-U"'"leF-"':I"rV (,I"" HIIWAJ'J LIBRARY

LEPTONIC AND HADRONIC BRANCHING FRACTIONS

A THESIS SUBMITTED TO THE GRADUATE DMSION OF THE UNIVERSITY OF HAWAI'I IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

PHYSICS

AUGUST 2007

by Due Ong

Thesis Committee:

Frederick Harris, Chairperson Thomas Browder

Stephen Olsen Klaus Sattler

We certify that we have read this thesis and that, in our opinion, it is satisfactory in scope and quality as a thesis for the degree of Master of Science in Phystcs

THESIS COMMI'ITEE

Chairperson

ACKNOWLEDGMENTS

I would like to thank Dr. Fred Harris for all of his guidance, the BES team at

IHEP, Yuan, C.Z., Ping, R.G., Uchida, K., Bassford, M., and Kowalczyk, J.

ABSTRACT

LEPTONIC AND HADRONIC BRANCHING FRACTIONS

FOR IN VIA ¢(2S) -+ 11'+11'- IN

Due Ong

Department of Physics and Astronomy

Master of Science

The BES II detector was used to collect 14 x 106 ¢(2S) events, in order to study the

dynamics of channonium bound states ¢(2S) and J N. The ratio of the branching

ratios ¢(2S) -+ 11'+11'- IN, IN -+ pP and ¢(2S) -+ ".+11'- IN, IN -+ e+e- is

determined. In addition, the ratio of the branching ratios ¢(2S) -+ 11'+11'- IN,

IN -+ JTfi and ¢(2S) -+ 11'+11'- IN, IN -+ fL+fL- is determined in two independent

ways. The angular distributions for each of these processes are also analyzed.

Contents

Table of Contents

1 Introduction 1.1 Overview. . 1.2 Weak Interaction . 1.3 Strong Interaction . . 1.4 Discovery of Charmonium Bound States

2 Physics 2.1 Motivation for the Experiment .. 2.2 Charmonium .. 2.3 Decay Process . . . . . . . 2.4 PDG Values . . . . . . . .

3 Experimental Apparatus

4

3.1 Beijing Electron-Positron Collider . 3.2 BES II Detector . .

3.2.1 Overview ........ . 3.2.2 Beam Pipe. . . . . . . . . 3.2.3 Vertex Chamber (VC) .. 3.2.4 Main Drift Chamber (MDCII) . . 3.2.5 Time-Of-Flight counter (TOF) . 3.2.6 Electromagnetic Shower Counters . . 3.2.7 Magnet System ............... . 3.2.8 Muon System . . . . . . . . . . . . . . . . . 3.2.9 Luminosity monitor (LUM) ..... . 3.2.10 Trigger system ................. .

Monte Carlo Data 4.1 Overview. 4.2 Method . 4.3 Monte Carlo Efficiencies

v

.

.

v

1 1 2 3 4

7 7 8

10 11

14 14 15 15 15 16 16 18 19 20 22 22 22

27 27 27 28

CONTENTS

5 Event Selection 5.1 Pion Selection . . . . . . . . . . . . .

5.1.1 Recoil Mass ......... . 5.2 Selection of High Momentum Tracks

5.2.1 Energy Loss Calibration ...... . 5.2.2 Dielectron Identification 5.2.3 Dimuon Identification 5.2.4 Diproton Identification

6 Results 6.1 Event Yields. . . . . . . . . . . 6.2 Branching Ratio Analysis . 6.3 Systematic Error . . . . . . . .

6.3.1 Common Sources ..... . 6.3.2 Dielectron Systematic Error 6.3.3 Dimuon Identification ... 6.3.4 Diproton Identification . . . . . . . . . . . . . 6.3.5 Ratio of Dimuon to Diproton ..

6.4 Summary of Branching Ratios 6.5 Angular Distributions. . . . . . . . . . . . .

6.5.1 Assumptions.............. 6.5.2 Previous Results .......... . 6.5.3 Systematic Error of Angular Distribution .

7 Conclusion

vi

30 31 31 33 35 36 39 42

47 47 48 49 49 50 51 51 52 53 53 55 55 56

63

Chapter 1

Introduction

1.1 Overview

In 1927 Paul Dirac derived a relativistic equation for the electron (the Dirac equation)

that contained negative-energy solutions along with positive ones. These negative-energy

electrons would later be labeled positrons, spawning the bt'ginning of high energy particle

physics experiments that employ antimatter. Antiparticles have the same mass as their

corresponding particle, but carry the opposite charge. Antiparticles also annihilate when in

contact with particles, giving rise to photons or other particle-antiparticle pairs [IJ.

The initial quarkl model of elementary particles, which stated that all hadrons such as

baryons (e.g. protons, neutrons) and mesons (e.g. pions and kaons) are made up of quarks,

was proposed in 1964. Hadrons are comprised of quarks, as opposed to leptons (e.g. electrons

and muons). Baryons are "heavy" hadrons that contain three quarks. Meson means ''middle­

weight," resulting from the fact that the first mesons' masses fell between that of the electron

1 The name was initially coined by Murray Gell-Mann. Quarks are elementary constituents of particles

such as mesons and baryons. Every quark has its own antiquark with charge opposite to the corresponding

quark [lJ.

1

CHAPTER 1. INTRODUCTION 2

and proton [lJ. At that time, the quarks came in three flavors: up, down, and strange.2 The

initial structure of the nucleon was initially studied by deep inelastic scattering experiments

at the Stanford Linear Accelerator Center (SLAC) in 1969 [I]. After a period of time, the

internal structure was established to be quark-like. This was analogous to Rutherford's

scattering experiment, which demonstrated the existence of a nucleus concentrated mostly

in the center of the atom [1].

1.2 Weak Interaction

The development of gauge theories with broken symmetries and the discovery of the weak

neutral current led to explanations of the weak interaction. The weak interaction has a

very short range (approximately 10-18 meters3), because its carrier particles (Wand Z

bosons) have large masses and consequentially short lifetimes (the Heisenberg Uncertainty

Principle with energy and time limits W and Z bosons to approximately 3xlO-2li seconds).

It acts on neutrinos, left-handed leptons, and quarks. The weak interaction is unique in

that it is capable of changing flavor. In addition, it is the only force that violates charge

symmetry C, parity symmetry P, and charge-parity symmetry CPo Charge symmetry is

the physical symmetry under a cl!ange in sign of all charges (charge conjugation) [1]. Parity

symmetry refers to the invariance of physical laws under the transformation where all spatial

coordinates flip sign [1]. The weak force was unified with the electromagnetic force to form

the Electroweak force, which merges these forces above the unification energy (102 GeV) [1].

The combination of Electroweak theories with the quark modelled to calculations that

predicted Z boson-mediated (neutral current) flavor-changing decays of a strange quark into

a down quark, corresponding to I1S = 1. However, sucl! decays were not observed. For ex­

ample, in neutral Kaons, the ratio of neutral- to charged-current decay rates is less than 10-5

2The three other more recently discovered flavors are charm, top, and bottom.

310-18 meters is 1000 times 8O!3IIer than the di3D1eter of an atomic nucleus

CHAPTER 1. INTRODUCTION 3

[2]. In 1970, the contradiction was resolved theoretically by the GIM mechanism (Sheldon

Glashow, John Iliopoulos, and Luciano Maiani) [3]. The GIM mechanism eliminated the

flavor-changing decays by introducing a fourth quark called charm, which possessed a charge

of +2/3. The introduction of the charm in the second quark doublet (charm, strange) in­

troduced terms into the neutral-current Lagrangian that cancelled the strangeness-changing

(AS = 1) terms. In 1974, theoretical predictions of a charm/anticharm meson were made

[1].

1.3 Strong Interaction

Some elementary particles such as hadrons are subject to the strong interaction or color force.

The theory behind this force is called Quantum ChromoDynamics (QCD). QCD describes

interactions at 10-15 meters (approximately the size of the diameter of a nucleus) between

quarks and gluons (mediators of the strong force) [1].

Spin is a body's intrinsic angular momentum beyond spatial coordinates. Fermions are

particles with half-integer spin, and must obey the Pauli Exclusion Principle (PEP), which

means they must occupy antisynImetric states, forbidding them from sharing quantum states.

Bosons are particles with integer spin and are not subject to the PEP [1]. The fermionic

nature of quarks was controversial because of its apparent violation of PEP. In 1964 this was

resolved by introducing color (red, green, and blue) as a new quantum state parameter [1].

One implication of QCD is called asymptotic freedom, which refers to the fact that gluons

and quarks interact weakly at high energies (shorter distances) [1]. Another property of

QCD called confinement explains why no free quark has been discovered. Color confinement

states that quarks must form triplets or pairs to result in net neutral color particles. Also,

as quarks separate, the strong force between them increases with distance, until the point

where it requires less energy to create another quark pair than to free the individual quarks.

CHAPTER 1. INTRODUCTION 4

PARTICLE QUARKS GLUONS

CHARGE TYPE(S) Color, Electric, Weak Color

WEAK FORCE Interacting Non-Interacting

FLAVOR Present Absent

SPIN 1/2: Fermions 1: Bosons

DYNAMICS Emit/Absorb Gluons Emit/Absorb Gluons

W Bosons, Photons Direct Interaction

Thus, quarks are forever bound in hadrons [1].

1.4 Discovery of Charmonium Bound States

Two independent groups claimed the discovery of the J N simultaneously, making it the

only elementary particle with a two-letter name. Both Burtonllichter's group at the Stan­

ford Linear Accelerator Center (SLAC) and Samuel Ting's group at Brookhaven National

Laboratory (BNL) announced their results on November 11, 1974, known as the November

Revolution [1].

The MARK I Stanford Positron Electron Asymmetric rung (SPEAR) was the collider

used at SLAC to create the event display shown in Figure 1.1. SLAC's self-naming process

observed in the spark chamber trace was ¢(2S) -+ 1T+1T- IN, J/¢ -+ e+e-. Ting, however,

named this particle J, which is one letter from the already discovered K strange meson

(kaon). Thus, the physics community came to a consensus that the particle be called the

J/¢ [1].4 The discovery of the IN led many to the conclusion that quarks were no longer

purely mathematical constructs, but rather particles that are subject to a potential [1].

