Measurements of baryon pair decays of chi(cJ) mesons

This is the accepted manuscript made available via CHORUS, the article has been published as:

Measurements of baryon pair decays of χ_{cJ} mesons

Phys. Rev. D 87, 032007 — Published 15 February 2013 DOI: 10.1103/PhysRevD.87.032007

Measurements of Baryon Pair Decays of χ

Mesons

M. Ablikim1_{, M. N. Achasov}6_{, O. Albayrak}3_{, D. J. Ambrose}39_{, F. F. An}1_{, Q. An}40_,

J. Z. Bai1_{, Y. Ban}26_{, J. Becker}2_{, J. V. Bennett}16_{, M. Bertani}17A_{, J. M. Bian}38_,

E. Boger19,a_{, O. Bondarenko}20_{, I. Boyko}19_{, R. A. Briere}3_{, V. Bytev}19_{, X. Cai}1_{, O.}

Cakir34A_{, A. Calcaterra}17A_{, G. F. Cao}1_{, S. A. Cetin}34B_{, J. F. Chang}1_{, G. Chelkov}19,a_,

G. Chen1_{, H. S. Chen}1_{, J. C. Chen}1_{, M. L. Chen}1_{, S. J. Chen}24_{, X. Chen}26_{, Y. B. Chen}1_,

H. P. Cheng14_{, Y. P. Chu}1_{, D. Cronin-Hennessy}38_{, H. L. Dai}1_{, J. P. Dai}1_{, D. Dedovich}19_,

Z. Y. Deng1_{, A. Denig}18_{, I. Denysenko}19,b_{, M. Destefanis}43A,43C_{, W. M. Ding}28_{, Y. Ding}22_,

L. Y. Dong1_{, M. Y. Dong}1_{, S. X. Du}46_{, J. Fang}1_{, S. S. Fang}1_{, L. Fava}43B,43C_{, C. Q. Feng}40_,

R. B. Ferroli17A_{, P. Friedel}2_{, C. D. Fu}1_{, Y. Gao}33_{, C. Geng}40_{, K. Goetzen}7_{, W. X. Gong}1_,

W. Gradl18_{, M. Greco}43A,43C_{, M. H. Gu}1_{, Y. T. Gu}9_{, Y. H. Guan}36_{, A. Q. Guo}25_,

L. B. Guo23_{, T. Guo}23_{, Y. P. Guo}25_{, Y. L. Han}1_{, F. A. Harris}37_{, K. L. He}1_{, M. He}1_,

Z. Y. He25_{, T. Held}2_{, Y. K. Heng}1_{, Z. L. Hou}1_{, C. Hu}23_{, H. M. Hu}1_{, J. F. Hu}35_{, T. Hu}1_,

G. M. Huang4_{, G. S. Huang}40_{, J. S. Huang}12_{, L. Huang}1_{, X. T. Huang}28_{, Y. Huang}24_,

Y. P. Huang1_{, T. Hussain}42_{, C. S. Ji}40_{, Q. Ji}1_{, Q. P. Ji}25_{, X. B. Ji}1_{, X. L. Ji}1_,

L. L. Jiang1_{, X. S. Jiang}1_{, J. B. Jiao}28_{, Z. Jiao}14_{, D. P. Jin}1_{, S. Jin}1_{, F. F. Jing}33_,

N. Kalantar-Nayestanaki20_{, M. Kavatsyuk}20_{, B. Kopf}2_{, M. Kornicer}37_{, W. Kuehn}35_,

W. Lai1, J. S. Lange35, M. Leyhe2, C. H. Li1, Cheng Li40, Cui Li40, D. M. Li46, F. Li1,

G. Li1_{, H. B. Li}1_{, J. C. Li}1_{, K. Li}10_{, Lei Li}1_{, Q. J. Li}1_{, S. L. Li}1_{, W. D. Li}1_{, W. G. Li}1_,

X. L. Li28_{, X. N. Li}1_{, X. Q. Li}25_{, X. R. Li}27_{, Z. B. Li}32_{, H. Liang}40_{, Y. F. Liang}30_,

Y. T. Liang35_{, G. R. Liao}33_{, X. T. Liao}1_{, D. Lin}11_{, B. J. Liu}1_{, C. L. Liu}3_{, C. X. Liu}1_,

F. H. Liu29_{, Fang Liu}1_{, Feng Liu}4_{, H. Liu}1_{, H. B. Liu}9_{, H. H. Liu}13_{, H. M. Liu}1_,

H. W. Liu1_{, J. P. Liu}44_{, K. Liu}33_{, K. Y. Liu}22_{, Kai Liu}36_{, P. L. Liu}28_{, Q. Liu}36_{, S. B. Liu}40_,

X. Liu21_{, Y. B. Liu}25_{, Z. A. Liu}1_{, Zhiqiang Liu}1_{, Zhiqing Liu}1_{, H. Loehner}20_{, G. R. Lu}12_,

H. J. Lu14_{, J. G. Lu}1_{, Q. W. Lu}29_{, X. R. Lu}36_{, Y. P. Lu}1_{, C. L. Luo}23_{, M. X. Luo}45_,

T. Luo37_{, X. L. Luo}1_{, M. Lv}1_{, C. L. Ma}36_{, F. C. Ma}22_{, H. L. Ma}1_{, Q. M. Ma}1_{, S. Ma}1_,

