



3.0




2.8


JPC= 0-+ 1--
L=O 0


1++ 2+


Figure 1-1.


Figure shows the charmonium system of resonances. The states are labeled by
a spectrosopic notation: 2S+1L3 where L S, P, D... for L 0, 1, 2..., and L and
S denote the orbital and spin angular momentum quantum numbers
respectively. Each state is characterized by additional quantum numbers of
total angular momentum (J), parity (P), and charge conjugation (C) by the
notation JPC. The transitions between states is shown by arrows.


No


1 O**









(a)









\111) Y V VV V V ~Hadrons




(b)

c 8


l y1T1 e 1 T~ Hadrons




(c)

C *








Figure 1-2. Figure shows the cc annihilation of into gluons and photons before
hadronization, (a) the decay through the 3-gluon (strong) channel, (b) the
radiative decay to 2-gluons and 1-photon, and (c) the electro-magnetic decay
into a pair of fermions, are shown.









CHAPTER 2
EXPERIMENTAL APPARATUS

In order to study the decay of Xc charmonium resonances which can only be produced

in a high energy environment, we need a complex technological infrastructure. This

challenging task involves the co-ordination between two inl ri ~ components which

constitute the apparatus: the accelerator and the detector. The former is responsible

for creating the desired charmonium resonances, while the latter detects the outcomes

of the almost instantaneous (=10-23 Sec) decays of the charm particles. This two-step

process requires a tremendous amount of activity and work-force involving physicists,

engineers, and technicians who not only produce and collect the data, but process and

store it in a manner that can be utilized by data analyst physicists at a later point in

time. Such a community of scientists involved in the collection, storage, maintenance, and

analysis of high energy physics data associated with a certain experiment constitutes a

collaborating team for the experiment.

We obtained the charmonium resonance data for this analysis using the experimental

facilities (collider and detector) housed by the Laboratory for Elementary Particle Physics

(LEPP) located on the campus of Cornell University in Ithaca, NY. The accelerator

facility at LEPP which produced the charmonium resonance data is the Cornell

Electron-Positron Storage Ring (CESR). The partner facility responsible for detecting

the outcomes of CESR collisions and located at the south end of CESR is known as the

CLEO detector (CLEO is not an acronym, but is named after Cleopatra a suitable

companion for CESR).

The CLEO collaboration is a team of over 150 high energy physicists from 25

universities studying the production and decay of beauty and charm quarks, and tau

leptons produced in CESR collisions.










2.1 The Cornell Electron-Positron Storage Ring

CESR is a circular electron-positron collider with a circumference of 768 meters,

located 12 meters below a parking lot and an athletic field on the Cornell University

campus. It is capable of producing collisions between electrons and their anti-particles,

positrons, with center-of-massl energies between :3 GeV and 12 GeV. The entire CESR

equipment consists of a linear accelerator (LINAC), synchrotron, and the storage ring

as shown in Figure 2-1. The electrons and positrons are produced in a :30 meter long

vacuum pipe called the LINAC. Electrons are generated by heating a filament until they

have sufficient energy to escape the filament surface. The electrons are then collected

by a pre-buncher which compresses the electrons into packets for acceleration in the

LINAC. The electron packets are accelerated in the LINAC using varying electric fields

generated by radio frequency (RF) cavities. The electrons are accelerated to an energy of

about :300 MeV at the end of the LINAC. Positrons are created by colliding a 140 AleV

electron beam halfway down the LINAC on a movable tungsten target. The result of this

impact is a spray of electrons, positrons and photons. The positrons are separated from

the electrons and accelerated in the remainder of the LINAC up to an energy of about

200 MeV. This accelerated hunch of electrons and positrons is introduced separately and

in opposite directions into the synchrotron. This process typically lasts for about ten

minutes, and is commonly referred to as a "run fill."

The synchrotron is a few meters smaller in radius than the storage ring and is

located in the same tunnel. In the synchrotron, the particles are accelerated in circular

orbits inside a vacuum pipe by four :$-meter long linear accelerators, and are contained

by a series of dipole bending magnets. As the particles are accelerated, the value of




1 the center of mass energy (ECMs) is a measure of the energy available to create new
particles. For an e Ie- collider, EcM = Eiseam. l-t~~ 2 1+ o c.A CLEO, ac-, is very
small, so EcMs M 2 Eiseam










the magnetic fields are adjusted in synchronism with the velocity to keep the particles

contained in the orbit. Once the particles are accelerated to the desired energy of 2 GeV,

they are transferred to the storage ring. The process of transferring the electron and

positron beams into the storage ring (CESR) is called "injection." In the storage ring,

electrons and positrons are guided by dipole bending magnets and are focused hv a series

of quadrupole and sextuple magnets. The beams lose energy by synchrotron radiation

which occurs as charged particles move in a curved path, so super-conducting RF cavities

which operate at a frequency of 500 1\Hz are used to maintain the beam energy (Ebeam),

thus keeping the particles in their orbits. 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. To avoid the

beam collisions anywhere besides the interaction region, the electrostatic separators hold

the electron and positron beams slightly apart from each other. This configuration is

known as pt.1..!"I) shaped orbit. The electrons and positrons are not continually placed

into the storage ring, but are rather located in "bunches", which are grouped into l .."

CESR can he configured to store up to 9 trains with a maximum of 5 bunches each. The

bunches in the trains are separated by 14 ns, and the trains themselves are separated by

284 ns.

The Interaction Region (IR) is a small region of space located at the center of

the CLEO detector where the electron and positron beams undergo collision. At the

interaction point enclosed by the CLEO detector, the beams do not collide head-on,

but with a small crossing angle (cne,) of a 2 mrad into the ring (see Figure 2-2). This

allows for hunch-by-bunch collisions of the electron and positron trains. For low-energy

running (near charm center of mass energies between 3-5 GeV), r-i 1. lr magnets induce

synchrotron radiation, but this has minimal effect on the beam trajectory.










For operation at lower beam energies, twelve wigglers have been installed into CESR

(only six out of twelve r-iva~l; r magnets were installed at the time the data used in

this an~ ll-h- was taken). Each r-i 1. lr consists of eight dipole magnets with maximum

magnetic field strengths of 2.1 tesla per magnet [2].

The ability to obtain a high collision rate is crucial for the success of the accelerator

and its partner experiment. The rate at which collisions occur is expressed in terms of

luminosity (number of collisions per second per unit area), as:


L = fa (2-1)


where f is the frequency of revolution for the bunches, a is the number of bunches for

each particle species, A is the cross-sectional area of beam overlap, and 1V+ and 1V- are

the numbers of positrons and electrons per bunch, respectively. In order to maximize the

luminosity, the beams are focused as narrow as possible in the IR. An important measure

of accelerator performance is the integrated luminosity over a period of time. One can

compute the number of events of a particular type of process by taking the product of

the integrated luminosity with the known cross-section for the given process [40], and one

can then count the number of times this process is detected in a certain time interval.

The two reference processes that are used at CLEO are, e+e- interacting to produce a

new e+e- pair, and e+e- annihilating to produce a pair of photons. Using the well known

cross-section for each process [41], the number of events is converted to a luminosity. We

refer to these as the Bhabha and yy (GamGam) luminosities respectively.

2.2 The Interaction

The collision of the electrons and positrons in the IR at high energies, causes an

interaction among the particles governed by their destiny. It is a challenge for the

physicist to uncover the outcome of this interpl .-- between matter and energy in order to

understand the underlying physics. What comes out of the interaction (matter anti-matter

annihilation) is very sensitive to the energies at which the e+e- beams collide. To










produce charmonium resonances, the e+e- are made to collide at center of mass energies

between 3-5 GeV2

Upon collision, the two beams either scatter, or annihilate and interact electro-magnetically

to create a virtual photons A virtual particle can have any mass as it does not conserve

the four-momentum of the e~e- pair, and is said to lie outside of its mass shell. This

virtual photon being unstable (existing for a time period governed by the uncertainty

principle), decays immediately into "real" (or "on-shell") daughters.

Even at the operating energies of; I 11< GeV (mass of ~(2S) ), the virtual photon

may either produce the resonance ~(2S), or produce continuum background and these

processes are experimentally indistinguishable. Figure 2-3 shows the production of ~(2S)

resonance in a CLEO-c exploratory scan of the ~(2S) hadronic cross section for eight

different beam energy values. It is also possible that the initial e+e- pair radiates two

photons, which subsequently collide.

Irrespective of the intermediate states, the final end product of such an e+e-

annihilation are relatively long-lived charged and neutral daughter particles. The particles

(and corresponding anti-particles wherever applicable) that can be directly detected using

particle detectors are electrons (e-), muons (p ), pions (xr+), kaons (K+), protons (p), and

photons(y). The process of interest in this analysis is

e+e- i i (2S) 7 %c, where Xc h~h-~ro zo, hPh-l wro, K~~rPKoro,

and & = xr, K, p. The remainder of this chapter and chapter 3, explain the method of

separating this process of interest from mimicking backgrounds.



2Specific energies are needed to produce specific resonances with JPC = 1--. The center
of mass energy required to produce the resonance nearly equals the mass of the resonance.

3 Although it is possible to produce a virtual Zo in this annihilation, the probability is
extremely small (oc a

4 COntinuum background is referred to events of the type e~e- i qq, where q =
n, d, a (hadronic), or events of the type e+e- i 1+1-, where 1 = e, p, -r (QED).









2.3 The CLEO Detector

In this section, we describe the experimental particle detector components responsible

for detecting the long-lived "on-shell" daughters of the interaction (section 2.2) which

fly off at relativistic speeds. The principles of particle detection are based upon the

scientific knowledge on matter-matter interaction. CLEO is a versatile, multipurpose

detector with excellent charged particle and photon detection capabilities. Each detector

component is a combination of sensors, which directly or indirectly recognize the signature

of a given species. A detailed discussion of detector technology [1, 2] is beyond the scope

of this document, nevertheless the basic governing principles are highlighted for each

detector part. The rest of this section is devoted to describing the CLEO III and CLEO-c

detectors, and the manner in which they measure the energy, moment and trajectory of

particles.

2.3.1 The CLEO III detector

The CLEO III apparatus is depicted in Fig 2-4, and is the generation of CLEO in

operation in 2001-2002. It is a general-purpose cylindrically symmetric assembly of many

detector elements built concentrically around the CESR interaction point [1].

The entire detector is approximately cube shaped, with one side measuring about

6 meters, and weighs over 1000 tons. Inside out from the beam axis, the CLEO III

detector components as shown in Figs 2-4 and 2-5 are: a silicon vertex detector, a drift

chamber [42], a ring imaging Cherenkov (RICH) detector [43], an electro-magnetic crystal

calorimeter, a super-conducting solenoid magnet (field strength of 1.5 T and direction

parallel to the beam line), and a muon chamber [44].




s There have been many generations of CLEO detectors that have evolved since the
original CLEO detector. Each 1!! ri ~ upgrade marks a new generation.










For the~ particles~ in whiIIhI we~ are~ interested.) (p~ K, Y)II 1,,ty S ) the most interesting

parts of the detector are the tracking system (silicon vertex detector and drift chamber),

the RICH and most importantly, the calorinteter.

The co-ordinate system used inside the CLEO detector is illustrated in Fig 2-6. The

.r-axis points towards the outside of the CESR ring (South), the y-axis points up towards

the sky, and the x-axis is along the incident positron beam direction (West). The origin

of the co-ordinate system lies in the IR within 1-2 nin of the ede- collision point. Owing

to its cylindrical syninetry around x, the polar angle 8 of a point P in space is defined as

the angle between the positive x-axis and the line formed between the origin and P (r in

Fig 2-6 B). Additionally, the azinmuthal angle is defined as the angle between the positive

.r-axis and the line front the origin to P projected onto the I;-plane.

In the following subsections we discuss some of the particle detection methodologies

intpleniented in the CLEO sub-detectors, and how raw detector data is transformed into

measurements of physics interest: particle energy, montenta, and trajectories.

2.3.1.1 Tracking system

The particles created at the interaction point pass the low-nlass heant pipe (Figure 2-4)

before they begin to encounter the active elements of the detector tracking system. The

CLEO III tracking system is responsible for tracking a charged particle's path and thus

giving the physicist a measure of the particle montentunt. The tracking system of the

CLEO III detector is composed of two sub-detectors. The first is the silicon vertex

detector measuring the x and the cotangent of the polar angle 8, surrounded by a central

drift chamber measuring the curvature. Both devices measure the azinmuthal angle 4 and

the impact parameter. This two-conmponent tracking system covers C, :' of the 4xr solid

angle around the IR. For the data presented in this analysis, the charged particle tracking

system operates in a 1.0 T magnetic field (subsection 2.3.1.4) along the beam axis, and

achieves a montentunt resolution of 0.1u' for 1 GeV/c tracks. The resolution is worse

for charged particles with montenta helow 120 1\eV/c, as they will not make it through










much of the outer volume of the tracking system. 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 I0' for hadrons (pion, kaon, and proton), and 5' for

electrons. The tracking system is not sensitive to neutral particles.

2.3.1.2 Silicon vertex detector

The silicon vertex detector provides information about tracks left by the incident

charged particles by collecting the charge left in the wake of the ionization produced by

these particles. The vertex detector is composed of silicon (the ionizing medium) strips

held perpendicular to the trajectories of most particles.

The silicon vertex detector (Fig 2-7) consists of four 300 pm thick detection 1... r~s

which circle around the beam line at radial distances of 2.5 cm, 3.8 cm, 7.0 cm, and 10.1

cm. Each of the four detector 111-;- rs (barrels) is constructed from independent chains

(called ladders) which are made by connecting individual silicon wafers (sensors) together.

Each silicon wafer is 27.0 mm in 4, 52.6 mm in z and 0.3 mm thick. Each lI ... consists

of a proportionally increasing number of detectors along 4 and z, a total of 447 silicon

identical double-sided detectors are used to make the four lIn-;-rs ( 7 along 4 and 3 along z

in the 2.5 cm 1... -r, 10 along 4 and 4 along z in the 3.8 cm lI... r, 18 along 4 and 7 along z

in the 7.0 cm lI ...r, and 26 along 4 and 10 along z in the 10.1 cm li ... ).

The charge is conducted out of the detector for amplification along traces which are

parallel to the beam-line on one side of the strip and perpendicular to it on the other, so

that the two-dimensional point of intersection may be reconstructed. The silicon vertex

detector provides accurate track position measurements close to the interaction point in

r (perpendicular distance from beam line), (azimuthal angle), and z (parallel distance

along the beam line) co-ordinates. The position resolution near the interaction point is 40

p-m in x-y, and 90 pm in z.










2.3.1.3 The central drift chamber

The central drift chamber covers a region in r of 13.2 cm to 82.0 ent front the

beam-line. The CLEO III central drift chamber (DR III) is filled with drift gas of 60:40

heliuni-propane mixture held at about 270 K(, and at a pressure slightly above one

atmosphere. The drift chamber is made up of 9796 drift cells and at the center of each

cell is a 20 put diameter gold-plated tungsten sense (anode) wire, and the sense wire is

surrounded by eight 110 pm diameter gold-plated aluntinunt field (cathode) wires. The

cell forms a nearly square shape 14 nin across as seen in Fig 2-8. The anodes are kept

at a positive potential (about 2100 V), which provides an electric field throughout the

volume of the drift chamber. The cathodes are kept grounded, thus shaping the electric

field such that the fields front neighboring anode wires do not interfere with each other.

During its passage through the DR III, the charged particle interacts electro-nlagnetically

with the gas molecules inside the chamber. When a charged particle passes through a cell,

the energy is transferred front the high energy particle to the gas molecule thereby ionizing

the gas by liberating the outer valence 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 enough energy to become a secondary ionizing electron itself

and ionizes more atoms front the surrounding gas molecules. This creates an avalanche

of electrons on the sense wire which provides a 10" amplification. The avalanche of

electrons thus created reaches 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 front the

avalanche is amplified and collected at the end of the anode wire. The amount of charge

collected, and the time between the initial ionization and charge deposition are measured.

A calibrated drift chamber then converts these measurements to a measurement of the

distance of closest approach of the particle to the sense wire. A calibration of the drift










chamber is then used to map the amount of charge collected to the specific ionization

measurement of the incident particle.

The drift chamber consists of 16 1 i -c r~s of axial sense wires (parallel to the beam-line)

and :31 sense wire 1.,-c cms which alternate in small stereo angles (stereo angle is defined

as the difference in between the wire end-plate and the vertical) to provide sensitivity

to the z-position of the tracks. The wires in a stereo 11s-<-r are tilted or skewed in the

direction. The stereo angle varies from 21 mrad to 28 mrad with respect to the beam axis

yielding a x-position resolution of :3-4 mm at each wire alternating in each subsequent

1 n,-c c. The drift position resolution is around 150 pm in r 4 and about 6 mm in x, and

the momentum resolution of 40 1\eV/c at p = 5.3 GeV/c is achieved [1, 2].

2.3.1.4 Super-conducting coil

The Silicon vertex detector and the central drift chamber as well as all the remaining

CLEO III detector components with the exception of the muon chambers, are permeated

by a uniform 1.5 T solenoidal magnetic field" pointing along the x-axis (East). A :3.5 m

long coil of inner diameter 2.9 m and radial thickness of 0.1 m is wound with a 5 mm x

16 mm super-conducting cable made from aluminum stabilized Cu-NbTi alloy kept in

super-conducting state by the liquid helium. The coil is wound in 2 l~i-c r~s, each having

650 turns, on an aluminum shell. Charged particle trajectories are helical in this field and

we measure the charge times momentum of particles through the radii of curvature of their

tracks. Thus the radius of curvature provides information about the momentum of the

particles.

2.3.1.5 dE/dx particle identification system

The nature of the energy loss of a charged particle due to ionization in the CC, is

used for finding the identity of the charged particle.




6 For all the data used in this analysis, a uniform magnetic field of 1.0 T was used.










At CLEO operating energies, the amount of energy loss per unit length (dE/dxr) is

related to the particle's velocity by an inverse square law, as determined by Bethe and

Bloch [45] Figure 2-9 depicts the relationship between the momentum and energy loss for

different charged species. Knowing the charged hadron track momentum and its dE/dxr

information, one can estimate the number of the standard deviations the dE/dxr is away

from a given particle hypothesis, and this information helps its identification. We also

observe from Figure 2-9 that after certain moment for each charged species, the dE/dxr

curve overlaps and becomes of less use for particle identification (PID). Thus, the ability

to use the dE/dxr information effectively for PID depends on the momentum of each

particle type. Distinguishing K from xr with dE/dxr becomes most effective at moment

< 600 1\eV/c, and separating p from K and xr is most effective at moment helow <

1 GeV/c. To reconstruct the trajectory of the charged hadrons through the detector,

a K~alman fitting procedure [46] is used. The helical charged particle trajectory in the

magnetic field, helps determine the particle momentum, and its position in space.

2.3.1.6 Ring imaging cherenkov detector

The RICH detector lies outside of the DR III, and has a solid angle coverage of 8 :'

It is shown in Figure 2-10. It is used most of the times in combination with the dE/dxr

information to discriminate between charged particles. C'I. i. ill:,v radiation is emitted

by a charged particle when it travels faster than light in a given medium. The charged

particle polarizes the molecules of the medium as it travels through it, and the polarized

molecules emit photons in order to relax to their ground state. A conical wavefront of light

is produced by the photons thus emitted, due to constructive interference of light. The

C'I. i. ill:,v photons are distributed in a conical shape, and the apex angle of the cone is

called the C'I. 1. ill:,v angle 8. It is related to the particle velocity /3, or alternatively to

the particle momentum P of mass m by,

1 1 nz2
cos 8 = -1 + ,and /3 > (2-2)
/3n n P2










where, n is the refractive index of the medium. The measurement of 8 is thus a

measurement of the particle's velocity, and is combined with the measured particle

momentum to determine its mass, and thus its identity.

In the RICH detector the C'I. i. ill:,v photons are not focused and so to measure 8,

they are allowed to propagate in a given space. The RICH components are: a radiator,

an expansion volume, and photon detectors. The radiator allows a charged particle

to radiate C'I. i. ill:.>v photons; its material is made up of lithium fluoride (LiF) plates

(for LiF, n = 1.5). The expansion volume is a region filled with nitrogen gas, and is

16 cm in length. The photon detectors are highly segmented multi-wire proportional

chambers (11WPC) filled with methane-TEA (tri-ethyl amine) gas mixture behind 2 mm

calcium fluoride (CaF2) windows, where the C'I, i. ill:,v cone is intercepted. The detector

covers the radial distance from 82 cm to 101 cm, and renders a total radiation length

of approximately 1"' The RICH is capable of measuring the C'I!. 1. ill:,v angles with

a resolution of few milliradians. This provides good separation between K and xr up to

nearly 3 GeV/c.

The information from the RICH photons, is translated into a likelihood (Li) for

a given particle hypothesis by taking into account each possible optical path traveled

by a photon. Figure 2-11 shows the RICH particle separation as a function of particle

momentum for different particle hypotheses. We observe from Figure 2-11 distinct

momentum thresholds for particle discrimination, determined by n. It is evident that

the K/xr separation using RICH PID becomes effective above 700 1\eV/c of particle

momentum, due to the fact that K does not radiate in the RICH at lower moment.

Similarly the threshold for p/xr separation is about 1 GeV/c. In this analysis, we combine

the dE/dxr and RICH PID systems to complement each other which will be discussed in

subsection 3.2.1. The combined dE/dxr-RICH PID procedure has a pion or kaon efficiency

> 90 .~ and a probability of pions faking kaons (or vice versa) < 5










2.3.1.7 Crystal calorimeter

Located outside of the RICH detector volume is the crystal calorimeter (CC). It

performs energy measurements by absorbing the energy produced in the interaction of

the particles with the traversing medium. The CC is sensitive to both photons, and

charged particles. Incident e* and y particles interact electro-magnetically with the

calorimeter mass, by either producing a shower cascade of equal total energy, or by

depositing a fraction of their energy. A calorimeter is responsible for measuring the

deposited energy. Other incident charged particles directly ionize the atoms in the

material of the calorimeter, while hadrons interact strongly with the atomic nucleus of the

calorimeter material producing a large number of neutral pions, which decay to photon

pairs producing electro-magfnetic showers. The CLEO detector CC is an electro-magfnetic

shower calorimeter, and is vital for the detection of photons in the analysis presented

in this dissertation, as all of our events of interest contain at least three, and often five

photons. As seen from Figure 2-5, the calorimeter constitutes a barrel region and two

end-cap regions. These regions are distinguished based on the polar angle, the barrel

(| cos(0)| < 0.81) and the end-cap (| cos(0)| > 0.81). The calorimeter consists of 7784

(6144 in the barrel and 1640 in the end-caps) thallium-doped CsI crystals, covering 95' .

of the solid angle. The barrel region < !i--r II-; are tapered towards the front face, and are

aligned to point towards the interaction point so that the photons originating from the

interaction point strike the barrel( < i--r .IIs at near normal incidence. The < !i--r .IIs in the

end-cap are rectangular in shape and are aligned parallel to the beam-line. Visible light

from the shower is collected on the back of the crystals, from which the incident energy is

reconstructed. The light yield from each of the crystals is converted into electrical signals

by four photo-diodes at the back of each of the < !i--r I1- and are calibrated to measure

the energy deposited by the incoming particles. Each of the crystals is 30 cm in length,

and covers about 16.2 radiation lengths. The shower energy resolution provided by the










CC (shown in Fig 2-12) is 2.2' (5' .) for photons with energy of 1 GeV (100 MeV). The

angular resolution for showers is about 10 mrad.

2.3.1.8 Muon detectors

Muons can travel through almost everything, and are usually the last particles

detected in a detector. The Muon detector system is used in the identification of muons,

and is placed outside the main body of the CLEO detector. The muon detector covers

85' of solid angle. Like the CC, the muon detector is arranged as a barrel and two

endcaps, and consists of plastic stream counters interspersed in 1 e. ris of iron. When

a charged particle passes through the muon detector, an electrical signal is generated

in a manner analogous to those signals generated in the drift chamber. There are

multi-purpose lIn-;-rs of iron which primarily serve to stop most particles which would

otherwise escape to the detector. Muons are able to penetrate the iron, and the depth

to which a muon travels helps to identify it. The parameter of interest for measuring

the amount of muon penetration is called "penetration (I. pll I which is the number of

hadronic interaction lengths' traversed by the particle track in the muon detector.

The heavy iron 111-;- rs also serve as the magnetic flux return yoke for the superconducting

coil. They also protect the inner detector components of the CLEO III detector from

non-muonic type of cosmic ray backgrounds.

2.3.1.9 The trigger system

A "Data Acquisition Sy--l, in records the events of physics interest that occur as a

result of the e+e- interaction in the detector. Such filteringf of events based upon their

nature and quality is essential for time and cost effectivity, as a lot of resources are spent

in reconstructing and recording the events, and maintaining them for future analysis work.

Read-out electronics are tl~__ ri I I to take a snapshot of the detector and record signals




SHadronic interaction length of a particle is its mean free path before undergoing a
hadronic interaction, in a given medium.










at the time a desired amount of activity is sensed in the drift chamber and the CC. The

tlr__ Ii-- ,lin- criteria are classified into various Il l--- !_ lines" which are used depending upon

the analysis in question. The ones that are responsible for collecting the events used in

this an~ ll-k- are listed below:

1. EL-TR ACK(, requiring at least one axial track, and in addition at least a shower

cluster inside the CC barrel with an energy above 150 MeV.

2. R ADTAU, requiring two or more stereo tracks and either a shower cluster with

energy above 750 MeV or two shower clusters each with energy above 150 MeV

inside the barrel region.

:3. TWO-TR ACK(, requiring at least two axial tracks. Only 5.;:' of the events

satisfying this condition were accepted as this tr~i ;r line was pre-scaled by a

factor of 19 in the CLEO III detector' We are unaffected by the loss of events due

to this pre-scaled tr~i ;r line as the other two trigger lines described above rescued

those events, due to the fact that each of our events in the analysis contained shower

clusters.

An advanced description of the trigger detector can he found in [47].

2.3.2 The CLEO-c detector

The CLEO-c detector is shown in Figure 2-1:3. The CLEO-c detector came into

operation at the launch of the CLEO-c era [2] in 2001, aimed at providing extremely high

precision in the study of the charmed mesons and the dynamics of the charmonium states

in the :3-5 GeV energy range. The CLEO-c detector is identical to the earlier CLEO III

detector in all aspects, with the exception of two modifications: the magnetic field is

lowered to a value of 1.0 T from 1.5 T in CLEO III, and an inner wire drift chamber




SAn axial (stereo) track is derived from the hit patterns on the axial (stereo) burlis of
the drift chamber.

This line was not pre-scaled in CLEO-c.










(ZD) replaces the Silicon vertex detector of CLEO III. These modifications improve the

detection of particles arising front charntoniunt decals, which have a lower montentunt

than those produced in the bottonioniunt range for which the CLEO III detector was

designed. A detailed description of the CLEO-c detector is given in [2].

2.3.2.1 ZD

The inner wire drift chamber consists of a low mass six-] n,-< c (stereo) wire drift

chamber at a small radius, suitable for these relatively low energies and is called the

ZD. It is located between the beam pipe (0.5 nin in thickness, radius of :35 nin) and

the main drift chamber (DR III). The ZD spans the region between 4.1 cm and 11.7 ent

front the beam pipe, and its inner (outer) wall is made of 1 cm (127 pnt ) thick aluntinunt

(nlylar). Figure 2-14 shows an isometric view of the ZD. It is made up of :300 drift cells,

each shaped in a near square of side 10 nin (Figure 2-8), and consisting of a sense wire

(20 I-ni diameter gold-plated tungsten) surrounded by eight field wires (110 ftn diameter

aluntinunt). An electric field is maintained by applying a potential difference of 1900 V

between the sense and field wires. The six 1.,-c cms of the ZD are all slightly tilted (rotated

in 4), arranged at a stereo angle in order to render accurate x information of the charged

track. The inner (outer) 1.,-c c is at 10.3o (15.40) stereo angle. The ZD is filled with a 60:40

heliuni-propane gas mixture, with radiation length of about :330 nt. The manner in which

the ZD detects charged particles is identical to that in the main drift chamber described

in subsection 2.3.1.3. For low transverse montentunt (PT less that about 70 MeV) tracks,

the ZD is the sole source of x information for the track. The position resolution of charged

particles in the x component attained hv the ZD is 680 pm, and it provides a montentunt

resolution of nearly 0. !' for charged particles at normal incidence (cos 8 = 0).

2.4 Monte Carlo Simulation

Monte Carlo simulation is the systematic use of samples of random numbers to

estimate the parameters of an unknown distribution by statistical sampling where the

dintensionality and or complexity of the problem make straightforward numerical solutions










impossible or impractical [48]. Thus Monte C' .) 1.'" is an integration technique used

to solve problems with many dimensions where parameterizing various dependencies is

complex.

A Monte Carlo (\l C) simulation of events is a one such technique where an event

is an interaction and the simulation can he of different levels of sophistication. It is

widely used in high-energy physics experiments to design detectors, and to simulate

how the detector responds to a particular process. It becomes an indispensable tool for

determining the I. .!" rate of a particular process (an interaction or decay). To determine

this rate, one needs to know the efficiency"l of the experiment to reconstruct this type of

process, and the level of background in the selected events. This is almost impossible to

determine analytically for a complex system as CLEO, and we solve this problem using

MC simulation.

A typical CLEO MC simulates the physics process occurring during a collision and

includes the production and tracking of the out-coming particles. The response of the

active detector elements is simulated including possible sources of backgrounds in the

experiment .

The p'ly--ses" simulation which occurs at the first stage uses information about

heam energies to simulate the collisions of the beam. We generate particles with an event

generator randomly (but according to the desired distributions), and obeying the laws

of physics. The produced particles are d. I li-. I1 using a list of possible final states called

"decay table" until only stable or long lived particles remain giving rise to an associated

"decay tree."




1o The name Monte Carlo refers to the tourist resort in Monaco, famous about its
casinos and .1,,0111.-- because of the involvement of randomness and chance.

"1 The fraction of events that actually occur that one reconstructs.










We then propagate the particles through the detector, modeling the interactions and

energy deposition using a detector simulation software called GEANT [49].

The last stage involves reconstructing tracks and showers from low level detector hits

using the the same algorithms that are used for data reconstruction (called PAss212 )

This entire process is very CPU-intensive.