The ¢(2S) and J N are both flavor5-neutral and electric charge-neutral mesons consisting

4The ,p(2S) was first discovered a.t SLAC alone, which meant there would he no "J" in its name. 5Flavor refers to the type of quark

CHAPTER 1. INTRODUCTION 5

-Figure 1.1: SPEAR Event Display for 1/>(28) -> 71"+71"- IN, IN -> e+e-. This is seen in the x-y projection, where z is the beam and magnetic field direction. The trigger and shower counters used to detect tracks are the objects in concentric alignment.

of a charm (c) quark and anti-charm (e) quark. This class of cC bound state mesons is called

Charmonium [1). The IN is often referred to as having "hidden charm" or "closed charm"

because it has a net charm of zero, since the c quark has charm +1 and the c quark has a

charm of -1. The first "bare" or "open" charmed mesons discovered were the DO with quark

content (cit) and the D+ with quark content (cd) [1).

References

[lJ D. Griffiths, Introduction to Elementary Particles, 1st ed. (Harper and Row Publishers,

Inc., New York, NY, 1987).

[2J D. H. Perkins, Introduction to High Energy Physics, 3rd ed. (Cambridge University Press,

Cambridge, UK, 2000).

[3J S. L. Glashow, J. lliopouJos, and L. Maiani, ''Weak Interactions with Lepton-Hadron

Symmetry," Phys. Rev. D 2, 1285-1292 (1970).

6

Chapter 2

Physics

2.1 Motivation for the Experiment

The leptonic decay modes of the J N are used as the signature for the presence of the J N in many experiments. Thus, precise branching ratio values are needed for J /'if; production

calculations. Furthermore, the branching ratio for J /'if; --+ pji is normalized to the leptonic

branching ratios in this analysis. Because protons are more stable than other elementary

particles, they are particularly of interest. However, baryons such as protons are currently

not well understood.

Another motivation for this analysis is to study the distributions of events as a function

of the angle between the particle and the beam. The general angular distributions of'if;(2S)

--+ 1r+1r- IN, IN --+ e+e-, 'if;(2S) --+ 1r+1r- IN, IN --+ j.t+p.-, and'if;(2S) --+ 1r+1r- IN,

J N --+ pji can be written as

dN 2 dcos6 oc l+acos 6 (2.1)

where 6 is the angle between the direction of the e, p. or p and the beam direction. The value

of a can be compared with various theoretical models based on first-order QeD [1]. This

can have implications for the validity of theoretical predictions.

7

CHAPTER 2. PHYSICS

2.2 Charmonium

3.8

2.8 L=O

DD Threshold

+ -7t 7t

lcl 3PI

XeO 3po,,",' .. .. •

~'------~v~------~j

L= 1 Orbital Angular Momentum

Figure 2.1: Charmonium bound states including '¢(2s) -+ 11"+11"- Jj'¢. Dashed lines indicate unob­served states and transitions.

8

The '¢(2S), also known as ,¢', has a rest mass of 3686.093 ± 0.034 MeV/e? The Jj'¢ has

a rest mass of 3096.916 ± 0.011 MeV /e?, approximately three times the mass of the proton

[2]. The J j'¢ has a mean lifetime of approximately 10-20 seconds, which is about 1000 times

longer than the typical hadron in this mass range [3]. The long lifetime is also unusual based

on Heisenberg Uncertainty Principle (HUP) arguments for energy and time.1 The J/,¢ has

an unexpectedly long lifetime because its mass is less than the masses of particles which

1 HUP states that AEAt~ "/2. This implies that sbort-lifetime excited states have non-negligible energy

uncertainties, ruling out tbe possibility of sharp spectral lines despite ideal conditions [3].

CHAPTER 2. PHYSICS 9

Figure 2.2: OZI suppression of J/1/J -> 1/"+1/"-1/"0 [3].

separately contain a charm and an anticharm quark such as the DO and D+ mesoni'. (See

Figure 2.1) Because the decay processes to open charm states are kinematically blocked, the

J /1/J can only decay into noncharm quarks, leailing to a suppression of the decay rate. In

addition, the width, which is inversely proportional to the lifetime, [4] is extremely narrow

at 93.4 ± 2.1 keV /e? [2]. This is due to OZI sppression of strong decays [5]. The OZI rnIe

states that if the diagram of a process can be cut along gluon lines without cutting particle

lines, then that process is suppressed [3]. (See Figure 2.2)

Vector mesons (C = -1) such as the J/1/J must decay through three gluon exchange (C =

-1) to conserve charge conjugation. The process J/1/J -> 2 gluons (C = +1) is not allowed

because of quantum mechanics. The three gluon exchange process makes up about 2/3 of

the partial width, while the remaining 1/3 consists of virtual photon decays.

The .,p(28) and J/1/J both have the same quantum numbers, 3S1o which means that the

2 DO has a rest mass of 1864.5 ± 0.4 MeV Ie- and the D+ has a rest mass of 1869.3 ±0.4 MeV Ie-

CHAPTER 2. PHYSICS 10

spin angular momentum is 1, the orbitaP angular momentum is 0, and the total angular

momentum is 1.4 Both the 1/1(28) and Jj1P have odd (-) parity and odd (-) charge conjugation

[2J.

2.3 Decay Process

One characteristic of elementary particles is the branching ratio of a decay process, which is

defined to be r Irt where r is the decay rate of an individual process and r t is the total decay

rate [3]. Charmonium decays provide an excellent opportunity to examine short distance

dynamics of heavy quark-antiquark pairs [6].

J/IjI

Figure 2.3: Emission of two gluons and hadronization of pions

The process 1/1(28) -+ J j1P + anything has a PDG branching ratio of ( 56.1 ± 0.9 ) x 10-2

[2]. Of these transitions, we analY2e the process 1/1(28) -+ 11"+11"- Jj1P, which makes up the

majority of aJI1/l(28) decay events with a branching ratio of (31.8 ± 0.6 ) x 10-2 [2]. The

decay 1/1(28) -+ 11"+11"- Jj1P occurs in two steps. First, the 1/1(28) emits two gluons. Then,

'Orbital 8JlgU!ar momentum is the motion of a particle's center of mass about a physical point [3]. 4Spectroscopic notation: 28+1 L j , where L can be S (1=0), P (1=1), D (1=2), F (1=3), etc [2].

CHAPTER 2. PHYSICS 11

Pion pairs are formed through a process called hadronization, as shown in Figure 2.3 [6].

The following decay chains are analyzed: J N -+ e+ e-, J N -+ f.L+ f.L-, and J N -+ pp.

2.4 PDG Values

The previous Particle Data Group (PDG) Branching Fraction measurements for 'I/>(2S) -.

11"+11"- IN, Jj'¢> -.leptons are summarized here [2].

Jj'¢> -+ e+e- BRANCHING RATIO (10-2) CITATION DETECTOR

5.945 ± 0.067 ± 0.042 Z. Li et al [7] CLEO

5.90 ± 0.05 ± 0.10 J. Z. Bal et al. [8] BES!

6.09± 0.33 D. Coffman et al. [9] MARK III

5.94± 0.06 World Average [2] PDG

Jj'¢> -+ f.L+f.L- BRANCHING RATIO (10-2)

5.960 ± 0.065 ± 0.050 Z. Li et al [7] CLEO

5.84 ± 0.06 ± 0.10 J. Z. Bal et al. [8] BES!

5.90 ± 0.15 ± 0.19 D. Coffman et al. [9] MARK III

5.93±0.06 World Average [2] PDG

Jj'¢> -+ pp BRANCHING RATIO (10-3 )

2.26 ± 0.01 ± 0.14 J. Z. Bal et al [1] BES II

1.91 ± 0.04 ± 0.30 D. Pa1lin et al. [10] DMII .

2.16 ± 0.07 ± 0.15 M. W. Eaton et al. [ll] LBL

2.17±0.08 World Average [2] PDG

References

[IJ J. Z. Bai et al., "The measurements of IN -> 'PP," Phys. Lett. B591, 42-48 (2004).

[2J W.-M. Yao et al., "Review of Particle Physics," J. Phys. G 33, 64, 891-897 (2006).

[3J D. Griffiths, Introduction to Elementary Panicles, 1st ed. (Harper and Row Publishers,

Inc., New York, NY, 1987).

[4J M. Bauer and P. A. Mello, "On the lifetime-width relation for a decaying state and the

uncertainty principle," In Proceedings of the National Academy of Sciences of USA, 73,

283-285 (1976).

[5J T. J. LeCompte, "Heavy quarkonia, Charm in nuclear collisions," presented at the

11th Coordinated Theoretical-Experimental Project (CTEQ) Summer School on QCD

Analysis and Phenomenology, (Madison, WI; June 2004).

[6J J. Z. Bai et al., "'1/1 (2s) -> 11"+11"- IN Decay Distributions," Phys. Rev. D 62 (2000).

[7J Z. Li et al., "Measurement of the branching fractions for IN -+ 1+1-," Physical Review

D (Particles and Fields) 71, 111103 (2005).

[8J J. Z. Bai et al., "Determination of the J N leptonic branching fraction via '1/1 (2s)

-+ 11"+11"- IN," Phys. Rev. D58, 092006 (1998).

12

REFERENCES 13

[9] D. Coffman et at., "Direct measurement of the J/1/J leptonic branching fraction," Phys.

Rev. Lett. 68, 282-285 (1992).

[10] D. Pa1lin et at., "Baryon pair production in J/1/J decays," Nucl. Phys. B292, 653 (1987).

[11] M. W. Eaton et al., "Decays of the 'I,b(3097) to Baryon-Antibaryon final states," Phys.

Rev. D29, 804 (1984).

Chapter 3

Experimental Apparatus

3.1 Beijing Electron-Positron Collider

The Institute of High Energy Physics (IREP) houses the Beijing Electron-Positron Collider

(BEPC), which is the source of the events observed in the Beijing Spectrometer. Figure 3.1

demonstrates the process of generating collisions between electrons (e-) and positrons (e+).

