Study of
J=
c
! p p and J=
c
! n n
M. Ablikim,1M. N. Achasov,5D. J. Ambrose,40F. F. An,1Q. An,41Z. H. An,1J. Z. Bai,1Y. Ban,27J. Becker,2N. Berger,1 M. Bertani,18J. M. Bian,39E. Boger,20,*O. Bondarenko,21I. Boyko,20R. A. Briere,3V. Bytev,20X. Cai,1A. Calcaterra,18
G. F. Cao,1J. F. Chang,1G. Chelkov,20,*G. Chen,1H. S. Chen,1J. C. Chen,1M. L. Chen,1S. J. Chen,25Y. Chen,1 Y. B. Chen,1H. P. Cheng,14Y. P. Chu,1D. Cronin-Hennessy,39H. L. Dai,1J. P. Dai,1D. Dedovich,20Z. Y. Deng,1 A. Denig,19I. Denysenko,20,†M. Destefanis,44W. M. Ding,29Y. Ding,23L. Y. Dong,1M. Y. Dong,1S. X. Du,47J. Fang,1 S. S. Fang,1L. Fava,44,‡F. Feldbauer,2C. Q. Feng,41R. B. Ferroli,18C. D. Fu,1J. L. Fu,25Y. Gao,36C. Geng,41K. Goetzen,7 W. X. Gong,1W. Gradl,19M. Greco,44M. H. Gu,1Y. T. Gu,9Y. H. Guan,6A. Q. Guo,26L. B. Guo,24Y. P. Guo,26Y. L. Han,1 X. Q. Hao,1F. A. Harris,38K. L. He,1M. He,1Z. Y. He,26T. Held,2Y. K. Heng,1Z. L. Hou,1H. M. Hu,1J. F. Hu,6T. Hu,1 B. Huang,1G. M. Huang,15J. S. Huang,12X. T. Huang,29Y. P. Huang,1T. Hussain,43C. S. Ji,41Q. Ji,1X. B. Ji,1X. L. Ji,1 L. K. Jia,1L. L. Jiang,1X. S. Jiang,1J. B. Jiao,29Z. Jiao,14D. P. Jin,1S. Jin,1F. F. Jing,36N. Kalantar-Nayestanaki,21 M. Kavatsyuk,21W. Kuehn,37W. Lai,1J. S. Lange,37J. K. C. Leung,35C. H. Li,1Cheng Li,41Cui Li,41D. M. Li,47F. Li,1
G. Li,1H. B. Li,1J. C. Li,1K. Li,10Lei Li,1N. B. Li,24Q. J. Li,1S. L. Li,1W. D. Li,1W. G. Li,1X. L. Li,29X. N. Li,1 X. Q. Li,26X. R. Li,28Z. B. Li,33H. Liang,41Y. F. Liang,31Y. T. Liang,37G. R. Liao,36X. T. Liao,1B. J. Liu,34B. J. Liu,1
C. L. Liu,3C. X. Liu,1C. Y. Liu,1F. H. Liu,30Fang Liu,1Feng Liu,15H. Liu,1H. B. Liu,6H. H. Liu,13H. M. Liu,1 H. W. Liu,1J. P. Liu,45K. Y. Liu,23Kai Liu,6Kun Liu,27P. L. Liu,29S. B. Liu,41X. Liu,22X. H. Liu,1Y. Liu,1Y. B. Liu,26 Z. A. Liu,1Zhiqiang Liu,1Zhiqing Liu,1H. Loehner,21G. R. Lu,12H. J. Lu,14J. G. Lu,1Q. W. Lu,30X. R. Lu,6Y. P. Lu,1 C. L. Luo,24M. X. Luo,46T. Luo,38X. L. Luo,1M. Lv,1C. L. Ma,6F. C. Ma,23H. L. Ma,1Q. M. Ma,1S. Ma,1T. Ma,1 X. Y. Ma,1Y. Ma,11F. E. Maas,11M. Maggiora,44Q. A. Malik,43H. Mao,1Y. J. Mao,27Z. P. Mao,1J. G. Messchendorp,21
J. Min,1T. J. Min,1R. E. Mitchell,17X. H. Mo,1C. Morales Morales,11C. Motzko,2N. Yu. Muchnoi,5Y. Nefedov,20 C. Nicholson,6I. B. Nikolaev,5Z. Ning,1S. L. Olsen,28Q. Ouyang,1S. Pacetti,18,§J. W. Park,28M. Pelizaeus,38K. Peters,7
J. L. Ping,24R. G. Ping,1R. Poling,39E. Prencipe,19C. S. J. Pun,35M. Qi,25S. Qian,1C. F. Qiao,6X. S. Qin,1Y. Qin,27 Z. H. Qin,1J. F. Qiu,1K. H. Rashid,43G. Rong,1X. D. Ruan,9A. Sarantsev,20,kJ. Schulze,2M. Shao,41C. P. Shen,38,{ X. Y. Shen,1H. Y. Sheng,1M. R. Shepherd,17X. Y. Song,1S. Spataro,44B. Spruck,37D. H. Sun,1G. X. Sun,1J. F. Sun,12 S. S. Sun,1X. D. Sun,1Y. J. Sun,41Y. Z. Sun,1Z. J. Sun,1Z. T. Sun,41C. J. Tang,31X. Tang,1E. H. Thorndike,40H. L. Tian,1
D. Toth,39M. Ullrich,37G. S. Varner,38B. Wang,9B. Q. Wang,27K. Wang,1L. L. Wang,4L. S. Wang,1M. Wang,29 P. Wang,1P. L. Wang,1Q. Wang,1Q. J. Wang,1S. G. Wang,27X. F. Wang,12X. L. Wang,41Y. D. Wang,41Y. F. Wang,1 Y. Q. Wang,29Z. Wang,1Z. G. Wang,1Z. Y. Wang,1D. H. Wei,8P. Weidenkaff,19Q. G. Wen,41S. P. Wen,1M. Werner,37 U. Wiedner,2L. H. Wu,1N. Wu,1S. X. Wu,41W. Wu,26Z. Wu,1L. G. Xia,36Z. J. Xiao,24Y. G. Xie,1Q. L. Xiu,1G. F. Xu,1 G. M. Xu,27H. Xu,1Q. J. Xu,10X. P. Xu,32Y. Xu,26Z. R. Xu,41F. Xue,15Z. Xue,1L. Yan,41W. B. Yan,41Y. H. Yan,16 H. X. Yang,1T. Yang,9Y. Yang,15Y. X. Yang,8H. Ye,1M. Ye,1M. H. Ye,4B. X. Yu,1C. X. Yu,26J. S. Yu,22S. P. Yu,29 C. Z. Yuan,1W. L. Yuan,24Y. Yuan,1A. A. Zafar,43A. Zallo,18Y. Zeng,16B. X. Zhang,1B. Y. Zhang,1C. C. Zhang,1
D. H. Zhang,1H. H. Zhang,33H. Y. Zhang,1J. Zhang,24J. G. Zhang,12J. Q. Zhang,1J. W. Zhang,1J. Y. Zhang,1 J. Z. Zhang,1L. Zhang,25S. H. Zhang,1T. R. Zhang,24X. J. Zhang,1X. Y. Zhang,29Y. Zhang,1Y. H. Zhang,1Y. S. Zhang,9
Z. P. Zhang,41Z. Y. Zhang,45G. Zhao,1H. S. Zhao,1J. W. Zhao,1K. X. Zhao,24Lei Zhao,41Ling Zhao,1M. G. Zhao,26 Q. Zhao,1S. J. Zhao,47T. C. Zhao,1X. H. Zhao,25Y. B. Zhao,1Z. G. Zhao,41A. Zhemchugov,20,*B. Zheng,42J. P. Zheng,1
Y. H. Zheng,6Z. P. Zheng,1B. Zhong,1J. Zhong,2L. Zhou,1X. K. Zhou,6X. R. Zhou,41C. Zhu,1K. Zhu,1K. J. Zhu,1 S. H. Zhu,1X. L. Zhu,36X. W. Zhu,1Y. M. Zhu,26Y. S. Zhu,1Z. A. Zhu,1J. Zhuang,1B. S. Zou,1J. H. Zou,1and J. X. Zuo1
(BESIII Collaboration)
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China
2Bochum Ruhr-University, 44780 Bochum, Germany
3Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
4China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
5G. I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
6
Graduate University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
7GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
8Guangxi Normal University, Guilin 541004, People’s Republic of China
9GuangXi University, Nanning 530004, People’s Republic of China
10Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
12Henan Normal University, Xinxiang 453007, People’s Republic of China
13Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
14Huangshan College, Huangshan 245000, People’s Republic of China
15Huazhong Normal University, Wuhan 430079, People’s Republic of China
16Hunan University, Changsha 410082, People’s Republic of China
17Indiana University, Bloomington, Indiana 47405, USA
18INFN Laboratori Nazionali di Frascati, Frascati, Italy
19Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, 55099 Mainz, Germany
20
Joint Institute for Nuclear Research, 141980 Dubna, Russia
21KVI/University of Groningen, 9747 AA Groningen, The Netherlands
22Lanzhou University, Lanzhou 730000, People’s Republic of China
23Liaoning University, Shenyang 110036, People’s Republic of China
24Nanjing Normal University, Nanjing 210046, People’s Republic of China
25Nanjing University, Nanjing 210093, People’s Republic of China
26Nankai University, Tianjin 300071, People’s Republic of China
27Peking University, Beijing 100871, People’s Republic of China
28Seoul National University, Seoul, 151-747 Korea
29Shandong University, Jinan 250100, People’s Republic of China
30Shanxi University, Taiyuan 030006, People’s Republic of China
31Sichuan University, Chengdu 610064, People’s Republic of China
32Soochow University, Suzhou 215006, People’s Republic of China
33Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
34The Chinese University of Hong Kong, Shatin, N. T., Hong Kong
35The University of Hong Kong, Pokfulam, Hong Kong
36
Tsinghua University, Beijing 100084, People’s Republic of China
37Universitaet Giessen, 35392 Giessen, Germany
38University of Hawaii, Honolulu, Hawaii 96822, USA
39University of Minnesota, Minneapolis, Minnesota 55455, USA
40University of Rochester, Rochester, New York 14627, USA
41University of Science and Technology of China, Hefei 230026, People’s Republic of China
42University of South China, Hengyang 421001, People’s Republic of China
43University of the Punjab, Lahore-54590, Pakistan
44University of Turin and INFN, Turin, Italy
45Wuhan University, Wuhan 430072, People’s Republic of China
46Zhejiang University, Hangzhou 310027, People’s Republic of China
47Zhengzhou University, Zhengzhou 450001, People’s Republic of China
(Received 4 May 2012; published 31 August 2012)
The decays J=c ! p p and J=c ! n n have been investigated with a sample of 225:2 106 J=c
events collected with the BESIII detector at the BEPCII eþe collider. The branching fractions are
determined to be BðJ=c ! p pÞ ¼ ð2:112 0:004 0:031Þ 103 and BðJ=c ! n nÞ ¼ ð2:07
0:01 0:17Þ 103. Distributions of the angle between the proton or antineutron and the beam
direction are well described by the form 1 þ cos2, and we find ¼ 0:595 0:012 0:015 for J=c !
p p and ¼ 0:50 0:04 0:21 for J=c ! n n. Our branching-fraction results suggest a large phase
angle between the strong and electromagnetic amplitudes describing the J=c ! N N decay.
DOI:10.1103/PhysRevD.86.032014 PACS numbers: 14.40.Pq, 12.38.Qk, 13.25.Gv
I. INTRODUCTION
The J=c meson is interpreted as a bound state of a charmed quark and a charmed antiquark (c c). The decay process J=c ! N N (N ¼ p or n) is an octet-baryon-pair decay mode, and should be a good laboratory for testing perturbative QCD (pQCD) because the three gluons in the OZI-violating strong decay correspond to the three q q pairs that form the final-state nucleons. The ratio of the branching fractions for the p p and n n final states provides information about the phase angle between the strong and the electromagnetic (EM) amplitudes governing the decay
*Also at the Moscow Institute of Physics and Technology,
Moscow, Russia
†On leave from the Bogolyubov Institute for Theoretical
Physics, Kiev, Ukraine
‡University of Piemonte Orientale and INFN (Turin)
§University and INFN of Perugia, Perugia, Italy
kAlso at the PNPI, Gatchina, Russia
[1–3]. Because the initial-state isospin is 0, the strong-decay amplitudes for the p p and n n final states must be equal. The J=c ! p p and J=c ! n n EM decays are expected to have amplitudes that are of about the same magnitude, but with opposite signs, like the magnetic mo-ments (as discussed in Sec.VII). Because the EM decays of J=c to p p and n n behave the same as nonresonant pro-duction of those final states, the magnitude of the EM decay amplitude of J=c can be estimated from the cross section for continuum production eþe! p p. If the strong and EM amplitudes are almost real, and therefore in phase, as predicted by pQCD [1–5], then interference would lead to a branching fraction for J=c ! n n about one-half as large as that for J=c ! p p. Conversely, if the strong and EM amplitudes are orthogonal, then the strong decay dominates and the branching fractions are expected to be equal. In previous experiments, J=c ! p p has been measured with good precision, while J=c ! n n has been measured with quite a large uncertainty [6,7]. They appear to be equal within errors, at odds with the pQCD expectation.