In this analysis, we use two types of MC:

1. "Signal MC" is generated to simulate a specific (signal) decay mode of interest. The

decay table allows only one (or few) decays of interest.

2. "Generic MC" that is generated to simulate all possible actual physical mix of

known processes and decays, and is mainly used to study background.

Of these two, we generated all signal MC (for studying signal processes and specific

background channels) using the EvTGEN generator [50], whereas the generic MC sample

was used from the library of MC events, generated for the entire CLEO collaboration for

use when analyzing this dataset.

Although MC is a vital tool in any was! ll--- one must remember that MC is not

real data and it can at best only try to mimic data. Thus one must study carefully the

reliability of the simulation by comparing the MC to data, and make corrections, or

incorporate discrepancies into the systematic error.

At this stage of the end of this chapter, all the analysis tools available to an

experimenter have been discussed. It is now up to one's discretion to use these tools

to explore the p'ly--ses" of an interaction by separating signal from background.











12 There is also a procedure known as PAss1 which ensures the quality of the data and is
implemented on the data at run time.





































__


9


+


Figure 2-2. Definition of crossing angle aca, at CLEO. The crossing angle is defined as the
angle between the positron beam and the nominal beam axis. The angle
between the electron and positron beams is 2 cam. The value of ace, a 2 mrad.













CLEO EXPLORATORY SCAN


Figure 2-3. C'!I. .) ~!In I t l cross section in an exploratory energy scan at CLEO is shown.
Eight different energy points in the d(2S) mass range have been selected. The
error bars represent statistical uncertainties associated with the measurement.

















+Y (up)


+Z ';..eSt


(South)


xc = r" sin B cos #

y = r sin B sin r

z = r cos 0

r = Vx +1 y* + z2 u

0 = arecos z/r

S= arctan y/l7


(9I

I,


Figure 2-6. The CLEO co-ordinate system is shown. A) represents the global co-ordinate
axes, and B) defines the relationship between the co-ordinates.

































3.75
7.50
10.75












1 cm
LJ



Figure 2-7. End view cross section of the CLEO III silicon vertex detector is shown. The
four detector 1, oric positions and arrangement along the beam pipe are shown.




























8 e




r


7mmin DR3; 5mm iin ZD


Figure illustrates the principle of working of the DR. The field and sense wire
arrangement in a typical DR cell is shown. The pattern of lines represents the
electric field which causes the ions and electrons to drift away front each other.
The liberated electrons produce an avalanche and move towards the sense
wire, and a hit is registered.


Figure 2-8.


i)Field wire
*Sensewire

Charedpair~ticle
trajectory





















1 0 ------------ ----------- -












L I I I I I I I II I
0 .

P GVc

Figre L 2-1 Fiu e sosteRC pril eaaio safnto o oetm()
fo atce bv terrsetv IC hehls h pril hehl
deItemntosaebsdo th vauofa( 15foLi)Thquniy n









Figre 1anFglre s of the respctiv particle s (p, e, Kp) afnd ,t h RSrstion of oet ()



the C'I. i. a!l:0,v angle determination for each particle type.
























4-
GEANT Monte Carlo y







-2 -



10- 101 1 10
E, (GeV)

Figure 2-12. Figure shows the CC energy resolution as a function of photon energy.































j~ERACTION


Figure 2-14. Figure shows an isometric view of the ZD detector.









CHAPTER 3
ANALYSIS TECHNOLOGY

The general tools required for data detection and analysis were discussed in

C'!s Ilter 2. This chapter describes the specific analysis technology emploi- II in this

research.

3.1 Dataset and MC Samples

The data samples used in this analysis are the ~(2S) resonance data with luminosities]

2.74 pb-l (CLEO III, data 24,26,28) and 2.89 pb-l (CLEO-c, data 32), a total of (3.08

+0.09) x 106 ~(2S) decays. The CLEO III and CLEO-c ~(2S) data have a C11l energy

spread of 1.5 MeV and 2.3 MeV respectively. Note that the apparent mis-match of

luminosities and event totals in the two configurations is due to different beam energy

spreads. Studies of MC simulations and the data reveal no significant differences in the

capabilities of the two detector configurations, therefore the CLEO III and CLEO-c

datasets are analyzed together.

The signal Monte Carlo samples used in this analysis were all generated using the

EvtGen [50] generator and Geant-based [49] detector simulation. Both the detector

configurations (CLEO-c and CLEO III) have slightly different efficiencies and resolutions.

We generated 10,000 events each for all the modes which contain two xro mesons, whereas

for all the remaining modes containing rl or Ko mesons, 15,000 events were generated

for each detector configuration for each of the three Xc mesons. The signal events were

all generated using the PHSP (phase space ) model of EvtGen for each exclusive mode

under study, and using the Xc intrinsic widths from [30]3 For the modes with rl and



1 The peak instantaneous luminosity achieved was 2 1031 cm-2S-1

2 A phase space model generates events with a uniform angular distribution of the final
state particles.

3 FOT Xc0, an intrinSIC Width of 14.9 MeV was used, as it was the MC default value.










KS~ these particles were allowed to decay generically that is, to the daughters in their

known ratios :30 and therefore the efficiency for such modes includes the intermediate
branching, fractions of,,~, the odesof r cnstrctionC of,,, th f n K The signal MC for

this enh l--- alone amounts to more than half a million events (540,000). In order to

account for the angular distribution corresponding to each of the three X c candidates

for the radiative decay d'(2S) 7 1,J, the MC was generated in accordance with an El

transition production cross section expectation of 1 + A co~s2 0) where A = 1, -1/3, +1/1:3

for .7 = 0, 1, 2 particles [51], and 8 is the radiated photon angle relative to the positron

beam direction.

We also generated events (20,000) for the study of an anticipated source of background

of the type ( (2S) i 7/#' ~~ro 0/ r+ r- o, using the EvtGen generator model

VVPIPI (vector decay into a vector and two pions) for the first step of the decay, and

the PHSP model for the latter step. Furthermore, we also analyzed a generic MC sample

with a luminosity equivalent to the data sample in order to check for possible feed-through

backgrounds. Both these background MC samples were based on the CLEO-c detector

configuration for convenience.

3.2 Final State Selection

In this section, we discuss the final state reconstruction criteria. The following final

states of the Xc candidate are reconstructed in this analysis, as we expect reasonable

efficiency and background in these final states:
h~h-~ro 0r, h~h-if rO, K~~r KO-o where-- b = xK,.I addition,,, we al

reconstruct the transition photon from ((2S) The final state variable plotted is the

mass of the hadron combination (Xc candidate) after application of all the selection

criteria and kinematic constraints described below.

3.2.1 Charged Particle Reconstruction

The three charged particles reconstructed in this analysis are xr, K, and p. Several

selections were applied. One or more selection criteria are also known as a "cut". Each cut










acts as a filter and provides a handle to eliminate possible backgrounds. However, with

each application of a cut, one also most often loses signal events, thus p .i-ing a price in the

form of efficiency. A good cut is one that eliminates maximum background with the least

possible signal loss. Following are the cuts used in reconstructing the charged particles in



1. Track quality criteria:

We used CLEO standard cuts to ensure the quality of charged tracks. A good track

is a track that satisfies the following conditions:

possesses a reasonable number of hits on the DR, the ratio of number of wire hits

to those expected must be > 0.3.

lies within the fiducial volume of the DR, i.e. has |cos(0)| < 0.93, where 8 is the

polar angle measured with respect to the beam direction.

We also require the number of t;ood" tracks to be either 2 or 4 based on the

number of charged hadrons in the final state.

We demand all tracks come from the beam spot with a momentum-dependent cut

on impact parameter4 that is less restrictive for low momentum tracks, for which

the resolution is poorer. The impact parameter is required to be less than a value

of (5-3.8p3) mm, (with p being the total momentum of the charged track measured

in GeV/c), and the minimum value of the cut is 1.2 mm. This means that this cut

slides from 5 mm at zero momentum to 1.2 mm at 1 GeV/c and then remains flat at

the value 1.2 mm thereafter.

2. C'!I. aged Particle Identification:

The CLEO particle identification information was used for the p, K and xr

separation. We defined the following parameters to use the available dE/dx and



4 It is the radial distance of the point of closest approach with respect to the beam spot
measured in mm.









RICH in combination.


PID1xp = L, L, (3-1)

where Li are the Likelihoods given by the measured C'I. 1. ill:,v angles of photons in

the RICH detector compared with predicted C'I. 1. ill:,v angles for that particular

particle type.

PID~zxp = ae a (3-2)

where ai is the ratio of the difference between the measured dE/dx and the

predicted dE/dx values with the error in the dE/dx determination for each particle

type.

Two more such parameters were defined for xr, K separation in an analogous

manner, all of which are used for xr identification. We further define four such

parameters each for K and p which are emploi-- II for K and p identification.

In order to identify the tracks as xr, K and p, we combine the dE/dx and RICH

using the above defined parameterization in the following manner:

* To use the RICH whenever the RICH information is available, we require

each particle momentum to be above its RICH threshold. We used 0.60 GeV/c,

0.62 GeV/c and 1 GeV/c as thresholds for pions, kaons and protons respectively.

* When dE/dx information is available, but RICH is not we require PID~ip < 0 and

PID~iK < 0 for i = xr, K, p for xr, K, p identification respectively.

* When dE/dx and RICH are both available, we require (PIDis, + PID~ip) < 0 and

(PID1iLK + PID~.iK) < 0 for i = xr, K, p for xr, K, p identification respectively.

* If both dE/dx and RICH are unavailable, we reject the track.

To suppress charged lepton QED backgrounds, we require additional cuts. We

reject electron candidates as follows: for all tracks, we compute the ratio of CC

energy to track momentum, Eco /p, and the difference between the measured

dE/dx and the expected dE/dx for the electron hypothesis, normalized to its









standard deviation, ae. We reject events with 0.92 < Eco /p < 1.05s and

|Ue| < 3. Furthermore, discrimination against muons is achieved by means of a cut

on the sum of the muon penetration depths of the tracks (corresponding to the two

charged hadrons occurring in the final state for each mode), to be less than 5. The

particle identification together with the lepton veto criteria are found to be more

than 97;' efficient for all the modes.

3.2.2 Neutral Particle Reconstruction

The neutral particles reconstructed in this analysis are y, wro, r and Ko The method

for reconstructing these neutrals is outlined below:

1. Photon selection:

Photon showers are defined as those having an energy profile in the CC consistent

with being a photon by requiring them to satisfy the condition of E90E250K(6 We

select the transition photon as having E > 30 MeV, being unmatched to any track

in the event and additionally checked to not be part of the xro or rl candidates. The

photon candidate has its 4-momentum calculated from the event vertex position.

The detection of the transition photon origination from the radiative decay of ~(2S)

( (2S) 7 %c) will enable us to reconstruct the complete event, which will improve

the resolution and signal to noise ratio for the final states and will give an additional

handle to eliminate backgrounds.

Photon candidates used in xro and rl reconstruction are additionally required to

possess more than 50 MeV of energy if found in the CC endcap region.



s For electrons this ratio is peaked at unity because by its nature, the almost massless
electron deposits all of its energy into the CC.

6 An E90E250K( is a selection cut which when true, implies that the energy deposited
by the photon shower in the inner 9 CC crystals (around the highest energy nearly the same as that deposited in 25 CC pattern for photon showers.









2. xro i y and rl i y reconstruction:

We reconstruct xro i y and rl i y candidates using a pair of photon candidates

having an energy deposition in the CC consistent with being a photon' possessing

an energy of at least 30 MeV (50 MeV if found in the endcap), and being unmatched

to any track in the event. The photon pair was kinematically fit to the nominal ;o

rl mass using the event vertex position defined by the event's charged tracks as the

origin of the photon trajectories A cut is placed on the mass fit of X2 < 10 (for

one degree of freedom). Figure 3-1 shows a marginal yet desired improvement in the

candidate resolution achieved after using the new event vertex position. Each photon

daughter of a xro (rl) candidate as described by the criteria above, was required to

possess a unique shower identifier (i.e. the photon shower involved was ensured to be

a unique daughter of the parent candidate and was not allowed to be a part of any

other final state particle).

3. rl "+"-"o reconstruction:

A pair of charged pions was reconstructed based upon the charged particle criteria

described in subsection 3.2.1, and combined with a xro candidate of the profile

discussed above to form an rl candidate. The rl i ozr+,- candidate was mass

constrained to the nominal rl mass, and a cut of X2 < 10 (per degree of freedom)

was placed on the fit.

4. KO, reconstruction:

We reconstruct the KS using its decay to a pair of good charged pion tracks

kinematically constrained to come from a common vertex. We require that the



SAn E90E25UnfOK( condition was applied. This criteria is the same as the E90E250K(
condition, but where ( i-- .IIs which are shared between clusters, have their energy split
between the clusters. Only part of the energy of these fringe crystals are counted in any
one cluster.

8 This procedure is described in Appendix of [53].









reconstructed invariant mass of the two pions he within 10 MeV (a :3.2 standard

deviations) of the nominal K) peak. A K) flightg path cut was found to be

unnecessary because it did not help the signal to noise ratio any further than that

already achieved spectacularly by means of the kinematic constraint and particle ID

procedures (shown in Fig :3-2).

3.2.3 K~inematic Constraint Fitting

The knowledge of complete event (reconstructed using the above charged and neutral

selection conditions) is exploited to its full advantage by applying the laws of conservation

of energy and momentum.

If we simply obtain the invariant mass of the four hadrons comprising the Xe, we

obtain a X candidate mass resolution of a :30 MeV. Alternatively, we could use the energy

of the transition photon, which has a one to one correspondence to the energy of the

Xe. This would, by itself, produce a resolution of the order of 7 MeV for the Xc masses.

To optimize the resolution, we use all the available information together. We do this

by means of a kinematic constraint whereby the X, decay particles and the photon are

together kinematically constrained [54] to match the 4-momentum of the beam. Note that

for the 4-momentum of the beam, we use a fixed value for the mass of the 4 (2S) with

the small beam crossing angle taken into account. The mass of the 4 (2S) is known very

precisely, and its natural width is only :337 keV [:30], which is small compared with the

other uncertainties in the experiment. This procedure improves the resolution of the X,

mass to around 5 AleV, depending upon mode. The cut on the X2 of this fit is a critical

one, and is optimized at a value of X2 < 25 (for 4 degrees of freedom). Fig :3-3 shows the

profile of this X2 Variable and indicates the agreement between the MC modeling of this
cut and data.



The transverse decay length of the KS with respect to the beam spot.










This cut strongly eliminates background (as seen in Fig 3-4 a,b), and the fitting

procedure greatly improves the mass resolution of the Xc (as seen in Fig 3-5 a,b). The

improvement in the photon energy spectrum due to the kinematic fitting procedure is seen

in Fig 3-6 a,b. The Xc invariant mass is found using the updated parameters due to the

constraint.

In < 101' of the events, we find a problem of multiple combinations of photons in

the final states (for example, in modes involving one or more xro or rl mesons) leading to

more than one Xc candidate per event, thus causing an apparent increase in the number of

final state Xc candidates. To overcome this problem, an additional criterion to reject such

candidates per event is applied by choosing only that candidate in each event which has

the least value of the above X2 of the fit to the total 4-momentum beam constraint. The

number of multiple candidates is highest for the y~r+x-xozor final state as seen in Fig 3-7

a,b.

3.3 Fitting Procedure

The final state variable (invariant mass of the Xc candidate) histograms were fitted

to three signal shape functions corresponding to each of the three Xc states, and an

additional constant background function. Each signal shape function consisted of a

Breit-Wigner convolved with a double Gaussian resolution functions which was obtained

from signal MC. The respective widths of the Breit Wigner functions are representatives of

the intrinsic widths of the resonances involved and are fixed to the values in [30] (Exo

10.4 MeV, Ex,c = 0.89 MeV, Ex.2 = 2.06 MeV.) The detector resolution (represented by a

double Gaussian) is obtained from the MC fit of the difference between the generated and

reconstructed mass (M 1.,, Mrec) for each Xc in each mode. Fig 3-8 represents the detector

resoutin fncton fr te mde o wozo Note that the detector resolution which




1o To obtain such a function, we used two "Breit-Wigner convoluted with single
G- .--!la functions.









is about 4.5 7.1 MeV is of the order of the natural width in the case of Xco, whereas

for X,1 and Xc2, the detector resolution dominates the observed spread in the signal. The

resolution is best for the K~~r K~r o mode and is least good for the xr+xr-xozo mode,

while it is not much different for the other modes. For a given mode, among the Xc states,

the resolution is least good for the co.

The Xc masses are kept fixed to their nominal values during the fitting, due to the

presence of many fitting parameters (18 signal parameters). In all cases, the reconstructed

masses are, when allowed to float, consistent with these values. Figs 3-9 3-11 show the
fitting functions described above for the mode Xc K~xKx in sina MC The above-'""""- '-

fitting procedure is used to fit the data (CLEO III and CLEO-c samples together) to

obtain the yields and also to find the number of reconstructed events in the case of MC for

evaluating the signal efficiencies.

3.4 Efficiencies and Yields

The efficiencies are obtained by studying the signal MC samples generated for each

of the final states. The efficiencies for CLEO III and CLEO-c detector configurations are

listed in Tables 3-1 and 3-2. It may be noted that these are rather different for CLEO III

and CLEO-c, yet we observe the uniform trend of higher efficiency for CLEO-c as seen

in previous analyses [38, 39]. The efficiencies of rl modes listed includes the rl i y and

rl "+"-"o branching ratios. The efficiency for the K~~r K~r o mode includes the

KS xr+x- branching ratio. The final efficiencies (E) are obtained by taking a weighted

average (weighted by the number of ~(2S) events) over the CLEO III and CLEO-c

datasets are listed in Table 3-3. The fractional errors on the efficiencies are considered

with other systematic uncertainties discussed later in (I Ilpter 4. The yields in the data

are obtained by using the fitting procedure discussed in the section 3.3. Clean signals

of Xco, Xcl and Xc2 arT found in case of most modes studied. Our background studies

based on a generic MC sample of ~(2S) decays, indicated negligible contamination and no

peaking backgrounds in all the modes studied, while our studies of the simulated sample of










~(2S) J/ xo ~r~o, ~/ + indicated such contamination. Figure 3-12 shows the

scatter plot of the invariant mass of the xr+xr-wo combination versus the Xc candidate mass

in data. The horizontal line at the J/~ mass indicates the presence of this background.

We do not get rid of these events, as they occur throughout the Xc mass region and thus

get accommodated by the background function used in the fitting procedure.

Figures 3-13 through 3-19 show the fit parameters of the data fitted histogframs, and

Figures 3-20 to 3-26 and Table 3-3 summarize the yields obtained in data.









Table 3-1: CLEO-c MC efficiencies (in .~) for each mode.
Mode Xo Xcl Xc2
x x~-wr~o a 18.9 18.2 18.6
K+K-wro a 13.5 14.2 13.5
ppro a13.0 14.6 14. 1
x~x-qxo9.68 9.09 9.55
K(+K-rl"o 6.72 6.37 6.24
ppyro6.41 6.39 6.21
K~~r K~ro 10.7 11.7 10.7
Note: The efficiencies for the rl modes include the branching fractions of B(rl i yy) and
B(rl i xr~-wo), and the efficiency for the KO mode includes, the KS o branching
ratio.


Table 3-2: CLEO-3 MC efficiencies (in .~) for each mode.
Mode Xo Xcl Xc2
x x~-wr~o a 16.1 16.6 16.6
K+K-wro a 11.8 12.0 11.9
ppro a12.4 13.1 12.9
x~x-qxo8.35 8.67 8.02
K+K-rl"o 5.57 5.87 5.94
ppyro5.46 6.07 5.44
K~~r KOxo 10.1 10.6 10.1
Note: The efficiencies for the rl modes include the branching fractions of B(rl i yy) and
B(r xr+xr-wo), and the efficiency for the Kts mode includes the Kts xr branhn
ratio.






















a







fiO
fi
cO
I

















CO


Ot






SOO


cbe



o :-


t ~c3nE~nho


Ln~Cr3b \
r~cj~om o


co


Cat t~~C
tN Moi10 d


a f
fo
I f

f+


ai f

$I












File */cdatlaxp/tem2/tem/ruksha na/ntp/mergedchic/f final mergedcleoc/1_0 ntp
ID IDB Symb Daternlme Area Mean
3 300 1 070518/1228 2656 0 1337
3 600 2 070518/1228 2566 0 1339


RMS
7 5935E-03
7 1583E-03


0~
0.090


0.115 0.140 0.165


0.190


~ro i y invariant mass (GeV/c2)


Figure 3-1. Reconstructed invariant mass distribution of the xro qq candidate is shown.
The default ~ro (solid black), is ovalle li0 by the candidate re-fit from the event
vertex (dotted red).























20 -



0
3.20


3.30 3.40 3.50


Mass Xc (GeV/c2)


Effect of the~ KS Afliht significance cut in data for the mode K~~rX Kyo. The
dotted (red) histogram is with no cut on this variable while the solid (black)
histogram-: is- afe a -Cu Tof KSfight significance > 5. We chose not to apply a
cut on KS fight significance.


Figure 3-2.



























400-



300--



S200 -



100 -




0 25 50 75 100






Figure 3-3. Profile of the kinematic constraint cut of X2 < 25 is shown for the mode
xr+xr-xozo, for the sideband subtracted Xeo candidate events. The signal MC
cut profile histogram (solid black) is overlaid by the corresponding scaled data
plot (blue points). The arrow marks the cut value.




























3.20 3.30 3.40 3.50


3.60


Mass ke. (GeV/c2)


3.20 3.30 3.40 3.50
Mass ke. (GeV/c2)


Figure 3-4.


Improvements in the signal to noise ratio, and the ke. mass resolution due to
the X2 < 25 cut are shown. Events with X2 < 1000 cut (solid black) and after
(dotted red) the application of the X2 < 25 cut while keeping all other
selection conditions imposed for the mode Ex+~-roro oin the A) ye~o signal MC,
and B) data are depicted.





























3.20 3.30 3.40 3.50

Mass Xco (GeV/c2)


3.20 3.30 3.40 3.50
Mass Xc (GeV/c2)


The unconstrained (constrained) Xc candidate invariant mass distributions are
shown in dotted black (solid red) histograms for the mode K~~r Ko o in the
A) Xeo signal MC, and B) data.


Figure 3-5.


































































































The transition photon energy distributions before (after) the kinematic fitting

procedure are shown in dotted black (solid red) histograms for the mode

K(~x K~o in the A) Xeo signal MC, and B) data.


Figure 3-6.


I _ rl____l __ _~___I_


I___


LI


I"


::

II
I '









I


nlrc~~c;


100 1-


50 1-


0.05 0.15 0.25



































Mass Xc (GeV/c2)


3.


B




















62


50



40



30



20



10


3.32 3.42

Mass Xc (GeV/c2)


Figure 3-7.


The effect of multiple candidate rejection criteria in signal MC is shown via
the dotted (red) histogram in contrast to the solid (black) histogram which
includes the multiply counted candidates for the modes A) xr+xr-xozo and B)
I(;rKO Ko O


KnIKo o -
0



0



0



0



0


























MINUIT Likelihood Fit to Plot
chicth+h-h~h0 final UPCHIMS-CHIGENM axis
File: Generated Internally
Plot Area Total/Flt 1641 8 /1641 8
Func Area Total/Flt 1641 7 /1641 7
Likelihood = 80.3
X2= 75.7 for 100 6 d.o.f.,
Errors Parabolic
Function 1: Two Gausslans (sigma)
AREA 1643 3 & 4166
MEAN -2 86184E-04 & 1 5881E-0
SIGMA1 5 96357E-03 1 7998E-0
AR2/AREA 0 12416 & 2 2757E-0
DELM 1 57704E-03 1 3997E-0
SIG2/SIG1 3 1372 & 0 2620
120, ,


3&100


12-APR-2007 09:24
Fit Status 3
EDM 9 520E-06


C.L.= 91.6%


+ 00000E+00
+ 0 0000E+00
+ 0 0000E+00
+ 0 0000E+00
+ 0 0000E+00
+ 0 0000E+00


14
14
12
13


Minos

00000E+00
0 0000E+00
0 0000E+00
0 0000E+00
0 0000E+00
0 0000E+00


-0.050


-0.025 0.000 0.025 0.050
mass, X mass,. X (GeV)


Figure 3-8. The double Gaussian functional representation of the detector resolution is
shown. The signal MC Xeo mass resolution for the mode pp~ro O is well

represented by a double Gaussian function.


























MINUIT Likelihood Fit to Plot
chiceKplKOpl0 final UpchlMs axis
File: Generated Internally
Plot Area Total/Flt 1013 1 / 1013 1
Func Area Total/Flt 1014 1 / 1014 1
Likelihood = 135.9
X2= 121.1 for 100 1 d.o.f.,
Errors Para
Function 1: smear
AREA 81838 & 29
*MEAN 3 4150 + 0 0
*GAMMA 149000E-02 & 0 0
* SIGMA 4 78890E-03 & 0 0(
Function 2: smear
#AREA 218 56 & 0 0
*MEAN 3 4150 + 0 0
*GAMMA 149000E-02 & 0 0
# SIGMA 1 05212E-02 & 0 0(
160 a 0i u


4&200


12-APR-2007 09:30
Fit Status 3
EDM 4 370E-07


C.L.= 6.5%


27 09
00000E+00
00000E+00
0 0000E+00

00000E+00
00000E+00
00000E+00
0 0000E+00


abolic

69
000E+00
000E+00
000E+00

000E+00
000E+00
000E+00
000E+00


Minos

26 61
00000E+00
00000E+00
0 0000E+00

00000E+00
00000E+00
00000E+00
0 0000E+00


3.32 3.42 3.52 3.62
Reconstructed Xo mass (GeV)


Figure 3-9. Double Gaussian convoluted with B-W functional representation of the signal

variable i.e. the fitted signal MC for Xeo candidate invariant mass distribution

for the mode K~~ Ko rO is shown.



























MINUIT Likelihood Fit to Plot
chiceKplKOpl0 final UpchlMs axis
File: Generated Internally
Plot Area Total/Flt 1514 7 /1514 7
Func Area Total/Flt 1514 1 / 1514 1
Likelihood = 84.5
X2= 101.1 for 100 3 d.o.f.,
Errors Para
Function 1: smear
AREA 1002 7 & 27
*MEAN 3 5105 & 0 0
*GAMMA 8 80000E-04 & 0 0
* SIGMA 4 52650E-03 & 0 0(
Function 2: smear
#AREA 49452 + 00(
*MEAN 3 5105 & 0 0
*GAMMA 8 80000E-04 & 0 0
# SIGMA 7 12471E-03 & 0 0(
Function 3: Chebyshev Polynomlal of Ord~
NORM 42 128 & 13
CHEBO1 -0 88948 & 0 4
500 : : :


4&200


26-MAR-2007 09:54
Fit Status 3
EDM 6 794E-06


C.L.= 36.8%


+ 2874
+ 00000E+00
+ 00000E+00
+ 0 0000E+00

+ 00000E+00
+ 00000E+00
+ 00000E+00
+ 0 0000E+00

+ 1427
+ 04980


abolic


Minos

2825
00000E+00
00000E+00
0 0000E+00

00000E+00
00000E+00
00000E+00
0 0000E+00

12 19
0 4412


30
000E+00
000E+00
000E+00

000E+00
000E+00
000E+00
000E+00
er 1
20
802


3.32 3.42 3.52 3.62
Reconstructed X,, mass (GeV)


Figure 3-10. Double Gaussian convoluted with B-W functional representation of the signal

variable i.e. the fitted signal MC for X,1 candidate invariant mass distribution

for the mode K~~ Ko rO is shown.



























MINUIT Likelihood Fit to Plot
chiceKplKOpl0 final UpchlMs axis
File: Generated Internally
Plot Area Total/Flt 1470 4 / 1470 4
Func Area Total/Flt 1471 2 /1471 2
Likelihood = 111.1
X2= 119.1 for 100 3 d.o.f.,
Errors Para
Function 1: smear
AREA 1181 0 & 32
*MEAN 3 5562 & 0 0
*GAMMA 200000E-03 & 0 0
* SIGMA 4 59130E-03 & 0 0(
Function 2: smear
#AREA 28557 + 00(
*MEAN 3 5562 & 0 0
*GAMMA 200000E-03 & 0 0
# SIGMA 9 53613E-03 & 0 0(
Function 3: Chebyshev Polynomlal of Ord~
NORM 26 944 & 15
CHEBO1 -1 6674 & 18
500 : : :


4&200


26-MAR-2007 10:38
Fit Status 3
EDM 1015E-05


C.L.= 6.3%


32 36
00000E+00
00000E+00
0 0000E+00

00000E+00
00000E+00
00000E+00
0 0000E+00

16 32
1308


abolic


Minos

31 80
00000E+00
00000E+00
0 0000E+00

00000E+00
00000E+00
00000E+00
0 0000E+00

13 91
3 109


3/
000E+00
000E+00
000E+00

000E+00
000E+00
000E+00
000E+00
er 1
09
08


3.32 3.42 3.52 3.62
Reconstructed X, mass (GeV)


Figure 3-11. Double Gaussian convoluted with B-W functional representation of the signal

variable i.e. the fitted signal MC for Xc2 candidate invariant mass distribution

for the mode K~~ Ko rO is shown.