~---------------------3~m----------------------~ '------- 202 m ---------68 m ---ilOoMl- 66 m

120 M.V LiDAt

\ 30 M.V

i'Ie-JDjector "-.' Prod1lctlOD Target

2nd

:--1P ___ B...,ES'#L1 Stmage~ Ring

Figure 3.1: Beijing Electron-Positron Collider schematic [1].

The 120 MeV Linear Accelerator (LinAc) creates positrons by colliding electrons with a

14

CHAPTER 3. EXPERiMENTAL APPARATUS 15

target. Both electrons and positrons are sent to the main Iinac to be accelerated into the

beam storage ring. The trajectories of the (e-) and (e+) orbits are tuned so that they meet

at the center of the detector, which is the BES Interaction Point (IP) [1].

3.2 BES II Detector

3.2.1 Overview

The Beijing Spectrometer (BES) is a cylindrical solenoidal detector at the Beijing Electron

Positron Collider (BEPC), designed to study final states of e+e- annibUations at the center of

mass energy from 2.0 to 5.6 Ge V [2]. The original configuration BES I consists of the following

subsystems: central drift chamber (CDC), main drift chamber (MDC), time-of-flight counters

(TOF) (barrel and endcap), electromagnetic shower counter (SC), muon chamber, luminosity

monitor (LUM), solenoid magnet, trigger, and online data acquisition system (DAQ). Aging

effects were seen with the luminosity of BEPC and BES performance, leading to upgrades

of both from 1993 to 1997. During this period, BES I was upgraded to BES II, with several

new subsystems. Figure 3.2 indicates the position of the subsystems from a side and axial

view, respectively [3].

3.2.2 Beam Pipe

The electrons and positrons in the storage ring circulate in a Beam Pipe (BP) with a 240.4

m circumference and a 7.5 cm inner radius at the BES Interaction Point. One 5.2 cm long

bunch of 6.8x1010 particles is sent for every beam. The bunches circle the storage ring in

opposite directions at a frequency of 1247.057 kHz. In the current BES II detector, the BP

is made of beryllium (Be), which was chosen because of its low atomic number in order to

minimize multiple scattering. The BP is 1.2 mm thick and its diameter is 9.8 em [1].

CHAPTER 3. EXPERIMENTAL APPARATUS 16

M uun Cuunten.

Muon Countet'$

_ !II_--_.--------------------

TOF

mF Coumer,.

Side view of the B ES detector End view of the BES detector

Figure 3.2: BESlI Detector side and end view.

3.2.3 Vertex Chamber (VC)

The first chamber outside of the BP is the Vertex Chamber (Ve), which consists of 12 layers

of straw-tubes. The VC used in BES 11 was refurbished from the MARl{ III detector. It

has an inner diameter of 10.8 cm and outer diameter of 26 cm. The hit (time) information

is used for the trigger. It is used in conjunction with the Main Drift Chamber (MDC) to

measure event vertices and improve upon tracking and momentum information. The layout

of the 640 straws is shown in Figure 3.3. The gas used is held at 3 atm and consists of an

equal mix of Ar and C2H6 . The operating voltage is between 3.7 and 3.9 kV, The average

colliding beam single hi t resolut ion is approximately 90 I-'m [31.

3.2.4 Main Drift Chamber (MDCII)

The next concentric chamber located outside the VC is the Main Drift Chamber. The

MDC's functions are to determine track trajectories, measure the energy los (dE/ dx) of

CHAPTER 3. EXPERIMENTAL APPARATUS

Composite Shell --'iM:~~

Axlal straws ottliQc~

stereo straws

IP 4.8 an 13.5 an

Figure 3.3: Vertex Chamber straw alignment, with axial layers (1-4 and 9-12) and stereo lay­ers (5-8) making an approximately 3 degree angle with respect to the axis [1].

17

charged particles, and provide information for the trigger system. The MDCI was upgraded

to Mocn by improving on drift cell size, cell arrangement, field shaping, and feedthrough

design [3].

When charged particles pass through the chamber gas (89/10/1 ratio of Ar/C02/CRt),

they ionize the gas and create charges. The ions and electrons drift to the wires, which can

be used to reconstruct the path they took. The radius of curvature of the trajectory is used

to determine the momentum, since the entire chamber inside to a uniform 0.4 T magnetic

field [1].

Mocn has an inner diameter of 31 cm, an outer diameter of 230 cm, and an effective

length of 212 cm. The 10 layers in the MOCn alternate between stereo (odd layers) and

axial wires (even layers). The stereo wires provide z..coordinate information about the tracks.

There are 22,936 total wires of four different types. Sense wires (3,216) are used to receive sig-

CHAPTER 3. EXPERIMENTAL APPARATUS 18

nals. Field wires (11,468) provide a constant electric field. Potential wires (5,308) minimize

interference between signals by separating sense wires. Guard wires (2,944) are responsible

for decreasing edge effects. Each of these sets of wires are organized in units called cells, as

shown in Figure 3.4. The overall pattern of wires may be seen in Figure 3.5. The momentum

resolution of the tracking system has been measured to be t::.p/p = 0.0178v'f+P2", with p

taking units of GeV /c [1].

Layer 4, Cell 14 Layer 3, Cell IS

Figure 3.4: Solid circles are sense wires and open cir.c1es are field wires. The calculated field lines are shown from an axial view [1].

3.2.5 Time-Or-Flight counter (TOF)

The next sUbsystem outside the MDC is the Time-Of-Flight counter (TOF), which consists

of plastic scintillators that are connected to photomultiplier tubes (PMT's) via clear lucite

Iightpipes. TOF information can be used to identify particles, in conjunction with the MDC.

The TOF is made up of a cylindrical part (barrel) and two circular parts (endcaps) [1].

The barrel portion of the TOF consists of 48 scintillation counters, arranged in a cylinder,

CHAPTER 3. EXPERlMENTAL APPARATUS

•

•

•

•

•

• • I.,. •

Figure 3.5: An axial view of a quarter circle of drill hole patterns in the MDCII [1].

19

with PMT's connected to the ends of each bar. The scintillator bars are 284 cm long, 15.6

cm wide and 5 cm thick. The scintillator used for TOFII was BC-408, while the PMT's

were Hamamatsu R2490-05. The changes were improvements on the BES 1's TOF system,

resulting in a decrease of the fluorescence decay time from 2.3 ns to 2.1 ns. A decrease in

the light guide length from 112 cm to 16 cm also contributed to improved resolution, which

was measured to be about 150 ps for cosmic rays [3].

3.2.6 Electromagnetic Shower Counters

Located just outside the TOF system, the Electromaguetic Shower Counters is also made up

of a Barrel Shower Counter (BSC) and two Endcap Shower Counters (ESC). The top portion

CHAPTER 3. EXPERIMENTAL APPARATUS 20

of Figure 3.6 illustrates the mechanical structure of the BSC. The absorber panels are made

of successive layers of AI-Pb-AI and are 385 cm long. There are 24 absorber layers of gas

tubes (4/1 ratio of Ar /C02) interleaved with 23 layers of lead absorbers, each consisting of

10 absorber panels in circumference. Each layer is further divided into 560 cells by 1.3 cm

x 0.08 em AI I-beams. Five hori2ontai support rings called "ribs" are the only regions with

limited response and poor Monte Carlo simulation. Thus, analysis of these rib regions are

excluded [1].

Layers with the same ¢ angle are grouped into six readout layers in the r direction, to

minimize the number of electronic readout channels. There are 6,720 total readout channels.

When a charged particle hits a gas tube, the energy deposited (total charge) is sampled

according to the Self Quenching Streamer (SQS) spectrum [3].

The BSC covers 80% of the solid angle (471"). Its energy resolution t:..E/E is 21%, where

E is in GeV. The axial position z has a resolution of 2.3 em, and the ¢ resolution is 7.9 mrad

[1].

3.2.7 Magnet System

The 0.4 T magnetic field is generated by a solenoidal magnet consisting of a conventional coil

and an iron flux return yoke. The magnet yoke also serves as the main structural support for

the BES detector. The 330 ton magnet system is made up of a barrel and two endcaps. The

barrel portion consists of three layers of iron with two layers of muon chambers mounted on

the outside of each layer. In addition to functioning as a magnetic flux return, the inner two

layers are also hadron absorbers. The structure has dimensions of 5.1 m x 6.65 m x 5.86 m

(length x width x height) [1].

CHAPTER 3. EXPERIMENTAL APPARATUS

A

A Copper Pin

Feed-Through Insulator

34 P Stainless Steel Wire

Square Aluminum Tube

2.8 DlID Pb Plate 0.5 mm Glue Layer

Figure 3.6: The top diagram is the Barrel Shower Counter and the bottom diagram is the Endcap Shower Counter [lJ.

21

CHAPTER 3. EXPERiMENTAL APPARATUS

3.2.8 Muon System

22

The outer most subsystem of BES is the muon identifier, which is responsible for identifying

both collider-generated exiting muons and entering cosmic ray muons. Figure 3.2 illustrate

the alternating layers of muon counters and magnet yokes. There are three absorber layers

and three muon chamber layers. Three pieces of magnet yoke of thicknesses 12, 14, and 14 cm

make up the absorber layers, each forming an octagon. Eight proportional gas tubes make

up one of the 189 chambers. Each chamber is further divided into 2 sub-layers, staggered

by half of a tube to minimize inefficiencies caused by muons that could potentially travel

between two adjacent chambers. The tubes are filled with a 9/1 mixture of Ar/CH4• The

first and-second layer both cover 67% of the solid angle, while the third layer covers 63%.

The wire efficiency is 95% [1].

3.2.9 Luminosity monitor (LUM)

The BES lmninosity monitor outputs both instantaneous lmninosity and integrated lmninos­

ity via the online system for beam calibration and data quality control. A layout of the two

pairs of scintillator/shower-counter arms, each consisting of a beam positioning counter (P),

a coincidence counter (C), and a shower counter (S) (electromagnetic energy) is shown in

Figure 3.7. The lmninosity is determined from a ratio of the rate of P triggering (in conjunc­

tion with S and C coincidence) over the geometrical acceptance of Pin Bhabha scattering.