The angular distribution for J=c ! N N can be written as a function of the angle between the nucleon or anti-nucleon direction and the beam as follows:
dN
d cos ¼ Að1 þ cos
2Þ;
where A is an overall normalization. These angular distri-butions reflect details of the baryon structure and have the potential to distinguish among different theoretical models [1–5].
In this paper, we report new studies of the process J=c ! N N made with the BESIII detector at the BEPCII electron-positron storage ring [8,9]. With the world’s largest sample of J=c decays, we obtain improved measurements for the J=c ! p p and J=c ! n n branch-ing fractions and angular distributions.
II. BEPCII AND BESIII
BEPCII is a two-ring eþecollider designed for a peak luminosity of 1033 cm2s1at a beam current of 0.93 A. The cylindrical core of the BESIII detector consists of a helium-gas-based drift chamber (MDC) for charged-particle tracking and charged-particle identification by dE=dx, a plastic scintillator time-of-flight system (TOF) for addi-tional particle identification, and a 6240-crystal CsI(Tl) Electromagnetic Calorimeter (EMC) for electron identifi-cation and photon detection. These components are all enclosed in a superconducting solenoidal magnet provid-ing a 1.0-T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive-plate-counter muon detector modules (MU) interleaved with steel. The geometrical acceptance for charged tracks and photons is 93% of 4, and the resolutions for charged-track momen-tum and photon energy at 1 GeV are 0.5% and 2.5%,
respectively. More details on the features and capabilities of BESIII are provided in Ref. [8].
III. DATA SAMPLE
Our data sample consists of 225:2 106 eþe! J=c
events collected during 2009. The estimated uncertainty in the number of events is 1:3% [10]. AGEANT4-based [11,12] detector simulation is used to produce Monte Carlo (MC) samples for signal and background processes that are generated with specialized models that have been pack-aged and customized for BESIII [13].EVTGEN[14] is used to study phase-space signal events for J=c ! p p and for exclusive backgrounds in J=c decays.BABAYAGA[15] is used to generate Bhabha and events as possible EM backgrounds. A large inclusive sample (200 106events)
is used to simulate hadronic background processes. The J=c resonance is generated by KKMC [16]. Known J=c decay modes are generated withEVTGEN, using branching fractions set to world-average values [6]. The remaining J=c decay modes are generated by LUNDCHARM [13], which is based on JETSET [17] and tuned for the charm-energy region. The decays J=c ! p p and J=c ! n n are excluded from this sample.
IV. GENERAL EVENT SELECTION
Charged tracks in BESIII are reconstructed from MDC hits. To optimize the momentum measurement, we select tracks in the polar angle range j cosj < 0:93 and require that they pass within10 cm of the interaction point in the beam direction and within1 cm in the plane perpendicu-lar to the beam.
Electromagnetic showers are reconstructed by clustering EMC crystal energies. Efficiency and energy resolution are improved by including energy deposits in nearby TOF counters. Showers used in selecting photons and in 0
reconstruction must satisfy fiducial and shower-quality requirements. Showers in the barrel region (j cosj < 0:8) must have a minimum energy of 25 MeV, while those in the endcaps (0:86 < j cosj < 0:92) must have at least 50 MeV. Showers in the region between the barrel and endcap are poorly reconstructed and are excluded. To eliminate showers from charged particles, a photon must be separated by at least 10from any charged track. EMC timing requirements suppress electronic noise and energy deposits unrelated to the event.
V. ANALYSIS OF J=c ! p p A. Event selection
Events with exactly two good charged tracks in the polar angle rangej cosj < 0:8 are selected. We exclude the two endcap regions to reduce systematic uncertainties in track-ing and particle identification. By ustrack-ing a loose particle-identification requirement for the positive track (probability of the p hypothesis greater than the probabilities for the þ
and Kþ hypotheses), and by requiring no particle identi-fication for the negative track, the efficiency is maximized and the systematic uncertainty is minimized. A vertex fit is performed to the two selected tracks to improve the momentum resolution, and the angle between the p andp is required to be greater than 178 . Finally, for both tracks, the measured momentum magnitude must be within 30 MeV=c ( 3) of the expected value of 1:232 GeV=c. Figure1shows comparisons between data and MC for the angle between the p and p and for their momenta.
This selection results in a signal of N ¼ 314651 561 candidate events. Figures1(b)and1(c)show the p and p momentum distributions for these events, along with the expected distributions for a pure MC J=c ! p p signal. Backgrounds overall are very small, and appear to be negligible in the accepted p and p momentum range. Three independent procedures are used to estimate this background: inclusive J=c MC, exclusive MC of potential background processes (Bhabha events and J=c decays to eþe, þ, KþK, p p, 0p p, and
c with c !
p p), and a sideband technique. The estimates range from 0.02% to 0.2% of the signal. We apply no subtraction and take the largest of the estimates (sideband) as a system-atic uncertainty in the final result. The raw distribution of
cos for the protons in the selected signal events is given in Fig.2.
B. Efficiency correction
To measure the J=c ! p p branching fraction and an-gular distribution, it is necessary to correct for the selection efficiency, which is dominated by track reconstruction and selection and by particle-identification efficiency. We use signal MC to obtain the efficiency, but use data to correct for imperfections in the simulation, thereby reducing the systematic uncertainty in the correction. We measure dif-ferences between the data and MC separately for the efficiencies of tracking and particle identification, leaving the other selection cuts in place or tightening them for cleaner selection. The correlation between the corrections in the tracking and particle-identification efficiencies has been shown in MC studies to be small, so we combine them into a single correction function that is applied to the MC-determined efficiency. Because the tracking and TOF response depend on the track direction, the efficiency correction is determined in bins of cos.