49:









1 -



3.2 3.32 3.2 .5 3
Mas of La GeVc2

Fiur 312 Sudesofananicpaedbakgoud ro J saterplt f h
inaran mas oftexxw obnto essteX addt asi
daai shw. Th horizna liea h / ms niae h rsneo
this ackgound









Y r. r. ~~~87














MINUIT Likelihood Fit to Plot 3&100
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 4015.0 / 4015.0
Func Area Total/Fit 4008.8 1 4008.8


19-APR-2007 11:42
Fit Status 3
E.D.M. 3.730E-05


C.L.=0.736E-02%/


Likelihood = 164.6
X2= 157.7 for100 4 do~f,
Errors Parabolic
Function 1: near
AREA 1373.8 f 37.55
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 7.04920E-(E. f 0.0000E+00
Function 2: suear
#AREA 377.57 f 0.0000E+00
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 1.55650E-(Li f 0.0000E+00
Function 3:sunear
AREA 519.90 f 25.58
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 6.55030E-(E. f 0.0000E+00
Function 4: suear
#AREA 84.771 f 0.0000E+00
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 1.80130E-(Li f 0.0000E+00
Function 5:eunear
AREA 826.05 f 28.47
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 6.40090E-(E. f 0.0000E+00
Function 6: suear
#AREA 77.493 f 0.0000E+00
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 2.05400E-(Li f 0.0000E+00
Function 7: Chebyshev Polynomial of Order 0
NORM 1948.3 f 103.4
250 .
200 E
150 E
100 E
50 E
IJJ


Minos

39.90
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

24.14
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

29.54
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

102.7


40.50
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

24.83
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

30.14
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


+ 105.0


3.22


3.32 3.42 3.52 3.62

Massxa


Figure 3-13. The fitted signal variable for the x x~-xrozo mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 3&100
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 425.00 / 425.00
Func Area Total/Fit 424.671i424.67


19-APR-2007 11:43
Fit Status 3
E.D.M. 3.112E-06


C.L.= 25.0%


+ 14.57
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 6.134
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 8.969
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 36.01


Likelihood = 120.1
X2= 105.0 for100 4 do~f,
Errors Parabolic
Function 1: smear
AREA 181.22 f 14.06
* MEAN 3.4148 f 0.0000E+00
* GAMMA 1.04000E-02 f 0.0000E+00
* SIGMA 6.70390E-03 f 0.0000E+00
Function 2: smear
# AREA 32.237 f 0.0000E+00
* MEAN 3.4148 f 0.0000E+00
* GAMMA 1.04000E-02 f 0.0000E+00
* SIGMA 1.54590E-02 f 0.0000E+00
Function 3: smear
AREA 31.232 f 5.749
* MEAN 3.5107 f 0.0000E+00
* GAMMA 8.90000E-04 f 0.0000E+00
* SIGMA 5.47720E-03 f 0.0000E+00
Function 4: smear
# AREA 13.896 f 0.0000E+00
* MEAN 3.5107 f 0.0000E+00
* GAMMA 8.90000E-04 f 0.0000E+00
* SIGMA 1.05490E-02 f 0.0000E+00
Function 5: smear
AREA 68.963 f 8.738
* MEAN 3.5562 f 0.0000E+00
* GAMMA 2.06000E-03 f 0.0000E+00
* SIGMA 6. 01450E-03 f 0.0000E+00
Function 6: smear
# AREA 7.9231 f 0.0000E+00
* MEAN 3.5562 f 0.0000E+00
* GAMMA 2.06000E-03 f 0.0000E+00
* SIGMA 2.23980E-02 f 0.0000E+00
Function 7: Chebyshev Polynomial of Order 0
NORM 231.84 f 34.66
40 .

E 30

20

cv 10
05


Minos

13.93
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

5.603
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

8.354
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


33.42


3.22


3.32 3.42 3.52 3.62

Massxa


Figure 3-14. The fitted signal variable for the K K-7rozro mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 3&100
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 136.00 / 136.00
Func Area Total/Fit 135.53 / 135.53


19-APR-2007 11:44
Fit Status 3
E.D.M. 5.109E-06


Likelihood = 118..8
X2= 117.0 for 100 4 do~f,
Errors Parabolic
Function 1: near
AREA 31.985 f 6.810
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 5.96360E-(E. f 0.0000E+00
Function 2: suear
#AREA 7.4805 f 0.0000E+00
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 1.87080E-(Li f 0.0000E+00
Function 3:sunear
AREA 10.463 f 3.804
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 6.09260E-(E. f 0.0000E+00
Function 4: suear
#AREA 1.0150 f 0.0000E+00
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 2.12810E-C=2 f 0.0000E+00
Function 5:eunear
AREA 27.232 f 5.443
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 5.66790E-(E. f 0.0000E+00
Function 6: suear
#AREA 1.9948 f 0.0000E+00
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 2.57150E-(Li f 0.0000E+00
Function 7: Chebyshev Polynomial of Order 0
NORM 140.22 f 24.38
15L I I .


C.L.= 7.2%


7.181
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

4.135
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

5.838
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


Minos


6.520
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

3.501
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

5.196
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


23.26 + 25.57


3.22


3.32 3.42 3.52 3.62

Massxa


Figure 3-15. The fitted signal variable for the pp~ro a mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 3&890
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 533.00 / 533.00
Func Area Total/Fit 532.93 / 532.93


19-APR-2007 11:47
Fit Status 3
E.D.M. 2.642E-06


C.L.= 3.2%


+ 9.261
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 7.810
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 7.971
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 63.73


Likelihood = 118.3
X2= 123.1 for 100 4 d.o.f.,
Errors Parabolic
Function 1: smear
AREA 39.491 f 9.056
* MEAN 3.4148 f 0.0000E+00
* GAMMA 1.04000E-02 f 0.0000E+00
* SIGMA 6.11950E-03 f 0.0000E+00
Function 2: smear
# AREA 14.427 f 0.0000E+00
* MEAN 3.4148 f 0.0000E+00
* GAMMA 1.04000E-02 f 0.0000E+00
* SIGMA 1.33410E-02 f 0.0000E+00
Function 3: smear
AREA 22.209 f 7.519
* MEAN 3.5107 f 0.0000E+00
* GAMMA 8.90000E-04 f 0.0000E+00
* SIGMA 6.40090E-03 f 0.0000E+00
Function 4: smear
# AREA 2.7690 f 0.0000E+00
* MEAN 3.5107 f 0.0000E+00
* GAMMA 8.90000E-04 f 0.0000E+00
* SIGMA 1.31410E-02 f 0.0000E+00
Function 5: smear
AREA 24.942 f 7.488
* MEAN 3.5562 f 0.0000E+00
* GAMMA 2.06000E-03 f 0.0000E+00
* SIGMA 5.75930E-03 f 0.0000E+00
Function 6: smear
# AREA 3.2912 f 0.0000E+00
* MEAN 3.5562 f 0.0000E+00
* GAMMA 2.06000E-03 f 0.0000E+00
* SIGMA 1.47670E-02 f 0.0000E+00
Function 7: Chebyshev Polynomial of Order 0
NORM 1066.8 f 62.64
> 20. .



S10 -
c -


Minos

8.664
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

7.139
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

7.287
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

61.54


3.22 3.32 3.42 3.52 3.62

Mass ;rar-n~o


Figure 3-16. The fitted signal variable for the xx igrl~o mode shows the X c candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 3&779
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 178.00 / 178.00
Func Area Total/Fit 177.83 / 177.83


19-APR-2007 11:48
Fit Status 3
E.D.M. 9.676E-07


C.L.= 98.4%


Likelihood =
X2= 68.6 for
Errors
Function 1: near
AREA 4
* MEAN 3
*GAMMA 1.
*SI3MA 6.
Function 2: suear
#AREA 7
* MEAN 3
*GAMMA 1.
*SI3MA 1.
Function 3:sunear
AREA 1
* MEAN 3
*GAMMA 8.
* SI3MA 5.
Function 4: suear
#ARE EA 5
*GAMMA 8.
* SI3MA 8.
Function 5:eunear
AREA 1
* MEAN 3
*GAMMA 2.
* SI3MA 5.
Function 6: suear
#ARE EA 5
*GAMMA 2.
* SI3MA 9.


791.2
100 4 d.o.f.


Parabolic

7.856
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

4.163
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

4.761
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


Minos


~9.005
1.4148
04000E-(Li
42410E-C=3

.3552
1.4148
04000E-(Li
97990E-(Li

5.592
1.5107
90000E-04
43430E-(E.

,.3953
1.5107
90000E-04
91230E-X3

7.858
1.5562
06000E-(E.
20830E-(E.

,.0353
1.5562
06000E-(E.
83330E-(E.


7.696
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

3.925
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

4.496
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

27.54


8.359
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

4.474
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

5.094
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


Function 7: Chebyshev Polynomial of Order0O
NORM 196.31 + 28.61

> I0

15

10

c:5

LJ 0


+ 29.81


3.22 3.32 3.42 3.52 3.62

Mass K+K-prlro

Figure 3-17. The fitted signal variable for the K K ig~o mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 3&668
chicah+h-h0h0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 42.000 / 42.000
Func Area Total/Fit 41.9991i41.999


19-APR-2007 11:49
Fit Status 3
E.D.M. 6.800E-07


C.L.= 32.2%


Likelihood = 92.6
X2= 101.9 for 100 4 do~f,
Errors Parabolic
Function 1: near
AREA 1.6865 f 2.540
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 5.96390E-(E. f 0.0000E+00
Function 2: suear
# AREA 0.24594 f 0.0000E+00
* MEAN 3.4148 f 0.0000E+00
*GAMMA 1.04000E-(Li f 0.0000E+00
*SI3MA 2.66590E-(Li f 0.0000E+00
Function 3:sunear
AREA 4.0739 f 2.208
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 4.82390E-(E. f 0.0000E+00
Function 4: suear
#AREA 1.5486 f 0.0000E+00
* MEAN 3.5107 f 0.0000E+00
*GAMMA 8.90000E-04 f 0.0000E+00
* SI3MA 8. 84220E-(E. f 0.0000E+00
Function 5:eunear
AREA 2. 0422 f 1.954
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 5.22530E-(E. f 0.0000E+00
Function 6: suear
# AREA 0.35222 f 0.0000E+00
* MEAN 3.5562 f 0.0000E+00
*GAMMA 2.06000E-(E. f 0.0000E+00
* SI3MA 8.83600E-(E. f 0.0000E+00


Minos


2.171
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

1.949
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

1.657
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

15.68


2.946
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

2.493
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

2.275
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


Function
NORM









uJ C


7: Chebyshev Polynomial of Order0O
80.222 f 16.69


+ 17.76


3.22 3.32 3.42 3.52 3.62

Mass ppyn


Figure 3-18. The fitted signal variable for the ppprlo mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.














MINUIT Likelihood Fit to Plot 4&200
chicaKpiK~pi0 final. UpchiMs axis
File: *psi2s~chicanotherneutral proc_20070322_f ullIdata. ntp
Plot Area Total/Fit 815.00 / 815.00
Func Area Total/Fit 814.82 / 814.82


19-APR-2007 11:45
Fit Status 3
E.D.M. 7.349E-06


C.L.= 39.2%


+ 18.18
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 9.343
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 12.76
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00
+ 0.0000E+00

+ 34.13


Likelihood = 107.6
X2= 99.2 for 100 4 do~f.
Errors
Function 1: smear
AREA 320.24
* MEAN 3.4148
* GAMMA 1.04000E-02
* SIGMA 4.78890E-03
Function 2: smear
# AREA 81.433
* MEAN 3.4148
* GAMMA 1.04000E-02
* SIGMA 1.05210E-02
Function 3: smear
AREA 96.421
* MEAN 3.5107
* GAMMA 8.90000E-04
* SIGMA 4. 52650E-03
Function 4: smear
# AREA 44.915
* MEAN 3.5107
* GAMMA 8.90000E-04
* SIGMA 7.12470E-03
Function 5: smear
AREA 171.26
* MEAN 3.5562
* GAMMA 2.06000E-03
* SIGMA 4.59130E-03
Function 6: smear
# AREA 40.325
* MEAN 3.5562
* GAMMA 2.06000E-03
* SIGMA 9.53610E-03


Parabolic

18.24
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

9.393
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

12.88
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00


Minos

17.58
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

8.837
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

12.21
0.0000E+00
0.0000E+00
0.0000E+00

0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00

31.39


Function 7: Chebyshev Polynomial of Order 0
NORM 167.75 + 32.82


60-

40-


20


3.22 3.32 3.42 3.52 3.62

Mass Kn~Co a~


Figure 3-19. The fitted signal variable for the K~~r Ko a mode shows the Xc candidate
invariant mass distribution. The fit is described in the text.















+-00


3.22


3.32 3.42 3.52 3.62
Mass,


Figure 3-20. Data yields for the x x~
distribution is shown.


xrozo mode. The fitted Xc candidate invariant mass















40





30





S20




10


0L
3.22


3.32 3.42 3.52 3.62
Mass,


Figure 3-21. Data yields for the K K-wro a mode. The fitted Xc candidate invariant mass
distribution is shown.


K+ K zno ~O







































OL
3.22


3.32 3.42 3.52 3.62
Mass,


Figure 3-22.


Data yields for the pproro mode.
distribution is shown.


The fitted Xc candidate invariant mass


pp 7Co o










































0L
3.22


3.32 3.42 3.52 3.62
Mass .nT+n-77r o


Figure 3-23. Data yields for the x x~-rlxo mode. The fitted Xc candidate invariant mass
distribution is shown.


+- 0




































0L
3.22


3.32 3.42 3.52 3.62
Mass

Figure 3-24. Data yields for the K K-rlxo mode.
distribution is shown.


The fitted Xc candidate invariant mass


K' K g7o





































0L
3.22


3.32 3.42 3.52 3.62
Mass pp77ro


Figure 3-25.


Data yields for the ppy~ro mode. The fitted Xc candidate invariant mass
distribution is shown.


PP 11 o





















60C -c 10 lelu le 1.01 10.3
c2 Yield 211.6+ 15.4












20 --







3.22 3.32 3.42 3.52 3.62
Mass K7T~CO ar


Figure 3-26. Data yields for the K~7 K~o mode. The fitted Xc candidate invariant mass
distribution is shown.









CHAPTER 4
SYSTEMATIC UNCERTAINTY STUDIES

In this chapter we discuss the dominant factors which contribute to the uncertainty

in the measurements made in this analysis. The errors associated with the nature of the

experimental apparatus, and those related to the tools and methods emploi-v I will be

discussed and evaluated.

Several sources of systematic uncertainties in the branching fractions are investigated

and are listed in Table 4-1. Limited MC statistics in determining the reconstruction

efficiencies introduces effects at the level of 1.In' to 3.01' Systematic uncertainties

assigned for tracking are based upon a 0.'7' uncertainty associated with each charged

track present in the event. Uncertainty in the charged particle identification efficiency

introduces an uncertainty in the branching ratios of 0.;:' per pion and 1.;:' for each kaon

and proton track in the final state. Secondary vertexing used for Ko reconstruction in one

of the modes introduces an additional "' error. A universal uncertainty of 1 is assigned

to all the modes due to the trigger simulation, while a global "' uncertainty is attributed

to the transition photon reconstruction for each of the final states. In addition, the

systematic uncertainties for wro,rl efficiencies are !' for each wro,rl meson in the final state.

A universal error of ::' was assigned to all the modes attributed due to the uncertainty

in the number of d(2S) particles, determined according to the method described in [31].

The robustness of the fitting procedure was checked by systematically re-fitting the

Xc invariant mass plots using floating masses, widths, and resolutions. The maximum

deviations in the yields were taken as the systematic error components arising due to the

fittingf procedure. The maximum deviations occurred in cases when either the masses and

widths, or the masses and resolutions, or the resolutions and widths were simultaneously

unconstrained. These vary between 0.'7' and 5.' as listed in Table 4-1 for all the modes.

We studied the cut on the X2 of the kinematic constraint for systematic effects. In order

to do so, we study three modes with high statistics viz. xr+x-wro o, K~~r K~o o and









K(+K-o O~oand note the efficiency of the X2 < 25 cut in both data and MC respectively.

Fig 3-3 shows the distribution of this X2 Variable in data (blue points) and MC (solid

black) overlaid for the largest signal statistics mode xr+xr-xozo (the data is normalized

with respect to the MC). We note from this distribution that the profile of this cut

matches well between data and MC indicating the correct modelling of the cut in MC. Our

findings for the inefficiency of the X2 < 25 cut for the modes xr+r- ozro, K+K-o O~oand

K nx Kro are 16.'7' .(10.0' ), 13.n' (10.1 .) and 9.1 (6.;: )rsetvlyfrd. !)

In accordance with these findings, we assign a maximum systematic uncertainty of 4.0I' .

which is slightly higher than, yet consistent with the corresponding values found in the

previous line of analyses based on this subject [38, 39].

Another source of systematic error is due to the fact that the MC was all generated

using 4-body phase space ignoring the possibility of the presence of intermediate

resonances (discussed in chapter 5 on substructure). A possible presence of substructure

could lead to a different angular distribution of the final state particles compared to the

case when no intermediate resonances are present. In such a situation where substructure

is present, and is most often the case in real data, the use of a flat MC (4-body phase

space) to determine the efficiency of a given mode will lead to incorrect results.

To account for such effects, MC simulations were generated for the three high
statistics channels (; x-;o;o, K+K-o o;r, K~x K' o orepnigtowihw

observed various intermediate resonances in data. We generated MC for substructure

modes: fo(980)xo 0r 0 2(1270)xo0r 0 o o~~ and fo(980)r+xr- for the non-resonant mode

x~x-oo K(**K ro and fo(980)K+K- for the non-resonant mode K+K-o o ; rlr for

the non-resonant mode xr+;-rlo; K*oKo o, K**Ko; K**K wo, p*K Ko, K*oK~;r

and K1(1270)Ko for the non-resonant mode K~~ KO- o- using phase spac modl in

the CLEO-c detector configuration (Figs ??- ?? show evidence for the presence of such

intermediate resonance signals in data). We obtained the efficiencies of both the resonant

and non-resonant modes by fitting the Xc signals obtained from MC events with and










without substructure. These efficiencies are listed in Table 4-2. Based on the differences in

efficiencies between final states with and without intermediate resonances, and assuming

that there can he no "additional meI.~~ -, i,.1 resonances that can he more than 5(1' of

the signal [52], we estimate the systematic error to be between 3.5' and 7. 1' as shown

in Table 4-1 for the modes we studied. For the remaining modes, we conservatively

assign a 7.5' systematic error based on an assumption that up to '7 "' of our events

contain substructure, and that the difference in efficiency of these resonant events to the

non-resonant is no more than 1(I' .
























t-LnoCe
C`d;d;


000V3


















coxor









e 01
C:r~



simin



O~~crj~1


00 01



*r301 *rj





1 mi





Cr3~ 00


cr30 j


cr3~0100i


.cN 0d


O
0." ~ m
C~O O
O o 5Dk
~? cb~~
.U~~Om.,
c~ ~ X ~ cb
G;~ .~ F u_~t~
mO~~E"
NY~~jill ~ a, oO
H k ~) bD.~'
~cl ~ bD ~ cb
o ~ o hO~
cb C~
C~
k
-k ~ k
~ cb fi- cb
.k U1


o

cb
k
t;=r
Cb
Oo
og
cb
E









Table 4-2.











Mode




fo(980);r
f2(1270)7i
fo(980)xr
K+K-;o
K**K xT
fo(980)K
;+;-rlo
rlr
K(~; K ~
K(*oKO ;o
K(*oK x T
K*fK wT
K**x TK
p*K K
K~; K s
Ky (1270)


MC efficiencieS E (in ~) for all modes are shown. The detector configuration
CLEO implies combined CLEO-c and CLEO III average efficiencies. The
efficiencies of both the resonant and non-resonant modes were obtained by
fitting the Xc invariant mass distributions obtained from the corresponding MC
samples. We refer to this method of finding the efficiencies of the subtructure
modes as unclippedd" in contrast to the background subtraction procedure used
to determine these efficiencies for calculating the substructure branching
fractions (the method is discussed in Section 5.2). The following efficiency
numbers were used to determine the systematic uncertainties due to the model
dependence based on the procedure described in the text.
Xco Xcl Xc2 detector
a 17.6 17.5 17.6 CLEO
17.4 16.9 16.8 CLEO
a 18.9 CLEO-c
zro 17.6 CLEO-c
o aT 19.8 CLEO-c
t+r- 17.7 CLEO-c
ar 13.5 CLEO-c
o 13.4 CLEO-c
+K- 15.5 CLEO-c
9.68 CLEO-c
11.1 CLEO-c
x~o 10.3 11.2 10.3 CLEO
,K*oi K~~r 11.0 11.1 11.5 CLEO
', K*o K ~;To 9.50 CLEO
o, K** i rK~ 10.3 9.66 CLEO
~, K** K~~ro 10.4 9.44 CLEO
11.0 10.8 10.8 CLEO
x~o 10.7 CLEO-c
KO, 10.4 CLEO-c









CHAPTER 5
SEARCH FOR INTERMEDIATE STATES (SITBSTRITCTITRE)

In this chapter, we explore the possibility of the presence of intermediate resonances

leading to the same final states.

5.1 Introduction and Scope

Knowledge of the substructure of the 4-hody final states is an important aspect in

his analysis. It is much of concern in any multi-hody analysis as it has the ability to

change the efficiency for detecting a final state. This is particularly a pervasive issue in

substructure modes involving a heavy resonance, as the remaining particles in the decay

have a limited phase space, thus rendering them difficult to be detected and thus affecting

the efficiency of the mode. Light intermediate resonances also change the efficiency, but to

a lesser extent.

1\ore importantly, knowledge of the substructure tells us about the manner in which

the decay proceeds.

Given the limited statistics in this analysis, we restrict ourselves to looking for the

gross features of the substructure. We searched for possible substructure and found

many interesting possibilities including few clear signal while others being hints of new

possibilities to explore with more incoming data. Figfs 5-2 through 5-:31 show the rich

substructure plots. All of these are sideband subtracted plots with cuts on the respective

X c mass windows, as described in the following section.

5.2 Substructure Analysis

Having found the evidence of the presence of intermediate states in most of the

our final states under study, we perform an analysis of such intermediate resonance and

states in three of our parent modes with decent statistics, xr+r-~ro 0o, K+K-~ro o and

K K~~~~o 0 As illustrated in Figure 5-1, the signal regions for Xo, Xcl, and Xc2 are

3.:370-:3.470 GeV/c2, :3.490-:3.5:35 GeV/c2 and :3.5:35-:3.590 GeV/c2, Tespectively. One-sided

sidebands of :3.300-:3.:360 GeV/c2, :3.470-3.490 GeV/c2and :3.590-3.625 GeV/c2, Tespectively,










are subtracted. Although the subtraction is small, it is necessary to avoid spurious

reflections in the substructure mass plots. Subsequently, we make various invariant

mass combinations of two and three mesons occurring in each parent mode final state

and search for significant humps in the resultant distributions. We calculate the signal

significance by estimating the ratio of the number of events in the signal invariant mass

distributions to their standard deviations. We claim signals for only those cases where

we observe a signal significance of > 4 a, and quote results only for those invariant mass

combinations in which we observe possibilities beyond the 2 and :3 hody phase space.

After identifying the intermediate states, we fit the distributions with Breit-Wigner

functions for each known intermediate state using its fixed mass and width listed in [:30],

and add an additional third order polynomial function to incorporate the backgrounds.

We obtain the efficiencies (e') for the intermediate states by generating 20,000 events

(10,000 events each for the CLEO-c and CLEO III detector configurations) using the

PHSP model of EvtGen. All results reported in the following are first observations of these

intermediate states. We discuss the results below in detail.

1. Intermediate states in XJ xx r+-roro final state:

The four 2-hody invariant mass combination (m,+,-, m,+,o, m,,n and m,ozo)

fitted distributions for the Xeo state in data are shown in Figures 5-2 through 5-5.

We find the evidence of clear signals of p* in Figures 5-4 and 5-5. There are signs

of fo(980) and f2(1270) states in Figures 5-2 and 5-3, which do not meet the 4 a

significance criterion. Similarly, we find the prominent p* signals in the case of Xet

and Xc2 aS Seen in Figures 5-6 through 5-9. Their yields and efficiencies e', listed in

Table 5-1, are used as inputs to the final branching fraction calculations.

2. Intermediate states in XJ iK+K-~ro a final state:

Various invariant mass combination (mK+K-, mK+,ro, mKe-gO and m,ozo) fitted

distributions for the Xeo and X,1 states in data are shown in Figures 5-10 through









5-15. These indicate the presence of intermediate resonances 4, fo(1500), fo(1710),

fo(980) and K**, none of which are significant enough to claim signals.

3. Intermediate states in Key iK~~rK P~o final state:

Figures 5-16 through 5-31 show various invariant mass combination (mK x+, Ex wo,

mx+r~KO, ,K wro, mK xro and mK xfxo)r 0 fitted distributions for the Xo, Xcl and Xc2
states. Clear signals of p*, and K* are seen in some of the modes listed in Table 5-1,

and we see a hint of K1(1270) in Xe K~~r xo distribution among others.

4. Intermediate states in XJ ixx Oxo~r final state:

Figures 5-32,5-33 show the presence of rlr resonance substructure in the invariant

mass combinations of xr+xr-wo for Xeo and Xc2. We forgo the analysis of these

substructure modes as they have been presented in our earlier work [38].

Systematic uncertainties for these intermediate resonance branching fractions include

the common sources of errors for the respective non-resonant final states whose values are

listed in Table 4-1.

















cb~

bDt;

O
oO~
Xmc~
O
~cbcb
~vk
C~ m
bD~~
~am
~ Ea
C~cb~
c~m,
~ae
c~-b
~ cb ~


~~ C~
C~
e 5D




.~ k cb
m

cc~
cb





mg"
~'EC
k
a
~~cb
kO~
k O
coam
cb
k
Vi~

O~c~
E UO ha

k~~

c~kC~
O
~ c~0 ~
ke
c~a
em~
m
c~ cb

r O




v~`w

.~ O O
og~




cb
-d "

cb~
r
m
a bD~





Ln


e
cb


00L~00 4
cocded 4 9?Cq 0


Cr3Cr3~3
cdcdd


~3~3~
cdcd~


Lnn~ C30



a ~ ar~


rTll


co $









200


150 -






~100--






50 -..-







3.30 3.40 3.50 3.60
Mass X, '' -rr no a7~



Figulre 5-1. Figure elucidates signal and sideband regions for the Xc states. Arrows mark
the signal regions whereas the shaded areas represent the one-sided sidebands.














MINUIT X2 Fit to Plot 3&102
chic->h+h-h~h0 final ml2 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 1543 7 / 1516 7
Func Area Total/Flt 1628 5 / 1499 9

X2= 70.3 for 69 6 dof.,
Errors Parabolic
Function 1: Brelt-Wlgner
AREA 83 450 f 21 45 -
;MEAN 0 98000 f 0 0000E+00 0
;WIDTH 7 00000E-02 f 0 0000E+00 O
Function 2: Brelt-Wlgner
AREA 96 940 f 36 03 -
;MEAN 12754 f 0 0000E+00 0
;WIDTH 0 18510 f 0 0000E+00 O
Function 3: Chebyshev Polynornial of Order 3
NORM 450 84 f 28 08 -
CHEBO1 -1 0813 f 01650 0
CHEBO2 0 15533 & 67882E-02 0
CHEBO3 014066 f 01076 0


1-APR-2007 11:53
Fit Status 3
EDM 1288E-06
C.L.= 24.7%
Minos

21 50 + 21 49
)0000E+00 + 0 0000E+00
)0000E+00 + 0 0000E+00

36 07 + 36 07
)0000E+00 + 0 0000E+00
)0000E+00 + 0 0000E+00

28 02 + 28 02
)0000E+00 + 0 0000E+00
)0000E+00 + 0 0000E+00
)0000E+00 + 0 0000E+00


Figure 5-2. Figure shows data for the decay Xo xx xr~-r~o mode. Invariant mass
combination of x xr- is shown.


1.2 Ma.2 _~ 3.2













MINUIT X2 Fit to Plot 3&1
chic->h+h-h~h0 final m34 axis
File: *psl2s_chicanotherneutralproc_20070:
Plot Area Total/Flt 1543 7 / 1526 7
Func Area Total/Flt 1550 2 / 1481 2

X2= 77.1 for 72 5 dof.,
Errors Para
Function 1: Brelt-Wlgner
AREA 73 346 f 20
;MEAN 0 98000 f 000C
= WIDTH 7 00000E-02 f 0 0
Function 2: Chebyshev Polynornial of Ord~
NORM 409 30 f 22
CHEBO1 -1 0527 f 011
CHEBO2 -0 18675 7 93
CHEBO3 0 23745 f 8 46


03


322_fulldata ntp


1-APR-2007 11:53
Fit Status 3
EDM 2 600E-06
C.L.= 18.8%


Ibolic

76
)00E+00
)00E+00
er 3
39
195
~02E-02
j60E-02


Minos

20 75 + 20 77
0 0000E+00 + 0 0000E+00
0 0000E+00 + 0 0000E+00


22 39
01214
8 2852E-02
8 5218E-02


22 40
01181
76152E-02
84374E-02


60





O
\ 40






20


0.2 1.2 Ms o2p 3.2


Figure 5-3. Figure shows data for the decay co
combination of xro o is shown.


i T T jT-roo mode. Invariant mass













MINUIT X2 Fit to Plot 3&140
chic->h+h-h~h0 final m23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 3087 3 / 3063 7
Func Area Total/Flt 2888 6 / 2998 3

X2= 104.2 for 67 5 d.o.f.,
Errors Parabolic
Function 1: Brelt-Wlgner
AREA 69712 f 5578 -
;MEAN 0 77580 f 0 0000E+00 0
= WIDTH 0 15030 f 0 0000E+00 O
Function 2: Chebyshev Polynornial of Order 3
NORM 492 60 f 36 88 -
CHEBO1 -1 4373 f 01937 0
CHEBO2 -0 98754 f 01634 0
CHEBO3 0 36366 f 01009 0
2001 1 I:: :


1-APR-2007 11:53
Fit Status 3
EDM 3 400E-06
C.L.=0.635E-01%


Minos

56 54
)0000E+00
)0000E+00

37 62
)2099
)1790
)1058


56 57
00000E+00
0 0000E+00

37 70
01913
01557
01011


150





O
S100






50


0.2 1.2 M s 7~2 3.2


Figure 5-4. Figure shows data for the decay Xo xx xr~-r~o mode. Invariant mass
combination of xr-wo is shown.













MINUIT X2 Fit to Plot 3&120
chic->h+h-h~h0 final ml3 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 3087 3 / 3066 7
Func Area Total/Flt 2998 9 / 3043 2

X2= 69.2 for 67 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 661 35 f 56 80 56 81
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 557 83 f 38 73 38 77
CHEBO1 -1 2556 f 01763 01846
CHEBO2 -0 74947 f 0 1354 O 1447
CHEBO3 0 37237 f 9 1427E-02 9 3745E-02
2001 1 I:: : :


1-APR-2007 11:53
Fit Status 3
EDM 1076E-07
C.L.= 24.9%


56 81
00000E+00
0 0000E+00

38 77
01695
0 1276
89699E-02


150





O
S100






50






0


1.2 M s,2 3.2


Figure 5-5. Figure shows data for the decay Xo xx xr~-r~o mode. Invariant mass
combination of x x~o is shown.