Figure 3.8 depicts two arms of the lmninosity monitor [1].

3.2.10 Trigger system

The trigger system is based on data from the TOFII, SC, MDClI, VC, and muon counters.

The VC trigger logic is illustrated in Figure 3.10. Trigger decisions are made from information

found in the four iunermost and four outermost layers. Track candidates are those with hits

CHAPTER 3. EXPERIMENTAL APPARATUS

DC,IP1 [' --- . .

- - _ _ - - _ Interacholl RegIOIl

. --.... -------- I

5 2

-"-"'-:1: - I _ • .-.. .. ---- ... ---

~ -- ... -.

Figure 3. 7: Schematic of the luminosity monitor, con­sisting of a beam positioning counter (P), a coincidence counter (e), and a shower counter (S) [IJ .

.::-

Figure 3.8: Two arms of the luminosity moni tor [3J.

23

CHAPTER 3. EXPERIMENTAL APPARATUS 24

that match either pair of adjacent layers in the inner layers with those in the outer layers

[3].

The signals from the nonstereo (even) layers are used to identify charged track candi­

dates for the MDCII trigger. To be considered a track candidate, it must pass through the

interaction point and have a radius of curvature greater than 83.3 cm, which translates to a

momentum greater than lOOMeV. The MDC trigger logic is shown in Figure 3.9. The details

of the trigger process may be found in [3].

l88. 402 ,_ou

I ,,2<1> I FrLTn I 1 16~

VETO

:r£

t.khl ~ 1 S/JpIaI Sipl T D!strio - T ... k f-t -- ~ ~ - ...... ~ Addms c-&s ~ L..:. ~ Tatl f. ~

f r (I) fiDdlDa (2, )r4 '. H~!mt~ f-+C::

r~r (Mmdo 1 MoJoriI1 --t48 {48 TOf Vl"

Figure 3.9: MDC trigger logic [3].

CHAPTER 3. EXPERlMENTAL APPARATUS

CAMAC TGlCkCaD" .... Logic Readins

5)(% Tmck TIL Gal<: f-I ~

Ceo f-t Comblna· 40 logic (- UddI SeIa:ritm , SeIectim -Gare~ r- f- MaIdling

SipIal Sclo:c1ion ~ F_ Switch Ie logic .

f T

Figure 3.10: Logic diagram of the VC trigger [3].

VCI

ve2

48

To Main Trisger

ToMOC Trisger

25

References

[1] D. Kong, "Measurement ofthe total cross-section for hadronic production by e+e- anni­

hilation at energies between 2-GeV to 5-GeV," Ph.D. dissertation, University of Hawaii,

UMI-99-90253 .

[2] J. Z. Bai et al., ''The BES detector," Nucl. Instr. Meth. A 344, 319-334 (1994).

[3] J. Z. Bai et al., "The BES upgrade," Nucl. Instr. Meth. A 458, 627-637 (2001).

26

Chapter 4

Monte Carlo Data

4.1 Overview

The Monte Carlo program (8IMBES) used in this analysis is based on GEANT3, and hag

been created to simulate the response of the sutrdetectors in the BE8II detector. When

compared with data, the program performs at a generally satisfactory level. The details of

these comparisons can be found in Ref. [1]. The schematic structure of 8IMBE8 is outlined

in Figure 4.1.

4.2 Method

The BES developed generator PPGEN is used for exclusive decay channels 1/1(28) -+ .".+.".­

J/1/J, J/1/J -+ e+e-, 1/1(28) -+ .".+.".- J/1/J, J/1/J -+ p,+p,-, and 1/1(28) -+ .".+.".- J/1/J, J/1/J -+ pjj

to generate raw MC data. This data is then reconstructed and sent through the same event

selection criteria ag the real data.

27

CHAPTER 4. MONTE CARLO DATA

I loitiaJimtion I De1ector Definition

1

IKIDematicsI

! •

1-.... 1 / 1

Event Generator (GENBES)

B-~-EJ Figure 4.1: Program schematic of SIMBES, where dashed boxes are optional

4.3 Monte Carlo Efficiencies

28

A total of 400000 Monte Carlo (MC) events are generated each for '1/1(28) ..... 11"+11"- IN,

IN ..... e+e- and '1/1(28) ..... 11"+11"- IN, IN ..... p,+p,-. In addition, 100000 MC events are

generated for 1/1(28) ..... 11"+11"- IN, IN ..... pji.

The experimental distributions must be corrected for detection efficiency in order to

compare them with theoretical models. To obtain these efficiencies, Monte Carlo data is run

through the same analysis program as experimental data. The ratio of detected to generated

MC data is used to determine the bin-by-bin efficiency correction. This efficiency correction

is applied to each bin of the data distributions. Selection criteria for all cases are defined in

Chapter 5. The MC-determined e+e-, p,+ p,- (muid and nomuid), pji selection efficiencies are

listed in Chapter 6.

References

[1] J. Z. Bai et al., "BESII Detector Simulation," Nue!. Instr. Meth. A 552, 344 (2005).

29

Chapter 5

Event Selection

Event selection for decay channels '¢(2S) -> 11"+11"- Jj'¢, Jj'¢ -> e+e-, '¢(2S) -> 11"+11"- Jj'¢,

Jj'¢ -> /1+/1-, and '¢(2S) -> 11"+11"- Jj'¢, Jj'¢ -> pp is based on the MDC, SC, MUID, and

TOF subsystems.

Hits in the MDC are used to reconstruct each charged track. Events are required to have

four charged tracks, and radial and beam vertex positions rmin < 1.5 cm and !z",in! < 15

cm, where rmin is the minimum radial distance of approach to the beam line for the four

tracks and z", ... is the minimum z distance to the interaction point. In order to include

events with tracks that would not individually satisfy these cuts, event selection is based

on the minimum r and z distances of each of the four tracks. Each track must also have a

good helix fit. This is chosen to ensure the correct error matrix in the kinematic fit [1]. The

kinematic fit refers to a four-constraint (4C) fit, which is based on requiring conservation of

both momenta and energy components for the decay candidates. This fit is used to improve

the experimental resolution.

30

CHAPTER 5. EVENT SELECTION

5.1 Pion Selection

31

In order to ensure that each charged track originates from the interaction region, Jv; + v;,2 <

2 cm and IV. I < 20 cm, where vr , Vy, and V. are the coordinates of the point of closest

approach of the track to the beam axis. The invariant m8BS M,,+,,- of the pion pair from the

1/;(2S) -> 71"+71"- J/1/J, J/1/J -> e+e- channel for data and MC distributions is shown in Figure

5.1 (c). Events were selected based on the following criteria.

• Pion total momentum p" < 0.45 Ge VIc is required. The pion momentum distributions

for the ± tracks are shown in Figure 5.1. We find reasonable agreement between data

andMC.

• Pion momentum transverse to the beam pxy" > 0.07 GeV Ie is required. This cut is

chosen to eliminate tracks that orbit around in the Main Drift Chamber.

• We require I cos 0,,1 < 0.8, where 0" represents the polar angle of the 71" in the laboratory

system. This cut is chosen because tracks with I cos 0,,1 > 0.8 are not well measured

by the MDC.

• The acollinearity angle between the 71"+ and 71"- in the laboratory system is defined to

be 0"". The cosO"" distribution is shown in Figure 5.1 for data. We require I cos 0",,1 <

0.9, in order to veto misidentified e+e- pairs from photon b) conversions.

5.1.1 Recoil Mass

• The m8BS recoiling against the two pions is defined to be

(5.1)

where E" = Jm~ +~, m" is the m8BS of the pion, and p,,- are the momenta of

the ±-charged tracks. The recoil ill8BS distributions from the 1/;(2S) -> 71"+71"-J I1/;,

CHAPTER 5. EVENT SELECTION

0 0.07 025 0.43

PIt + (GaV/e)

2000

(e) !l !l c:

1000 c:

CD

~ Iii

O~eLLLLLLLLLLL~

0.30 0.40 0.50 0.60

7t1t- Mass (GaV/e2)

0 0.07 025 0.43

P,,- (GeV/e)

I

16000 r- -

(d)

8000 =-.... ,. { ~ -'~01"": . ... "", ....... ...,...""'-"""--- .,"

I i O~-L~~~-L~~

0.00 0.50

cosS""

1.00

32

Figure 5.1: *(28) ..... 7rT 7r-IN, IN ..... eTe- pion momenta (± tracks) for data (points with error bars) and Monte Carlo (histogram) are shown in (a) and (b). The M,,+,,- invariant mass distributions of the pion pair for data and MC are shown in (c). The cosine of the (acollinearity) angle between 7r+ and 7r- for data before particle identification is shown in (d). The selection for cos 0"" only includes the good helix fit requirement and I cos 0,,1 > 0.8.

CHAPTER 5. EVENT SELECTION 33

3000

(a) (b)

2500 S 2000 t:

~ 1000

o 1.....J.._!!l:.-'--.i----<..:~ _ _..J o 1.....J.._!!l:.-'--.i----<..:~ ..... _..J

3.050 3.100 3.150 3.050 3.100 3.150

e + a- Mrecou (GaV/c2) )1+)1- Mrecou (GaV/c2

)

Figure 5.2: ?j;(2S) -> 11"+11"-J/?j;, IN -t e+e- mllBS recoiling against 11"+11"- pair is shown in (a). ?j;(2S) -> 11"+11"- IN, IN -> p+,F mllBS recoiling against 11"+11"- pair is shown in (b). Data are points with error bars and Me are histograms. We find that the Me does not agree perfectly with the data, but the systematic error for the recoiling IDIlBS requirement is negligible.

IN -> e+e- and ?/J(2S) -> 11"+11"- IN, IN -+ p+p- channels for data and Me are

shown in Figure 5.2. In the final selection, the recoil mllBS must fall within 50 MeV / c?

of the IN IDIlBS of 3.097 GeV/c? There is reasonable agreement between data and

Me, and the IN peak is mostly clean.

5.2 Selection of High Momentum Tracks

• The two other candidate tracks decaying from the J N must have high momentum

compared to the pion momentum and be greater than 0.8 GeV /c .