We divide the full angular range (j cosj < 0:8) into 16 equal bins and for each bin compute the efficiency for the successful reconstruction of the p or p track as follows:
trk ¼
N2
N1þ N2
;
where N1(N2) is the number of J=c ! p p events with 1
(2) good charged track(s) detected. For N1, we require only
one good charged track which is identified as a p or p. Note that in this case, unlike the J=c ! p p selection, we can apply particle identification to the p selection to improve purity, since any inconsistency between data and MC would cancel in the efficiency. Figure 3 shows the data/ MC comparison for the tracking efficiencies and the com-puted correction factor data
trk =MCtrk for each cos bin for p
andp.
back-to-back angle (Degree)
Events/0.1 Degree 0 20 40 60 80 100 3 10 × P(p) (GeV) Events/5 MeV 1 10 2 10 3 10 4 10 5 10 ) (GeV) p P( 178 179 180 181 1.0 1.1 1.2 1.3 1.4 1.0 1.1 1.2 1.3 1.4 Events/5 MeV 1 10 2 10 3 10 4 10 5 10
FIG. 1 (color online). Comparisons between data (points) and MC (histograms) for properties of the p and p tracks for selected
J=c ! p p signal events: (a) angle between the p and p, (b) p momentum, and (c) p momentum.
cosθ -0.5 0.0 0.5 Events/0.1 0 5000 10000 15000 20000 25000
FIG. 2. Angular distribution of the selected J=c ! p p
We can similarly measure the particle-identification ef-ficiency for the p in each cos bin, considering only J=c ! p p events in which there are two good charged tracks, with the negatively-charged track identified as an antiproton. We define the efficiency as follows:
pid ¼
Np
Npþ N6p
;
where Np is the number of selected events in which the
proton has been successfully identified and N6p is the
number of events without the proton identified. To select a more pure sample we tighten the selection on the p and p momenta to be within 20 MeV=c ( 2) of the expected value. Figure 4 shows the data/MC comparison for the proton particle identification efficiency and the resulting correction factor datapid=MCpid.
In each cos bin, the corrected MC-determined effi-ciency to be applied to data is computed with the following formula: ¼ MC data ptrk MCptrk datappid MCppid dataptrk MCptrk :
To diminish the effect of bin-to-bin scatter due to statistical fluctuations, we fit the corrected efficiency as a function of cos with a fifth-order polynomial, as shown in Fig.5.
C. Angular distribution and branching fraction We fit the measured angular distribution of the proton from J=c ! p p to the function Að1 þ cos2ÞðcosÞ, where A is the overall normalization and ðcosÞ is the
cosθ Eff. 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.02 1.04 cosθ Eff . Corr . 0.96 0.98 1.00 1.02 1.04 -0.5 0.0 0.5 -0.5 0.0 0.5
FIG. 4 (color online). (a) p particle-identification efficiency for data (points) and MC (circles), and (b) the computed efficiency
correction factor data
pid=MCpid. cosθ Eff. 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 cosθ -0.5 0.0 0.5 -0.5 0.0 0.5 Eff. Corr. 0.96 0.98 1.00 1.02 1.04 cosθ Eff. 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 cosθ -0.5 0.0 0.5 -0.5 0.0 0.5 Eff. Corr. 0.94 0.96 0.98 1.00 1.02 1.04 1.06
FIG. 3 (color online). (a) The proton tracking efficiency for data (points) and MC (circles), and (b) the correction data
trk =MCtrk; (c) and
corrected MC-determined efficiency function (Sec. V B). The angular distribution and the fit are shown in Fig.6. The 2 for the fit is 16, with 14 degrees of freedom, and the
value determined for the angular-distribution parameter is ¼ 0:595 0:012, where the error is statistical only.
The raw yield of J=c ! p p events obtained by count-ing protons in the angular range cos ¼ ½0:8; 0:8 is Nð0:8; 0:8Þ ¼ 314651 561. The efficiency-corrected yield obtained by fitting the cos distribution over this range is Ncorð0:8; 0:8Þ ¼ 357786 638. The fitted value
of is used to determine the total number of J=c ! n n events in the full angular range of cos ¼ ½1:0; 1:0 as follows: Ncorð1:0; 1:0Þ ¼ Ncorð0:8; 0:8Þ R1:0 1:0ð1 þ cos2Þd R0:8 0:8ð1 þ cos2Þd ¼ 475567 848:
Combining this final yield with the number of J=c events in our sample (ð2:252 0:029Þ 108Þ, we find
the branching fraction to be
B ðJ=c ! p pÞ ¼ ð2:112 0:004Þ 103;
where the error is statistical only.
D. Systematic errors and results
To determine the uncertainty in the efficiency cor-rection, we use toy MC experiments to obtain distribu-tions in the branching fraction and that reflect the statistical errors of the bin-by-bin efficiency values. We perform this study by varying each bin randomly accord-ing to a normal distribution for each MC experiment, redoing the polynomial fit and then remeasuring the efficiency-corrected yield. The results have normal distri-butions and they are fitted with Gaussian functions to estimate the associated uncertainties in the branching fraction and , which are found to be 4:69 106 and 0.011, respectively.
The full magnitude of the p p momentum sideband background estimate (0.2%) is taken to be the uncertainty in the branching fraction due to the background correction. We fit the sideband-subtracted angular distribution and determine a new value for the angular parameter , taking the change relative to the standard result (0.004) as the systematic error.
To estimate the systematic error due to the detector angular resolution, we perform a study with the signal MC. The ‘‘true’’ generated proton cos is fitted before and after smearing with a MC-derived angular resolution function. The differences in the fitted values (0.010) and in the branching fractions (4 106) are taken as the systematic uncertainties from this source.
The branching fraction also incurs two systematic un-certainties that do not affect . A small systematic uncer-tainty enters due to the correction for the j cosj < 0:8 requirement, which depends on the determined value of and its error. The dominant uncertainty in the branching fraction is due to the estimated 1.3% error in the number of J=c events in our sample [10].
To study the effect from continuum production, we write the total cross section p pas
cosθ MC eff. 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 cosθ Corrected MC eff. 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 -0.5 0.0 0.5 -0.5 0.0 0.5
FIG. 5. J=c ! p p selection efficiency as a function of cos (a) before correction, and (b) after correction. The line shows the
smoothed efficiency obtained by fitting the data to a fifth-order polynomial.
cosθ -0.5 0.0 0.5 Events/0.1 0 5000 10000 15000 20000 25000 30000
FIG. 6. The points represent the measured distribution of cos
for the p in J=c ! p p candidate events, with error bars that are the quadratic sums of the statistical and efficiency uncertainties. The line represents the fit of the distribution to the functional form given in the text, and is used to determine the normalization and the angular-distribution parameter .
p p¼ j ffiffiffiffiffiffiffiffiffiffiffi cont:p p q þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12eetot p s m2þ imtot ðEpþ eiSÞj2;
where Ep and S are the EM and strong amplitudes of
J=c ! p p and is the phase angle between them. cont:
p p is the p p cross section contributed by the continuum
under the J=c peak. These values are taken from the calculation in Sec. VII. The difference with and without cont:p p is assigned as the systematic error.