T. Ma1_{, X. Y. Ma}1_{, F. E. Maas}11_{, M. Maggiora}43A,43C_{, Q. A. Malik}42_{, Y. J. Mao}26_,

Z. P. Mao1_{, J. G. Messchendorp}20_{, J. Min}1_{, T. J. Min}1_{, R. E. Mitchell}16_{, X. H. Mo}1_,

C. Morales Morales11_{, N. Yu. Muchnoi}6_{, H. Muramatsu}39_{, Y. Nefedov}19_{, C. Nicholson}36_,

M. Pelizaeus2_{, H. P. Peng}40_{, K. Peters}7_{, J. L. Ping}23_{, R. G. Ping}1_{, R. Poling}38_,

E. Prencipe18_{, M. Qi}24_{, S. Qian}1_{, C. F. Qiao}36_{, L. Q. Qin}28_{, X. S. Qin}1_{, Y. Qin}26_,

Z. H. Qin1_{, J. F. Qiu}1_{, K. H. Rashid}42_{, G. Rong}1_{, X. D. Ruan}9_{, A. Sarantsev}19,c_,

B. D. Schaefer16_{, M. Shao}40_{, C. P. Shen}37,d_{, X. Y. Shen}1_{, H. Y. Sheng}1_{, M. R. Shepherd}16_,

X. Y. Song1_{, S. Spataro}43A,43C_{, B. Spruck}35_{, D. H. Sun}1_{, G. X. Sun}1_{, J. F. Sun}12_,

S. S. Sun1_{, Y. J. Sun}40_{, Y. Z. Sun}1_{, Z. J. Sun}1_{, Z. T. Sun}40_{, C. J. Tang}30_{, X. Tang}1_,

I. Tapan34C_{, E. H. Thorndike}39_{, D. Toth}38_{, M. Ullrich}35_{, G. S. Varner}37_{, B. Q. Wang}26_,

D. Wang26_{, D. Y. Wang}26_{, K. Wang}1_{, L. L. Wang}1_{, L. S. Wang}1_{, M. Wang}28_{, P. Wang}1_,

P. L. Wang1_{, Q. J. Wang}1_{, S. G. Wang}26_{, X. F. Wang}33_{, X. L. Wang}40_{, Y. F. Wang}1_,

Z. Wang1_{, Z. G. Wang}1_{, Z. Y. Wang}1_{, D. H. Wei}8_{, J. B. Wei}26_{, P. Weidenkaff}18_,

Q. G. Wen40_{, S. P. Wen}1_{, M. Werner}35_{, U. Wiedner}2_{, L. H. Wu}1_{, N. Wu}1_{, S. X. Wu}40_,

W. Wu25_{, Z. Wu}1_{, L. G. Xia}33_{, Z. J. Xiao}23_{, Y. G. Xie}1_{, Q. L. Xiu}1_{, G. F. Xu}1_,

G. M. Xu26_{, Q. J. Xu}10_{, Q. N. Xu}36_{, X. P. Xu}31_{, Z. R. Xu}40_{, F. Xue}4_{, Z. Xue}1_{, L. Yan}40_,

W. B. Yan40_{, Y. H. Yan}15_{, H. X. Yang}1_{, Y. Yang}4_{, Y. X. Yang}8_{, H. Ye}1_{, M. Ye}1_,

M. H. Ye5_{, B. X. Yu}1_{, C. X. Yu}25_{, H. W. Yu}26_{, J. S. Yu}21_{, S. P. Yu}28_{, C. Z. Yuan}1_,

Y. Yuan1_{, A. A. Zafar}42_{, A. Zallo}17A_{, Y. Zeng}15_{, B. X. Zhang}1_{, B. Y. Zhang}1_{, C. Zhang}24_,

C. C. Zhang1_{, D. H. Zhang}1_{, H. H. Zhang}32_{, H. Y. Zhang}1_{, J. Q. Zhang}1_{, J. W. Zhang}1_,

J. Y. Zhang1_{, J. Z. Zhang}1_{, R. Zhang}36_{, S. H. Zhang}1_{, X. J. Zhang}1_{, X. Y. Zhang}28_,

Y. Zhang1_{, Y. H. Zhang}1_{, Z. P. Zhang}40_{, Z. Y. Zhang}44_{, Zhenghao Zhang}4_{, G. Zhao}1_,

H. S. Zhao1_{, J. W. Zhao}1_{, K. X. Zhao}23_{, Lei Zhao}40_{, Ling Zhao}1_{, M. G. Zhao}25_{, Q. Zhao}1_,

Q. Z. Zhao9_{, S. J. Zhao}46_{, T. C. Zhao}1_{, Y. B. Zhao}1_{, Z. G. Zhao}40_{, A. Zhemchugov}19,a_,

B. Zheng41_{, J. P. Zheng}1_{, Y. H. Zheng}36_{, B. Zhong}23_{, Z. Zhong}9_{, L. Zhou}1_,

X. K. Zhou36_{, X. R. Zhou}40_{, C. Zhu}1_{, K. Zhu}1_{, K. J. Zhu}1_{, S. H. Zhu}1_{, X. L. Zhu}33_,

Y. C. Zhu40_{, Y. M. Zhu}25_{, Y. S. Zhu}1_{, Z. A. Zhu}1_{, J. Zhuang}1_{, B. S. Zou}1_{, J. H. Zou}1

(BESIII Collaboration)

1 _{Institute of High Energy Physics, Beijing 100049, People’s Republic of China} 2 _{Bochum Ruhr-University, D-44780 Bochum, Germany}