• In order to select only IN -+ two charged particle decays, we select p+ > 1.3 GeV/e

or p_ > 1.3 Ge V / c or (p+ + p_) > 2.3 Ge V / c. The Pe+ versus Pe- distribution from

the ?j;(2S) -> 11"+11"- IN, IN -+ e+e- channel for data and Me are shown in Figure

5.3. The corresponding distributions for ?j;(2S) -t 11"+11"-J N, J N -t p+ p-, and

?j;(2S) -> 11"+11"- J N, J N -> pP are also shown in Figure 5.3.

CHAPTER 5. EVENT SELECTION 34

1.9 1.9

~ ~

.g u

=ii :> Cl 1.4

(B 1.4 ~ ~

~ ~ , .

0.9 0.9 0.9 1.4 1.9 0.9 1.4 1.9

Pe" (GeV/c) Me Pe" (GeV/c)

1.9 1.9

~ ~

~ ~ ':" ... Cl S2.

,1", - 1.4 1.4

~"- +,,-0.

(cl' .•.... (d) • : ;"

0.9 0.9 ~ '.' .

0.9 1.4 1.9 0.9 1.4 1.9

P~" (GeV/c) Me P~" (GeV/c)

1.9 1.9

~

: .. (e) ~

(f) u .g :> - ... =ii Q) . :~: .. "

Cl 1.4 Cl 1.4 - ~

+0. + 0.

0. 0.

0.9 0.9 0.9 1.4 1.9 0.9 1.4 1.9

pp" (GeV/c) Me pp" (GeV/c)

Figure 5.3: p+ VB. p- for (a, c, e) data 8Jld (b, d, f) Me.

CHAPTER 5. EVENT SELECTION 35

Parameter Data Me

e+ Mean 0.367 ± 0.0107 0.378 ± 0.00872

e+O"«o) 1.11± 0.00754 1.12± 0.00594

e+O"(>O) 0.875 ± 0.00703 0.896 ± 0.00565

cMean 0.196 ± 0.0105 0.373 ± 0.00872

e-0"«0) 1.10 ± 0.00749 1.10 ± 0.00597

e-O"(>O) 0.904 ± 0.00673 0.903± 0.00564

Table 5.1: Bifurcated Gaussian fit results before correction. These values are used to calibrate data and Me xse values.

5.2.1 Energy Loss Calibration

One of the most useful tools in particle identification is dE/dx, which is the energy loss per

distance traveled. Because dE/dx depends on mass, one can separate out different particles

[2]. For electron-positron pairs (e±), the number of standard deviations from the expected

energy loss is defined to be xse±.

1 12 [(dE/dx)-:..a. - (dE/dx)"t:.r,]2 [((dE/dx)~ - (dE/dx);"']2

xse = + +. 0" 0"-(5.2)

(dE/dx)'IMaB and (dE/dx)ezp are the measured and expected energy losses for electrons, and

O"± is the experimental dE/dx resolution. The Ixsel2 values are calibrated according to a

MNFIT bifurcated gaussian fit to the xse± distributions. This is illustrated in Figure 5.4

The original values of xse± are corrected according to the fitted values in Table 5.1, so

that the means of both data and Me coincide with the origin in xse±-space and the standard

deviations are 1.

CHAPTER 5. EVENT SELECTION 36

2 ...

.... '61lO

'200

BOO

... 0

4 .. .. 0 2 4

(a) xse+ data (b) xse- data

(c) xse+ MC (d) xse- MC

Figure 5.4: xse:l: for energy loss dEl dx, fitted with a bifurcated gaussian.

5.2.2 Dielectron Identification

In order to contain tracks in the BSC, we require I cos 6.1 < 0.75, where 6. is the polar angle

of the electron. In addition, we require that the invariant IIlllB8 of the dielectron determined

from the kinematic fit falls within 100 MeV Ie-of the J N mass. The cosine of the dielectron

acoplanarity angle in the J N rest frame cos 6 .. must be less than -0.996 in order to ensure

that the e+ and e- are back-to-back (6;' > 175°). These selection criteria are neccessary to

CHAPTER 5. EVENT SELECTION 37

remove background. In addition, the systematic errors associated with these requirements

mostly cancel when taking the ratio of branching ratios.

A combination of the energy loss information from the MDC (xse±) and the Shower

Counter Energy (SCe±) is used to select e+e- pairs. This is due to poor MC simulation of

energy deposition in the rib regions described in Section 3.2.6. Figure 5.5 illustrates (xse+)

VB. (xse-) before and after the SCE±/Pe± selection criteria outlined below. Figure 5.5 also

shows SCE_/pc VB. SCE+/Pe+ before and after the xse± selection.

After the energy loss correction, the xse± selection is based on the following criteria.

• If xse+ < 0 and xse- < 0, then values that fall within a quarter-circle of radius 2 are

selected. This is used to eliminate hadron pairs that would have xse peaks at negative

values.

• For all other cases, values that fall within the remaining larger circle of radius 3 are

accepted.

There are three possibilities for selecting dielectron candidates.

1. Double electron identified case: If both tracks do not hit the BSC rib region, then the

ratios of electron energy deposited in the BSC to their respective momenta for the e+ e­

candidate pairs SCE±/Pe± are selected, as indicated in Figure 5.6. This requirement

is used to veto events with low SCE±/Pe± values such as 1/>(2S) -> 11"+11"- IN, IN-> two hadrons.

2. Double electron identified case: If one of the tracks hits the BSC rib region, the dE/dx

information from the MDC of both e+ and e- must agree with the respective expected

values. The invariant mass of the e+e- must also fall within 250 MeY/e? of the IN mass. In addition, if one track is identified to be in the rib region, then the other track

must have a SCE/p > 0.5 .

CHAPTER 5. EVENT SELECTION 38

4 4

2 2

0 0

-2 -2

-4 -4 -2 0 2 4

-4 -4 -2 0 2 4

(0) xse- vs. xse . (b) xse- vs. xse'

2 2

1.5 1.5

0.5 0.5

o o 0.5 1 1.5 2 o o 0.5 1 1.5 2

(c) SCE-/p- vs. SCE'/p' (d) SCE-/p- vs. SCE'/p'

Figure 5.5: 'I/1(2S) -+ 11"-<-11"- IN, J/'I/1 -+ eTe- selection criteria: (a) xse- vs. xseT before selection, (b) xse- vs. xse+ with SCE±/Pe± selection, (c) SCE_/Pe- vs. SCE+/Pe+ before selection, (d) SCK/Pe- vs. SCE+/Pe+ with xse± selection

3. Single electron identified case: One of the tracks must have SC E±/Pe± > the maximum

of 0.6/Pe±. and 0.4, and the invariant mass must fall within 250 MeV/e?- of the IN mass.

We define a quantity R:

(5.3)

The momentum distributions Pe+ and Pe-, the invariant mass of the e+ e- calculated using

a 4C kinematic fit, and R for data (high momentum tracks) and MC ('I/1(2S) -+ 11"+11"- Jf.,p,

J N -+ e+ e-) are shown in Figure 5.7. Although R is not used to identify dielectron events,

it is used later in dimuon identification in order to veto dielectron events. (See nomuid)

CHAPTER 5. EVENT SELECTION 39

2

1.5 SCEJp ..

1 1

0.5

0 1 SCEJP .. 0 0.5 1 1.5 2

Figure 5.6: The SCE+/Pe+ VB. SCE_/Pe- distribution is shown with selection consis­tent with 'if;(2S) -> 1[+1[-Jj¢, Jj¢ -> e+e-. Tracks with SCE±/Pe± less than 1 are re­quired to fall within an ellipse of axes Rcut(±). Rcut(±) is defined to be (1- [maximum of (0.6/Pe±,0.4)]), in order to eliminate hadrons, which have low SCE±/Pe± ratios. The SCE+/Pe+ VB. SCE_/Pe- distribution before this selection is shown in Figure 5.5.

5.2.3 Dimuon Identification

Dimuon pairs are selected in two independent ways:

1. Using the MUm system, defined to be muid

• I cos 11,,1 < 0.60, where II" is the polar angle of the muon. This is used to contain tracks

in the MUm system.

• At least one of the /J.+/J.- tracks must have N hit > 1. where Nhit is the number of

MUm layers with matched hits (ranging from 0 to 3).

• If only one track satisfies this condition, then the invariant mass of the p,+ p,- must fall

within 250 MeV / r:?- of the J j¢ mass.

II. Not using the MUm system, defined to be nomuid

• Events satisfying I cos II!, 1 < 0.75 are required.

CHAPTER 5. EVENT SELECTION 40

1600 1600

800 800

0 0 120 1.60 120 1.60

Pe+ (GeV/e) Pe- (GeV/e)

, I

1800 6000 - -

(e) J!l S r:: 4000 - - r:: ~ CD

> 800 W W

2000 - -

J I\' . 0 0 3.00 3.10 320 0.00 0.40 0.60

e+e- Mass (GeV/e2) R (e+e- Me)

Figure 5.7: Momenta for e+ and e- are shown in (a) and (b), where histograms are MC and error bars are data. The invariant mass of the e+e- is shown in (c), while R for data (high momentum tracks) and MC (¢(2S) ..... 11"+11"-Jj¢, Jj¢ -+ e+e-) are shown in (d). These histograms reflect the final selection criteria for dielectron pairs.

• We require that the invariant mass of the dimuon determined from the kinematic fit

falls within 100 MeV/r? ofthe Jj¢ mass.

• The cosine of the dimuon acoplanarity angle in the J/¢ rest frame cosOee must be less

than -0.996 in order to ensure that the Jl+ and Jl- are back-to-back «(}:I' > 175°).

• We require 0.9 < R < 1.4 for dimuon events. The R (see Equation 5.3) distributions

CHAPTER 5. EVENT SELECTION 41

S 1600

S 1600

c c Q) g! > W W

800 800

, 0 0 1.20 1.60 1.20 1.60

PI1+ (GaV/c) PI1- (GaV/c)

10000 , I

3000

(C) (d) S ~ 2000 c g! 5000 f- -

~ W

1000 f-

0 .)1 ....