Finally, we change by 1 (includes systematic error) and reevaluate the branching-fraction to estimate the systematic error in the branching-fraction measurement.
TableIprovides a summary of all identified sources of systematic uncertainty, which are assumed to be uncorre-lated, and their quadrature sum. The final results for our J=c ! p p measurements are as follows:
¼ 0:595 0:012 0:015; and BðJ=c ! p pÞ ¼ ð2:112 0:004 0:031Þ 103:
The branching-fraction measurement is consistent with the previous world average [6] and improves the overall precision by about a factor of 2.5. The value of is also consistent with previous experiments (Table II) and is improved significantly.
VI. ANALYSIS OFJ=c ! n n A. Event selection
We search for J=c ! n n candidates by selecting events that have no good charged tracks originating in the inter-action region. The antineutron annihilation ‘‘star’’ in the EMC provides a signature for these events that is much
more identifiable than the hadronic shower produced by a neutron. We therefore first select events with showers characteristic of n interactions, and then search in these events for energy deposited by n hadronic interactions on the opposite side of the detector.
The most energetic shower in the event is assigned to be the n candidate and is required to have an energy in the range 0.6–2.0 GeV. To optimize the discrimination against backgrounds, we apply a fiducial cut ofj cosj < 0:8 to the n candidate. This ensures that the n energy is fully con-tained in the EMC for most signal events. To suppress photon backgrounds, we impose a requirement on the second moment of the candidate shower, defined as S ¼ iEir2i=iEi, where Ei is the energy deposited in the ith
crystal of the shower and riis the distance from the center
of that crystal to the center of the shower. To be accepted, the n candidate must satisfy S > 20 cm2. To further exploit
the distinctive n shower topology, we require the number of EMC hits in a 50 cone around the n candidate shower direction to be greater than 40.
Events with accepted n candidates are searched for EMC showers on the opposite side of the detector that are con-sistent with being the neutron in a J=c ! n n decay. The energy of this shower must be between 0.06 and 0.6 GeV, a range found to be characteristic of the EMC neutron re-sponse in MC studies. If multiple showers are present, the one that is most back-to-back with respect to the n candi-date is selected. To further suppress backgrounds from all-neutral J=c decays, continuum production and EM pro-cesses, we require Eextra ¼ 0, where Eextra is the total
deposited energy in the EMC, excluding that of the n shower and any additional energy in the 50 cone.
The expected signal for J=c ! n n is an enhancement near 180 in the distribution of the angle between the n shower and the direction of the n. The distributions of this angle and of the cosine of the polar angle of the n shower ( cos) for selected candidates are shown in Fig. 7. The enhancement near 180 in the distribution of the angle between the n and n constitutes the J=c ! n n signal. Since there is nonnegligible background, the number of J=c ! n n events must be determined by fitting. Distributions of the angle between the n and n are con-structed in bins of cos and fitted with signal and back-ground functions.
Data-driven methods are used to determine the effi-ciency and signal shapes for J=c ! n n. We select J=c ! pð nÞ and charge-conjugate (c.c.) events in data to ob-tain n and n samples to evaluate the selection efficiency. We use the p and p in J=c ! p p events that have been selected using information from just the MDC to get un-biased information on the shape and efficiency of the n and n response in the EMC, since antiproton and antineutron hadronic interactions are similar.
Generic J=c MC is used to assess the background. Figure 7(a) shows that there is no peaking in the
TABLE I. Systematic errors for J=c ! p p.
Sources Effect on Effect onB(103)
Efficiency Correction 0.011 0.005 Background 0.004 0.002 cos Resolution 0.010 0.004 Value 0.004 Number of J=c 0.026 continuum 0.015 Total 0.015 0.031
TABLE II. Previous measurements of in J=c ! p p.
Collaboration Mark1 [18] 1:45 0:56 Mark2 [19] 0:61 0:23 Mark3 [20] 0:58 0:14 DASP [21] 1:70 1:70 DM2 [22] 0:62 0:11 BESII [23] 0:676 0:055
distribution of the angle between the n and n for this background. We also consider possible exclusive back-ground channels: J=c ! 0n n, J=c ! n n, eþe !
, J=c ! þ, J=c ! þ, J=c ! p p, and J=c ! c (c ! n n). None of these potential
back-ground sources exhibits peaking in the distribution of the angle between the n and n.
B. Efficiency determination
We use specially chosen event samples from data to determine the efficiencies for each requirement in the J=c ! n n selection. The overall efficiency is then com-puted bin-by-bin in cos as the product of these compo-nents and is applied as a correction in obtaining the angular distribution and branching fraction.
We select J=c ! p n events to study the efficiency of the n selection. Events with exactly two good charged tracks identified as p and are selected. Information
from the TOF detector and dE=dx information from the MDC are combined to do the particle identification. The p and are required to have a missing mass within 30 MeV of the nominal n mass. The missing momentum of the p and is required to be in the range 1:1–1:2 GeV=c to ensure a sample that is as similar as possible to the n in J=c ! n n (momentum 1:232 GeV=c). The number of events passing the above selection gives Nexp, the expected
n yield. The number of n candidates selected from these events (criteria defined in Sec.VI A) that match the miss-ing momenta of the accompanymiss-ing p and within 10 gives the observed yield Nobs. The efficiency for n selec-tion is datan ¼ Nobs=Nexp.
To validate this procedure and ensure consistency be-tween the n in J=c ! p nand that in the signal process J=c ! n n, we select higher-purity n candidates in J=c ! n n (J=c ! p n) with a stringent cut of 177 on the angle between the n and n. (For J=c ! p n the cut is on the angle between the n and the missing momen-tum of the p and .) Comparisons of the selection variables (energy deposit in EMC, number of EMC hits in a 50 cone about the n shower, and the shower second moment) for these two n samples are shown in Fig.8. Each distribution is plotted after the cuts on the other variables have been imposed. There is good agreement, verifying that the n in J=c ! pð nÞis a good match to the n in the signal process J=c ! n n, and that this process provides a reliable efficiency correction.
