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-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