0 3.00 3.10 3.20 0.90 1.10 1.30 1.50

/-1+/-1- Mass (GaV/c2) R C/lV)

Figure 5.8: Momenta for (nomuid) /L+ and /L- are shown in (a) and (b), where histograms are MC and error bars are data. The invariant mass of the /L+/L- is shown in (c), while R for data (bigh momentum tracks) and MC (1/I(2S) -> 11"+11"- J/1/J, J/1/J ..... /L+/L-) are shown in (d). Because there is some disagreement between Me and data for these distributions, the systematic error of the R requirement is determined in section 6.3

CHAPTER 5. EVENT SELECTION 42

for data and Me are shown in Figure 5.8. Dielectron events have R < 0.6 and can be

vetoed with this criterion [3J. (See Figure 5.7)

• Etot is defined to be the total energy of all four charged tracks, which should correspond

to the energy of the 'I/J(2S). We require Etot > 3.5 GeV/e? in order to select events

consistent with 'I/J(2S) --+ 11'+11'- J /'if;. The Etot distributions for data and Me are shown

in Figure 5.10

The nomuid momentum distributions p,,+ and p,,-, the invariant IIlllSS of the J-L+ J-L- cal­

culated using a 4C kinematic fit, and R (before selection) for data and MC for the process

'I/J(2S) -> 11'+11'- J/'if;, IN -> J-L+J-L- are shown in Figure 5.8.

5.2.4 Diproton Identification

Because the collection of decay channels 'I/J(2S) -> 11'+11'- J /'I/J, J /'if; -> two hadrons consists

of several channels such as 'I/J(2S) -> 11'+11'- J /'if;, J /'if; -+ K+ K- and 'I/J(2S) -+ 11'+11'- J /'if;,

J /'if; -> 11'+11'-, a time-of-flight requirement identifying 'I/J(2S) -> 11'+11'- J /'if;, J /'if; -> 'PP is

used. The flight time for diproton events tezp can be calculated using the known masses

of p, K, and 11'. The absolute difference between the measured and expected time for 'PP

is defined to be D.t(pP) = Itmeas - tezp(pP)I. Likewise, D.t(K±) = Itmeas - tezp(K±)1 and

D.t(1I'±) == Itmeas - tezp(1I'±)I.

• Events satisfying I cos /Jp I < 0.75 are required.

• The events selected as 'I/J(2S) -> 11'+11'- J /'if;, J /'if; -> 'PP must have D.t(pP) < D.t(K±)

and D.t(pP) < D.t(1I'±) [4J. The Me differences in flight times D.t's for 11'+, K+, and p+

are shown in Figure 5.9.

• In order to remove the remaining background, we require the 4C kinematic fitted

momentum pji invariant mass within 100 MeV /e? of the J/'I/J mass. This requirement

CHAPTER 5. EVENT SELECTION

1200 1000 800 600 400 200

o o

1400 1200 1000 800 600 400 200

o

(b)

o

3000 ':-2500 ~

2000 1500 1000 500

o o 1

43

(e)

I

2 3 123 Me M./ (ns)

1 2 3

Me llt./ ens) Me llt.: ens)

Figure 5.9: TOF time difference distributions with pji MC: (a) assuming pion mass (.6.t,,+,,-) (b) assuming kaon mass (.6.tK+K-), and (c) assuming proton mass (.6.tpjj ).

is determined from pji invariant mass histograms using '¢>(28) -+ 7r+7r-IN, IN -+

K+ K- and '¢>(28) -+ 7r+7r-J N, J N -+ 7r+7r- Monte Carlo events.

• The acoplanarity angle between the P and p in the J N CM frame cos8~ < -0.996 is

required, which corresponds to requiring the P and p to be back-to-back (9~ > 175°).

This is nsed to remove background from events with extra neutral tracks, such as

J N -+ pji'lr0 .

• We require Etot > 3.5 GeV/r? in order to select events consistent with '¢>(28) .....

7r+7r-J I'¢>. The Etot distributions for data and MC are shown in Figure 5.10.

The momentum distributions Pp and Pi;' the invariant mass of the pji calculated nsing a

4C kinematic fit, and the cosine of the angle between the p and p for data and MC for the

process '¢>(28) -+ 7r+7r- IN, IN -+ pji are shown in Figure 5.11.

CHAPTER 5. EVENT SELECTION 44

30000

(a) !!3 20000 c: ~

W

10000

OL-~~ __ ~-L~L-~~ __ ~-L __ L-~~ __ ~-L __ ~~

o 1 3 4

160

!!3 c: ~ 80 W

(b) 2000 (c) !!3 t c: • ~ • W

1000 • • • ,

0~~2L~~~~~~ .....

O~~-L~--~~--~

3.40 3.80 3.40 3.80

Diproton Etot (GeV/c2) nomuid Erot (GeV/c2

)

Figure 5.10: (a) Etot. for data before selection, (b) pji, and (c) /1+/1-. (b) and (c) contain MC (histograms) and data (points with error bars) after selection. Because the MC does not agree perfectly with the data for Etot , we determine the systematic error in section 6.3

CHAPTER 5. EVENT SELECTION

80

40

o • 0.90

(a)

I •

1.30 1.70

Pp+ (GeV/c)

300 ""--'-"'--'---,""--'-"'-'---'

200 f- (c) -

100 - -

o ......... ~~WlJ~Lr~~.'~.\...........J 3.00 3.10 320

P V Fit IvMass (GeV/c2)

45

40

1.30 1.70

Pp- (GeV/c)

(d)

5OOr- -

Figure 5.11: Momenta for p and p are shown in (a) and (b), where histograms are MC and error bars are data. The invariant mBBS of the pP is shown in (c), while the cosine of the angle between the p and p in the J N CM frame is shown in (d).

References

[1] J. Z. Bai et al., "Measurement of the Branching Fraction of J /'if; ..... 11'+11'-11'0," Physical

Review D 70, 012005 (2004).

[2] D. Kong, "Measurement of the total cross-section f{)r hadronic production by e+e- anni­

hilation at energies between 2-GeV to 5-GeV," Ph.D. dissertation, University of Hawaii,

UMI-99-90253 .

[3] J. Z. Bai et al., "'¢>(2S) decays into J/'if; plus two photons," Physical Review D (Particles

and Fields) 70, 012006 (2004).

[4] J. Z. Bai et al., "The measurements of J/'¢> ..... W," Phys. Lett. B591, 42-48 (2004).

46

Chapter 6

Results

6.1 Event Yields

The event yields for each decay channel are. determined from the invariant II1lI8S distribution

calculated using momenta determined from a 4C kinematic fit, as shown in Figures 5.7, 5.8,

and 5.11. Because the MC and data distributions do not match perfectly, we do not fit the

data with the MC distribution. Also, there are no radiative tails on the dielectron invariant

mass distribution because the 4C kinematic fit constrains the dielectron sample to those that

do not radiate greatly.

Since the distributions are clean, we use sideband subtraction to determine the number.

Background is removed from the raw number Nraw by Bubtracting the number of events in

a sideband region outside the peak, Nba.ckgruund. The sideband is defined to be 3.0 to 3.05

and 3.15 to 3.2 GeV/C'-. The statistical error in the numbers of events N is determined

from combining the error from the raw number ..; N raw and the background J Nba.ckground in

quadrature. N e+e- is the number of events identified as dielectron, N,,+,,-muid is the number

of events identified as dimuon using the MUID system, N,,+,,-""""'id is the number of events

identified as dimuon without using the MUID system, and Npp is the number of events

47

CHAPTER 6. RESULTS 48

identified as diproton. The event yields and corresponding efficiencies are summarized in

Table 6.1.

J/1/J-> Numbers of Events (N) Efficiencies (€) Branching Ratios

e+e- 55313 ± 232 21.6% (5.7 ± 0.26) x 10-2

p.+p.-muid 50385± 223 20.9% (5.4 ± 0.24) x 10-2

p.+p.-nomuid 70204±259 28.5% (5.5 ± 0.24) x 10-2

pfj 2048±47 25.1% (1.8 ± 0.1) x 10-3

Table 6.1: Numbers of events for e+e-,p.+p.-(muid and nomuid), and pfj selection after sideband subtraction. The uncertainties in the branching ratios include the systematic error on the '1/;(28) number of 4%, the uncertainty of the Me event yield, and the uncertainty of the PDG J /1/J branching ratio of 1.9%. These branching ratios are used as a consistency check.

6.2 Branching Ratio Analysis

BR('I/;(28) -> 11"+11"- J/1/J, J/1/J -> e+e-) = Ntot Ne+e- m<:

1/>(28) X €e+e-

BR(1/J(28) -> 11"+11"- J/1/J, J/1/J -> p.+p.-) = Ntot Np+p-tru! 1/>(28) X €p+l'-

N. BR('I/;(2S) -> 11"+11"- J/1/J, J/1/J -> pfj) = N'f1. pjj me

1/>(28) X €pjj

(6.1)

(6.2)

(6.3)

Rather than using N:;'(28) from an inclusive analysis, the ratios of branching ratios are calcu­

lated. The advantage of taking the ratios of branching ratios is that many systematic errors

that are present in both branching ratios cancel. Also, this comparison ratio is no longer a

function of N:;'(28). BR(J/1/J -> pfj) _ Npjj x €:;'fe­

BR(J/1/J -> e+e-) - Ne+e- x €;;;f

BR(J/1/J ..... pfj) Npjj x €;:::'p_ BR(J/1/J -> p.+p.-) - Np+p- X €;;;f

(6.4)

(6.5)

CHAPTER 6. RESULTS 49

The branching ratios were calculated with the number of'l/l(2S) events being (14 ± .56) x

106 and the branching ratio of'l/l(2S) -> 11"+11"- IN being (31.8 ± 0.6 )xlO-2 [1]. The

BR(JN->'fIP) • d te . ed t b (3 19 ± 0 085 ± 0 21) 10-2 d th BR(JN-rrP) • BR(JN_+e ) IS e nmn 0 e. . . x an e BR(J/TP-p.+p.-muid'J IS

determined to be (3.34±0.085±0.25) X 10-2• The first error is statistical, and the second error

is systematic. The statistical error for the ratios of branching ratios includes the uncertainty

on the '1/1(28) number, the uncertainty of the MC event yield, and the uncertainty of the

PDG 'I/I(2S) -> 11"+11"- J N branching ratio.