We apply the same technique to calculate the efficiency for selecting the neutron (data
n ), in this case using a sample
of J=c ! pðnÞþ selected from data. A comparison of the distribution of the EMC energy for neutrons from J=c ! pðnÞþ with that from J=c ! n n is shown in Fig.9. In this case the momentum difference between the two n samples results in a greater difference in the EMC energy than was observed in the n case. This disagreement is a source of systematic error, which we try to minimize by the use of the very loose energy cut on the n shower. Angle between n and n (Degree)
180 175 170 165 160 Events/1 degree 0 2000 4000 6000 8000 10000 12000
Cosine polar angle of n
1.0 0.5 0.0 -0.5 -1.0 Events/0.05 0 500 1000 1500 2000 2500 3000 3500
FIG. 7 (color online). Distributions for J=c ! n n candidate
events summed over all cos bins (points) and background from inclusive MC (solid lines): (a) angle between the n and n, and (b) cos for the n shower.
) (GeV) n E( Events/50 MeV 0 500 1000 1500 2000 2500
Hits in 50-degree cone
Events/2 0 500 1000 1500 2000 2500 3000 ) 2 Second moment (cm 0.0 0.5 1.0 1.5 2.0 2.5 0 50 100 150 0 20 40 60 80 100 2 Events/2 cm 0 1000 2000 3000 4000 5000
FIG. 8 (color online). Comparisons of distributions of selection variables for n from J=c ! n n (solid line) with those from
J=c ! p n(points): (a) deposited energy in the EMC, (b) the number of EMC hits in the 50cone around the n shower, and (c) the
For the Eextra cut, we use J=c ! p p to obtain the
efficiency (data
Eextra). The requirements are identical to those described in Sec. VA. Our selection of J=c ! p p does not depend on information from the calorimeter, so the behavior of p p in the EMC can be used to verify the efficiency of the Eextra cut for J=c ! n n. Figure 10
shows the comparison of the Eextra distributions for
J=c ! p p and J=c ! n n. We require the angle be-tween the n and n to be greater than 177 to suppress background for this comparison. We find that the propor-tion of Eextra¼ 0 events in J=c ! p p and J=c ! n n
agree well. The ratio of J=c ! p p events with or with-out the requirement Eextra ¼ 0 is calculated as the
effi-ciency of the Eextra cut.
Finally, we determine the overall efficiency from the product of the three component efficiencies described above:
¼ datan datan dataEextra:
To facilitiate measurement of the angular distribution as well as the yield, the product efficiency is determined in 16 bins in cos (cosine of the n polar angle) from -0.8 to 0.8. Figure11shows the efficiency for each cut and the product as a function of cos. The loss of n efficiency near cos ¼ 0:8 is caused by the requirement on the number of EMC hits in a 50cone around the shower. To smooth the bin-to-bin statistical fluctuations in the effi-ciency correction, we fit with a fifth-order polynomial [Fig. 11(d)]. E(n) (GeV) 0.0 0.2 0.4 0.6 Events/50 MeV 0 200 400 600 800 1000
FIG. 9 (color online). Comparison of the distribution of the
deposited energy in the EMC for n showers from J=c ! n n
(points) with that from J=c ! pnþ (solid line).
(GeV) extra E 0.0 0.2 0.4 0.6 0.8 1.0 Events/20MeV 1 10 2 10 3 10 4 10
FIG. 10 (color online). Comparison of the distribution of Eextra
in J=c ! n n (points) with that from J=c ! p p (solid line).
cosθ eff. n 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 cosθ n eff. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 cosθ eff. extra E 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 cosθ -0.5 0.0 0.5 -0.5 0.0 0.5 -0.5 0.0 0.5 -0.5 0.0 0.5 Total eff. 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
FIG. 11. Component selection efficiencies for J=c ! n n as a function of cos: (a) n selection, (b) n selection, and (c) Eextra cut;
C. Angular distribution and branching fraction The number of J=c ! n n events in each cos bin is obtained by fitting the distribution of the angle between the n and n. The signal shape is determined with the J=c ! p p sample. Because of the 1.0-T magnetic field in the BESIII detector, the angular distribution in J=c ! p p must be corrected before being applied to J=c ! n n. The signal shape () for fitting the distribution of the angle between n and n can be expressed in terms of dp
(dp) and dp (dp), the polar and azimuthal angles
between the shower position and the extrapolated EMC position of p ( p), as follows: ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 cos2 pÞd2p pþ d2p p q ;
where p is the polar angle of the proton track, dp p¼
dpþ dp and dp p¼ dpþ dp. The background
shape is fixed to the shape of the inclusive background, while signal and background normalizations are allowed to float in each cos bin. A sample fit for one cos bin is shown in Fig.12.
After obtaining the bin-by-bin signal yields, we fit the resulting cos distribution with the function Að1 þ cos2ÞðcosÞ, where A gives the overall normalization
and ðcosÞ is the corrected efficiency. The resulting an-gular distribution and fit are shown in Fig.13. The 2 for
the fit is 13 for 14 degrees of freedom, and the value determined for the angular-distribution parameter is ¼ 0:50 0:04 (statistical error only).
The raw number of J=c ! n n events in the range cos ¼ ½0:8; 0:8 is Nð0:8; 0:8Þ ¼ 35891 211. The efficiency-corrected yield obtained from the cos fit is Ncorð0:8; 0:8Þ ¼ 354195 2078. The fitted value of
is used to determine the total number of J=c ! n n events in the full angular range of cos ¼ ½1:0; 1:0 as follows: Ncorð1:0; 1:0Þ ¼ Ncorð0:8; 0:8Þ R1:0 1:0ð1 þ cos2Þd R0:8 0:8ð1 þ cos2Þd ¼ 466590 2737:
Combining this total yield with the number of J=c events in our sample, we find the branching fraction to be
B ðJ=c ! n nÞ ¼ ð2:07 0:01Þ 103;
where the error is only statistical.
D. Systematic errors and results
The different nðnÞ momentum distributions in J=c ! p n (c.c.) and J=c ! n n may introduce systematic uncertainties in the nðnÞ efficiency determina-tion. We change the missing-momentum range from ð1:1–1:2Þ GeV=c to ð1:0–1:1Þ GeV=c when selecting the nðnÞ sample from J=c ! p n (c.c.) and take the resulting differences in and the branching fraction as systematic errors. This estimation is cross-checked with a lower-statistics sample obtained from a separate BESIII data sample collected at the cð3686Þ resonance. High-momentum nðnÞ candidates are selected from the decay cð3686Þ ! þJ=c, J=c ! p n (c.c.). The
aver-age nðnÞ efficiencies obtained with this sample are con-sistent with those from J=c ! p n (c.c.) within statistical errors.