3 _{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA} 4 _{Central China Normal University, Wuhan 430079, People’s Republic of China}

Beijing 100190, People’s Republic of China

6 _{G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia} 7 _{GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany}

8 _{Guangxi Normal University, Guilin 541004, People’s Republic of China} 9 _{GuangXi University, Nanning 530004, People’s Republic of China} 10 _{Hangzhou Normal University, Hangzhou 310036, People’s Republic of China} 11 _{Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany}

12 _{Henan Normal University, Xinxiang 453007, People’s Republic of China}

13_{Henan University of Science and Technology, Luoyang 471003, People’s Republic of China} 14 _{Huangshan College, Huangshan 245000, People’s Republic of China}

15 _{Hunan University, Changsha 410082, People’s Republic of China} 16 _{Indiana University, Bloomington, Indiana 47405, USA} 17 _{(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati,}

Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy

18 _{Johannes Gutenberg University of Mainz,}

Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

19 _{Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia} 20 _{KVI, University of Groningen, NL-9747 AA Groningen, The Netherlands}

21 _{Lanzhou University, Lanzhou 730000, People’s Republic of China} 22 _{Liaoning University, Shenyang 110036, People’s Republic of China} 23 _{Nanjing Normal University, Nanjing 210023, People’s Republic of China}

24 _{Nanjing University, Nanjing 210093, People’s Republic of China} 25 _{Nankai University, Tianjin 300071, People’s Republic of China}

26 _{Peking University, Beijing 100871, People’s Republic of China} 27 _{Seoul National University, Seoul, 151-747 Korea}

28 _{Shandong University, Jinan 250100, People’s Republic of China} 29 _{Shanxi University, Taiyuan 030006, People’s Republic of China} 30 _{Sichuan University, Chengdu 610064, People’s Republic of China}

31 _{Soochow University, Suzhou 215006, People’s Republic of China} 32 _{Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China}

33 _{Tsinghua University, Beijing 100084, People’s Republic of China}

34 _{(A)Ankara University, Dogol Caddesi, 06100 Tandogan, Ankara, Turkey; (B)Dogus}

University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey

35 _{Universitaet Giessen, D-35392 Giessen, Germany}

36 _{University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China} 37 _{University of Hawaii, Honolulu, Hawaii 96822, USA}

38 _{University of Minnesota, Minneapolis, Minnesota 55455, USA} 39 _{University of Rochester, Rochester, New York 14627, USA}

40 _{University of Science and Technology of China, Hefei 230026, People’s Republic of China} 41 _{University of South China, Hengyang 421001, People’s Republic of China}