6.3 Systematic Error

The difference between the Monte Carlo simulations and data gives rise to systematic errors.

If the MC agrees perfectly with data, then the systematic error would be zero. However, we

find discrepancies between MC and data. Some of the systematic errors cancel when taking

the ratio of branching ratios. The remaining systematic errors are addressed separately for

dimuon and diproton decay channels below.

6.3.1 Common Sources

• Because we take the ratio of branching ratios, the systematic error from selecting 11"+11"-

in '1/1(28) -> 11"+11"- J N cancels. (See Section 5.1)

• The MDC tracking efficiency has a systematic error of 2% per track. This cancels when

taking the ratiO of branching ratios.

• The systematic error of the momenta selection p± > 0.8 GeV Ie cancels when taking

the ratio of branching ratios.

• The I cos () I < 0.75 selection cancels in ratio. This angular range is used for dielectron,

dimuon (nomuid), and diproton.

CHAPTER 6. RESULTS 50

• The selection of the invariant mass within 100 MeV/~ of the Ji1/J maBS using the

momenta determined from a 4C kinematic fit cancels when taking the ratio

• The systematic error of the cosine of the acollinearity angle cos (J* < -0.996 requirement

cancels in the ratio of branching ratios.

6.3.2 Dielectron Systematic Error

• The systematic error of the selection for both tracks identified as e+ e- outside the

rib region is determined to be 0.64%. This was done by making a tight selection on

SCE±/P± and comparing the efficiencies of the data and MC distributions of xse±.

The systematic error of the selection for both tracks identified as e+ e- where one track

hits the rib region is determined to be 0.69%. This was done by making a tight selection

on xse± and comparing the efficiencies of the data and MC distributions of SC E±/p±.

These individual systematic errors were combined according to the percentages of each

possibility (outside rib region: 67% and one track hits the rib region: 32%) to give a

total systematic error of 0.67%.

• The systematic error of the case where one track is identified as e+ e- is determined to

be 0.12%. This was found from comparing the dielectron branching ratio between all

three possibilities (1-3) and only the double-electron cases (1,2). (See section 5.2.2)

• The invariant mass distribution of the dielectron does not agree perfectly between MC

and data. The systematic error of the sideband subtraction was determined to be

0.26%. This was found by comparing the MC and data efficiencies for the dielectron

invariant maBS with and without sideband subtraction.

CHAPTER 6. RESULTS 51

6.3.3 Dimuon Identification

1. The overall systematic error using the MUID system is estimated by comparing the

dimuon branching ratio from muid (0.05368) and namuid (0.0521). The resulting

systematic error is 3.0%.

2. The following systematic errors from dimuon identification are found without using

the MUll system (namuid):

• In order to select the dimuon pair, we require R = J(SCE+/p+ -1)2 + (SCE_/p_ - 1)2 >

1.0. The data and MC efficiencies for a clean sample of dimuon events (required to

have Nhit > 2) was used to determine the systematic error. Although the difference

between these efficiencies is determined to be less than 1%, we conservatively estimate

that the systematic error is 1%. This is similar to the systematic error analysis in Ref.

[2].

• The systematic error of the selection of the total energy of the four tracks Etot >

3.5 GeV /c2 was determined by comparing the efficiencies with and without using the

MUID system. The efficiency for the muid data sample is estimated to be 0.943 while

the efficiency for the namuid MC sample is estimated to be 0.961. The resulting

systematic error is 1.91%

• The systematic error of the sideband subtraction for the dimuon was determined to be

negligible. This was done by comparing the MC and data efficiencies for the dimuon

invariant mass with and without sideband subtraction.

6.3.4 Diproton Identification

• The uncertainty caused by the TOF pP identification is estimated to be 0.3% [3]. This

was determined in Ref. [3] for the process J N --> pP, which yielded a much larger

CHAPTER 6. RESULTS 52

event sample size.

• The systematic error from the value of a in the MC for J N -+ pjj is negligible. This

is because changing a from 0.70 to 1.0 leads to a negligible change in the ratio of

branching ratios.

• The systematic error of the sideband subtraction for the diproton was determined to

be 1.9%. This was done by comparing the MC and data efficiencies for the diproton

invariant mass with and without sideband subtraction.

• The Blot > 3.5 Ge VIr? selection gives a negligible systematic error for the diproton

sample.

6.3.5 Ratio of Dimuon to Diproton

• The systematic error of the momenta selection (p+ > 1.3 GeV Ie or p_ > 1.3 GeV Ie or (p+ +p_) > 2.3 GeVle) is 0.2%. This was determined from changing the momenta

selection to (p+ > 1.3 GeVle or p_ > 1.3 GeVle or (p+ + p_) > 2.2 GeVle) and

comparing the ratio of branching ratios.

• The hadronic interaction systematic error for BR(p.f:J.'!..uid) from various simulation

models (GCALOR/GEANT-FLUKA) gives asystematic error of 6.4%. This was deter­

mined by comparing the ratio of branching ratios for GCALOR (0.03655) and GEANT­

FLUKA (0.03402). The ratio from the GEANT-FLUKA MC is used in the final result

for dimuon and diproton. This is because GEANT-FLUKA performs better than

GCALOR for diproton pairs.

CHAPTER 6. RESULTS 53

Selection IN-> Systematic Error (%)

R p,+p,- 1

Etot p,+p.- 1.91

TOF PID TIP 0.3 [3J

Sideband TIP 1.9

Etot TIP negligible

a value pfJ negligible

p++p- p,+ p,- ,pfJ 0.2

Hadronic Interaction p,+p,- ,TIP 6.4

Total Error 7.0

Table 6.2: Branching ratio systematic errors for J N -> p,+ p,- and J /1/J -> TIP events. Be­cause the Etot systematic error is negligible for TIP, there is an almost negligible systematic error correlation between p,+ p,- and TIP. All of the remaining systematic errors are inde­pendent of each other, resulting in a ne/9jtble systematic error correlation. Therefore, the systematic error on the ratio of BR(J7:~+;J!t!m.Uid) can be determined by combining all of the systematic errors in quadrature.

6.4 Summary of Branching Ratios

The branching ratio for J N --+ TIP is determined by:

_ BR(JN --+ TIP) + _ BR(JN --+ pp) = BR(JN -> p,+p,-ncnnuid) x BR(JN --+ p, p, PDG) (6.6)

where BR(p,+p,-PDG) is (5.93 ± 0.06) x 10-2 [lJ. The ratio of branching ratios and the

branching ratio of J N -> TIP are summarized in Table 6.3.

6.5 Angular Distributions

The cosine of the angle between the e+e- direction and the dipion system in the e+e- CM

system is defined to be cos Ox. The cosine of the angle between the 1[+ and the J/1/J direction

CHAPTER 6. RESULTS 54

BR(JL'/Hl!P.l BR(J N-I-'+ I-'-nomuid) (3.32 ± 0.077 ± 0.23) x 10-2

BR(JjV; -> pfi) (1.97 ± 0.15) x 10-3

BR(JjV; -> pfi)* (2.26 ± 0.14) x 10-3 [3]

BR(JjV; -> pfi)PDG (2.17 ± 0.08) x 10-3 [1]

Table 6.3: Ratio of Branching Ratios, where the first error is statistical and the second is systematic. BR(JjV; -> pfi) contains a combined error. BR(JjV; -> pji)* refers to a BES II inclusive analysis using the total number of J jV; events [3].

11'(28) ? n+ n- JIll', J/II'? Jl+ Jl-

eO

Figure 6.1: '1/;(28) -+ 11"+11"- JjV;, JjV; -+ /L+/L- angles. Circles indicate CM frame.

in the dipion CM frame is cos 0;. The cosine of the angle of the positive high momentum

track (e+,/L+, or p) and the JjV; direction in the JjV; rest frame is defined to be (cos 0;+,

COS 0;+, cos 0;). These angles are illustrated in Figure 6.5.

CHAPTER 6. RESULTS

6.5.1 Assumptions

55

The process I/J(2S) -> 11"+11"- IN, IN -> 1+1- is considered to take place via sequential

two-body decays; I/J(2S) -> X + IN, X -> 11"+11"-, and IN -> 1+1-. The Monte Carlo

assumes the following;

1. The invariant mass of the dipion system is empirically determined by;

~. ex (phase space) x (m!" - 4m~)2

where phase space refers to the momenta available to the decaying particles. Phase

space can also be represented by a spherical surface whose radius depends on the

masses.

2. The orbital angular momentum between the 11"+ and 11"- and between the dipion system

and the J /I/J in the 11"+11"- system is zero.

3. The X and the J/I/J are distributed uniformly in cos 0 in the e+e- rest frame.

4. The 11"+11"- are distributed uniformly in cos 0;+.

5. Leptons have a 1 + cos2 OJ distribution, where 1 represents e+ or J.L+.

6. The J N decay has a final state radiative correction in the J N rest frame on the order

of a3 •

6.5.2 Previous Results

According to BES I data, there is agreement between MC and data for cos Ox and the

assumed 1 + acos2 0j distribution for leptons in 1f;(2S) -> 11"+11"- IN, IN --+ 1+1-. It was

also determined that there was disagreement between the data and MC for the cos 0;+

distribution. The MC assumes that the relative angular momentum between the 11"+11"- and

CHAPTER 6. RESULTS 56

the J N is zero. Instead of the flat distribution of the MC, we find that the value of 0< is non­

zero. This is due to the fact that the relative angular momentum of the 11"+11"- is not purely

S-wave. The parameters for the BES I analysis for leptons involves combining the dielectron

and dimuon events. The partial wave amplitudes MI,L,B were determined from simultaneous

)(2 fits of the three distributions cosO;, cos 0;+, and cos Ox. Considering only the lowest

angular momentum amplitudes, we determine values for 0< below [4]. Each of the following

Distribution 0<

cos Ox -0.019 ± 0.031

cos 0;+ 0.26 ± 0.074

cos OJ 0.96 ± 0.023

Table 6.4: BES I angular distribution 0< values determined from partial wave amplitudes [4].

angular distributions is fitted with 1 + 0«x2), where x represents cos 0". The fit range is

restricted to a smaller portion of the total angular range. The MC cos 0;+ distribution is

weighted with 1 + 0.2(X2), in order to approximate the data more accurately. The angular

distributions for J N --+ e+ e- are shown in Figure 6.2 for MC and data. There is reasonable

agreement between data and MC, and with previous resnlts in Ref. [4). IN --+ p,+p,­

angular distributions are shown in Figures 6.3 and 6.4 for the muid and nomuid cases. The

angular distributions for J N --+ pP are shown in Figure 6.5 for MC and data. The values

for 0< are summarized below.