MINUIT X2 Fit to Plot 3&120
chic->h+h-h~h0 final ml3 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 1038 0 / 1031 2
Func Area Total/Flt 962 62 / 1064 9

X2= 81.6 for 67 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 355 66 f 42 12 41 92
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 93 080 f 2938 3102
CHEBO1 -2 1647 f 1 132 1 740
CHEBO2 -2 9214 f 1274 2036
CHEBO3 0 39258 f 0 3237 04943


1-APR-2007 11:53
Fit Status 3
EDM 1351E-06
C.L.= 4.8%


41 90
00000E+00
0 0000E+00

31 07
0 9341
1030
0 3318


80










S 40










0


1.2 M s,2 3.2


Figure 5-6. Figure shows data for the decay Xct xx xr~-r~o mode. Invariant mass
combination of x x~o is shown.













MINUIT X2 Fit to Plot 3&140
chic->h+h-h~h0 final m23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 1038 0 / 1028 2
Func Area Total/Flt 983 18 / 1029 4

X2= 44.2 for 67 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 356 63 f 40 90 40 98
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 11542 f 3394 3407
CHEBO1 -1 1067 f 0 8079 1 081
CHEBO2 -1 9257 f 0 9284 1 314
CHEBO3 0 56633 f 0 3063 03644


1-APR-2007 11:53
Fit Status 3
EDM 1097E-05
C.L.= 95.7%


40 87
00000E+00
0 0000E+00

3414
06677
07254
0 2831


80










O
S40











0


1.2 M s,2 3.2


Figure 5-7. Figure shows data for the decay Xct xx xr~-r~o mode. Invariant mass
combination of xr-wo is shown.













MINUIT X2 Fit to Plot 3&120
chic->h+h-h~h0 final ml3 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 1810 6 /1801 1
Func Area Total/Flt 1744 9 / 1755 9

X2= 62.7 for 72 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 51932 f 3873 3873
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 271 02 f 19 86 19 87
CHEBO1 -0 83650 f 0 1383 O 1414
CHEBO2 -1 0741 f 01562 01670
CHEBO3 0 49374 f 01058 01068
1501 I ,


1-APR-2007 11:54
Fit Status 3
EDM 9 161E-09
C.L.= 62.8%


38 73
00000E+00
0 0000E+00

19 87
0 1362
01469
01055


0.2 1.2 M s 7~2 3.2


Figure 5-8. Figure shows data for the decay Xc2 0 0r~-~or mode. Invariant mass
combination of x x~o is shown.













MINUIT X2 Fit to Plot 3&140
chic->h+h-h~h0 final m23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 1810 6 / 1805 1
Func Area Total/Flt 1708 6 / 1745 3

X2= 74.6 for 71 5 dof.
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 51262 f 3999 3999
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 259 62 f 2155 2157
CHEBO1 -1 1221 f 01809 01885
CHEBO2 -1 1514 f 01877 02032
CHEBO3 0 42425 f 01162 01183
1201 I ,


1-APR-2007 11:54
Fit Status 3
EDM 1057E-07
C.L.= 22.0%


39 99
00000E+00
0 0000E+00

21 57
01752
01749
01151


1.2 M s,2 3.2


Figure 5-9. Figure shows data for the decay Xc2 0 0r~-~or mode. Invariant mass
combination of xr-wo is shown.














MINUIT X2 Fit to Plot 3&102
chic->h+h-h~h0 final ml2 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 187 33 / 187 33
Func Area Total/Flt 187 90 / 185 45

X2= 46.1 for 81 7 dof.
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 0 40560 f 0 5288 O 5316
;MEAN 1 0195 f 0 0000E+00 00000E+00
= WIDTH 4 26000E-03 f 0 0000E+00 O 0000E+00
Function 2: Brelt-Wlgner
AREA 10 777 f 10 22 10 26
;MEAN 15070 f 0 0000E+00 00000E+00
= WIDTH 0 10900 f 0 0000E+00 O 0000E+00
Function 3: Brelt-Wlgner
AREA 30 304 f 1424 1425
;MEAN 1 7140 f 0 0000E+00 00000E+00
= WIDTH 0 14000 f 0 0000E+00 O 0000E+00
Function 4: Chebyshev Polynornial of Order 3
NORM 56 597 f 12 24 12 29
CHEBO1 -7 06859E-02 f 0 5618 O 4986
CHEBO2 -0 56756 f 0 5337 O 6432
CHEBO3 0 31359 f 0 4734 O 4279


1-APR-2007 12:42
Fit Status 3
EDM 1098E-06
C.L.= 99.6%


0 5318
00000E+00
0 0000E+00

10 26
00000E+00
0 0000E+00

1425
00000E+00
0 0000E+00

12 29
06220
0 4651
0 5202


1.3 1.8 2.3 2.8
Mass K K<-


Figure 5-10. Figure shows data for the decay Xo K K+-7ro aO mode. Invariant mass
combination of K K- is shown.













MINUIT X2 Fit to Plot 3&120
chic->h+h-h~h0 final ml3 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 376 67 / 377 33
Func Area Total/Flt 338 69 / 336 35

X2= 67.6 for 63 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 47 997 f 13 32 13 30
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 68 384 f 37 57 36 59
CHEBO1 0 96576 f 1743 1145
CHEBO2 -1 9178 f 1 725 3594
CHEBO3 1 1772 f 1 125 O 7450
30 .


1-APR-2007 12:42
Fit Status 3
EDM 7 775E-07
C.L.= 18.2%


13 29
00000E+00
0 0000E+00

36 62
3526
1 102
2 259


20





10






10


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-11. Figure shows data for the decay Xo K K+-wro a mode. Invariant mass
combination of K xro is shown.













MINUIT X2 Fit to Plot 3&1.
chic->h+h-h~h0 final m23 axis
File: *psl2s_chicanotherneutralproc_20070:
Plot Area Total/Flt 376 67 / 376 67
Func Area Total/Flt 290 66 / 350 15

X2= 38.6 for 65 5 dof.,
Errors Para
Function 1: Brelt-Wlgner
AREA 27510 f 12
;MEAN 0 89166 f 000C
= WIDTH 5 08000E-02 f 0 0
Function 2: Chebyshev Polynornial of Ord~
NORM 31 739 f 19
CHEBO1 53778 f 47
CHEBO2 -6 5823 f 49
CHEBO3 4 8120 f 3 7
24 o..,- n .


21

322_fulldata ntp


1-APR-2007 12:42
Fit Status 3
EDM 1129E-06
C.L.= 98.6%


Ibolic

00
)00E+00
)00E+00
er 3
93
61
99
06


Minos

12 00
0 0000E+00
0 0000E+00

19 34
2923
12 36
2 278


11 99
00000E+00
0 0000E+00

1934
11 60
3026
9 022


16








i, 8




05


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-12. Figure shows data for the decay Xo K K+-wro a mode. Invariant mass
combination of K-wro is shown.













MINUIT X2 Fit to Plot 3&103
chic->h+h-h~h0 final m34 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 188 33 / 188 33
Func Area Total/Flt 184 44/180 12

X2= 63.0 for 76 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 26 679 f 9941 9940
;MEAN 0 98000 f 0 0000E+00 00000E+00
= WIDTH 7 00000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 73 039 f 11 57 11 59
CHEBO1 -0 46179 f 0 3273 O 3482
CHEBO2 -0 25277 f 0 2492 O 2797
CHEBO3 0 39153 f 0 2574 O 2653
20:::::::::::::::


1-APR-2007 12:42
Fit Status 3
EDM 1271E-06
C.L.= 73.8%


9943
00000E+00
0 0000E+00

11 57
0 3159
02279
0 2563


0.2 0.7 1 .2 1.7 2.2
MOSS ro ar


Figure 5-13. Figure shows data for the decay Xo K K+-wro a mode. Invariant mass
combination of xro o is shown.













MINUIT X2 Fit to Plot 3&120
chic->h+h-h~h0 final ml3 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 82 000 / 80 000
Func Area Total/Flt 102 43 / 99 285

X2= 30.4 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 25 585 f 8 111 8 117
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 20 148 f 19 58 19 67
CHEBO1 -3 85384E-02 f 2 859 2 573
CHEBO2 -1 4241 f 2572 00000E+00
CHEBO3 -0 15396 f 1 448 1 882


1-APR-2007 12:42
Fit Status 3
EDM 1466E-05
C.L.= 99.9%


8 120
00000E+00
0 0000E+00

19 67
0 0000E+00
1 328
0 0000E+00


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-14. Figure shows data for the decay Xc K K-wro a mode. Invariant mass
combination of K xro is shown.




































II


I








II

II






. I . I . I . I . I


MINUIT X2 Fit to Plot 3&121
chic->h+h-h~h0 final m23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_2070322_full data ntp
Plot Area Total/Flt 82 000 / 82 000
Func Area Total/Flt 121 77 /101 89

X2= 22.9 for 65 5 dof.,
Errors Parabolic
Function 1: Brelt-Wlgner
AREA 7 8346 f 6 416 -
;MEAN 0 89166 f 0 0000E+00 0
= WIDTH 5 08000E-02 f 0 0000E+00 O
Function 2: Chebyshev Polynornial of Order 3
NORM 39730 f 1655 -
CHEBO1 9 62190E-03 f 1 237 -
CHEBO2 -0 31267 f 0 6796 -
CHEBO3 -7 86260E-03 f 0 6918 O


1V


1-APR-2007 12:42
Fit Status 3
EDM 4 746E-06
C.L.=100.0%


Minos

6 415
)0000E+00
)0000E+00

16 53
1 090
1 130
)6474


6 418
00000E+00
0 0000E+00

1654
1 690
04935
0 8910


0.2 0.7 1.2Ms 1 /


2.2 2.7


Figure 5-15. Figure shows data for the decay Xc K K-wro a mode.
combination of K-wro is shown.


Invariant mass













MINUIT X2 Fit to Plot 4&102
chic->KplKOpl0 final rnl2 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 360 67 / 360 67
Func Area Total/Flt 374 83 / 315 69

X2= 85.1 for 72 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 52 469 f 12 06 12 06
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 11305 f 2311 2304
CHEBO1 -0 47695 f 0 3324 02868
CHEBO2 -0 29864 f 0 3282 O 4049
CHEBO3 0 47747 f 0 2834 O 2437
30 ., ~ .


2-APR-2007 09:19
Fit Status 3
EDM 2 707E-06
C.L.= 6.7%


12 06
00000E+00
0 0000E+00

23 04
03995
02759
0 3418


20





10






10


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass KwT





Figure 5-16. Figure shows data for the decay Xo K~~rP~~o mode. Invariant mass
combination of K~~r is shown.













MINUIT X2 Fit to Plot 4&107
chic->KplKOpl0 final rn24 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 360 67 / 360 67
Func Area Total/Flt 384 10 / 316 17

X2= 58.5 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 179 74 f 22 67 22 70
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 94 962 f 3636 3659
CHEBO1 0 29419 f 0 5961 O 9202
CHEBO2 0 40089 f 0 2862 O 4557
CHEBO3 0 42407 f 0 2372 03441
50 .. ,


2-APR-2007 09:20
Fit Status 3
EDM 8 994E-06
C.L.= 53.2%


22 67
00000E+00
0 0000E+00

36 61
04592
0 2138
01938


a 25







0


0.2 0.7 1.2 1.{,~ 2.2 2.7


Figure 5-17. Figure shows data for the decay Xo K~~rP~~o mode. Invariant mass
combination of xr~xo is shown.













MINUIT X2 Fit to Plot 4&106
chic->KplKOpl0 final rn23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 360 67 / 360 67
Func Area Total/Flt 344 24 / 309 57

X2= 74.7 for 62 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 64146 f 12 81 12 81
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 81 397 f 28 05 27 95
CHEBO1 -1 0436 f 0 6825 06071
CHEBO2 -0 98490 f 0 7674 1 155
CHEBO3 -0 29736 f 0 4206 O 3882


2-APR-2007 09:20
Fit Status 3
EDM 4 537E-08
C.L.= 5.7%


12 82
00000E+00
0 0000E+00

27 95
08627
0 5741
0 5133


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass rKs





Figure 5-18. Figure shows data for the decay Xo K~~rP~~o mode. Invariant mass
combination of x*~Ko is shown.













MINUIT X2 Fit to Plot 4&105
chic->KplKOpl0 final rnl4 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 360 67 / 360 67
Func Area Total/Flt 297 11 / 311 84

X2= 67.8 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 42 488 f 10 04 10 03
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 54 583 f 1880 1868
CHEBO1 20549 f 1534 1183
CHEBO2 -2 3968 f 1290 1929
CHEBO3 2 1629 f 1 140 O 8744
24 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 2 732E-08
C.L.= 22.8%


10 03
00000E+00
0 0000E+00

1868
2200
09599
1 643


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-19. Figure shows data for the decay Xo K~~rP~~o mode. Invariant mass
combination of K~~ro is shown.













MINUIT X2 Fit to Plot 4&103
chic->KplKOpl0 final rn34 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 360 67 / 359 67
Func Area Total/Flt 272 58 / 319 70

X2= 64.9 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 39 977 f 11 14 11 12
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 31 077 f 1892 1822
CHEBO1 46491 f 4107 2532
CHEBO2 -5 6597 f 4264 9886
CHEBO3 42129 f 3177 1 960
24 ., ~ .


2-APR-2007 09:19
Fit Status 3
EDM 1744E-05
C.L.= 31.1%


11 16
00000E+00
0 0000E+00

1814
9389
2593
7259


0.2 0.7 1.2as 1.7~r 2.2 2.7






Figure 5-20. Figure shows data for the decay Xo K~~rP~~o mode. Invariant mass
combination of Ko rO is shown.













MINUIT X2 Fit to Plot 4&106
chic->KplKOpl0 final rn23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 / 139 75
Func Area Total/Flt 146 59 / 135 13

X2= 29.0 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 25 239 f 8157 8167
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 37 239 f 20 97 20 66
CHEBO1 0 64633 f 1675 1147
CHEBO2 -0 77267 f 1 122 2 450
CHEBO3 0 47506 f 0 9030 O 6437
15 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 3 545E-05
C.L.=100.0%


8137
00000E+00
0 0000E+00

20 77
3447
07236
1 790


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass rKs





Figure 5-21. Figure shows data for the decay Xc K~~rP~~o mode. Invariant mass
combination of x*~Ko is shown.













MINUIT X2 Fit to Plot 4&105
chic->KplKOpl0 final rnl4 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 /141 75
Func Area Total/Flt 165 48 / 118 06

X2= 31.3 for 59 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 29 293 f 7 746 7 746
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 53 989 f 18 92 18 89
CHEBO1 -1 1985 f 1 051 1 093
CHEBO2 7 95039E-02 f 0 4187 O 6256
CHEBO3 -0 58882 f 0 5606 O 6077
20 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 2 968E-05
C.L.= 99.4%


7750
00000E+00
0 0000E+00

18 92
1 149
0 3185
05892


r 10






0D


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-22. Figure shows data for the decay Xc K~~rP~~o mode. Invariant mass
combination of K~~ro is shown.













MINUIT X2 Fit to Plot 4&103
chic->KplKOpl0 final rn34 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 /141 75
Func Area Total/Flt 118 98 / 134 39

X2= 35.4 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 16 911 f 7170 7168
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 19 744 f 19 38 18 88
CHEBO1 44219 f 6248 3870
CHEBO2 -2 9805 f 4159 00000E+00
CHEBO3 26189 f 3415 2058
12 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 1109E-05
C.L.= 99.5%


7158
00000E+00
0 0000E+00

18 95
00000E+00
2088
00000E+00


8






d 4



0









-4


0.2 0.7 1.2as 1.7~r 2.2 2.7


Figure 5-23. Figure shows data for the decay Xc K~~rP~~o mode. Invariant mass
combination of Ko rO is shown.













MINUIT X2 Fit to Plot 4&102
chic->KplKOpl0 final rnl2 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 /141 75
Func Area Total/Flt 131 18 /131 01

X2= 42.9 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 37 941 f 8541 8542
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 23 954 f 14 89 14 75
CHEBO1 10521 f 2216 1603
CHEBO2 -1 5203 f 1 784 4521
CHEBO3 0 34163 f 1 134 09089
24 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 1598E-07
C.L.= 95.3%


8542
00000E+00
0 0000E+00

14 75
4833
1 113
2239


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass KwT


Figure 5-24. Figure shows data for the decay Xc K~~rP~~o mode. Invariant mass
combination of K~~r is shown.













MINUIT X2 Fit to Plot 4&107
chic->KplKOpl0 final rn24 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 / 140 75
Func Area Total/Flt 148 24 /156 35

X2= 25.8 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 79 494 f 1647 1689
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 19 556 f 40 83 46 76
CHEBO1 -2 0279 f 8032 00000E+00
CHEBO2 -1 3056 f 5090 00000E+00
CHEBO3 -0 37665 f 2 480 O 0000E+00
20 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 1032E-05
C.L.=100.0%


1686
00000E+00
0 0000E+00

46 73
00000E+00
00000E+00
00000E+00


cu10





0


0.2 0.7 1.2 1.{,~ 2.2 2.7


Figure 5-25. Figure shows data for the decay Xc K~~rP~~o mode. Invariant mass
combination of xr~xo is shown.













MINUIT X2 Fit to Plot 4&109
chic->KplKOpl0 final rnl24 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 141 75 / 140 75
Func Area Total/Flt 123 58 / 121 28

X2= 34.1 for 56 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 12255 f 6949 6886
;MEAN 12730 f 0 0000E+00 00000E+00
= WIDTH 9 00000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 29 038 f 57 70 52 77
CHEBO1 17322 f 7467 00000E+00
CHEBO2 -0 84253 f 3 884 O 0000E+00
CHEBO3 -9 28473E-02 f 1 312 O 0000E+00
121 u I ,


2-APR-2007 09:20
Fit Status 3
EDM 1256E-05
C.L.= 96.7%


6885
00000E+00
0 0000E+00

52 62
00000E+00
00000E+00
00000E+00


1.2 MsKao2.2 3.2


K(~x K~o mode. Invariant mass


Figure 5-26. Figure shows data for the decay Xct i
combination of K~~r xo is shown.













MINUIT X2 Fit to Plot 4&102
chic->KplKOpl0 final rnl2 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 209 14 / 206 14
Func Area Total/Flt 212 32 / 190 44

X2= 37.7 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 62 969 f 10 53 10 53
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 47 467 f 21 30 21 15
CHEBO1 1 06754E-02 f 1 040 07694
CHEBO2 -0 65473 f 0 8572 1 513
CHEBO3 0 54258 f 0 6955 O 5162
30 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 8 614E-06
C.L.= 98.9%


10 53
00000E+00
0 0000E+00

21 16
1 728
05975
1 153


20





10






a 0


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass KwT


Figure 5-27. Figure shows data for the decay Xc2 K~~r K~o mode. Invariant mass
combination of K~~r is shown.














MINUIT X2 Fit to Plot 4&107
chic->KplKOpl0 final rn24 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 209 14 / 209 14
Func Area Total/Flt 242 05 / 202 06

X2= 34.1 for 75 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 62 861 f 15 90 15 90
;MEAN 0 77580 f 0 0000E+00 00000E+00
= WIDTH 0 15030 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 75 261 f 24 21 24 29
CHEBO1 0 62003 f 0 3834 05376
CHEBO2 0 20165 f 0 3070 O 4422
CHEBO3 0 62957 f 0 1711 O 2092


2-APR-2007 09:21
Fit Status 3
EDM 1635E-06
C.L.=100.0%


15 90
00000E+00
0 0000E+00

24 25
03068
0 2391
0 1565


16









cu
r
(D
d 8
r,

c
a,
15







o


0.2 0.7 1.2 1.{,~ 2.2 2.7


Figure 5-28. Figure shows data for the decay Xc2 K~~r K~o mode. Invariant mass
combination of xr~xo is shown.













MINUIT X2 Fit to Plot 4&106
chic->KplKOpl0 final rn23 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 209 14 / 209 14
Func Area Total/Flt 189 14 /195 91

X2= 31.5 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 51141 f 9788 9795
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 29 952 f 18 97 18 73
CHEBO1 13182 f 2502 1715
CHEBO2 -2 3475 f 2300 6016
CHEBO3 10860 f 1477 1025
30 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 7 349E-06
C.L.= 99.9%


9776
00000E+00
0 0000E+00

18 78
5842
1411
3407


20





10




0D


0.2 0.7 1 .2 1 .7 2.2 2.7
Mass rKs


Figure 5-29. Figure shows data for the decay Xc2 K~~r K~o mode. Invariant mass
combination of x*~Ko is shown.













MINUIT X2 Fit to Plot 4&105
chic->KplKOpl0 final rnl4 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 208 14 / 205 14
Func Area Total/Flt 184 86 / 181 11

X2= 42.3 for 65 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 39 325 f 8 733 8 731
;MEAN 0 89166 f 0 0000E+00 00000E+00
= WIDTH 5 08000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 38 669 f 17 96 17 69
CHEBO1 1 3046 f 1 670 1 188
CHEBO2 -1 3614 f 1 236 2 218
CHEBO3 1 2616 f 1 076 O 7696
20 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 7 922E-06
C.L.= 96.0%


8726
00000E+00
0 0000E+00

17 67
2878
08448
1 845


10
O





10


0.2 0.7 1.2Ms 1.{a 2.2 2.7


Figure 5-30. Figure shows data for the decay Xc2 K~~r K~o mode. Invariant mass
combination of K~~ro is shown.













MINUIT X2 Fit to Plot 4&103
chic->KplKOpl0 final rn34 axis
F ie: *psl2s_ch ica nothe rne utralIproc_20070322_full data ntp
Plot Area Total/Flt 209 14 / 209 14
Func Area Total/Flt 184 62 / 182 55

X2= 41.5 for 70 5 dof.,
Errors Parabolic Minos
Function 1: Brelt-Wlgner
AREA 38 659 f 8957 8953
;MEAN 0 89610 f 0 0000E+00 00000E+00
= WIDTH 5 07000E-02 f 0 0000E+00 O 0000E+00
Function 2: Chebyshev Polynornial of Order 3
NORM 40 555 f 14 76 14 70
CHEBO1 0 58419 f 0 9306 O 7034
CHEBO2 -1 1703 f 0 9126 1 406
CHEBO3 0 34263 f 0 5180 O 4077
24 ., ~ .


2-APR-2007 09:20
Fit Status 3
EDM 2 699E-06
C.L.= 99.0%


8959
00000E+00
0 0000E+00

14 68
1 404
0 6761
0 7518


0.2 0.7 1.2as 1.7~r 2.2 2.7


Figure 5-31. Figure shows data for the decay Xc2 K~~r K~o mode. Invariant mass
combination of Ko rO is shown.












File: *psi2s_chicanotherneutralproc_20070322_fuldt~t
ID IDB Symb Date/Time Area Mean
3 107 1 070402/1503 76.00 1.623



chicah+h-h0h0 final. ml24 axis


R.M.S.
0.9000


30





20





10





0


1.0 2.00r+r~~ 3.0


Figure 5-32. Figure shows data for the decay Xc i xr~-rlxo mode. Invariant mass
combination of x x~-wro for Xeo i xr~-rlxo is shown. We do not discuss this
state any further as it has been studied in our earlier work [38].












chic h+h-h0h0 final. ml24 axis
IIII IIII IIII I
Xc2 L'L 1:


IIIIIl..I ...1.I
O 1.0 2.00rr~r~;~ 3.0


File: *psi2s_chicanotherneutralproc_20070322_fuldt~t
ID IDB Symb Date/Time Area
3 107 1 070402/1504 27.43


Mean
2.193


R.M.S.
0.4698


8 1-


Figure 5-33. Figure shows data for the decay Xc i xr~-rlxo mode. Invariant mass
combination of x x~-wro for Xc2 i 0r~-lr iS Shown. We do not discuss this
state any further as it has been studied in our earlier work [38].


ia


nn









CHAPTER 6
MEASUREMENT RESULTS

In this chapter, we convert the observations and analyses of data (yields and

efficiencies ) from previous chapters into meaningful measurements of physical quantities

of interest. We arrive at branching fractions and upper limits wherever applicable for the

seven modes under study.

The systematic uncertainties listed in Table 4-1 were all added in quadrature. The

ones due to the branching fractions of ~(2S) i acJ [31] are quoted separately. For most

of the final states, we convert the yields in Tables 3-3 and 5-1 to branching fractions

usmng:


Yield
B(xe> i) = (6-1)
Ngb(2S) ei B( (2S)i 7%c ) [31]
where NVyieta yield in data; Ngb(2S) number of ~(2S) = 3.08 x 106; e E liSted in

Table 3-3 for four-hadron modes, or e' listed in Table 5-1 for substructure modes, and i

represents a particular four-hadron or substructure decay mode.

To calculate the branching fractions for the inclusive four-hadron final states for

the modes xr+xr-xozo and K~~r Ko a which have rich substructure, we use a modified

procedure. Since the p~~r xo resonant mode yields clearly dominate the four-hadron

final state yields for the x x~-xrozo mode (Tables 3-3 and 5-1), we use the efficiency, E Of

the p~; ;o sub-mode listed in Table 5-1 and equation 6-1 to determine the ;+;-;o;o

four-hadron branching fraction. These efficiencieS E were obtained by fitting the Xc

signals in substructure simulations using the same fitting procedure as that used for the

four-hadron signal simulations



1 The efficiency e' is lower than E Since the sideband subtraction procedure used for
obtaining the efficiency e' results in some loss of efficiency.










To calculate the K~~r Ko a branching fraction, we modify the procedure by taking

into account that this channel has many intermediate resonances (Table 5-1). We replace
th~e 1rat~io N~i eza/ e4C in? equa~tio n 6 1 wit an-'' eff ci nc corrected- yield'- (Y: K' x xo

by adding the individual efficiency corrected contributions due to all resonant and

non-resonant channels computed as:

Yield .5yil
YK xfrKoxro = K foo k 62
EK xfrKoxro k=1 tk (I EK xrfKoxro (

where k runs over the substructure modes we consider, K*oK~ro, K*oK~~r K**K ro,

I*iTK** K), and p*K K)

The branching fractions thus obtained, and taking into account the systematic

uncertainties from C'!. Ilter 4, we get the results summarized in Table 6-1. Where we do

not find evidence of a signal, we present a CII' C.L. upper limit by determining the value

that includes CII' of the probability density function (p.d.f) obtained by convolving the

p.d.f for the branching fraction with a Gaussian systematic error. To do this, we take the

p.d.f in mn_fit2 and divide each entry by the efficiency smeared by the total systematic

uncertainty, and find the branching fraction that includes CII' of the total area.

The reported four-hadron branching ratios include possible intermediate resonances

cascading to the given final state, as well as direct non-resonant decays to the final state.

The reported three-hadron intermediate resonance mode branching fractions are inclusive

of other hidden resonances which could lead to the same three-hadron final states and

therefore do not represent the amplitudes for the three-body non-resonant branching

fractions .

A comparison of some of the results in this dissertation with existing measurements

from other experiments are listed in Table 6-2. We compare the Xes p fro~r for

J = 0, 1, 2 branching fractions measured in this analysis (Table 6-1) with Xes pozr+,-




2 This is a plotting and fitting software [55] used by high energy physicists.









for J = 0, 1, 2 in [30] ((1.6 + 0.5) (0.39 + 0.35) and (0.7 + 0.4) for J = 0, 1 and

2 respectively), and find our measurements to be of better precision and similar strength

within experimental errors, as expected from isospin symmetry. Furthermore, we also

find our measurement of a (Xc2 K*oK~~r ) (Table 6-3) to be higher yet consistent

within experimental errors with B (Xc2 K*oK~~r ) of [30]. We also observe that the

isospin formalism works well for the modes XJ K*Kxr where Xes K*oKozro and

XJ K*fK xTo are expected to have equal partial widths (compare these for Xso and

Xc2 StateS in Table 6-3 since for the latter mode, we do not have > 4 o- signals for Xl).

Moreover, our measurements for the B (Xc2 K*oK~~ ), B (Xco K**x TKo), and B

(Xc2 IK**x ~Ko) (Table 6-3) are in good agreement with the isospin expectations Of


| < K*oKo o|Xc > |2 : | < K*oK~;r|Xc > |2


1: 2


(6-3)


and


| < K*oKo o|Xc > |2 : | < K**x'rKo|Xc > |2


1 : 2


(6-4)


3 See Appendix A for a discussion of these isospin expectations.















xm








o" c



age
co




~co



at ,


3 a

mo<















m i


000
00
00



000
00
co



00



co
co S

co
co




00


ooo

ooo

00

co








oa S


0000





0 00


~0000 3



0 00

o co
o1 co




Ln



01 00

coco

coco




0000
++++















i o
a o f


a
d
aI
+r

00











co








0


od
V-
o
+


a





a
a 3


an
O

a
aI






o





03
d


$I

0
e










Tabl 6-2 Co-mparison of results.


Mode


p x-;o
p-; +;o
po r+ -
K*oKfiT
K*oKfiT


Source

this analysis
this analysis
PDG,
this analysis
PDG


Xo
B.F ( .)
1.48 + 0.24
1.56 + 0.24
1.6 + 0.5


%01
B.F ( .)
0.78 + 0.14
0.78 + 0.14
0.39 + 0.35


Xc2
B.F ( .)
1.12 + 0.18
1.11 + 0.18
0.7 + 0.4
0.90 + 0.25
0.48 + 0.28


Table 6-3. Results related by isospin are shown. Branching fractions and combined error
measurements for the isospin related K*Kxr intermediate modes are listed.