A second source of systematic error in the n (n) effi-ciency is the effect of the requirement that the shower be within 10 of the expected direction. We estimate the systematic errors due to this requirement by removing it and determining the changes in the results. We sum these two systematic error in quadrature to obtain the total sys-tematic errors due to the selection of n (n). For the determination, the n and n errors are 0.04 and 0.09, respec-tively, and for the branching fraction they are 5 105and 1:2 104. For the branching fraction the n efficiency is the largest source of uncertainty in our measurement.
As we did for J=c ! p p, we use a toy MC method to estimate systematic errors due to the statistical uncertain-ties in the efficiency. For , this systematic error is 0.17,
Events / 1 degree 0 100 200 300 400 500 600 (Degree) n Angle between n and
160 165 170 175 180
FIG. 12 (color online). Fit to the angle between the n and n for
cos in ½0:3; 0:2. cosθ -0.5 0.0 0.5 Events/0.1 0 500 1000 1500 2000 2500 3000 3500 4000
FIG. 13. The points represent the measured distribution of
cos for the n in J=c ! n n candidate events, with error bars that are the quadratic sums of the statistical and efficiency uncertainties. The line represents the fit of the distribution to the functional form given in the text, and is used to determine the normalization and the angular-distribution parameter .
the largest contributor to the overall uncertainty of the measurement. For the branching fraction this error it is 7:1 105and is the second-largest contributor.
We change the background shape for each exclusive MC background channel and repeat the fit of the angle between n and n. The largest variation observed for any case considered is assigned as the systematic error.
Our signal shape in fitting the n n angle was obtained from J=c ! p p. The correction of the p p angular distribution into one appropriate for n n in J=c ! n n is a source of systematic uncertainty. To assess this we used a sideband subtraction instead of the fit to the angular distribution. We normalize the yield of MC background in the signal region (170–180) by the numbers of events in the sideband range (160–170) for data and MC back-ground. Then we take the background-subtracted number of events in the signal region (170–180) as the yield in each cos bin. The differences between this alternative method and the standard method are assigned as systematic errors.
The angular resolution can introduce systematic uncer-tainty both through the binning and through thej cosj < 0:8 cut. We use the J=c ! p p sample to evaluate the cos resolution for J=c ! n n. In the data d cos ¼ cospext
cospemc is calculated as the equivalent of the resolution in
cos for n, where cospext represents the extrapolated
position of the p at the EMC and cos pemc is the
recon-structed position in the EMC. Here we assume that the position reconstruction of n in the EMC is similar to that for p, because both are dominated by hadronic interac- tions. To estimate the systematic error, we smear the cos of n with the distribution of d cos and redo the fit in each bin, and the fit to the angular distribution. The resulting changes are taken as the systematic errors.
For the all-neutral n n final state the trigger efficiency is another potential source of uncertainty. We correct the efficiency curve with the MC-determined trigger efficiency and redo the fit. The resulting changes in the branching fraction and are taken as systematic uncertainties due to trigger efficiency.
To consider the systematic error from interference be-tween the J=c peak and the continuum, we write the total cross section n nas n n ¼ j ffiffiffiffiffiffiffiffiffiffiffi cont: n n q þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12eetot p s m2þ im tot ðEn eiSÞj2;
where En and S are the EM and strong amplitudes for
J=c ! n n and is the phase angle between them. cont: n n
is the n n cross section contributed by continuum under the J=c peak. These values are taken from Sec.VIIand, as discussed there, the EM amplitude En should be opposite
to Ep. The cross section ðeþe! n nÞ close to J=c is
assumed to lie between ðeþe! p pÞ and ðeþe ! p pÞ ðn=pÞ2, so the En, which is in proportion to
ffiffiffiffiffiffiffiffiffiffiffi cont: n n
p
, ranges from Ep to Epðn=pÞ, where n and
pare the magnetic moments of the neutron and proton.
To estimate the uncertainty from the continuum, we take the larger one, cont:
n n cont:p p , therefore also En Ep. The
difference with and without cont:
n n is assigned as systematic
error.
Finally, we change by 1 (including the systematic error) and reevaluate the branching fraction to estimate the systematic error in the branching-fraction measurement.
Table III summarizes the systematic uncertainties and their sum in quadrature. The final results for our J=c ! n n measurements are as follows:
¼ 0:50 0:04 0:21; and BðJ=c ! n nÞ ¼ ð2:07 0:01 0:17Þ 103:
The branching-fraction measurement is consistent with the previous world average [6] and improves the overall precision by about a factor of 2.3.
VII. SUMMARY
We have used the world’s largest sample of J=c decays to make new measurements of the branching fractions and production-angle distributions for J=c ! p p and J=c ! n n, obtaining the branching fractions BðJ=c ! p pÞ ¼ ð2:112 0:004 0:031Þ 103 and BðJ=c ! n nÞ ¼
ð2:07 0:01 0:17Þ 103. These results represent
sig-nificant improvements over previous measurements. The angular distributions for both decays are well described by the functional form 1 þ cos2, with measured values of ¼ 0:595 0:012 0:015 for J=c ! p p, and ¼ 0:50 0:04 0:21 for J=c ! n n.
The p p angular distribution can be decomposed as jCM
pj2ð1 þ cos2Þ þ ð2Mp=MJ=cÞ2jCEpj2sin2, where CMp
and CE
p are the total helicity1 and 0 decay amplitudes.
In terms of the angular parameter , the ratio of amplitudes is jCE p=CMpj ¼ MJ=c=ð2MpÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 Þ=ð1 þ Þ p . With our measured values for , we find jCE
p=CMpj ¼ 0:832
0:015 0:019 and jCEn=CMnj ¼ 0:95 0:05 0:27,
TABLE III. Systematic errors for J=c ! n n.
Sources Effect on Effect on B (103)
n selection 0.04 0.05
n selection 0.09 0.12
Efficiency correction statistics 0.17 0.07
Background 0.03 0.03 Signal shape 0.02 0.06 cos resolution 0.05 0.01 Trigger 0.03 0.01 value 0.01 Number of J=c 0.03 Continuum 0.01 Total 0.21 0.17
respectively. These measurements permit discrimination among the different proposed models [24–30].