42 _{University of the Punjab, Lahore-54590, Pakistan}

43 _{(A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern}

Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy

44 _{Wuhan University, Wuhan 430072, People’s Republic of China} 45 _{Zhejiang University, Hangzhou 310027, People’s Republic of China} 46 _{Zhengzhou University, Zhengzhou 450001, People’s Republic of China}

a _{Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia} b _{On leave from the Bogolyubov Institute for Theoretical Physics, Kiev 03680, Ukraine}

c _{Also at the PNPI, Gatchina 188300, Russia}

Abstract

Using 106 million ψ′ _{decays collected with the BESIII detector at the BEPCII, three decays of}

χcJ (J = 0, 1, 2) with a baryon pairs (Λ¯Λ, Σ0Σ¯0, Σ+Σ¯−) in the final state have been studied. The

branching fractions are measured to be B(χc0,1,2→ Λ¯Λ) = (33.3±2.0±2.6)×10−5, (12.2±1.1±1.1)×

10−5_{, (20.8±1.6±2.3)×10}−5_{; B(χ}

c0,1,2→ Σ0Σ¯0) = (47.8±3.4±3.9)×10−5, (3.8±1.0±0.5)×10−5,

(4.0 ± 1.1 ± 0.5) × 10−5_{; and B(χ}

c0,1,2 → Σ+Σ¯−) = (45.4 ± 4.2 ± 3.0) × 10−5, (5.4 ± 1.5 ± 0.5) × 10−5,

(4.9 ± 1.9 ± 0.7) × 10−5_{, where the first error is statistical and the second is systematic. Upper}

limits on the branching fractions for the decays of χc1,2 → Σ0Σ¯0, Σ+Σ¯−, are estimated to be

B(χc1 → Σ0Σ¯0) < 6.2 × 10−5, B(χc2 → Σ0Σ¯0) < 6.5 × 10−5, B(χc1 → Σ+Σ¯−) < 8.7 × 10−5 and

B(χc2 → Σ+Σ¯−) < 8.8 × 10−5 at the 90% confidence level.

I. INTRODUCTION

In the standard quark model, χcJ (J = 0, 1, 2) mesons are c¯c states in an L = 1

con-figuration. Experimental studies on χcJ decay properties are essential to test

perturba-tive Quantum Chromodynamics (QCD) models and QCD-based calculations. The

impor-tance of the color octet mechanism (COM) for χcJ decays has been pointed out for many

years [1], and theoretical predictions of two-body exclusive decays have been made based

on it. The predictions of COM theory for some χcJ decays into baryon pairs (B ¯B) disagree

with measured values. For example, the branching fraction of χc0 → Λ¯Λ is predicted to be

(93.5 ± 20.5) × 10−5 _{according to Ref. [2], and (11.9 ∼ 15.1) × 10}−5 _{according to Ref. [3],}

while the world average of experimental measurements is (33.0 ± 4.0) × 10−5 _{[4]. One finds}

that the theoretical prediction is either about two times larger, or several times smaller than

the experimental measurement. Although some experimental results on χcJ exclusive decays

have been reported [5–7], many decay modes of χcJ → B ¯B have not been observed yet, such

as χc1,2 → Σ0Σ¯0, Σ+Σ¯−, or measured with poor precision. For further testing of the COM

in the decays of the P-wave charmonia, measurements of other baryon pair decays of χcJ,

such as χcJ → Λ¯Λ, Σ0Σ¯0 and Σ+Σ¯−, are desired.

In addition, measurements of χc0 → B ¯B are helpful for further understanding the helicity

selection rule (HSR) [8], which prohibits χc0 decays into baryon-antibaryon pairs. However,

the measured branching fractions for χc0 → B ¯B do not vanish, for example χc0 → p¯p [4],

which demonstrates a strong violation of HSR in charmonium decays. It is necessary to

measure the decays of χc0 → B ¯B in other channels to provide additional tests of the HSR.

While χcJ mesons are not produced directly in e+e− annihilations, the large branching

fractions of ψ′ _{→ γχ}

cJ make e+e− collision at the ψ′ peak a very clean environment for χcJ

investigation. In this paper, the results of two-body decays of χcJ → Λ¯Λ, Σ0Σ¯0 and Σ+Σ¯−

final states are presented. This analysis is based on 106 million ψ′ _{events [9] collected with}

BESIII at the BEPCII. A sample of 44 pb−1 _{of data taken at} √_{s = 3.65 GeV is used for}

II. BESIII DETECTOR AND MONTE CARLO SIMULATION

BEPCII is a double-ring e+_e− _{collider that has reached peak luminosity of about 0.6 ×}

1033 _cm−2_s−1 _{at the peak energy of ψ(3770). The cylindrical core of the BESIII detector}

consists of a helium-based main drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance for charged particles and photons is 93% over 4π stereo angle, and the charged-particle momentum and photon energy resolutions at 1 GeV are 0.5% and 2.5%, respectively. The detector is described in more detail in Ref. [10].