Mode

K*oKo TO
K*oK x T
K**K xTo
K**x TKo


Xo
B.F ( .)
0.56+0.15

0.74+0.18
0.96+0.25


%01
B.F ( .)
0.38+0.11


Xc2
B.F ( .)
0.59+0.14
0.90+0.25
0.57+0.13
0.90+0.25









CHAPTER 7
CONCLUSION AND SUMMARY

In summary, the branching fractions for Xca xr+x-o o~r, XcJ K+K-o o~r, XJ

;r;-rl;o, XJ K+K-rl;o, and XJ K~;rKo ar for J = 0, 1, 2 and, XJ i ,9xo ar

frJ=0, 2, are measured for the first time. For the modes Xc pp~rozo and XJ

pporo" for J = 0, 1, 2 where we do not find enough evidence of a signal, we present upper

limits (UL) at CI'I C.L. We also measure for the first time the branching fractions of

the intermediate resonance modes: XJ p r-~ro and p-xr+xo, XJ K*oKozro, and

XJ p*K Ko for J = 0, 1, 2; Xc2 K*oKfiT ; XcJ K**K xToand XcJ K**xPTKo

for J = 0, 2. Our measurements can account for up to >' of the hadronic width of the

Xc states. These newly discovered exclusive decay channels for which there are as yet

no specific predictions, are helpful phenomenologfical inputs to theoretical QCD models

trying to understand the decay mechanisms of Xc states, and the role of the COM in these

decays. These measurements improve our existing knowledge of the exclusive many body

decay modes of the Xc states and constitute a large portion of the hadronic width of these

P-wave charmonia states. We urge the theorists to extract useful information and come up

with an understanding of the governing decay dynamics of the Xc states using our results

together with the ones already existing in this sector.

The four-hadron final states xr+xr-xozo and K~~ Ko ro, are almost entirely saturated

with rich substructure of intermediate resonances. Our measurements will serve as

significant new additions in the relevant sections of the Particle Data Book. While these

measurements are already ini.~ i. -1 it, these results will further serve as useful guidelines

for the reconstruction of these states in new upcoming data at these energies.









APPENDIX A
ISOSPIN ANALYSES

Here we demonstrate the use of the isospin symmetry (discussed in ('! .pter 1) to

find the relative proportions of XJ K*Kxr decays related by isospin. In particular, we

present the calculations using the isospin formalism and arrive at equations 6-3 and 6-4

of C'!s Ilter 6.

Notation: |1, Iz > are iso-spin eigenstates, where I and Iz denote the isospin and its z

component respectively in isospin space.

1. Isospin analysis for ,J K*oK~r:

Below we estimate the relative proportions of the decays, X, c; K*oKo ro and



(a) Isospin amplitude of XJ K*oKo ar
11
Ko2' 2




S1 -1
XcJ dYJI K""o 2 2
|0, O >



d xo |1, 0 >



Figure A-1. Feynman diagram and isospin eigen states for XJ K*oKo O





|K*oKogo > = |K*o > |KoiT a
1 --1 1 1
2' 2 2 2


2' 2 V3/, 2 '2 1 2 2





















I< K*o gozo Xcsl > 2 1
6:

(b) Isospin amplitude of XJ K*oK+x-.


Usingf standard Clebsh Gordan coefficients, we get


|2,0>+ |1,0>


-
|1,0>


- |0,0


|K*oKozo >


Thus ,


< K*o gozo XcJ >


< 0, 0|0, O >


(A-1)


11
K+ 2' 2'



S 1
K *o ->
S2' 2




n- 1, -1 >


XcJ
|0, O >


Figure A-2. Feynman diagram and isospin eigen states for XJ K*oK x-.





|K*oK x- > = |K*o > |K xr- >


1
> -
2'


11
2' 2
1 1
2' 2


Y3 2'


Y32'


Using standard Clebsh Gordan coefficients, we get


|2,0 >


|1_,0 > + |0,0


|K*oK x- >


1
2


- |1_,0>








Thus ,


< K*oK x-|Xe> > =


K)oK .-|Xe >1 (A-2)

Dividing equation A-1 by A-2 we deduce,


Bi (Xai K"oKo o) 1
(A-3)
Bi (Xai K*oK+;7-) 2




























































I< K'* Kr to >~j 2 1
6;


2. Isospin analysis for XJ K**Kxr

Below we estimate the relative proportions of the decays, X,J i K* K-~ro and

cJ IK* xT-Ko

(a) Isospin amplitude of XJ K**K-;ro


1 --1
-~ K- |>
*U 2' 2
,S


11
2'+ 21




O o | O >


XcJ
0, O >


Figure A-3. Feynman diagram and isospin eigen states for XJ K* K-;ro


|K* K-ro >


|K*
1 1


2'2


Using standard Clebsh Gordan coefficients, we get


|K* K-ro >= | > > |1,l0 > |10> |0,0 >


Thus ,


~< 0 0|0,0>


< K* K-ro toJ >


(A-4)


> |K-;To

1-12
>- | ->10> -
32' 2 2































































I< K* x- go keJ 2 =


(b) Isospin amplitude of XJ K**x-Ko


-- 7 1 -


11
Ko -
2' 2


XcJ
10, O >


11
K* ->
2' 2


Figure A-4. Feynman diagram and isospin eigen states for XJ K* x-Ko


|K*
11
2' 2
1 1
2' 2


|K*+;T-Ko >


> |xT-Ko

> ~2'1 2

1 3 -1 1 -1
Y3 2' 2)Y 2' 2


We consider only the term having |' 1 > |1 ,> as it is the only one which

will decompose into a term in |0, 0 >, and using standard Clebsh Gordan

coefficients, we get


< K* xT-KoI~cl>


|1, > 0,


Thus ,


S< 0. 0|0,0:>


(A-5)











B (XcJ K*+K-iTo) 1
B (Xa~ K h*+i-Ko) 2


B (Xci K*oKo oU) 1
B (XcJ K*+K-iTo) 1


Bi (Yci K~noKo o) 1
B (Xci K*+i-Ko) 2


Dividing equation A-4 by A-5 we deduce,


(A-6)


We arrive at the following relations usingf equations A-1, A-4 and A-5:


(A-7)


(A-8)









REFERENCES

[1] G. Viehhauser, Nucl. Instrum. Methods A 462, 146 (2001).

[2] R. A. Briere, G. P. Clo! n,~ T. Ferguson, G. Tatishvilli, H. Vogel, J. P. Alexander et al.
(CLEO-c Collaboration), LEPP Report No. CLNS 01/1742, 2001 (unpublished).

[3] D. Griffiths, Introduction to El~ I,,n ,.Jlit;, Particles (John Wiley & Sons, 1987).

[4] D. H. Perkins, Introduction to High Energy Ph; -; (Addison-Wesley, 1987).

[5] R. N. Cahn and G. Goldhaber, The Explerimental Foundations of Particle Ph ; .i
(Cambridge Univ. Press, Cambridge, 1989).

[6] J. Hewett, SLAC-PUB-7930, hep-ph/9810316 (1997).

[7] R. Cahn, Rev. Mod. Phys. 68, 951 (1996).

[8] T. P. C'I. ing and L.-F. Li, Gauge Theory of Elementary Particle Ph;, (Claredon
Press, 1984); E. Golowich, J. F. Donoghue and B. R. Holstein, D ,imen of the
Standard M~odel (Cambridge University Press, 1992).

[9] P. W. Higgs, Phys. Rev. Lett. 12, 132 (1964); P. W. Higgs, Phys. Rev. 145, 1156
(1966).

[10] J. Erler, Phys. Rev. D 63, 071301 (2001).

[11] Rohlf, J. William, M~odern Ph ;, from a to ZO (John Wiley & Sons, 1994).

[12] W. Marciano and H. Pagels, Phys. Rep. 36, 137 (1978).

[13] D. J. Gross, Nucl. Phys. Proc. Suppl. 74, 426 (1999).

[14] K(. G. Wilson, Phys. Rev. D 10, 2445 (1974).

[15] R. P. Feynman, QED: The Str r,:ll. Theory of Light and M~atter (Princeton
University Press, 1985); R. P. Feynman, Quantum fl~i~l.. ,.i,,rii i.; (Addison-Wesley,
1998); S. S. Schweber, QED and the M~en Who M~ade It: D;,.on Feynman,
Schwinger, and Tomonaga (Princeton University Press, 1994).

[16] F. Halzen and A. D. Martin, Quarks and Lep~tons: An Introducl.. ;, Course in
Modern Particle Ph ;;i- (John Wiley & Sons, 1984).

[17] I. J. Aitchison and A. J. Hey, Gauge Ti,; .-<.-, in Particle Ph; -; (Adam Hilger
Limited, 1982 .

[18] J. P. Uzan, Rev. Mod. Phys. 75, 403 (2003).

[19] P. Z. Quintas, W. C. Leung, S. R. Mishra, F. J. Sciulli, C. Arroyo, K(. T. Bachmann
et al., Phys. Rev. Lett. 71, 1307 (1993).










[20] L. W. Jones, Rev. Mod. Phys. 49, 717 (1977).

[21] M. Gell-Mann, Phys. Lett. 8, 214 (1964).

[22] B. J. Bjorken and S. L. Glashow, Phys. Lett. 11, 255 (1964); S. L. Glashow,
J. Iliopoulos and L. Maiani, Phys. Rev. D 2, 1285 (1970).

[23] J. J. Aubert, U. Becker, P. J. Biggs, J. Burger, M. C!. is, G. Everhart et al., Phys.
Rev. Lett. 33, 1404 (1974); J. E. Augustin, A. M. Bo-, .7 1:i M. Breidenbach,
F. Bulos, J. T. Dakin, G. J. Feldman et al., Phys. Rev. Lett. 33, 1406 (1974);
G. S. Abrams, D. Briggs, W. C'!!n~io.-l:y, C. E. Friedberg, G. Goldhaber,
R. J. Hollebeek et al., Phys. Rev. Lett. 33, 1453 (1974).

[24] T. Appelquist and D. Politzer, Phys. Rev. Lett. 34, 43 (1975).

[25] J. S. Whitaker, W. Tanenbaum, G. S. Abrams, M. S. Alam, A. M. Boi-- .71:fi
M. Breidenbach et al., Phys. Rev. Lett. 37, 1596 (1976); C. J. Biddick,
T. H. Burnett, G. E. Masek, E. S. Miller, J. G. Smith, J. P. Stronski et al., Phys.
Rev. Lett. 38, 1324 (1977).

[26] E. D. Bloom and C. W. Peck, Ann. Rev. Nucl. Part. Sci. 33, 143 (1983); M. Oreglia,
E. Bloom, F. Bulos, R. C!. -1inal1 J. Gaiser, G. Godfrey et al., Phys. Rev. D 25,
2259 (1982).

[27] J. L. Richardson, Phys Lett. 82B, 272 (1979); C. Quigg and J. L. Rosner, Phys.
Rep. 56, 167 (1979); E. Eichten, K(. Gottfried, T. K~inoshita, K(. D. Lane and
T. M. Yan, Phys. Rev. D 17, 3090 (1980).

[28] R. Shankar, Princip~les of Quantum M~echanics (K~luwer Academic/Plenum
Publishers, 1994).

[29] A. M. Green (Editor), Hadronic Ph;,i. From Lattice QCD (World Scientific
Publishing, 2004); D. G. Richards, nucl-th/0006020 (2000).

[30] W. M. Yao, C. Amsler, D. Asner, R. M. Barnett, J. Beringer, P. R. Burchat, et
al. (Particle Data Group), J. Phys. G 33, 1 (2006).

[31] S. B. Athar, P. Avery, L. Brey- I-N. i.- 11, R. Patel, V. Potlia, H. Stoeck et al.,
(CLEO Collaboration), Phys. Rev. D 70, 112002 (2004).

[32] H. W. Huang and K(. T. Chao, Phys. Rev. D 54, 6850 (1996).

[33] A. Petrelli, Phys. Lett. B 380, 159 (1996).

[34] J. Bolz, P. K~roll and G. A. Schuler, Phys. Lett. B 392, 198 (1997).

[35] S. M. H. Wong, Nucl. Phys. A 674, 185 (2000).

[36] S. M. H. Wong, Eur. Phys. J. C 14, 643 (2000).









[37] C. Amsler and F. E. Close, Phys. Rev. D 53, 295 (1996).

[38] G. S. Adams, M. Anderson, J. P. Cummings, I. Danko, J. Napolitano, Q. He et al.,
(CLEO Collaboration), Phys. Rev. D 75, 071101 (2007).

[39] S. B. Athar, R. Patel, V. Potlia, J. Yelton, P. Rubin, C. Cawlfield et al.,
(CLEO Collaboration), Phys. Rev. D 75, 032002 (2007).

[40] G. L. K~ane, M~odern Elementary Particle Ph ; The Fundamental Particles and
Forces ? (Perseus Publishing, 1993).

[41] M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory
(Perseus Books, 1995).

[42] D. Peterson, K(. Berkelman, R. Briere, G. Ch.! n, D. Cronin-Hennessy, S. Csorna et
al., Nucl. Instrum?. Melth~ods Ph~ys. Res., Sct. Ai 478, 142 (2002).

[43] M. Artuso, R. Ayad, K(. Bukin, A. Efimov, C. Boulahouache, E. Dambasuren et
al., Nucl. Instrum. Meth. Phys. Res., Sect A 554, 147 (2005), M. Artuso, R. Ayad,
K(. Bukin, A. Efimov, C. Boulahouache, E. Dambasuren et al., Nucl. Instrum.
Methods Phys. Res., Sect. A 502, 91 (2003).

[44] Y. K~ubota, J. K(. Nelson, D. Perticone, R. Poling, S. Schrenk, M. S. Alam et al.,
(CLEO Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 320, 66 (1992).

[45] W. R. Leo, Techniques for Nuclear and Particle Ph ;, Expleriments (Springer,
1994).

[46] Robert K~utschke and Anders Ryd, CLEO Collaboration internal document, CBX
96-20 (1996).

[47] M.A.Selen, R.M.Hans and M.J. Haney, IEEE Trans. Nucl. Sci. 48, 562 (2001).
R.M.Hans, C.L. Plager, M.A. Selen and M.J. Haney, IEEE Trans. Nucl. Sci. 48, 552
(2001).

[48] R. K(. Bock and W. K~rischer, The Data A,...el;,-: Brief Book (Springer, Heidelberg,
1998).

[49] R. Brun, Geant 3.21, CERN Program Library Long Writeup W5013, 1993
(unpublished) .

[50] D. J. Lange, Nucl. Instrum. Meth. Phys. Res., Sect. A 462, 152 (2001).

[51] L. S. Brown and R. N. Cahn, Phys. Rev. D 13, 1195 (1976).

[52] Luis Breva-N -~ i.- 11, John Yelton CLEO Collaboration internal document, CBX 02-1,
(2002).

[53] V. S. Potlia, Ph.D. Thesis, (2006).









[54] P. Avery, CLEO Collaboration internal document, CBX 98-37, (1998), CBX 91-72,
(1991).

[55] I. C. Brock, CLEO Collaboration Software Note, CSN-94/245, (1996).









BIOGRAPHICAL SKETCH

Rukshana Patel was born in her native place Bharuch in Gui II Ir,, India, in September

1976. Her parents raised her in Mumbai, the commercial capital of India. Her mother

Rashida Patel who has been a very successful high school teacher and her perfect role

model, taught her life's most important lessons and values.

She received her high school education from St. Joseph's High School and then went

on to do her junior and degree College from Jai Hind College-Mumbai. After receiving

her Bachelor of Science degree (physics and instrumentation us! lj ur), she went to Mumbai

U~niversity-K~alina, Mumbai to pursue her Master of Science degree (nuclear physics

1!! I in i-). Through all the years of her education and personality development, Rukshana

was a favorite to her teachers, who guided and motivated her to pursue her dreams. She

also obtained her bachelor's in education (science teaching) from K~apila K~handawala

College-Mumbai and worked as a junior college instructor and degree college guest

lecturer at Jai Hind College, her alma matter.

The N----- -r turning point in her career was the decision to obtain a doctoral degree

in physics at the University of Florida (UF)-Gainesville beginning Fall 2001. This meant

much more than an outstanding academic achievement for her, it was an ultimate learning

experience of life. At UF, she found her husband Dr. Shadab Siddiqui (also a gator).

Having earned her doctorate, Rukshana now aspires to serve the science community

by utilizing her teaching and inter-personal skills combined with her technical knowledge

and motivation, in many creative v- .--s. Her dream is to be able to competently balance

between career and home-making, and be the best in all her roles in life.





PAGE 1

1

PAGE 2

2

PAGE 3

3

PAGE 4

I,theauthorofthisdissertationowemyheartfeltgratitudetoallthosewhoplayedaroleinmakingthisapieceofwork.IbeginbythankingtheAlmightyGodforshoweringhismercyovermeatalltimes,especiallyduringthetwistsandturnsofgraduatelife.TheonepersonIcan'tthankenoughismyadvisorDr.Yelton,whostoodbymelikeafortressinallthehardshipsthatcamemyway.WhereshallIbeginwith,thedaywhenheputhisfaithinmeandintroducedmetoanewworldofanalysisbyteachingmeinsmallsteps,orthedaysofhisendlesspatiencewhenheletmegrowatmyownpacewhileguidingmeinmanysubtleanduniqueways.HeistrulyagreatmentorandItrulyadmirehim,asinspiteofhisbusyfacultyschedulehemanagestoactuallydoanalysishimselffromscratch,becauseofwhichheremainedawareofeveryproblemthatIwasfacedwithinmyresearchandprovidedmeansformetotacklethem.Heisagreatfacilitator,providingmewithmanyopportunitiestopresentmyworkatexternalmeetings.IwouldliketothankmycommitteemembersDr.PaulAvery,Dr.AndrewKorytov,Dr.DavidReitze,Dr.JohnSchueller,andDr.RichardWoodardfortheirinterest,timeandexpertise,andfortheirinputsinthisdissertation.IowemanythankstoallmyteachersparticularlyDr.Dufty,Dr.FryandDr.Ingersentforthecorecourses.IalsothankDr.DuftyandDr.Meiselformotivatingmeduringthedicultinitialtwosemestersatgraduateschool.ManythanksareduetoDr.Woodardforteachingmetostrugglehardandforboostingmycondenceduringhisrigorouseldtheoryclassandforbeingateacherofhiskind.IthankDr.KorytovandDr.MitselmakherfortheirwonderfulandenrichingparticlephysicscourseswhichIsatthroughoverandovermorethanonceforthethrillandexcitementtheycarried.IwouldliketothanktheentireCLEOcollaborationfortheirsupportandsometimesrigoroussuggestionswhichareakeytowardsmakingthisworkofpublicationquality.IthankmyCLEOinternalcommittee,MattShepherd,DavidKreinickandHectorMendez 4

PAGE 5

5

PAGE 6

6

PAGE 7

page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 ABSTRACT ........................................ 14 CHAPTER 1THEORY ....................................... 15 1.1Introduction ................................... 15 1.2RelevantParticlePhysicsLiterature ...................... 15 1.2.1TheStandardModel .......................... 16 1.2.2Symmetries ............................... 21 1.2.3MesonsandResonances ......................... 23 1.2.4Charmonium ............................... 23 1.2.5QuantumChromodynamicsintheCharmoniumEnergyRegime .. 26 1.3MotivationforExclusiveCharmoniumDecays ................ 26 2EXPERIMENTALAPPARATUS .......................... 32 2.1TheCornellElectron-PositronStorageRing ................. 33 2.2TheInteraction ................................. 35 2.3TheCLEODetector .............................. 37 2.3.1TheCLEOIIIdetector ......................... 37 2.3.1.1Trackingsystem ....................... 38 2.3.1.2Siliconvertexdetector .................... 39 2.3.1.3Thecentraldriftchamber .................. 40 2.3.1.4Super-conductingcoil ..................... 41 2.3.1.5dE=dxparticleidenticationsystem ............. 41 2.3.1.6Ringimagingcherenkovdetector .............. 42 2.3.1.7Crystalcalorimeter ...................... 44 2.3.1.8Muondetectors ........................ 45 2.3.1.9Thetriggersystem ...................... 45 2.3.2TheCLEO-cdetector .......................... 46 2.3.2.1ZD ............................... 47 2.4MonteCarloSimulation ............................ 47 3ANALYSISTECHNOLOGY ............................ 64 3.1DatasetandMCSamples ........................... 64 3.2FinalStateSelection .............................. 65 7

PAGE 8

.................... 65 3.2.2NeutralParticleReconstruction .................... 68 3.2.3KinematicConstraintFitting ...................... 70 3.3FittingProcedure ................................ 71 3.4EcienciesandYields ............................. 72 4SYSTEMATICUNCERTAINTYSTUDIES .................... 102 5SEARCHFORINTERMEDIATESTATES(SUBSTRUCTURE) ........ 107 5.1IntroductionandScope ............................. 107 5.2SubstructureAnalysis ............................. 107 6MEASUREMENTRESULTS ............................ 144 7CONCLUSIONANDSUMMARY .......................... 149 APPENDIX AISOSPINANALYSES ................................ 150 REFERENCES ....................................... 156 BIOGRAPHICALSKETCH ................................ 160 8

PAGE 9

Table page 1-1StandardModelfermions. .............................. 29 1-2StandardModelforcesandgaugebosons. ...................... 29 3-1CLEO-cMCeciencies(in%)foreachmode. ................... 74 3-2CLEO-3MCeciencies(in%)foreachmode. ................... 74 3-3YieldsandcombinedCLEO-candCLEOIIIeciencies(%)of4-hadronnalstates. ......................................... 75 4-1Systematicuncertainties(in%)areshown. ..................... 105 4-2MCeciencies"(in%)forallmodesareshown. ................. 106 5-1Yieldsandeciencies(in%)forsubstructuremodes. ............... 110 6-1Branchingfractions(B.F.)withstatisticalandsystematicuncertainties. ..... 147 6-2Comparisonofresults. ................................ 148 6-3Resultsrelatedbyisospinareshown. ........................ 148 9

PAGE 10

Figure page 1-1Figureshowsthecharmoniumsystemofresonances. ................ 30 1-2Figureshowstheccannihilationof(2S) ..................... 31 2-1AschematicoftheCESRapparatusisshown. ................... 50 2-2DenitionofcrossinganglecaatCLEO. ..................... 51 2-3CharmoniumcrosssectioninanexploratoryenergyscanatCLEO. ....... 52 2-4Figureshowsacut-openfrontviewoftheCLEOIIIdetector. .......... 53 2-5FigureshowstheCLEOdetectorsideview(quarter)cross-section. ........ 54 2-6TheCLEOco-ordinatesystemisshown. ...................... 55 2-7EndviewcrosssectionoftheCLEOIIIsiliconvertexdetectorisshown. .... 56 2-8FigureillustratestheprincipleofworkingoftheDR. ............... 57 2-9FigureshowsaplotofthedE=dxasafunctionofparticlemomentum. ..... 58 2-10FigureshowstheRICHdetector. .......................... 59 2-11FigureshowstheRICHparticleseparation. .................... 60 2-12FigureshowstheCCenergyresolutionasafunctionofphotonenergy. ..... 61 2-13Figureshowsacut-openfrontviewoftheCLEO-cdetector. ........... 62 2-14FigureshowsanisometricviewoftheZDdetector. ................ 63 3-1Reconstructedinvariantmassdistributionofthe0!candidate. ...... 76 3-2EectoftheK0SightsignicancecutindataforthemodeKK0S0. .... 77 3-3Proleofthekinematicconstraintcutof2<25. ................. 78 3-4Improvementsinthesignaltonoiseratio,andthecmassresolutionduetothe2<25cut. .................................... 79 3-5Theunconstrained(constrained)ccandidateinvariantmassdistributions. ... 80 3-6Thetransitionphotonenergydistributionsbefore(after)thekinematicttingprocedure. ....................................... 81 3-7Theeectofmultiplecandidaterejectioncriteria. ................. 82 3-8ThedoubleGaussianfunctionalrepresentationofthedetectorresolution. .... 83 10

PAGE 11

........................................ 84 3-10DoubleGaussianconvolutedwithB-Wfunctionalrepresentationofthesignalvariable. ........................................ 85 3-11DoubleGaussianconvolutedwithB-Wfunctionalrepresentationofthesignalvariable. ........................................ 86 3-12StudiesofananticipatedbackgroundfromJ=. .................. 87 3-13Thettedsignalvariableforthe+00mode. ................. 88 3-14ThettedsignalvariablefortheK+K00mode. ................ 89 3-15Thettedsignalvariableforthepp00mode. ................... 90 3-16Thettedsignalvariableforthe+0mode. ................. 91 3-17ThettedsignalvariablefortheK+K0mode. ................. 92 3-18Thettedsignalvariableforthepp0mode. ................... 93 3-19ThettedsignalvariablefortheKK0S0mode. ................ 94 3-20Datayieldsforthe+00mode. ........................ 95 3-21DatayieldsfortheK+K00mode. ........................ 96 3-22Datayieldsforthepp00mode. .......................... 97 3-23Datayieldsforthe+0mode. ......................... 98 3-24DatayieldsfortheK+K0mode. ........................ 99 3-25Datayieldsforthepp0mode. ........................... 100 3-26DatayieldsfortheKK0S0mode. ....................... 101 5-1Figureelucidatessignalandsidebandregionsforthecstates. .......... 111 5-2Figureshowsdataforthedecayc0!+00mode. ............. 112 5-3Figureshowsdataforthedecayc0!+00mode. ............. 113 5-4Figureshowsdataforthedecayc0!+00mode. ............. 114 5-5Figureshowsdataforthedecayc0!+00mode. ............. 115 5-6Figureshowsdataforthedecayc1!+00mode. ............. 116 5-7Figureshowsdataforthedecayc1!+00mode. ............. 117 11

PAGE 12

............. 118 5-9Figureshowsdataforthedecayc2!+00mode. ............. 119 5-10Figureshowsdataforthedecayc0!K+K00mode. ............ 120 5-11Figureshowsdataforthedecayc0!K+K00mode. ............ 121 5-12Figureshowsdataforthedecayc0!K+K00mode. ............ 122 5-13Figureshowsdataforthedecayc0!K+K00mode. ............ 123 5-14Figureshowsdataforthedecayc1!K+K00mode. ............ 124 5-15Figureshowsdataforthedecayc1!K+K00mode. ............ 125 5-16Figureshowsdataforthedecayc0!KK0S0mode. ............ 126 5-17Figureshowsdataforthedecayc0!KK0S0mode. ............ 127 5-18Figureshowsdataforthedecayc0!KK0S0mode. ............ 128 5-19Figureshowsdataforthedecayc0!KK0S0mode. ............ 129 5-20Figureshowsdataforthedecayc0!KK0S0mode. ............ 130 5-21Figureshowsdataforthedecayc1!KK0S0mode. ............ 131 5-22Figureshowsdataforthedecayc1!KK0S0mode. ............ 132 5-23Figureshowsdataforthedecayc1!KK0S0mode. ............ 133 5-24Figureshowsdataforthedecayc1!KK0S0mode. ............ 134 5-25Figureshowsdataforthedecayc1!KK0S0mode. ............ 135 5-26Figureshowsdataforthedecayc1!KK0S0mode. ............ 136 5-27Figureshowsdataforthedecayc2!KK0S0mode. ............ 137 5-28Figureshowsdataforthedecayc2!KK0S0mode. ............ 138 5-29Figureshowsdataforthedecayc2!KK0S0mode. ............ 139 5-30Figureshowsdataforthedecayc2!KK0S0mode. ............ 140 5-31Figureshowsdataforthedecayc2!KK0S0mode. ............ 141 5-32Figureshowsdataforthedecayc!+0mode. .............. 142 5-33Figureshowsdataforthedecayc!+0mode. .............. 143 A-1FeynmandiagramandisospineigenstatesforcJ!K0K00. ......... 150 12

PAGE 13

......... 151 A-3FeynmandiagramandisospineigenstatesforcJ!K+K0. ......... 153 A-4FeynmandiagramandisospineigenstatesforcJ!K+K0. ......... 154 13

PAGE 14

WemeasureexclusivehadronicdecaysoftheP-wavespin-tripletcharmoniumstatescJ,whereJ=0;1;2,into4-hadronnalstateswithtwochargedandtwoneutralmesons.ThecJareproducedinradiativedecaysof3.08million(2S)observedintheCLEOIII[ 1 ]andCLEO-c[ 2 ]detectors.WereportrstmeasurementsofthebranchingfractionsofthecJforthemodes+00,K+K00,+0,K+K0,KK00forJ=0;1;2,andpp00forJ=0;2;andpresentupperlimitsat90%C.L.forthemodepp00forJ=1andpp0forJ=0;1;2.Wealsomeasureforthersttimethebranchingfractionsviaintermediateresonancesforthe4-bodynalstates:0,K0K00,andKK0forJ=0;1;2;K0KforJ=2;KK0andKK0forJ=0;2.TheresultspresentedwillserveasusefulphenomenologicalinputstoperturbativeQCDbasedcalculationstryingtounderstandthedecaydynamicsofthesecharmoniumstates. 14

PAGE 15

Particlephysicistsstudytheelementaryconstituentsofmatter,andtheirinteractionsbyproducingandstudyingelementaryparticlesathighenergiesinthelaboratory. Althoughtheexperimentaltriumphsofelementaryparticlephysicscanbetracedtotheyear1897withthediscoveryoftheelectron[ 3 4 ];theeraofthemidtwentiethcenturywasmarkedbythediscoveries 5 ].Theseeminglylargechaoticjungleofnewparticlesyelledouttothephysiciststheirneedforanorganizedclassicationofsomekindtoexplaintheirrolesandexistenceinnature.Itallcametosomerestwiththeinventionofamodelthatwasabletoexplainthemedleyintermsoffewfundamentalparticles.Anewtheoryemergedduringthelastthreedecades,andsucceededindescribingalloftheknownelementaryparticleinteractionsexceptgravity.Thischapterdoesaliteraturereviewofsomeofthefundamentalconceptsusefulforunderstandingtheworkconductedinthisdissertation,andconcludeswiththemotivationforthiswork. 3 ]). 15

PAGE 16

6 ]inspiteofthefactthatitusesnineteenunderivednumericalparameterinputsanddoesnotanswersomequestions,renderingthetheoryincomplete[ 7 ].ThisParticlePhysicsreviewsectionconcludeswithadiscussionoftheCharmoniumsystemwhichistheheartofthisdissertation. 8 ]ofParticlePhysicsisthemoderntheorythatattemptstoexplainallthephenomenaofparticlephysicsintermsofthepropertiesandinteractionsofasmallnumberofpoint-line(elementary)particleswhichpossessintrinsicproperties.Thistheoryemergedbythe1980's,andalloftheknownelementaryparticleinteractionsandtheirgoverningforces,exceptgravitycanbederivedfromtheSM. IntheSM,thedynamicsofallthematterintheuniversecanbeexplainedusingfewfundamentalelements(matterparticles,andforcemediatingparticles)whichareclassiedintotwobroadcategories:fermionsandbosons.TheSMfermions 2particles,whiletheSMbosons(whicharetheforcemediators)haveanintrinsicspinvalueof1 1. Leptons: Therearesixleptonswhichcomeinthreegenerationsoravors;theelectron(e)anditsneutrino(e),themuon()andanassociatedmuonneutrino(),andthetau()anditsneutrino(). 16