The relative phase between the strong and EM ampli-tudes can be obtained by comparing BðJ=c ! p pÞ and BðJ=c ! n nÞ. The J=c EM decay amplitudes are related to the corresponding continuum cross sections close to the J=c as follows: E2
NðJ=c ! ! N NÞ ¼ BðJ=c !
Þ ðeþe! N NÞ=ðeþe! Þ. Present data [31] suggest that ðeþe! p pÞ ð9 3Þ pb, if fitted with a smooth W10 as expected at high enough center-of-mass energies W. For ðeþe ! n nÞ the only available data [32,33] are close to threshold. In the following it is assumed that the neutron timelike dominant magnetic form factor is negative at these center-of-mass energies, like the magnetic moment, as predicted dispersion relations [34]. The cross section ðeþe ! n nÞ close to J=c is assumed to lie between ðeþe! p pÞ, as is seen in the present data close to threshold, and ðeþe! p pÞ ðn=pÞ2, as in the spacelike region [35]. Taking into
account these hypotheses and their overall uncertainties, and neglecting the contribution of continuum amplitudes, the strong amplitude S is given by
S2¼ ½ðBðJ=c ! p pÞ E2 pÞEn
þ ðBðJ=c ! n nÞ E2
nÞEp=ðEnþ EpÞ
¼ ð2:038 0:094Þ 103;
and the phase between the strong and EM amplitudes is found to be
¼ cos1½ðBðJ=c ! p pÞ S2 E2
pÞ=ð2SEpÞ
¼ ð88:7 8:1Þ:
The uncertainty in the phase is mostly due to the BðJ=c ! n nÞ systematic error. This determination con-firms the orthogonality of the strong and EM amplitudes within the precision of our measurement.
ACKNOWLEDGMENTS
The BESIII collaboration thanks the staff of BEPCII and the computing center for their hard efforts. This work is supported in part by the Ministry of Science and Technology of China under Contract No. 2009CB825200; Joint Funds of the National Natural Science Foundation of China under Contracts Nos. 11079008, 11179007; National Natural Science Foundation of China (NSFC) under Contracts Nos. 10625524, 10821063, 10825524, 10835001, 10935007, 11125525; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Program of CAS; Istituto Nazionale di Fisica Nucleare, Italy; U. S. Department of Energy under Contracts Nos. DE-FG02-04ER41291, 91ER40682, 94ER40823, DE-FG02-05ER41374; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0
[1] R. Baldini, C. Bini, and E. Luppi,Phys. Lett. B 404, 362
(1997).
[2] C. Z. Yuan, P. Wang, and X. H. Mo,Phys. Lett. B 567, 73
(2003).
[3] P. Wang, C. Z. Yuan, and X. H. Mo, Phys. Rev. D 69,
057502 (2004).
[4] V. L. Chernyak and I. R. Zhitnitsky,Nucl. Phys. B246, 52
(1984).
[5] C. Carimalo,Int. J. Mod. Phys. A 2, 249 (1987).
[6] K. Nakamura et al. (Particle Data Group),J. Phys. G 37,
075021 (2010).
[7] A. Antonelli et al. (FENICE Collaboration),Phys. Lett. B
334, 431 (1994).
[8] M. Ablikim et al. (BESIII Collaboration),Nucl. Instrum.
Methods Phys. Res., Sect. A 614, 345 (2010).
[9] D. M. Asner et al., Physics at BESIII, edited by K. T. Chao and Y. F. Wang [Int. J. Mod. Phys. A 24, S1 (2009)].
[10] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D
83, 012003 (2011).
[11] S. Agostinelli et al. (GEANT4 Collaboration), Nucl.
Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
Geant4 version: v09-03p0; Physics List simulation engine: BERT; Physics List engine packaging library: PACK 5.5.
[12] J. Allison et al.,IEEE Trans. Nucl. Sci. 53, 270 (2006).
[13] R. G. Ping,Chinese Phys. C 32, 8 (2008).
[14] D. J. Lange,Nucl. Instrum. Methods Phys. Res., Sect. A
462, 152 (2001).
[15] Giovanni Balossini et al.,Nucl. Phys. B758, 227 (2006).
[16] S. Jadach, B. F. L. Ward, and Z. Was, Comput. Phys.
Commun. 130, 260 (2000); Phys. Rev. D 63, 113009 (2001).
[17] T. Sjostrand,Comput. Phys. Commun. 82, 74 (1994).
[18] I. Peruzzi et al.,Phys. Rev. D 17, 2901 (1978).
[19] M. W. Eaton et al.,Phys. Rev. D 29, 804 (1984).
[20] J. S. Brown, Ph.D. thesis, University of Washington, 1984. [21] R. Brandelik et al., Physica C (Amsterdam) 1, 233 (1976).
[22] D. Pallin et al. (DM2 Collaboration),Nucl. Phys. B292,
653 (1987).
[23] J. Z. Bai et al. (BES Collaboration),Phys. Lett. B 591, 42
(2004).
[24] M. B. Wise, M. Claudson, and S. L. Glashow,Phys. Rev. D
[25] V. L. Chernjak and J. R. Zhitnisky, Phys. Rep. 112, 173 (1984).
[26] M. Gari and N. G. Stefanis,Phys. Lett. B 175, 462 (1986).
[27] I. D. King and C. T. Sachraida, Nucl. Phys. B279, 785
(1987).
[28] C. Carimalo,Int. J. Mod. Phys. A 2, 249 (1987).
[29] V. L. Chernjak, A. A. Oglobi, and J. R. Zhitnisky, Z. Phys. C 42, 565 (1989).
[30] N. G. Stefanis and M. Bergmann,Phys. Rev. D 47, R3685
(1993).
[31] B. Aubert et al. (BABAR Collaboration),Phys. Rev. D 73,
012005 (2006).
[32] A. Antonelli et al. (FENICE Collaboration),Nucl. Phys.
B517, 3 (1998).
[33] Alexander E. Obrazovsky, (on behalf of the SND collaboration) Proceedings of the XIV International Conference on Hadron Spectroscopy (Munich, Germany, 2011), pp. 13–17.
[34] R. Baldini, S. Dubnicka, P. Gauzzi, S. Pacetti, E.
Pasqualucci, and Y. Srivastava, Eur. Phys. J. C 11, 709
(1999).
[35] John Arrington, Proceedings of QCD Bound States Workshop (Argonne National Lab, Argonne, IL, 2009), pp. 15–19.