6.5.3 Systematic Error of Angular Distribution

The systematic error on the fitted value for 0< for J / if; --+ pP mainly arises from the fit

parameters of the weight curve (2.6% [3]), tracking reconstruction from MDC wire resolution

MC models (5.2% [3)), and a pP momentum background study (2.2% [3)). The sum of these

CHAPTER 6. RESULTS

20000

15000

10000 (0)

5000

o ·1 -D.5 0 0.5 1

Me e + e- cos(8;1

20000

10000 (b)

0.1 .0_5 0 0.5 1 Me e + e- cos(8n +)

~-----~ 15000

15000

10000

5000

o

15000

10000

5000

o ·1

(c)

IoIl.CHAN Cl.2823E+0& ndf4.538 I 18

Pf 0.1212£+05:1: SQ.13 P2 D.BB2 :I: CU9 2-01

-D.5 0 0.5 Me e+ e- cos(8/)

(e)

ALLCHAND..2572£+06 :/nIlf .stl.l1 16

P1 o..123O£+~:I: 104.9 P2 0.1 10:1: -01

·0_5 0 0.5 1 e + e- cos(81/)

10000

(d)

5000

o ·1 -D.5 0 0.5 1

e + e- cos(8;1

10000

5000

o -D.5

57

Figure 6.2: J N -> e+e- bin-by-bin efficiency corrected angular distributions for MC (a-c) and data (d-f). The fit ranges are: (a,d) (-1:1), (b,e) (-0.85:0.85), (c,f) (-0.68:0.68).

CHAPTER 6. RESULTS

20000

15000

10000

5000

o

10000

5000

15000

10000

5000

o

(0)

-1 -0.5 0 0.5 1

-1

MC,.t 1-"- cos(8)

(c)

(e)

'-df10.4l I 18 P1 97118.:1:

13 0.

+

.... 7 4E 01

-0.5 0 0.5 1 muid 11+ 11- cos(81t +)

20000

10000 (b)

o -1 -0.5 0 0.5 1 MC 11+ 11- cos(81t+)

10000

5000

o

8000

6000

4000

2000

(d)

-1 -0.5 0 0.5 1 muidl1+ 11- cos(8)

AU.CHANo.t315E+D8 ndf'4"" I 18

PI SM5.ll:

o Li~~==~I~~~ -0.5 -0.25 0 0.25 0.5

muid 11+ 11- cos(8l1 +)

58

Figure 6.3: IN ..... p.+p.- bin-by-bin efficiency corrected 8Jlgular distributions for muid MC (a-c) 8Jld data (d-f). The fit r8Jlges are: (a,d) (-1:1), (b,e) (-0.85:0.85), (c) (-0.62:0.62), (f) (-0.6:0.6) .

CHAPTER 6. RESULTS 59

20000 20000

15000

10000 (0) 10000 (b)

5000

o -1 -0.5 0 0.5 1

o -1 -0.5 0 0.5 1

MCnomuidli+ Ii- cos(9) MC nomuid Ii + Ii - cos(91t +)

... + ... 15000

~ +

10000 I-

10000 (c) (d)

5000 r--5000

ALLCHANQ.2492E+08

o -0.5 0 0.5

!! ... , ...... !.. ,. Pl D.1243[+o!z b. 8.!.34 P2 :i: 1 BOlf.-Gl o

-1 -0.5 0 0.5 1 MC nomuid Ii + Ii - cos(911 +) nomuidJl+ Jl- cos(9)

15000

~ 10000 10000

(e) 5000 (f)

5000

o -1 -0.5 0 0.5 1

o -0.5 0 0.5

nomuid Jl + Ii - cos(91t +) nomuidJl+ Jl- cos(9I1+)

Figure 6.4: J /'1/1 -+ p,+p,- bin-by-bin efficiency corrected angular distributions for nomuid Me (arc) and data (d-f). The fit ranges are: (a,d) (-1:1), (b,e) (-0.85:0.85), (c) (-0.68:0.68), (f) (-0.62:0.62).

CHAPTER 6. RESULTS

4000 (0)

2000

o ·1 -0.5 0 0.5 1

MCp+ p. cos(9J

4000

3000

2000 (c)

1000

o -0.5 0 0.5

MCp+ p. cos(9/)

600

400

200 (e)

o ·1 -0.5 0 0.5 1

p+p. cos(97t+)

4000 (b)

2000

oL,.~~~~~ ·1 -0.5 0 0.5 1

MC p + p. cos(97t +)

600 ~------,

400

200 (d)

o ·1 -0.5 0 0.5 1

p+ p. cos(9J

400

300

200

100 (f)

10.4.5 o L-~~~~~~~I~~ -0.5 . 0 0.5

P + p. cos(9p +)

60

Figure 6.5: J N ..... pji bin·by-bin efficiency corrected angular distributions for Me (a·c) and data (d-f). The fit ranges are: (a,d) (·1:1), (b,e) (.0.85:0.85), (c) (-0.68:0.68), (f) (.0.6:0.6).

CHAPTER 6. RESULTS 61

'if;(2S) ..... 11+11- Jj'if;, Jj'if; ..... e+e- C<

cos 9x 0.027 ± 0.019

cos 9; 0.13 ± 0.026

cos 9;+ 0.94 ± 0.047

'if;(2S) ..... 11+11- Jj'if;, Jj'if; ..... p,+p,-muid C<

cos9x -0.0052 ± 0.016

cos 9; 0.19 ± 0.022

cos 9;+ 1.57 ± 0.065

'if;(2S) ..... 11+11- Jj'if;, Jj'if; ..... p,+p,-nomuid C<

cos 9x 0.048 ± 0.018

cos 9; 0.18 ± 0.025

cos 9;+ 1.36 ± 0.061

'if;(2S) ..... 11+11- Jj'if;, Jj'if; ..... pji C<

cos 9x -0.014 ± 0.D78

cos 9; 0.053 ± 0.099

cos 9* l' 0.41 ± 0.19

Table 6.5: c< values for cos Ox, cos 0;, and (cos 9;+, cos 9;+, or cos 9;). The errors on c<

for all cases except cos 9; are statistical only. The error on cos 9; includes statistical and systematic errors.

systematic errors in quadrature is 6.2% [3]. These errors are small compared to the statistical

error of 46.5%.

The c< systematic error is then combined in quadrature with the statistical errors, which is

summarized below for 'if;(2S) ..... 1T+1T- J /'if;, J /'if; ..... pji. The c< uncertainty for the dielectron

and the dimuon cases are statistical only.

References

[1] W.-M. Yao et al:, "Review of Particle Physics," J. Phys. G 33, 64, 891-897 (2006).

[2] J. Z. Boi et al., "7/1(28) decays into J N plus two photons," Physical Review D (Particles

and Fields) 70, 0120[J6 (2004).

[3] J. Z. Soi et al., "The measurements of IN -+ pP," Phys. Lett. B591, 42--48 (2004).

[4] J. Z. Boi et al .. "7/1 (2s) -+ 7r+7r- J/7/J Decay Distributions," Phys. Rev. D 62 (2000).

62

Chapter 7

Conclusion

The determined value of BR(Jj'Ij; -+ pp) of (1.97±0.15) x 10-3 agrees with the PDG (2007)

value of BR(J j'Ij; -+ pfi) of (2.17 ± 0.08) x 10-3 within one standard deviation. Although the

combined error for the value of BR(J j'Ij; -+ pp) is slightly larger than that ofthe BES II direct

measurement of BR(Jj'Ij; -+ pfi), the systematic error is different. Figure 7.1 summarizes

these results.

The angular distributions for cos ex and cos e; are consistent with Me angular distrib,:­

tions. The cos 9 x Q values are consistent with zero, and the cos 9; Q values are consistent for

all dilepton cases. The BES I combined lepton analysis for Q of the cos 9x distribution gives

-0.019 ± 0.031. The Q of the cos9; distribution gives 0.26 ± 0.074. [I] We find reasonable

agreement with these values for Q.

The Q value for cos9;+ is similar to 1. However, Q for cos9;+ (muid and namuid) do

not agree with the assumed value of 1. A similar analysis using BES I data for a combined

lepton value (cos9;++cos9;+) for Q gives 0.96 ± 0.023, where the error is combined. [I] This

disagreement could be due to the fact that the efficiency for detecting muons is dependent

on the angle.

The Q value for cos 9; is consistent with that reported in a J j'Ij; -+ pfi BES II analysis

63

CHAPTER 7. CONCLUSION

2.5,.----------------------,

2.4

2.3·

2.2·

2.1

2·

1.9"

Diproton branching ratio (x 10.3)

J/\" ~ pp BESII

2.26

This Result

1.97

PDG World Average r

12.17

1.81-----------------------1

64

Figure 7.1: Diproton branching ratio comparison of result, PDG value, and J/'I/J -> Pii BESII result.

(0.676 ± 0.036 ± 0.042 [2]) within one standard deviation.

References

[1] J. Z. Bai et al., "'IjJ (2s) ..... 71"+71"- Jf'IjJ Decay Distributions," Phys. Rev. D 62 (2000).

[2] J. Z. Bai et al., "The measurements of Jj'if; ..... W," Phys. Lett. B591, 42-48 (2004).

65