PAGE 17

2. Quarks: Therearesixtypesoravorsofquarks,arrangedinthreegenerations;up(u)anddown(d),charm(c)andstrange(s),top(t)andbottom(b). chargecharge+2 3e1 3e0B@ud1CA;0B@cs1CA;0B@tb1CA 3e(rstrow)or1 3e(secondrow). 3. Mediators: Thesearespin-1bosonswhicharealsoknownastheforcecarriers:acharge-lessphoton(),threegaugebosons IntheSMtheorytherealsoexistsaHiggsboson[ 9 ]withspin-0,howeverthereisnodirectevidenceexperimentally[ 10 ]foritsexistenceyet 17

PAGE 18

1-1 liststhepropertiesoftheSMfermions.Inadditiontocarryingafractionalelectriccharge,eachquarkmemberalsopossessesacolor Furthermore,allthetwelvefermions(leptonsandquarks)haveanassociatedanti-particlewhichhasthesamemassandspin,butoppositeelectriccharge(infact,alltheadditivequantumnumbersundergoachangeinsignaswemovefromparticletoanti-particle).Theanti-particlesofthechargedleptonsarerepresentedbythesamesymbolastheparticlesthemselves,butwithanoppositechargesign(theanti-particleofanelectronisthepositronandisrepresentedase+).Thecharge-lessanti-neutrinosandallanti-quarksarerepresentedbyanoverheadbarsymbol(forexample,ananti-electronneutrinoiswrittenase,andacharmanti-quarkiswrittenasc). AccordingtotheSM,therearethreetypesoffundamental 3 ].Table 1-2 listssomeofthepropertiesoftheSMforces. Amongthese,thestrongforceisthestrongestplayerandoperatesoverashortinteractionrangeandisdescribedbyatheoryknownasQuantumChromodynamics(QCD)[ 12 ].Thisstrongforceholdsquarkstogetherinsideprotonsandneutrons 18

PAGE 19

13 ]discoveredbyGross,WilczekandPolitzerwhowereawardedtheNobelPrizeinPhysicsin2004forthiswork).Howeverattheotherendofasymptoticfreedom,isthephenomenonofquarkconnement[ 14 ].Atlowenergies,thestrengthoftheinteractionincreaseswithdecreasingenergy,andbecomesstrongenoughto\conne"thequarksandgluonstogetherinsidehadrons. Theelectro-magneticforceisalongrangeforceobeyinganinversesquarelaw 15 ]theory.Anexampleoftheelectro-magneticforceistheforceofattractionbetweennucleiandelectronsinsideanatom.Theelectro-weak[ 16 17 ]theorydescribestheelectro-magneticandweakforcesastwomanifestationsofoneunderlyingforce.Theweakforceiseectiveonlyoverextremelyshortdistances,isweakerinstrengththanbothelectro-magneticandstrongforces,andisresponsibleforthedecayofheavynuclei. ThefermionsintheSMinteractwitheachotherinvariouswaysdeterminedbytheirproperties.Thechargedleptonsparticipateinelectro-magneticandweakinteractions,whiletheirneutralcounterparts(theneutrinos)interactonlyweakly.Thequarksbeingallchargedandcolored,interactbothelectro-magneticallyandstrongly,andalsoweakly Table 1-2 listssomeofthepropertiesoftheforcemediatorsintheSM.Themasslessphotonsmediatetheelectro-magneticforcebetweenparticlespossessingelectriccharge.Themasslessgluonsactasmediatorsbetweenstronglyinteractingparticles.Theeight 19

PAGE 20

3 ].Themassivegaugebosonsareresponsibleformediatingtheweakforcebetweenparticlesofdierentavors(allquarksandleptons).Inadditiontomediatingtheweakforce,beingchargedthemselves,theWbosonsparticipateinelectro-magneticinteractions. Aparameterofinterestindicatingtherelativestrengthofaforceiscalledacouplingconstant[ 18 ]-adimensionlessquantity.Table 1-2 summarizestheseforthethreeSMforces.Ironically,noneofthesecoupling\constants"arerealconstants.Instead,theyvarywiththeenergyscaleatwhichtheparticularinteractioninquestionoccurs,andaresaidto\run"withenergy.Inordertounderstandthis\running"qualitatively,wemustunderstandtheactionoftheforceeld(sayanelectriceldduetoachargedparticle)onvirtualparticlescarryingtherelevantcharge.Vacuumpolarizationeectscanexplainthisconcept.Thevacuumconsistsofvirtualelectron-positronpairs,andanexternalelectricchargehastheeectofpolarizingit.Thussuchamediumwithvirtualelectricdipoleshastheeectofscreeningtheactualchargeduetoapartialcancelationoftheeld.Consequentlyverynearthechargedparticleinquestionthis\screening"eectissmallleadingtoanoverallincreaseintheeectivestrengthoftheeld. InQCDthesametrendisobservedwithvirtualquark-anti-quarkpairswhichtendtoscreenthecolorchargeofthe\colored"particleinquestion.However,QCDhasanadditionalcomplicationduetothefactthatinadditiontothequarks,eventhegluonsare\colored"andarecapableofcausinginteractions,possiblyinadierentfashion.Thevirtualgluonsinthevacuumalsopolarizeit,butthistimetheeectofthepolarizationiscalled\anti-screening",wherebytheeectiveeldstrengthisescalated.Sincethevirtual 20

PAGE 21

19 ] 3 16 ],herewepresentashortsummaryoftherelevantconcepts. Asymmetryrelatedtoquarkavorisknownas\isospin"symmetry 2)withinthisspace.Thealgebraicoperationsforisospinareidenticaltothoseusedforangularmomenta 13 ]islogarithmic.13 21

PAGE 22

16 2andtheneutronis1 2 17 2),andsodothecandsquarksI=1 2.Thestrongandtheelectro-magneticinteractionforcesconservethethirdcomponentofisospin,Iz.Thisisaconsequenceofthefactthatbothstrongandelectro-magneticinteractionsconservequarkavor.Ontheotherhand,thetotalisospinIisagoodsymmetryonlyofstronginteractions.Theweakinteractiondoesnotconserveisospin.AnapplicationofisospinanalysisinthisdissertationcanbefoundinAppendix A Wenowdiscusstwodiscrete(non-continuous)symmetryoperationswhichplayaspecialroleinthedynamicsoftheproductionanddecayofparticles:Parity(P)andChargeconjugation(C).Thespatialinversionofpositioncoordinateswithrespecttotheoriginisobtainedbythe^Poperator. ^P~r=^P(x;y;z)=(x;y;z)=~r(1{1) ThephysicalquantitieswhichchangeanoverallsignundertheparityoperationhaveaparityeigenvalueorintrinsicparityofP=1.Velocities,accelerationandlinearmomentumareexamplesofsuchquantities.ThosewhichdonotundergoasignreversalunderP,suchanorbitalangularmomentum(bothpositionandlinearmomentumundergospatialinversion,leavingtheoverallorbitalangularmomentumunchanged)haveanintrinsicparityP=+1.Notethattwosuccessiveparitytransformationsleaveasystemunchanged,thusmimickinganidentityoperation,withpossibleeigenvaluesofP=1.Stateswiththispropertyarecalledeigenstatesoftheparityoperator(hadronsare 22

PAGE 23

3 ].TheparityofaparticlewithadeniteorbitalangularmomentumLisaneigenstateof^Pwithaneigenvalueof(1)Ltimesitsintrinsicparity.Theintrinsicparityoffermionsisdenedbyconvention,andcannotbederived.Byconvention,quarks(anti-quarks)haveP=+1(P=1).Theparityofacompositesystemofquarksistheproductoftheintrinsicparitiesofeachcomponentquarktimesafactorof(1)L,whereListheorbitalangularmomentumofthequarksysteminthehadron.TheparitiesofthephotonandgluoncanbederivedandgiveavalueofP=1forboththesemediators.Parityisasymmetryofstrongandelectro-magneticinteractions. Anotherdiscretesymmetryofinterestisthechargeconjugationsymmetry(C).Thechargeconjugationoperator^C,reversesthesignofallinternalquantumnumbers,thustransformingtheparticleintoitscorrespondinganti-particle.Thus, ^Cjparticle>=janti-particle>(1{2) Likeavorfermion-anti-fermionsystemsareeigenstatesof^CwitheigenvalueofC=(1)L+S,whereLandSdenotetheorbitalandspinangularmomentaasusual.TheintrinsicvalueofCforbothphotonsandgluonsis1[ 3 16 ]. 20 ].Quarksthereforearefoundincolorlesscombinationsoftwo(mesons)orthree(baryons)calledhadrons[ 21 ].Thisisthephenomenonofconnement[ 14 ].Othercolorneutralobjectsarealsopossible,howevertheyarerareandexoticandwillnotbediscussedhere. 3 ],quarkoniumistheQCDcounterpartboundbystronginteractions.Boundstatesinvolvinglightquarks 23

PAGE 24

Charmoniumresonanceswerediscoveredexperimentally 23 ].ThatthesecharmoniumresonancesareinfactccboundstateswasinterpretedbyT.AppelquistandD.Politzer[ 24 ],andsoonarichspectrumofthesehiddencharm 1-1 showsthespectrumofcharmoniumstates.Aspectroscopicnotationisusedtodenoteeachofthesecharmoniumstates:2S+1LJwhereL=S;P;D:::forL=0;1;2:::(S=0;1aseachquarkconstituentisafermion). Inadditiontothisspectroscopicnotation,thesestatesareeachcharacterizedbyadditionalquantumnumbersoftotalangularmomentum(J 22 ].19 24

PAGE 25

1-2 .Sincetheinitialstateiscolorless,ccannihilationviaasinglegluonisnotallowedasagluoniscolored.Furthermore,ccannihilationviaasinglephotonispossible(Figure 1-2 c),butissuppressedrelativetoaccannihilationthatproceedsthroughthestrongchannel.Next,weconsidertheannihilationviatwogluons,whichalthoughacolorneutralcombinationdoesnotconserveCvalue.Sotheonlypossibledominantgluonchannelisthe3-gluonchannel(Figure 1-2 b).Decayviaasinglephotonand2gluonsisalsoallowedasthisparticularchoiceconservesCaswellasiscolorneutral(Figure 1-2 a).ThislatterchannelisalsoknownasaradiativedecayandisoneofinterestinthisanalysisandismostusefulforobservingthestateswithJPC=J++,from(2S): 25 ].Thesewerelaterconformedandstudiedinaseriesofexperiments[ 26 ],andtheinterpretationoftheJ/and(2S)statesasnon-relativisticboundstatesofaheavyquark-anti-quarksystemwassolidied. Soonafterthediscoveryofthesecharmoniastates,variouspotentialmodels[ 27 ]wereintroducedinanattempttounderstandthecharmoniumspectrumasastronglyinteractinganalogofpositronium(e+eboundstate).ConsiderthefollowingpotentialV(r)motivatedbyasymptoticfreedomforsmallccseparation(r)andconnementforlargeseparation, 25

PAGE 26

Inordertoaccountfornestructureinthecharmoniumspectrum,forinstancethesplittingbetweenthectripletstates,thespin-orbitinteractionsmustbetakenintoconsideration. Potentialmodelsweresuccessfulindescribingthegrossfeaturesofthecharmoniumspectrum.Foradetaileddiscussion,see[ 27 ]. 1.2.1 ,wediscussedaboutthephenomenaofasymptoticfreedomandquarkconnement,andtheconsequent\running"ofS.Intheasymptoticfreedomregimeofshortdistances,quarksbehaveasalmostfreeparticles,andthereforeinthisregimeonecanapplyperturbationtheory[ 28 ]forhardprocessesinvolvinglargemomentumtransfers.ThesmallnessofSatsuchenergieswarrantstheuseoftheperturbativeQCDtechnique.However,inthelowenergyregimewhereSisnolongersmall,thesolutiondivergesandperturbationtheorybreaksdown.HencebelowthescaleofQCDwhereoneenterstheconnementregime,onehastoresorttoothernon-perturbativemethods[ 29 ]. Heavyquarkonia,suchascharmonia(cc)andbottomonia(bb)arenon-relativisticsystemswithlowcharacteristicquarkvelocities(S0.3).Thusthesesystemsareveryusefulexperimentalprobesfortestingnon-perturbativeQCDcalculations. 26

PAGE 27

2 ]whichisaimedatprovidingextremelyhighprecisioninthestudiesofcharmedmesonsandthedynamicsofcharmoniumstatesinthisenergyrange. Thecurrentlyavailablecmeasurementsaresparse[ 30 ];especiallywhencomparedwithotherS-wavecharmonialikeJ=.ThedatatakenbyCLEO-catthe(2S)resonancehasmadeavailableabountyofcJstateswhichareproducedviatheradiativedecay(2S)!cJwithbranchingratiosofeacharound9%[ 31 ]. Hadronicdecaysofthecoeranumberofpotentiallyinterestingmeasurements.Thus,thisisanexploratoryendeavor.PastresearchindicatesthattheColorOctetMechanism(COM)isimportantandgovernsthedecayoftheseP-wavecharmoniastates[ 32 { 36 ].QCDpredictionsoftwobodyexclusivecdecayswiththeinclusionoftheCOMexistandaretestedusingtheavailableexperimentaldata.TheseshowsupportfortheCOM.Inthislight,newandprecisecmeasurementswillcontributetowardsabetterunderstandingoftheCOMandnatureofP-wavedynamics.Moreover,thesumofallknownc0two-bodyBR's<2.5%,whichsuggeststhatalargeportionofthechadronicwidthmaybeduetomany-bodydecaymodes.Thisstudyof4-bodymodesatCLEOisanattempttodiscoversuch\notyetobserved"decays.InordertobuildacomprehensiveunderstandingabouttheP-wavedynamics,boththeoreticalpredictionswiththeinclusionoftheCOMandpreciseexperimentalmeasurementsforcmany-bodynalstatesarerequired.AllthesetogetherwillprovideatestingforQCDmodelsandcalculationsincludingeectoftheCOM.Furthermore,decaysofcJ,inparticularc0;2provideadirectwindowonglueballdynamics[ 37 ]whichhavebeenasubjectofinterest 27

PAGE 28

Thisanalysisfollowsthegeneralmethodofourearlierworkon0[ 38 ]and3-body[ 39 ]decaysofc,extendingittohighermultiplicitystates.Thefourbodyexclusivecdecaymodesstudiedinthisarticlecontaintwoneutralandtwochargedhadronsinthenalstate,andarebeingmeasuredforthersttime.Wealsotakearstlookatthegrossfeaturesoftherichsubstructureofthemodes. 28

PAGE 29

StandardModelfermions. LeptonsQuarks SymbolMass SymbolMass Table1-2: StandardModelforcesandgaugebosons. ForceRangeRelativeCouplingCarrier CarrierCarrier(m)strengthconstant[ 11 ] masselectric (GeV=c2)charge Electro-1102=1=137 Strong10151S=1g Note:Thevalueofthecouplingconstantslistedhereareatthescaleoflowmomentatransfers. 29

PAGE 30

Figureshowsthecharmoniumsystemofresonances.Thestatesarelabeledbyaspectrosopicnotation:2S+1LJwhereL=S;P;D:::forL=0;1;2:::,andLandSdenotetheorbitalandspinangularmomentumquantumnumbersrespectively.Eachstateischaracterizedbyadditionalquantumnumbersoftotalangularmomentum(J),parity(P),andchargeconjugation(C)bythenotationJPC.Thetransitionsbetweenstatesisshownbyarrows. 30

PAGE 31

(b) (c) Figure1-2. Figureshowstheccannihilationofintogluonsandphotonsbeforehadronization,(a)thedecaythroughthe3-gluon(strong)channel,(b)theradiativedecayto2-gluonsand1-photon,and(c)theelectro-magneticdecayintoapairoffermions,areshown. 31

PAGE 32

Inordertostudythedecayofccharmoniumresonanceswhichcanonlybeproducedinahighenergyenvironment,weneedacomplextechnologicalinfrastructure.Thischallengingtaskinvolvestheco-ordinationbetweentwomajorcomponentswhichconstitutetheapparatus:theacceleratorandthedetector.Theformerisresponsibleforcreatingthedesiredcharmoniumresonances,whilethelatterdetectstheoutcomesofthealmostinstantaneous(1023sec)decaysofthecharmparticles.Thistwo-stepprocessrequiresatremendousamountofactivityandwork-forceinvolvingphysicists,engineers,andtechnicianswhonotonlyproduceandcollectthedata,butprocessandstoreitinamannerthatcanbeutilizedbydataanalystphysicistsatalaterpointintime.Suchacommunityofscientistsinvolvedinthecollection,storage,maintenance,andanalysisofhighenergyphysicsdataassociatedwithacertainexperimentconstitutesacollaboratingteamfortheexperiment. Weobtainedthecharmoniumresonancedataforthisanalysisusingtheexperimentalfacilities(collideranddetector)housedbytheLaboratoryforElementaryParticlePhysics(LEPP)locatedonthecampusofCornellUniversityinIthaca,NY.TheacceleratorfacilityatLEPPwhichproducedthecharmoniumresonancedataistheCornellElectron-PositronStorageRing(CESR).ThepartnerfacilityresponsiblefordetectingtheoutcomesofCESRcollisionsandlocatedatthesouthendofCESRisknownastheCLEOdetector(CLEOisnotanacronym,butisnamedafterCleopatra-asuitablecompanionforCESR). TheCLEOcollaborationisateamofover150highenergyphysicistsfrom25universitiesstudyingtheproductionanddecayofbeautyandcharmquarks,andtauleptonsproducedinCESRcollisions. 32

PAGE 33

2-1 .Theelectronsandpositronsareproducedina30meterlongvacuumpipecalledtheLINAC.Electronsaregeneratedbyheatingalamentuntiltheyhavesucientenergytoescapethelamentsurface.Theelectronsarethencollectedbyapre-buncherwhichcompressestheelectronsintopacketsforaccelerationintheLINAC.TheelectronpacketsareacceleratedintheLINACusingvaryingelectriceldsgeneratedbyradiofrequency(RF)cavities.Theelectronsareacceleratedtoanenergyofabout300MeVattheendoftheLINAC.Positronsarecreatedbycollidinga140MeVelectronbeamhalfwaydowntheLINAConamovabletungstentarget.Theresultofthisimpactisasprayofelectrons,positronsandphotons.ThepositronsareseparatedfromtheelectronsandacceleratedintheremainderoftheLINACuptoanenergyofabout200MeV.Thisacceleratedbunchofelectronsandpositronsisintroducedseparatelyandinoppositedirectionsintothesynchrotron.Thisprocesstypicallylastsforabouttenminutes,andiscommonlyreferredtoasa\runll." Thesynchrotronisafewmeterssmallerinradiusthanthestorageringandislocatedinthesametunnel.Inthesynchrotron,theparticlesareacceleratedincircularorbitsinsideavacuumpipebyfour3-meterlonglinearaccelerators,andarecontainedbyaseriesofdipolebendingmagnets.Astheparticlesareaccelerated,thevalueof 33

PAGE 34

TheInteractionRegion(IR)isasmallregionofspacelocatedatthecenteroftheCLEOdetectorwheretheelectronandpositronbeamsundergocollision.AttheinteractionpointenclosedbytheCLEOdetector,thebeamsdonotcollidehead-on,butwithasmallcrossingangle(ca)of2mradintothering(seeFigure 2-2 ).Thisallowsforbunch-by-bunchcollisionsoftheelectronandpositrontrains.Forlow-energyrunning(nearcharmcenterofmassenergiesbetween3-5GeV),wigglermagnetsinducesynchrotronradiation,butthishasminimaleectonthebeamtrajectory. 34

PAGE 35

2 ]. Theabilitytoobtainahighcollisionrateiscrucialforthesuccessoftheacceleratoranditspartnerexperiment.Therateatwhichcollisionsoccurisexpressedintermsofluminosity(numberofcollisionspersecondperunitarea),as: wherefisthefrequencyofrevolutionforthebunches,nisthenumberofbunchesforeachparticlespecies,Aisthecross-sectionalareaofbeamoverlap,andNe+andNearethenumbersofpositronsandelectronsperbunch,respectively.Inordertomaximizetheluminosity,thebeamsarefocussedasnarrowaspossibleintheIR.Animportantmeasureofacceleratorperformanceistheintegratedluminosityoveraperiodoftime.Onecancomputethenumberofeventsofaparticulartypeofprocessbytakingtheproductoftheintegratedluminositywiththeknowncross-sectionforthegivenprocess[ 40 ],andonecanthencountthenumberoftimesthisprocessisdetectedinacertaintimeinterval.ThetworeferenceprocessesthatareusedatCLEOare,e+einteractingtoproduceanewe+epair,ande+eannihilatingtoproduceapairofphotons.Usingthewellknowncross-sectionforeachprocess[ 41 ],thenumberofeventsisconvertedtoaluminosity.WerefertotheseastheBhabhaand(GamGam)luminositiesrespectively. 35

PAGE 36

Uponcollision,thetwobeamseitherscatter,orannihilateandinteractelectro-magneticallytocreateavirtualphoton Evenattheoperatingenergiesof3.686GeV(massof(2S));thevirtualphotonmayeitherproducetheresonance(2S),orproducecontinuumbackground 2-3 showstheproductionof(2S)resonanceinaCLEO-cexploratoryscanofthe(2S)hadroniccrosssectionforeightdierentbeamenergyvalues.Itisalsopossiblethattheinitiale+epairradiatestwophotons,whichsubsequentlycollide. Irrespectiveoftheintermediatestates,thenalendproductofsuchane+eannihilationarerelativelylong-livedchargedandneutraldaughterparticles.Theparticles(andcorrespondinganti-particleswhereverapplicable)thatcanbedirectlydetectedusingparticledetectorsareelectrons(e),muons(),pions(+),kaons(K+),protons(p),andphotons().Theprocessofinterestinthisanalysisis 3 ,explainthemethodofseparatingthisprocessofinterestfrommimickingbackgrounds. W).4 36

PAGE 37

2.2 )whichyoatrelativisticspeeds.Theprinciplesofparticledetectionarebaseduponthescienticknowledgeonmatter-matterinteraction.CLEOisaversatile,multipurposedetectorwithexcellentchargedparticleandphotondetectioncapabilities.Eachdetectorcomponentisacombinationofsensors,whichdirectlyorindirectlyrecognizethesignatureofagivenspecies.Adetaileddiscussionofdetectortechnology[ 1 2 ]isbeyondthescopeofthisdocument;neverthelessthebasicgoverningprinciplesarehighlightedforeachdetectorpart.TherestofthissectionisdevotedtodescribingtheCLEOIIIandCLEO-cdetectors,andthemannerinwhichtheymeasuretheenergy,momentaandtrajectoryofparticles. 2-4 ,andisthegenerationofCLEOinoperationin2001-2002.Itisageneral-purposecylindricallysymmetricassemblyofmanydetectorelementsbuiltconcentricallyaroundtheCESRinteractionpoint[ 1 ]. Theentiredetectorisapproximatelycubeshaped,withonesidemeasuringabout6meters,andweighsover1000tons.Insideoutfromthebeamaxis,theCLEOIIIdetectorcomponentsasshowninFigs 2-4 and 2-5 are:asiliconvertexdetector,adriftchamber[ 42 ],aringimagingCherenkov(RICH)detector[ 43 ],anelectro-magneticcrystalcalorimeter,asuper-conductingsolenoidmagnet(eldstrengthof1.5Tanddirectionparalleltothebeamline),andamuonchamber[ 44 ]. 37

PAGE 38

Theco-ordinatesystemusedinsidetheCLEOdetectorisillustratedinFig 2-6 .Thex-axispointstowardstheoutsideoftheCESRring(South),they-axispointsuptowardsthesky,andthez-axisisalongtheincidentpositronbeamdirection(West).Theoriginoftheco-ordinatesystemliesintheIRwithin1-2mmofthee+ecollisionpoint.Owingtoitscylindricalsymmetryaroundz,thepolarangleofapointPinspaceisdenedastheanglebetweenthepositivez-axisandthelineformedbetweentheoriginandP(~rinFig 2-6 B).Additionally,theazimuthalangleisdenedastheanglebetweenthepositivex-axisandthelinefromtheorigintoPprojectedontothexy-plane. InthefollowingsubsectionswediscusssomeoftheparticledetectionmethodologiesimplementedintheCLEOsub-detectors,andhowrawdetectordataistransformedintomeasurementsofphysicsinterest:particleenergy,momenta,andtrajectories. 2-4 )beforetheybegintoencountertheactiveelementsofthedetectortrackingsystem.TheCLEOIIItrackingsystemisresponsiblefortrackingachargedparticle'spathandthusgivingthephysicistameasureoftheparticlemomentum.ThetrackingsystemoftheCLEOIIIdetectoriscomposedoftwosub-detectors.Therstisthesiliconvertexdetectormeasuringthezandthecotangentofthepolarangle,surroundedbyacentraldriftchambermeasuringthecurvature.Bothdevicesmeasuretheazimuthalangleandtheimpactparameter.Thistwo-componenttrackingsystemcovers93%ofthe4solidanglearoundtheIR.Forthedatapresentedinthisanalysis,thechargedparticletrackingsystemoperatesina1.0Tmagneticeld(subsection 2.3.1.4 )alongthebeamaxis,andachievesamomentumresolutionof0.6%for1GeV/ctracks.Theresolutionisworseforchargedparticleswithmomentabelow120MeV/c,astheywillnotmakeitthrough 38

PAGE 39

Thesiliconvertexdetector(Fig 2-7 )consistsoffour300mthickdetectionlayerswhichcirclearoundthebeamlineatradialdistancesof2.5cm,3.8cm,7.0cm,and10.1cm.Eachofthefourdetectorlayers(barrels)isconstructedfromindependentchains(calledladders)whicharemadebyconnectingindividualsiliconwafers(sensors)together.Eachsiliconwaferis27.0mmin,52.6mminzand0.3mmthick.Eachlayerconsistsofaproportionallyincreasingnumberofdetectorsalongandz;atotalof447siliconidenticaldouble-sideddetectorsareusedtomakethefourlayers(7alongand3alongzinthe2.5cmlayer,10alongand4alongzinthe3.8cmlayer,18alongand7alongzinthe7.0cmlayer,and26alongand10alongzinthe10.1cmlayer). Thechargeisconductedoutofthedetectorforamplicationalongtraceswhichareparalleltothebeam-lineononesideofthestripandperpendiculartoitontheother,sothatthetwo-dimensionalpointofintersectionmaybereconstructed.Thesiliconvertexdetectorprovidesaccuratetrackpositionmeasurementsclosetotheinteractionpointinr(perpendiculardistancefrombeamline),(azimuthalangle),andz(paralleldistancealongthebeamline)co-ordinates.Thepositionresolutionneartheinteractionpointis40minx-y,and90minz. 39

PAGE 40

2-8 .Theanodesarekeptatapositivepotential(about2100V),whichprovidesanelectriceldthroughoutthevolumeofthedriftchamber.Thecathodesarekeptgrounded,thusshapingtheelectriceldsuchthattheeldsfromneighboringanodewiresdonotinterferewitheachother.DuringitspassagethroughtheDRIII,thechargedparticleinteractselectro-magneticallywiththegasmoleculesinsidethechamber.Whenachargedparticlepassesthroughacell,theenergyistransferredfromthehighenergyparticletothegasmoleculetherebyionizingthegasbyliberatingtheoutervalenceshellelectrons.Theliberatedelectrons\drift"intheelectriceldtowardstheclosestsensewire.Thethinsensewiremaintainedatahighpotentialproducesaverystrongelectriceldinitsvicinity.Astheelectronapproachesthesensewire,itgainsenoughenergytobecomeasecondaryionizingelectronitselfandionizesmoreatomsfromthesurroundinggasmolecules.Thiscreatesanavalancheofelectronsonthesensewirewhichprovidesa107amplication.Theavalancheofelectronsthuscreatedreachesthesensewireinaveryshortamountoftime(lessthanananosecond)andthesensewireregistersa\hit".Thecurrentontheanodewirefromtheavalancheisampliedandcollectedattheendoftheanodewire.Theamountofchargecollected,andthetimebetweentheinitialionizationandchargedepositionaremeasured.Acalibrateddriftchamberthenconvertsthesemeasurementstoameasurementofthedistanceofclosestapproachoftheparticletothesensewire.Acalibrationofthedrift 40

PAGE 41

Thedriftchamberconsistsof16layersofaxialsensewires(paralleltothebeam-line)and31sensewirelayerswhichalternateinsmallstereoangles(stereoangleisdenedasthedierenceinbetweenthewireend-plateandthevertical)toprovidesensitivitytothez-positionofthetracks.Thewiresinastereolayeraretiltedorskewedinthedirection.Thestereoanglevariesfrom21mradto28mradwithrespecttothebeamaxisyieldingaz-positionresolutionof3-4mmateachwirealternatingineachsubsequentlayer.Thedriftpositionresolutionisaround150minrandabout6mminz,andthemomentumresolutionof40MeV/catp=5:3GeV/cisachieved[ 1 2 ]. 41

PAGE 42

45 ]Figure 2-9 depictstherelationshipbetweenthemomentumandenergylossfordierentchargedspecies.KnowingthechargedhadrontrackmomentumanditsdE=dxinformation,onecanestimatethenumberofthestandarddeviationsthedE=dxisawayfromagivenparticlehypothesis,andthisinformationhelpsitsidentication.WealsoobservefromFigure 2-9 thataftercertainmomentaforeachchargedspecies,thedE=dxcurveoverlapsandbecomesoflessuseforparticleidentication(PID).Thus,theabilitytousethedE=dxinformationeectivelyforPIDdependsonthemomentumofeachparticletype.DistinguishingKfromwithdE=dxbecomesmosteectiveatmomenta600MeV/c,andseparatingpfromKandismosteectiveatmomentabelow1GeV/c.Toreconstructthetrajectoryofthechargedhadronsthroughthedetector,aKalmanttingprocedure[ 46 ]isused.Thehelicalchargedparticletrajectoryinthemagneticeld,helpsdeterminetheparticlemomentum,anditspositioninspace. 2-10 .ItisusedmostofthetimesincombinationwiththedE=dxinformationtodiscriminatebetweenchargedparticles.Cherenkovradiationisemittedbyachargedparticlewhenittravelsfasterthanlightinagivenmedium.Thechargedparticlepolarizesthemoleculesofthemediumasittravelsthroughit,andthepolarizedmoleculesemitphotonsinordertorelaxtotheirgroundstate.Aconicalwavefrontoflightisproducedbythephotonsthusemitted,duetoconstructiveinterferenceoflight.TheCherenkovphotonsaredistributedinaconicalshape,andtheapexangleoftheconeiscalledtheCherenkovangle.Itisrelatedtotheparticlevelocity,oralternativelytotheparticlemomentumPofmassmby, cos=1 42

PAGE 43

IntheRICHdetectortheCherenkovphotonsarenotfocussedandsotomeasure,theyareallowedtopropagateinagivenspace.TheRICHcomponentsare:aradiator,anexpansionvolume,andphotondetectors.TheradiatorallowsachargedparticletoradiateCherenkovphotons;itsmaterialismadeupoflithiumuoride(LiF)plates(forLiF,n=1:5).Theexpansionvolumeisaregionlledwithnitrogengas,andis16cminlength.Thephotondetectorsarehighlysegmentedmulti-wireproportionalchambers(MWPC)lledwithmethane-TEA(tri-ethylamine)gasmixturebehind2mmcalciumuoride(CaF2)windows,wheretheCherenkovconeisintercepted.Thedetectorcoverstheradialdistancefrom82cmto101cm,andrendersatotalradiationlengthofapproximately12%.TheRICHiscapableofmeasuringtheCherenkovangleswitharesolutionoffewmilliradians.ThisprovidesgoodseparationbetweenKanduptonearly3GeV/c. TheinformationfromtheRICHphotons,istranslatedintoalikelihood(Li)foragivenparticlehypothesisbytakingintoaccounteachpossibleopticalpathtraveledbyaphoton.Figure 2-11 showstheRICHparticleseparationasafunctionofparticlemomentumfordierentparticlehypotheses.WeobservefromFigure 2-11 distinctmomentumthresholdsforparticlediscrimination,determinedbyn.ItisevidentthattheK=separationusingRICHPIDbecomeseectiveabove700MeV/cofparticlemomentum,duetothefactthatKdoesnotradiateintheRICHatlowermomenta.Similarlythethresholdforp=separationisabout1GeV/c.Inthisanalysis,wecombinethedE=dxandRICHPIDsystemstocomplementeachotherwhichwillbediscussedinsubsection 3.2.1 .ThecombineddE=dx-RICHPIDprocedurehasapionorkaoneciency>90%,andaprobabilityofpionsfakingkaons(orviceversa)<5%. 43

PAGE 44

2-5 ,thecalorimeterconstitutesabarrelregionandtwoend-capregions.Theseregionsaredistinguishedbasedonthepolarangle,thebarrel(jcos()j<0.81)andtheend-cap(jcos()j0.81).Thecalorimeterconsistsof7784(6144inthebarreland1640intheend-caps)thallium-dopedCsIcrystals,covering95%ofthesolidangle.Thebarrelregioncrystalsaretaperedtowardsthefrontface,andarealignedtopointtowardstheinteractionpointsothatthephotonsoriginatingfromtheinteractionpointstrikethebarrelcrystalsatnearnormalincidence.Thecrystalsintheend-caparerectangularinshapeandarealignedparalleltothebeam-line.Visiblelightfromtheshoweriscollectedonthebackofthecrystals,fromwhichtheincidentenergyisreconstructed.Thelightyieldfromeachofthecrystalsisconvertedintoelectricalsignalsbyfourphoto-diodesatthebackofeachofthecrystals,andarecalibratedtomeasuretheenergydepositedbytheincomingparticles.Eachofthecrystalsis30cminlength,andcoversabout16.2radiationlengths.Theshowerenergyresolutionprovidedbythe 44

PAGE 45

2-12 )is2.2%(5%)forphotonswithenergyof1GeV(100MeV).Theangularresolutionforshowersisabout10mrad. Theheavyironlayersalsoserveasthemagneticuxreturnyokeforthesuperconductingcoil.TheyalsoprotecttheinnerdetectorcomponentsoftheCLEOIIIdetectorfromnon-muonictypeofcosmicraybackgrounds. 45

PAGE 46

1. EL-TRACK,requiringatleastoneaxial 2. RADTAU,requiringtwoormorestereotracks,andeitherashowerclusterwithenergyabove750MeVortwoshowerclusterseachwithenergyabove150MeVinsidethebarrelregion. 3. TWO-TRACK,requiringatleasttwoaxialtracks.Only5.3%oftheeventssatisfyingthisconditionwereacceptedasthistriggerlinewaspre-scaledbyafactorof19intheCLEOIIIdetector Anadvanceddescriptionofthetriggerdetectorcanbefoundin[ 47 ]. 2-13 .TheCLEO-cdetectorcameintooperationatthelaunchoftheCLEO-cera[ 2 ]in2001,aimedatprovidingextremelyhighprecisioninthestudyofthecharmedmesonsandthedynamicsofthecharmoniumstatesinthe3-5GeVenergyrange.TheCLEO-cdetectorisidenticaltotheearlierCLEOIIIdetectorinallaspects,withtheexceptionoftwomodications:themagneticeldisloweredtoavalueof1.0Tfrom1.5TinCLEOIII,andaninnerwiredriftchamber 46

PAGE 47

2 ]. 2-14 showsanisometricviewoftheZD.Itismadeupof300driftcells,eachshapedinanearsquareofside10mm(Figure 2-8 ),andconsistingofasensewire(20mdiametergold-platedtungsten)surroundedbyeighteldwires(110mdiameteraluminum).Anelectriceldismaintainedbyapplyingapotentialdierenceof1900Vbetweenthesenseandeldwires.ThesixlayersoftheZDareallslightlytilted(rotatedin),arrangedatastereoangleinordertorenderaccuratezinformationofthechargedtrack.Theinner(outer)layerisat10.3(15.4)stereoangle.TheZDislledwitha60:40helium-propanegasmixture,withradiationlengthofabout330m.ThemannerinwhichtheZDdetectschargedparticlesisidenticaltothatinthemaindriftchamberdescribedinsubsection 2.3.1.3 .Forlowtransversemomentum(PTlessthatabout70MeV)tracks,theZDisthesolesourceofzinformationforthetrack.ThepositionresolutionofchargedparticlesinthezcomponentattainedbytheZDis680m,anditprovidesamomentumresolutionofnearly0.4%forchargedparticlesatnormalincidence(cos=0). 47

PAGE 48

48 ].ThusMonteCarlo AMonteCarlo(MC)simulationofeventsisaonesuchtechniquewhereaneventisaninteractionandthesimulationcanbeofdierentlevelsofsophistication.Itiswidelyusedinhigh-energyphysicsexperimentstodesigndetectors,andtosimulatehowthedetectorrespondstoaparticularprocess.Itbecomesanindispensabletoolfordeterminingthe\real"rateofaparticularprocess(aninteractionordecay).Todeterminethisrate,oneneedstoknowtheeciency AtypicalCLEOMCsimulatesthephysicsprocessoccurringduringacollisionandincludestheproductionandtrackingoftheout-comingparticles.Theresponseoftheactivedetectorelementsissimulatedincludingpossiblesourcesofbackgroundsintheexperiment. The\physics"simulationwhichoccursattherststageusesinformationaboutbeamenergiestosimulatethecollisionsofthebeam.Wegenerateparticleswithaneventgeneratorrandomly(butaccordingtothedesireddistributions),andobeyingthelawsofphysics.Theproducedparticlesaredecayedusingalistofpossiblenalstatescalled\decaytable"untilonlystableorlonglivedparticlesremaingivingrisetoanassociated\decaytree." 48

PAGE 49

49 ]. Thelaststageinvolvesreconstructingtracksandshowersfromlowleveldetectorhitsusingthethesamealgorithmsthatareusedfordatareconstruction(calledpass2 Inthisanalysis,weusetwotypesofMC: 1. \SignalMC"isgeneratedtosimulateaspecic(signal)decaymodeofinterest.Thedecaytableallowsonlyone(orfew)decaysofinterest. 2. \GenericMC"thatisgeneratedtosimulateallpossibleactualphysicalmixofknownprocessesanddecays,andismainlyusedtostudybackground. Ofthesetwo,wegeneratedallsignalMC(forstudyingsignalprocessesandspecicbackgroundchannels)usingtheEvtGengenerator[ 50 ],whereasthegenericMCsamplewasusedfromthelibraryofMCevents,generatedfortheentireCLEOcollaborationforusewhenanalyzingthisdataset. AlthoughMCisavitaltoolinanyanalysis,onemustrememberthatMCisnotrealdataanditcanatbestonlytrytomimicdata.ThusonemuststudycarefullythereliabilityofthesimulationbycomparingtheMCtodata,andmakecorrections,orincorporatediscrepanciesintothesystematicerror. Atthisstageoftheendofthischapter,alltheanalysistoolsavailabletoanexperimenterhavebeendiscussed.Itisnowuptoone'sdiscretiontousethesetoolstoexplorethe\physics"ofaninteractionbyseparatingsignalfrombackground. 49

PAGE 50

AschematicoftheCESRapparatusisshown.TheimportantelementsofCESRaretheLINAC,thesynchrotron,andthestoragering. 50

PAGE 51

DenitionofcrossinganglecaatCLEO.Thecrossingangleisdenedastheanglebetweenthepositronbeamandthenominalbeamaxis.Theanglebetweentheelectronandpositronbeamsis2ca.Thevalueofca2mrad. 51

PAGE 52

Figure2-3. CharmoniumcrosssectioninanexploratoryenergyscanatCLEOisshown.Eightdierentenergypointsinthe(2S)massrangehavebeenselected.Theerrorbarsrepresentstatisticaluncertaintiesassociatedwiththemeasurement. 52

PAGE 53

Figureshowsacut-openfrontviewoftheCLEOIIIdetector.Variousdetectorcomponentsarelabeled.Themostimportantsub-detectorsforthisdissertationworkarethevertexdetector,driftchamber,theRICHandtheCalorimeter. 53

PAGE 54

FigureshowstheCLEOdetectorsideview(quarter)cross-section.Themostimportantsub-detectorsforthisdissertationworkarethetrackingdetectors,theRICHandtheCalorimeter. 54

PAGE 55

B Figure2-6. TheCLEOco-ordinatesystemisshown.A)representstheglobalco-ordinateaxes,andB)denestherelationshipbetweentheco-ordinates. 55

PAGE 56

EndviewcrosssectionoftheCLEOIIIsiliconvertexdetectorisshown.Thefourdetectorlayerpositionsandarrangementalongthebeampipeareshown. 56

PAGE 57

FigureillustratestheprincipleofworkingoftheDR.TheeldandsensewirearrangementinatypicalDRcellisshown.Thepatternoflinesrepresentstheelectriceldwhichcausestheionsandelectronstodriftawayfromeachother.Theliberatedelectronsproduceanavalancheandmovetowardsthesensewire,andahitisregistered. 57

PAGE 58

FigureshowsaplotofthedE=dxasafunctionofparticlemomentum.Threedistinctbandsfor,Kandpareseenasonemovesfromlefttoright. 58

PAGE 59

FigureshowstheRICHdetectorcrosssectionalviewintherplane.Thedetectorcomponents:LiFradiatorplate,expansiongas,andMWPCphotondetectorsareseen.Alsoshownisthetrajectoryofachargedtrackandtheemittedphotons. 59

PAGE 60

FigureshowstheRICHparticleseparationasafunctionofmomentum(P),forparticlesabovetheirrespectiveRICHthresholds.Theparticlethresholddeterminationsarebasedonthevalueofn(=1:5forLiF).ThequantityontheordinateistheratioofthedierencebetweenthemeasuredCherenkovanglesoftherespectiveparticles(;e;K;p)and,totheRMSresolutionoftheCherenkovangledeterminationforeachparticletype. 60

PAGE 61

FigureshowstheCCenergyresolutionasafunctionofphotonenergy. 61

PAGE 62

Figureshowsacut-openfrontviewoftheCLEO-cdetector.Variousdetectorcomponentsarelabeled.NotethatthevertexdetectorofCLEOIIIisnowreplacedbyaninnerdriftchamber. 62

PAGE 63

FigureshowsanisometricviewoftheZDdetector. 63

PAGE 64

ThegeneraltoolsrequiredfordatadetectionandanalysiswerediscussedinChapter 2 .Thischapterdescribesthespecicanalysistechnologyemployedinthisresearch. ThesignalMonteCarlosamplesusedinthisanalysiswereallgeneratedusingtheEvtGen[ 50 ]generatorandGeant-based[ 49 ]detectorsimulation.Boththedetectorcongurations(CLEO-candCLEOIII)haveslightlydierentecienciesandresolutions.Wegenerated10,000eventseachforallthemodeswhichcontaintwo0mesons,whereasforalltheremainingmodescontainingorK0mesons,15,000eventsweregeneratedforeachdetectorcongurationforeachofthethreecmesons.ThesignaleventswereallgeneratedusingthePHSP(phasespace 30 ] 64

PAGE 65

30 ],andthereforetheeciencyforsuchmodesincludestheintermediatebranchingfractionsofthemodesofreconstructionoftheandK0S.ThesignalMCforthisanalysisaloneamountstomorethanhalfamillionevents(540,000).Inordertoaccountfortheangulardistributioncorrespondingtoeachofthethreeccandidatesfortheradiativedecay(2S)!cJ,theMCwasgeneratedinaccordancewithanE1transitionproductioncrosssectionexpectationof1+cos2(),where=1;1=3;+1=13forJ=0;1;2particles[ 51 ],andistheradiatedphotonanglerelativetothepositronbeamdirection. Wealsogeneratedevents(20,000)forthestudyofananticipatedsourceofbackgroundofthetype(2S)!J=00,J=!+0,usingtheEvtGengeneratormodelVVPIPI(vectordecayintoavectorandtwopions)fortherststepofthedecay,andthePHSPmodelforthelatterstep.Furthermore,wealsoanalyzedagenericMCsamplewithaluminosityequivalenttothedatasampleinordertocheckforpossiblefeed-throughbackgrounds.BoththesebackgroundMCsampleswerebasedontheCLEO-cdetectorcongurationforconvenience. 65

PAGE 66

1. Trackqualitycriteria: WeusedCLEOstandardcutstoensurethequalityofchargedtracks.Agoodtrackisatrackthatsatisesthefollowingconditions: Wealsorequirethenumberof\good"trackstobeeither2or4basedonthenumberofchargedhadronsinthenalstate. Wedemandalltrackscomefromthebeamspotwithamomentum-dependentcutonimpactparameter 2. ChargedParticleIdentication: TheCLEOparticleidenticationinformationwasusedforthep,Kandseparation.WedenedthefollowingparameterstousetheavailabledE=dxand 66

PAGE 67

whereLiaretheLikelihoodsgivenbythemeasuredCherenkovanglesofphotonsintheRICHdetectorcomparedwithpredictedCherenkovanglesforthatparticularparticletype. whereiistheratioofthedierencebetweenthemeasureddE=dxandthepredicteddE=dxvalueswiththeerrorinthedE=dxdeterminationforeachparticletype. Twomoresuchparametersweredenedfor,Kseparationinananalogousmanner,allofwhichareusedforidentication.WefurtherdenefoursuchparameterseachforKandpwhichareemployedforKandpidentication. Inordertoidentifythetracksas,Kandp,wecombinethedE=dxandRICHusingtheabovedenedparameterizationinthefollowingmanner:TousetheRICHwhenevertheRICHinformationisavailable,werequireeachparticlemomentumtobeaboveitsRICHthreshold.Weused0.60GeV/c,0.62GeV/cand1GeV/casthresholdsforpions,kaonsandprotonsrespectively. TosuppresschargedleptonQEDbackgrounds,werequireadditionalcuts.Werejectelectroncandidatesasfollows:foralltracks,wecomputetheratioofCCenergytotrackmomentum,ECC=p,andthedierencebetweenthemeasureddE=dxandtheexpecteddE=dxfortheelectronhypothesis,normalizedtoits 67

PAGE 68

1. Photonselection: PhotonshowersaredenedasthosehavinganenergyproleintheCCconsistentwithbeingaphotonbyrequiringthemtosatisfytheconditionofE9OE25OK Photoncandidatesusedin0andreconstructionareadditionallyrequiredtopossessmorethan50MeVofenergyiffoundintheCCendcapregion. 68

PAGE 69

Wereconstruct0!and!candidatesusingapairofphotoncandidateshavinganenergydepositionintheCCconsistentwithbeingaphoton 3-1 showsamarginalyetdesiredimprovementinthecandidateresolutionachievedafterusingtheneweventvertexposition.Eachphotondaughterofa0()candidateasdescribedbythecriteriaabove,wasrequiredtopossessauniqueshoweridentier(i.e.thephotonshowerinvolvedwasensuredtobeauniquedaughteroftheparentcandidateandwasnotallowedtobeapartofanyothernalstateparticle). 3. Apairofchargedpionswasreconstructedbaseduponthechargedparticlecriteriadescribedinsubsection 3.2.1 ,andcombinedwitha0candidateoftheprolediscussedabovetoformancandidate.The!0+candidatewasmassconstrainedtothenominalmass,andacutof2<10(perdegreeoffreedom)wasplacedonthet. 4. WereconstructtheK0Susingitsdecaytoapairofgoodchargedpiontrackskinematicallyconstrainedtocomefromacommonvertex.Werequirethatthe 53 ]. 69

PAGE 70

3-2 ). Theknowledgeofcompleteevent(reconstructedusingtheabovechargedandneutralselectionconditions)isexploitedtoitsfulladvantagebyapplyingthelawsofconservationofenergyandmomentum. Ifwesimplyobtaintheinvariantmassofthefourhadronscomprisingthec,weobtainaccandidatemassresolutionof30MeV.Alternatively,wecouldusetheenergyofthetransitionphoton,whichhasaonetoonecorrespondencetotheenergyofthec.Thiswould,byitself,producearesolutionoftheorderof7MeVforthecmasses.Tooptimizetheresolution,weusealltheavailableinformationtogether.Wedothisbymeansofakinematicconstraintwherebythecdecayparticlesandthephotonaretogetherkinematicallyconstrained[ 54 ]tomatchthe4-momentumofthebeam.Notethatforthe4-momentumofthebeam,weuseaxedvalueforthemassofthe(2S),withthesmallbeamcrossingangletakenintoaccount.Themassofthe(2S)isknownveryprecisely,anditsnaturalwidthisonly337keV[ 30 ],whichissmallcomparedwiththeotheruncertaintiesintheexperiment.Thisprocedureimprovestheresolutionofthecmasstoaround5MeV,dependinguponmode.Thecutonthe2ofthistisacriticalone,andisoptimizedatavalueof2<25(for4degreesoffreedom).Fig 3-3 showstheproleofthis2variableandindicatestheagreementbetweentheMCmodelingofthiscutanddata. 70

PAGE 71

3-4 a,b),andthettingproceduregreatlyimprovesthemassresolutionofthec(asseeninFig 3-5 a,b).TheimprovementinthephotonenergyspectrumduetothekinematicttingprocedureisseeninFig 3-6 a,b.Thecinvariantmassisfoundusingtheupdatedparametersduetotheconstraint. In10%oftheevents,wendaproblemofmultiplecombinationsofphotonsinthenalstates(forexample,inmodesinvolvingoneormore0ormesons)leadingtomorethanoneccandidateperevent,thuscausinganapparentincreaseinthenumberofnalstateccandidates.Toovercomethisproblem,anadditionalcriteriontorejectsuchcandidatespereventisappliedbychoosingonlythatcandidateineacheventwhichhastheleastvalueoftheabove2ofthettothetotal4-momentumbeamconstraint.Thenumberofmultiplecandidatesishighestforthe+00nalstateasseeninFig 3-7 a,b. 30 ](c0=10:4MeV,c1=0:89MeV,c2=2:06MeV.)Thedetectorresolution(representedbyadoubleGaussian)isobtainedfromtheMCtofthedierencebetweenthegeneratedandreconstructedmass(MgenMrec)foreachcineachmode.Fig 3-8 representsthedetectorresolutionfunctionforthemodec0!pp00.Notethatthedetectorresolutionwhich 71

PAGE 72

Thecmassesarekeptxedtotheirnominalvaluesduringthetting,duetothepresenceofmanyttingparameters(18signalparameters).Inallcases,thereconstructedmassesare,whenallowedtooat,consistentwiththesevalues.Figs 3-9 3-11 showthettingfunctionsdescribedaboveforthemodec!KK0S0insignalMC.Theabovettingprocedureisusedtotthedata(CLEOIIIandCLEO-csamplestogether)toobtaintheyieldsandalsotondthenumberofreconstructedeventsinthecaseofMCforevaluatingthesignaleciencies. 3-1 and 3-2 .ItmaybenotedthattheseareratherdierentforCLEOIIIandCLEO-c,yetweobservetheuniformtrendofhighereciencyforCLEO-casseeninpreviousanalyses[ 38 39 ].Theecienciesofmodeslistedincludesthe!and!+0branchingratios.TheeciencyfortheKK0S0modeincludestheK0S!+branchingratio.Thenaleciencies(")areobtainedbytakingaweightedaverage(weightedbythenumberof(2S)events)overtheCLEOIIIandCLEO-cdatasetsarelistedinTable 3-3 .ThefractionalerrorsontheecienciesareconsideredwithothersystematicuncertaintiesdiscussedlaterinChapter 4 .Theyieldsinthedataareobtainedbyusingthettingprocedurediscussedinthesection 3.3 .Cleansignalsofc0,c1andc2arefoundincaseofmostmodesstudied.OurbackgroundstudiesbasedonagenericMCsampleof(2S)decays,indicatednegligiblecontaminationandnopeakingbackgroundsinallthemodesstudied,whileourstudiesofthesimulatedsampleof 72

PAGE 73

3-12 showsthescatterplotoftheinvariantmassofthe+0combinationversustheccandidatemassindata.ThehorizontallineattheJ=massindicatesthepresenceofthisbackground.Wedonotgetridoftheseevents,astheyoccurthroughoutthecmassregionandthusgetaccommodatedbythebackgroundfunctionusedinthettingprocedure. Figures 3-13 through 3-19 showthetparametersofthedatattedhistograms,andFigures 3-20 to 3-26 andTable 3-3 summarizetheyieldsobtainedindata. 73

PAGE 74

CLEO-cMCeciencies(in%)foreachmode. Modec0c1c2 Note:TheecienciesforthemodesincludethebranchingfractionsofB(!)andB(!+0),andtheeciencyfortheK0SmodeincludestheK0S!+branchingratio. Table3-2: CLEO-3MCeciencies(in%)foreachmode. Modec0c1c2 Note:TheecienciesforthemodesincludethebranchingfractionsofB(!)andB(!+0),andtheeciencyfortheK0SmodeincludestheK0S!+branchingratio. 74

PAGE 75

YieldsandcombinedCLEO-candCLEOIIIeciencies(%)of4-hadronnalstates. Modec0c1c2 Note:TheecienciesforthemodesincludethebranchingfractionsofB(!)andB(!+0),andtheeciencyfortheK0SmodeincludestheK0S!+branchingratio.Thefractionalerrorsontheecienciesareconsideredwithothersystematicuncertainties,andarelistedinTable 4-1

PAGE 76

Events=MeV Reconstructedinvariantmassdistributionofthe0!candidateisshown.Thedefault0(solidblack),isoverlayedbythecandidatere-tfromtheeventvertex(dottedred). 76

PAGE 77

Events=4MeV EectoftheK0SightsignicancecutindataforthemodeKK0S0.Thedotted(red)histogramiswithnocutonthisvariablewhilethesolid(black)histogramisafteracutofK0Sightsignicance5.WechosenottoapplyacutonK0Sightsignicance. 77

PAGE 78

#Events Proleofthekinematicconstraintcutof2<25isshownforthemode+00,forthesidebandsubtractedc0candidateevents.ThesignalMCcutprolehistogram(solidblack)isoverlaidbythecorrespondingscaleddataplot(bluepoints).Thearrowmarksthecutvalue. 78

PAGE 79

Events=4MeV Events=4MeV Improvementsinthesignaltonoiseratio,andthecmassresolutionduetothe2<25cutareshown.Eventswith2<1000cut(solidblack)andafter(dottedred)theapplicationofthe2<25cutwhilekeepingallotherselectionconditionsimposedforthemode+00intheA)c0signalMC,andB)dataaredepicted. 79

PAGE 80

Events=4MeV Events=4MeV Theunconstrained(constrained)ccandidateinvariantmassdistributionsareshownindottedblack(solidred)histogramsforthemodeKK0S0intheA)c0signalMC,andB)data. 80

PAGE 81

Thetransitionphotonenergydistributionsbefore(after)thekinematicttingprocedureareshownindottedblack(solidred)histogramsforthemodeKK0S0intheA)c0signalMC,andB)data. 81

PAGE 82

Events=4MeV Events=4MeV TheeectofmultiplecandidaterejectioncriteriainsignalMCisshownviathedotted(red)histogramincontrasttothesolid(black)histogramwhichincludesthemultiplycountedcandidatesforthemodesA)+00andB)KK0S0. 82

PAGE 83

ThedoubleGaussianfunctionalrepresentationofthedetectorresolutionisshown.ThesignalMCc0massresolutionforthemodepp00iswellrepresentedbyadoubleGaussianfunction. 83

PAGE 84

DoubleGaussianconvolutedwithB-Wfunctionalrepresentationofthesignalvariablei.e.thettedsignalMCforc0candidateinvariantmassdistributionforthemodeKK0S0isshown. 84

PAGE 85

DoubleGaussianconvolutedwithB-Wfunctionalrepresentationofthesignalvariablei.e.thettedsignalMCforc1candidateinvariantmassdistributionforthemodeKK0S0isshown. 85

PAGE 86

DoubleGaussianconvolutedwithB-Wfunctionalrepresentationofthesignalvariablei.e.thettedsignalMCforc2candidateinvariantmassdistributionforthemodeKK0S0isshown. 86

PAGE 87

StudiesofananticipatedbackgroundfromJ=.Ascatterplotoftheinvariantmassofthe+0combinationversustheccandidatemassindataisshown.ThehorizontallineattheJ=massindicatesthepresenceofthisbackground. 87

PAGE 88

Thettedsignalvariableforthe+00modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 88

PAGE 89

ThettedsignalvariablefortheK+K00modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 89

PAGE 90

Thettedsignalvariableforthepp00modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 90

PAGE 91

Thettedsignalvariableforthe+0modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 91

PAGE 92

ThettedsignalvariablefortheK+K0modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 92

PAGE 93

Thettedsignalvariableforthepp0modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 93

PAGE 94

ThettedsignalvariablefortheKK0S0modeshowstheccandidateinvariantmassdistribution.Thetisdescribedinthetext. 94

PAGE 95

Datayieldsforthe+00mode.Thettedccandidateinvariantmassdistributionisshown. 95

PAGE 96

DatayieldsfortheK+K00mode.Thettedccandidateinvariantmassdistributionisshown. 96

PAGE 97

Datayieldsforthepp00mode.Thettedccandidateinvariantmassdistributionisshown. 97

PAGE 98

Datayieldsforthe+0mode.Thettedccandidateinvariantmassdistributionisshown. 98

PAGE 99

DatayieldsfortheK+K0mode.Thettedccandidateinvariantmassdistributionisshown. 99

PAGE 100

Datayieldsforthepp0mode.Thettedccandidateinvariantmassdistributionisshown. 100

PAGE 101

DatayieldsfortheKK0S0mode.Thettedccandidateinvariantmassdistributionisshown. 101

PAGE 102

Inthischapterwediscussthedominantfactorswhichcontributetotheuncertaintyinthemeasurementsmadeinthisanalysis.Theerrorsassociatedwiththenatureoftheexperimentalapparatus,andthoserelatedtothetoolsandmethodsemployedwillbediscussedandevaluated. SeveralsourcesofsystematicuncertaintiesinthebranchingfractionsareinvestigatedandarelistedinTable 4-1 .LimitedMCstatisticsindeterminingthereconstructionecienciesintroduceseectsatthelevelof1.6%to3.0%.Systematicuncertaintiesassignedfortrackingarebasedupona0.7%uncertaintyassociatedwitheachchargedtrackpresentintheevent.Uncertaintyinthechargedparticleidenticationeciencyintroducesanuncertaintyinthebranchingratiosof0.3%perpionand1.3%foreachkaonandprotontrackinthenalstate.SecondaryvertexingusedforK0Sreconstructioninoneofthemodesintroducesanadditional2%error.Auniversaluncertaintyof1%isassignedtoallthemodesduetothetriggersimulation,whileaglobal2%uncertaintyisattributedtothetransitionphotonreconstructionforeachofthenalstates.Inaddition,thesystematicuncertaintiesfor0,ecienciesare4%foreach0,mesoninthenalstate.Auniversalerrorof3%wasassignedtoallthemodesattributedduetotheuncertaintyinthenumberof(2S)particles,determinedaccordingtothemethoddescribedin[ 31 ].Therobustnessofthettingprocedurewascheckedbysystematicallyre-ttingthecinvariantmassplotsusingoatingmasses,widths,andresolutions.Themaximumdeviationsintheyieldsweretakenasthesystematicerrorcomponentsarisingduetothettingprocedure.Themaximumdeviationsoccurredincaseswheneitherthemassesandwidths,orthemassesandresolutions,ortheresolutionsandwidthsweresimultaneouslyunconstrained.Thesevarybetween0.7%and5.8%aslistedinTable 4-1 forallthemodes.Westudiedthecutonthe2ofthekinematicconstraintforsystematiceects.Inordertodoso,westudythreemodeswithhighstatisticsviz.+00,KK0S0and 102

PAGE 103

3-3 showsthedistributionofthis2variableindata(bluepoints)andMC(solidblack)overlaidforthelargestsignalstatisticsmode+00(thedataisnormalizedwithrespecttotheMC).WenotefromthisdistributionthattheproleofthiscutmatcheswellbetweendataandMCindicatingthecorrectmodellingofthecutinMC.Ourndingsfortheineciencyofthe2<25cutforthemodes+00,K+K00andKK0S0are16.7%(10.0%),13.6%(10.1%)and9.1%(6.3%)respectivelyfordata(MC).Inaccordancewiththesendings,weassignamaximumsystematicuncertaintyof4.0%whichisslightlyhigherthan,yetconsistentwiththecorrespondingvaluesfoundinthepreviouslineofanalysesbasedonthissubject[ 38 39 ]. AnothersourceofsystematicerrorisduetothefactthattheMCwasallgeneratedusing4-bodyphasespaceignoringthepossibilityofthepresenceofintermediateresonances(discussedinchapter 5 onsubstructure).Apossiblepresenceofsubstructurecouldleadtoadierentangulardistributionofthenalstateparticlescomparedtothecasewhennointermediateresonancesarepresent.Insuchasituationwheresubstructureispresent,andismostoftenthecaseinrealdata,theuseofaatMC(4-bodyphasespace)todeterminetheeciencyofagivenmodewillleadtoincorrectresults. Toaccountforsucheects,MCsimulationsweregeneratedforthethreehighstatisticschannels(+00,K+K00,KK0S0)correspondingtowhichweobservedvariousintermediateresonancesindata.WegeneratedMCforsubstructuremodes:f0(980)00,f2(1270)00,0andf0(980)+forthenon-resonantmode+00;KK0andf0(980)K+Kforthenon-resonantmodeK+K00;forthenon-resonantmode+0;K0K00,KK0,KK0,KK0,K0KandK1(1270)K0forthenon-resonantmodeKK0S0usingphasespacemodelintheCLEO-cdetectorconguration(Figs????showevidenceforthepresenceofsuchintermediateresonancesignalsindata).Weobtainedtheecienciesofboththeresonantandnon-resonantmodesbyttingthecsignalsobtainedfromMCeventswithand 103

PAGE 104

4-2 .Basedonthedierencesinecienciesbetweennalstateswithandwithoutintermediateresonances,andassumingthattherecanbeno"additionalunobserved"resonancesthatcanbemorethan50%ofthesignal[ 52 ],weestimatethesystematicerrortobebetween3.5%and7.4%asshowninTable 4-1 forthemodeswestudied.Fortheremainingmodes,weconservativelyassigna7.5%systematicerrorbasedonanassumptionthatupto75%ofoureventscontainsubstructure,andthatthedierenceineciencyoftheseresonanteventstothenon-resonantisnomorethan10%. 104

PAGE 105

Systematicuncertainties(in%)areshown. Source+00K+K00pp00+0K+K0pp0KK0S0

PAGE 106

MCeciencies"(in%)forallmodesareshown.ThedetectorconfugurationCLEOimpliescombinedCLEO-candCLEOIIIaverageeciencies.Theecienciesofboththeresonantandnon-resonantmodeswereobtainedbyttingthecinvariantmassdistributionsobtainedfromthecorrespondingMCsamples.Werefertothismethodofndingtheecienciesofthesubtructuremodesas\unclipped"incontrasttothebackgroundsubtractionprocedureusedtodeterminetheseecienciesforcalculatingthesubstructurebranchingfractions(themethodisdiscussedinSection 5.2 ).Thefollowingeciencynumberswereusedtodeterminethesystematicuncertaintiesduetothemodeldependencebasedontheproceduredescribedinthetext. Modec0c1c2detector 106

PAGE 107

Inthischapter,weexplorethepossibilityofthepresenceofintermediateresonancesleadingtothesamenalstates. Moreimportantly,knowledgeofthesubstructuretellsusaboutthemannerinwhichthedecayproceeds. Giventhelimitedstatisticsinthisanalysis,werestrictourselvestolookingforthegrossfeaturesofthesubstructure.Wesearchedforpossiblesubstructureandfoundmanyinterestingpossibilitiesincludingfewclearsignalwhileothersbeinghintsofnewpossibilitiestoexplorewithmoreincomingdata.Figs 5-2 through 5-31 showtherichsubstructureplots.Allofthesearesidebandsubtractedplotswithcutsontherespectivecmasswindows,asdescribedinthefollowingsection. 5-1 ,thesignalregionsforc0,c1,andc2are3.370-3.470GeV/c2,3.490-3.535GeV/c2and3.535-3.590GeV/c2,respectively.One-sidedsidebandsof3.300-3.360GeV/c2,3.470-3.490GeV/c2and3.590-3.625GeV/c2,respectively, 107

PAGE 108

30 ],andaddanadditionalthirdorderpolynomialfunctiontoincorporatethebackgrounds.Weobtaintheeciencies(0)fortheintermediatestatesbygenerating20,000events(10,000eventseachfortheCLEO-candCLEOIIIdetectorcongurations)usingthePHSPmodelofEvtGen.Allresultsreportedinthefollowingarerstobservationsoftheseintermediatestates.Wediscusstheresultsbelowindetail. 1. IntermediatestatesincJ!+00nalstate: Thefour2-bodyinvariantmasscombination(m+,m+0,m0andm00)tteddistributionsforthec0stateindataareshowninFigures 5-2 through 5-5 .WendtheevidenceofclearsignalsofinFigures 5-4 and 5-5 .Therearesignsoff0(980)andf2(1270)statesinFigures 5-2 and 5-3 ,whichdonotmeetthe4signicancecriterion.Similarly,wendtheprominentsignalsinthecaseofc1andc2asseeninFigures 5-6 through 5-9 .Theiryieldsandeciencies0,listedinTable 5-1 ,areusedasinputstothenalbranchingfractioncalculations. 2. IntermediatestatesincJ!K+K00nalstate: Variousinvariantmasscombination(mK+K,mK+0,mK0andm00)tteddistributionsforthec0andc1statesindataareshowninFigures 5-10 through 108

PAGE 109

.Theseindicatethepresenceofintermediateresonances,f0(1500),f0(1710),f0(980)andK,noneofwhicharesignicantenoughtoclaimsignals. 3. IntermediatestatesincJ!KK0S0nalstate: Figures 5-16 through 5-31 showvariousinvariantmasscombination(mK,m0,mK0S,mK0,mK0S0andmK0)tteddistributionsforthec0,c1andc2states.Clearsignalsof,andKareseeninsomeofthemodeslistedinTable 5-1 ,andweseeahintofK1(1270)inc1!K0distributionamongothers. 4. IntermediatestatesincJ!+0nalstate: Figures 5-32 5-33 showthepresenceofresonancesubstructureintheinvariantmasscombinationsof+0forc0andc2.Weforgotheanalysisofthesesubstructuremodesastheyhavebeenpresentedinourearlierwork[ 38 ]. Systematicuncertaintiesfortheseintermediateresonancebranchingfractionsincludethecommonsourcesoferrorsfortherespectivenon-resonantnalstateswhosevaluesarelistedinTable 4-1 109

PAGE 110

Yieldsandeciencies(in%)forsubstructuremodes."representstheeciencyobtainedbyttingthecsignalsusingthesameprocedureasthatusedforthefour-hadronmodes,insubstructuresimulatedsamples(alsolistedinTable 4-2 ).Eciency0wasobtainedbyttingtheresonantsignalsafterapplyingthesidebandsubtractionproceduredescribedinthetext. Modec0c1c2

PAGE 111

Figureelucidatessignalandsidebandregionsforthecstates.Arrowsmarkthesignalregionswhereastheshadedareasrepresenttheone-sidedsidebands. 111

PAGE 112

Figureshowsdataforthedecayc0!+00mode.Invariantmasscombinationof+isshown. 112

PAGE 113

Figureshowsdataforthedecayc0!+00mode.Invariantmasscombinationof00isshown. 113

PAGE 114

Figureshowsdataforthedecayc0!+00mode.Invariantmasscombinationof0isshown. 114

PAGE 115

Figureshowsdataforthedecayc0!+00mode.Invariantmasscombinationof+0isshown. 115

PAGE 116

Figureshowsdataforthedecayc1!+00mode.Invariantmasscombinationof+0isshown. 116

PAGE 117

Figureshowsdataforthedecayc1!+00mode.Invariantmasscombinationof0isshown. 117

PAGE 118

Figureshowsdataforthedecayc2!+00mode.Invariantmasscombinationof+0isshown. 118

PAGE 119

Figureshowsdataforthedecayc2!+00mode.Invariantmasscombinationof0isshown. 119

PAGE 120

Figureshowsdataforthedecayc0!K+K00mode.InvariantmasscombinationofK+Kisshown. 120

PAGE 121

Figureshowsdataforthedecayc0!K+K00mode.InvariantmasscombinationofK+0isshown. 121

PAGE 122

Figureshowsdataforthedecayc0!K+K00mode.InvariantmasscombinationofK0isshown. 122

PAGE 123

Figureshowsdataforthedecayc0!K+K00mode.Invariantmasscombinationof00isshown. 123

PAGE 124

Figureshowsdataforthedecayc1!K+K00mode.InvariantmasscombinationofK+0isshown. 124

PAGE 125

Figureshowsdataforthedecayc1!K+K00mode.InvariantmasscombinationofK0isshown. 125

PAGE 126

Figureshowsdataforthedecayc0!KK0S0mode.InvariantmasscombinationofKisshown. 126

PAGE 127

Figureshowsdataforthedecayc0!KK0S0mode.Invariantmasscombinationof0isshown. 127

PAGE 128

Figureshowsdataforthedecayc0!KK0S0mode.InvariantmasscombinationofK0isshown. 128

PAGE 129

Figureshowsdataforthedecayc0!KK0S0mode.InvariantmasscombinationofK0isshown. 129

PAGE 130

Figureshowsdataforthedecayc0!KK0S0mode.InvariantmasscombinationofK00isshown. 130

PAGE 131

Figureshowsdataforthedecayc1!KK0S0mode.InvariantmasscombinationofK0isshown. 131

PAGE 132

Figureshowsdataforthedecayc1!KK0S0mode.InvariantmasscombinationofK0isshown. 132

PAGE 133

Figureshowsdataforthedecayc1!KK0S0mode.InvariantmasscombinationofK00isshown. 133

PAGE 134

Figureshowsdataforthedecayc1!KK0S0mode.InvariantmasscombinationofKisshown. 134

PAGE 135

Figureshowsdataforthedecayc1!KK0S0mode.Invariantmasscombinationof0isshown. 135

PAGE 136

Figureshowsdataforthedecayc1!KK0S0mode.InvariantmasscombinationofK0isshown. 136

PAGE 137

Figureshowsdataforthedecayc2!KK0S0mode.InvariantmasscombinationofKisshown. 137

PAGE 138

Figureshowsdataforthedecayc2!KK0S0mode.Invariantmasscombinationof0isshown. 138

PAGE 139

Figureshowsdataforthedecayc2!KK0S0mode.InvariantmasscombinationofK0isshown. 139

PAGE 140

Figureshowsdataforthedecayc2!KK0S0mode.InvariantmasscombinationofK0isshown. 140

PAGE 141

Figureshowsdataforthedecayc2!KK0S0mode.InvariantmasscombinationofK00isshown. 141

PAGE 142

Figureshowsdataforthedecayc!+0mode.Invariantmasscombinationof+0forc0!+0isshown.Wedonotdiscussthisstateanyfurtherasithasbeenstudiedinourearlierwork[ 38 ]. 142

PAGE 143

Figureshowsdataforthedecayc!+0mode.Invariantmasscombinationof+0forc2!+0isshown.Wedonotdiscussthisstateanyfurtherasithasbeenstudiedinourearlierwork[ 38 ]. 143

PAGE 144

Inthischapter,weconverttheobservationsandanalysesofdata(yieldsandeciencies)frompreviouschaptersintomeaningfulmeasurementsofphysicalquantitiesofinterest.Wearriveatbranchingfractionsandupperlimitswhereverapplicableforthesevenmodesunderstudy. ThesystematicuncertaintieslistedinTable 4-1 werealladdedinquadrature.Theonesduetothebranchingfractionsof(2S)!cJ[ 31 ]arequotedseparately.Formostofthenalstates,weconverttheyieldsinTables 3-3 and 5-1 tobranchingfractionsusing: 31 ](6{1) whereNyieldyieldindata;N(2S)numberof(2S)=3.08106;e"listedinTable 3-3 forfour-hadronmodes,or0listedinTable 5-1 forsubstructuremodes,andirepresentsaparticularfour-hadronorsubstructuredecaymode. Tocalculatethebranchingfractionsfortheinclusivefour-hadronnalstatesforthemodes+00andKK00whichhaverichsubstructure,weuseamodiedprocedure.Sincethe0resonantmodeyieldsclearlydominatethefour-hadronnalstateyieldsforthe+00mode(Tables 3-3 and 5-1 ),weusetheeciency,"ofthe0sub-modelistedinTable 5-1 andequation 6{1 todeterminethe+00four-hadronbranchingfraction.Theseeciencies"wereobtainedbyttingthecsignalsinsubstructuresimulationsusingthesamettingprocedureasthatusedforthefour-hadronsignalsimulations 144

PAGE 145

5-1 ).WereplacetheratioNyieldi=eiinequation 6{1 withaneciencycorrectedyield(Y0KK00)byaddingtheindividualeciencycorrectedcontributionsduetoallresonantandnon-resonantchannelscomputedas: wherekrunsoverthesubstructuremodesweconsider,K0K0S0,K0K,KK0,KK0S,andKK0S. Thebranchingfractionsthusobtained,andtakingintoaccountthesystematicuncertaintiesfromChapter 4 ,wegettheresultssummarizedinTable 6-1 .Wherewedonotndevidenceofasignal,wepresenta90%C.L.upperlimitbydeterminingthevaluethatincludes90%oftheprobabilitydensityfunction(p.d.f)obtainedbyconvolvingthep.d.fforthebranchingfractionwithaGaussiansystematicerror.Todothis,wetakethep.d.finmn t Thereportedfour-hadronbranchingratiosincludepossibleintermediateresonancescascadingtothegivennalstate,aswellasdirectnon-resonantdecaystothenalstate.Thereportedthree-hadronintermediateresonancemodebranchingfractionsareinclusiveofotherhiddenresonanceswhichcouldleadtothesamethree-hadronnalstatesandthereforedonotrepresenttheamplitudesforthethree-bodynon-resonantbranchingfractions. AcomparisonofsomeoftheresultsinthisdissertationwithexistingmeasurementsfromotherexperimentsarelistedinTable 6-2 .WecomparethecJ!0forJ=0;1;2branchingfractionsmeasuredinthisanalysis(Table 6-1 )withcJ!0+ 55 ]usedbyhighenergyphysicists. 145

PAGE 146

30 ]((1.60.5)%,(0.390.35)%,and(0.70.4)%forJ=0;1and2respectively),andndourmeasurementstobeofbetterprecisionandsimilarstrengthwithinexperimentalerrors,asexpectedfromisospinsymmetry.Furthermore,wealsondourmeasurementofB(c2!K0K)(Table 6-3 )tobehigheryetconsistentwithinexperimentalerrorswithB(c2!K0K)of[ 30 ].WealsoobservethattheisospinformalismworkswellforthemodescJ!KKwherecJ!K0K00andcJ!KK0areexpectedtohaveequalpartialwidths(comparetheseforc0andc2statesinTable 6-3 sinceforthelattermode,wedonothave4signalsforc1).Moreover,ourmeasurementsfortheB(c2!K0K),B(c0!KK0),andB(c2!KK0)(Table 6-3 )areingoodagreementwiththeisospinexpectation and A foradiscussionoftheseisospinexpectations. 146

PAGE 147

Branchingfractions(B.F.)withstatisticalandsystematicuncertaintiesareshownrespectively.Thesymbol\"indicatesproductofB.F.'s.Thethirderrorineachcaseistheoneduetothe(2S)!cJBF.Upperlimitsshownareat90%C.Landincludeallthesystematicerrors.Themeasurementsofthethree-hadronnalstatesareinclusivebranchingfractions,anddonotrepresenttheamplitudesforthethree-bodynon-resonantbranchingfractions. Modec0c1c2

PAGE 148

Comparisonofresults. Modec0c1c2Source B.F(%)B.F(%)B.F(%) Table6-3. Resultsrelatedbyisospinareshown.BranchingfractionsandcombinederrormeasurementsfortheisospinrelatedKKintermediatemodesarelisted. Modec0c1c2 148

PAGE 149

Insummary,thebranchingfractionsforcJ!+00,cJ!K+K00,cJ!+0,cJ!K+K0,andcJ!KK00forJ=0;1;2and,cJ!pp00forJ=0;2,aremeasuredforthersttime.Forthemodesc1!pp00andcJ!pp0forJ=0;1;2wherewedonotndenoughevidenceofasignal,wepresentupperlimits(UL)at90%C.L.Wealsomeasureforthersttimethebranchingfractionsoftheintermediateresonancemodes:cJ!+0and+0,cJ!K0K00,andcJ!KK0forJ=0;1;2;c2!K0K;cJ!KK0andcJ!KK0forJ=0;2.Ourmeasurementscanaccountforupto8%ofthehadronicwidthofthecstates.Thesenewlydiscoveredexclusivedecaychannelsforwhichthereareasyetnospecicpredictions,arehelpfulphenomenologicalinputstotheoreticalQCDmodelstryingtounderstandthedecaymechanismsofcstates,andtheroleoftheCOMinthesedecays.ThesemeasurementsimproveourexistingknowledgeoftheexclusivemanybodydecaymodesofthecstatesandconstitutealargeportionofthehadronicwidthoftheseP-wavecharmoniastates.Weurgethetheoriststoextractusefulinformationandcomeupwithanunderstandingofthegoverningdecaydynamicsofthecstatesusingourresultstogetherwiththeonesalreadyexistinginthissector. Thefour-hadronnalstates+00andKK00,arealmostentirelysaturatedwithrichsubstructureofintermediateresonances.OurmeasurementswillserveassignicantnewadditionsintherelevantsectionsoftheParticleDataBook.Whilethesemeasurementsarealreadyinteresting,theseresultswillfurtherserveasusefulguidelinesforthereconstructionofthesestatesinnewupcomingdataattheseenergies. 149

PAGE 150

Herewedemonstratetheuseoftheisospinsymmetry(discussedinChapter 1 )tondtherelativeproportionsofcJ!KKdecaysrelatedbyisospin.Inparticular,wepresentthecalculationsusingtheisospinformalismandarriveatequations 6{3 and 6{4 ofChapter 6 Notation:jI;Iz>areiso-spineigenstates,whereIandIzdenotetheisospinanditszcomponentrespectivelyinisospinspace. 1. IsospinanalysisforcJ!K0K: Belowweestimatetherelativeproportionsofthedecays,cJ!K0K00andcJ!K0K+. (a) IsospinamplitudeofcJ!K0K00. FigureA-1. FeynmandiagramandisospineigenstatesforcJ!K0K00. 2;1 2>j1 2;1 2>j1;0>=j1 2;1 2>r 3j3 2;1 2>r 3j1 2;1 2>!

PAGE 151

3j2;0>+r 3j1;0>r 6j1;0>r 6j0;0> 6<0;0j0;0> 6 (A-1) (b) IsospinamplitudeofcJ!K0K+. FigureA-2. FeynmandiagramandisospineigenstatesforcJ!K0K+. 2;1 2>j1 2;1 2>j1;1>=j1 2;1 2>r 3j3 2;1 2>r 3j1 2;1 2>! 6j2;0>r 6j1;0>r 3j1;0>+r 3j0;0>

PAGE 152

3<0;0j0;0> 3 (A-2) Dividingequation A{1 by A{2 wededuce, 2 (A-3) 152

PAGE 153

IsospinanalysisforcJ!KK (a) IsospinamplitudeofcJ!K+K0. FigureA-3. FeynmandiagramandisospineigenstatesforcJ!K+K0. 2;1 2>j1 2;1 2>j1;0>=j1 2;1 2>r 3j3 2;1 2>+r 3j1 2;1 2>! 3j2;0>r 3j1;0>+r 6j1;0>r 6j0;0> 6<0;0j0;0> 6 (A-4) 153

PAGE 154

IsospinamplitudeofcJ!K+K0. FigureA-4. FeynmandiagramandisospineigenstatesforcJ!K+K0. 2;1 2>j1;1>j1 2;1 2>=j1 2;1 2>r 3j3 2;1 2>r 3j1 2;1 2>! 2;1 2>j1 2;1 2>asitistheonlyonewhichwilldecomposeintoaterminj0;0>,andusingstandardClebshGordancoecients,wegetr 3j1 2;1 2>j1 2;1 2>=r 3j1;0>+r 3j0;0> 3<0;0j0;0> 3 (A-5) 154

PAGE 155

A{4 by A{5 wededuce, 2 (A-6) Wearriveatthefollowingrelationsusingequations A{1 A{4 and A{5 : 1 (A-7) 2 (A-8) 155

PAGE 156

[1] G.Viehhauser,Nucl.Instrum.MethodsA462,146(2001). [2] R.A.Briere,G.P.Chen,T.Ferguson,G.Tatishvilli,H.Vogel,J.P.Alexanderetal.(CLEO-cCollaboration),LEPPReportNo.CLNS01/1742,2001(unpublished). [3] D.Griths,IntroductiontoElementaryParticles(JohnWiley&Sons,1987). [4] D.H.Perkins,IntroductiontoHighEnergyPhysics(Addison-Wesley,1987). [5] R.N.CahnandG.Goldhaber,TheExperimentalFoundationsofParticlePhysics(CambridgeUniv.Press,Cambridge,1989). [6] J.Hewett,SLAC-PUB-7930,hep-ph/9810316(1997). [7] R.Cahn,Rev.Mod.Phys.68,951(1996). [8] T.P.ChengandL.-F.Li,GaugeTheoryofElementaryParticlePhysics(ClaredonPress,1984);E.Golowich,J.F.DonoghueandB.R.Holstein,DynamicsoftheStandardModel(CambridgeUniversityPress,1992). [9] P.W.Higgs,Phys.Rev.Lett.12,132(1964);P.W.Higgs,Phys.Rev.145,1156(1966). [10] J.Erler,Phys.Rev.D63,071301(2001). [11] Rohlf,J.William,ModernPhysicsfromatoZ0(JohnWiley&Sons,1994). [12] W.MarcianoandH.Pagels,Phys.Rep.36,137(1978). [13] D.J.Gross,Nucl.Phys.Proc.Suppl.74,426(1999). [14] K.G.Wilson,Phys.Rev.D10,2445(1974). [15] R.P.Feynman,QED:TheStrangeTheoryofLightandMatter(PrincetonUniversityPress,1985);R.P.Feynman,QuantumElectrodynamics(Addison-Wesley,1998);S.S.Schweber,QEDandtheMenWhoMadeIt:Dyson,Feynman,Schwinger,andTomonaga(PrincetonUniversityPress,1994). [16] F.HalzenandA.D.Martin,QuarksandLeptons:AnIntroductoryCourseinModernParticlePhysics(JohnWiley&Sons,1984). [17] I.J.AitchisonandA.J.Hey,GaugeTheoriesinParticlePhysics(AdamHilgerLimited,1982). [18] J.P.Uzan,Rev.Mod.Phys.75,403(2003). [19] P.Z.Quintas,W.C.Leung,S.R.Mishra,F.J.Sciulli,C.Arroyo,K.T.Bachmannetal.,Phys.Rev.Lett.71,1307(1993). 156

PAGE 157

L.W.Jones,Rev.Mod.Phys.49,717(1977). [21] M.Gell-Mann,Phys.Lett.8,214(1964). [22] B.J.BjorkenandS.L.Glashow,Phys.Lett.11,255(1964);S.L.Glashow,J.IliopoulosandL.Maiani,Phys.Rev.D2,1285(1970). [23] J.J.Aubert,U.Becker,P.J.Biggs,J.Burger,M.Chen,G.Everhartetal.,Phys.Rev.Lett.33,1404(1974);J.E.Augustin,A.M.Boyarski,M.Breidenbach,F.Bulos,J.T.Dakin,G.J.Feldmanetal.,Phys.Rev.Lett.33,1406(1974);G.S.Abrams,D.Briggs,W.Chinowsky,C.E.Friedberg,G.Goldhaber,R.J.Hollebeeketal.,Phys.Rev.Lett.33,1453(1974). [24] T.AppelquistandD.Politzer,Phys.Rev.Lett.34,43(1975). [25] J.S.Whitaker,W.Tanenbaum,G.S.Abrams,M.S.Alam,A.M.Boyarski,M.Breidenbachetal.,Phys.Rev.Lett.37,1596(1976);C.J.Biddick,T.H.Burnett,G.E.Masek,E.S.Miller,J.G.Smith,J.P.Stronskietal.,Phys.Rev.Lett.38,1324(1977). [26] E.D.BloomandC.W.Peck,Ann.Rev.Nucl.Part.Sci.33,143(1983);M.Oreglia,E.Bloom,F.Bulos,R.Chestnut,J.Gaiser,G.Godfreyetal.,Phys.Rev.D25,2259(1982). [27] J.L.Richardson,PhysLett.82B,272(1979);C.QuiggandJ.L.Rosner,Phys.Rep.56,167(1979);E.Eichten,K.Gottfried,T.Kinoshita,K.D.LaneandT.M.Yan,Phys.Rev.D17,3090(1980). [28] R.Shankar,PrinciplesofQuantumMechanics(KluwerAcademic/PlenumPublishers,1994). [29] A.M.Green(Editor),HadronicPhysicsFromLatticeQCD(WorldScienticPublishing,2004);D.G.Richards,nucl-th/0006020(2000). [30] W.M.Yao,C.Amsler,D.Asner,R.M.Barnett,J.Beringer,P.R.Burchat,etal.(ParticleDataGroup),J.Phys.G33,1(2006). [31] S.B.Athar,P.Avery,L.Breva-Newell,R.Patel,V.Potlia,H.Stoecketal.,(CLEOCollaboration),Phys.Rev.D70,112002(2004). [32] H.W.HuangandK.T.Chao,Phys.Rev.D54,6850(1996). [33] A.Petrelli,Phys.Lett.B380,159(1996). [34] J.Bolz,P.KrollandG.A.Schuler,Phys.Lett.B392,198(1997). [35] S.M.H.Wong,Nucl.Phys.A674,185(2000). [36] S.M.H.Wong,Eur.Phys.J.C14,643(2000). 157

PAGE 158

C.AmslerandF.E.Close,Phys.Rev.D53,295(1996). [38] G.S.Adams,M.Anderson,J.P.Cummings,I.Danko,J.Napolitano,Q.Heetal.,(CLEOCollaboration),Phys.Rev.D75,071101(2007). [39] S.B.Athar,R.Patel,V.Potlia,J.Yelton,P.Rubin,C.Cawleldetal.,(CLEOCollaboration),Phys.Rev.D75,032002(2007). [40] G.L.Kane,ModernElementaryParticlePhysics:TheFundamentalParticlesandForces?(PerseusPublishing,1993). [41] M.E.PeskinandD.V.Schroeder,AnIntroductiontoQuantumFieldTheory(PerseusBooks,1995). [42] D.Peterson,K.Berkelman,R.Briere,G.Chen,D.Cronin-Hennessy,S.Csornaetal.,Nucl.Instrum.MethodsPhys.Res.,Sect.A478,142(2002). [43] M.Artuso,R.Ayad,K.Bukin,A.Emov,C.Boulahouache,E.Dambasurenetal.,Nucl.Instrum.Meth.Phys.Res.,SectA554,147(2005);M.Artuso,R.Ayad,K.Bukin,A.Emov,C.Boulahouache,E.Dambasurenetal.,Nucl.Instrum.MethodsPhys.Res.,Sect.A502,91(2003). [44] Y.Kubota,J.K.Nelson,D.Perticone,R.Poling,S.Schrenk,M.S.Alametal.,(CLEOCollaboration),Nucl.Instrum.MethodsPhys.Res.,Sect.A320,66(1992). [45] W.R.Leo,TechniquesforNuclearandParticlePhysicsExperiments(Springer,1994). [46] RobertKutschkeandAndersRyd,CLEOCollaborationinternaldocument,CBX96-20(1996). [47] M.A.Selen,R.M.HansandM.J.Haney,IEEETrans.Nucl.Sci.48,562(2001).R.M.Hans,C.L.Plager,M.A.SelenandM.J.Haney,IEEETrans.Nucl.Sci.48,552(2001). [48] R.K.BockandW.Krischer,TheDataAnalysisBriefBook(Springer,Heidelberg,1998). [49] R.Brun,Geant3.21,CERNProgramLibraryLongWriteupW5013,1993(unpublished). [50] D.J.Lange,Nucl.Instrum.Meth.Phys.Res.,Sect.A462,152(2001). [51] L.S.BrownandR.N.Cahn,Phys.Rev.D13,1195(1976). [52] LuisBreva-Newell,JohnYeltonCLEOCollaborationinternaldocument,CBX02-1,(2002). [53] V.S.Potlia,Ph.D.Thesis,(2006). 158

PAGE 159

P.Avery,CLEOCollaborationinternaldocument,CBX98-37,(1998);CBX91-72,(1991). [55] I.C.Brock,CLEOCollaborationSoftwareNote,CSN-94/245,(1996). 159

PAGE 160

RukshanaPatelwasborninhernativeplaceBharuchinGujarat,India,inSeptember1976.HerparentsraisedherinMumbai,thecommercialcapitalofIndia.HermotherRashidaPatelwhohasbeenaverysuccessfulhighschoolteacherandherperfectrolemodel,taughtherlife'smostimportantlessonsandvalues.ShereceivedherhighschooleducationfromSt.Joseph'sHighSchoolandthenwentontodoherjunioranddegreeCollegefromJaiHindCollegeMumbai.AfterreceivingherBachelorofSciencedegree(physicsandinstrumentationmajor),shewenttoMumbaiUniversityKalina,MumbaitopursueherMasterofSciencedegree(nuclearphysicsmajor).Throughalltheyearsofhereducationandpersonalitydevelopment,Rukshanawasafavoritetoherteachers,whoguidedandmotivatedhertopursueherdreams.Shealsoobtainedherbachelor'sineducation(scienceteaching)fromKapilaKhandawalaCollegeMumbaiandworkedasajuniorcollegeinstructoranddegreecollegeguestlectureratJaiHindCollege,heralmamatter.ThebiggestturningpointinhercareerwasthedecisiontoobtainadoctoraldegreeinphysicsattheUniversityofFlorida(UF)GainesvillebeginningFall2001.Thismeantmuchmorethananoutstandingacademicachievementforher,itwasanultimatelearningexperienceoflife.AtUF,shefoundherhusbandDr.ShadabSiddiqui(alsoagator).Havingearnedherdoctorate,Rukshananowaspirestoservethesciencecommunitybyutilizingherteachingandinter-personalskillscombinedwithhertechnicalknowledgeandmotivation,inmanycreativeways.Herdreamistobeabletocompetentlybalancebetweencareerandhome-making,andbethebestinallherrolesinlife. 160