The BESIII detector is modeled with a Monte Carlo (MC) simulation based on geant4[11,

12]. The ψ′ _{resonance is produced with kkmc [13], while the subsequent decays are}

gen-erated with evtgen [14] according to the branching fractions provided by the Particle Data Group (PDG) [4], and the remaining unmeasured decay modes are generated with lundcharm [15].

III. EVENT SELECTION

The investigated final states include Λ(¯Λ), p(¯p), neutral π0_{mesons and a radiative photon}

from the decay ψ′ _{→ γχ}

cJ, where Λ(¯Λ) decays to π−p(π+p), while π¯ 0 is reconstructed in

the decay to π0 _{→ γγ. Candidate events are required to satisfy the following selection}

criteria. A charged track should have good quality in the track fitting and be within the angle coverage of the MDC (| cos θ| < 0.92). Photons are reconstructed from isolated showers in the EMC. The energy deposited in the nearby TOF counter is included to improve the reconstruction efficiency and energy resolution. Photon energies are required to be greater than 25 MeV in the EMC barrel region (| cos θ| < 0.8), and greater than 50 MeV in the EMC endcap (0.86 < | cos θ| < 0.92). The showers in the angular range between the barrel and the endcap are poorly reconstructed and excluded from the analysis. Moreover, the EMC timing of the photon candidate must be in coincidence with collision events, 0 ≤ t ≤ 700 ns, to suppress electronic noise and energy deposits unrelated to the events.

A. χcJ →Λ ¯Λ

Candidate events contain at least two positively-charged tracks, two negatively-charged

tracks and one photon. The Λ(¯Λ) candidates are reconstructed from pairs of oppositely

charged tracks, which are constrained to secondary vertices and have invariant masses closest

to the nominal Λ mass. The χ2 _{of the secondary vertex fit must be less than 500. The}

candidate photon and the Λ¯Λ pair are subjected to a four constraint (4C) kinematic fit

under the hypothesis of ψ′ _{→ γΛ¯Λ to reduce background and improve the mass resolution.}

When additional photons are found in an event, all possible combinations are iterated over,

and the one with the best kinematic fit χ2

4C is kept. Furthermore, χ24C < 50 is required to

suppress potential background from ψ′ _{→ Σ}0_Σ¯0_{. The χ}2

4C selection criterion is determined

by optimizing the figure of merit (F OM), F OM = S

√

S+B, where S is the number of signal

events and B is the number of background events based on the MC simulation. Figure 1 (a)

shows the comparison of χ2

4C between data and MC simulation, which is normalized with the

number of events satisfying the χ2 _{requirement. Figure 1 (b) shows the scatter plots of M}

pπ−

versus Mpπ¯ + from the data. Clear Λ¯Λ signals can be seen. The square around the Λ nominal

mass with a width of 20 MeV/c2 _{is taken as the signal region, which is also determined by}

maximizing the F OM. From events with two or more photons, additional selection criteria

are applied to suppress backgrounds from Σ0_Σ¯0 _{decays. The ψ}′ _{→ Σ}0_Σ¯0 _{candidates are}

selected by minimizing p(MγΛ− MΣ0)2+ (M_{γ ¯Λ}− M_Σ¯0)2 from all combinations. However,

some backgrounds remain in the signal region from ψ′ _{→ Σ}0_Σ¯0 _{events in which one photon}

from the Σ0_{decays is not reconstructed. To remove these, events falling into |M}

γΛ−MΣ0| < 6

MeV/c2 _{and |M}

γ ¯Λ− MΣ¯0| < 6 MeV/c2 have been discarded.

B. χcJ →Σ0Σ¯0

Candidate events have at least two positively-charged tracks, two negatively-charged

tracks and three photons. The charged track selection and Λ(¯Λ) reconstruction are the

same as described above for the χcJ → Λ¯Λ decay. The mass window of Λ(¯Λ) is optimized

to be |Mpπ − MΛ| < 7 MeV/c2. The candidate photons and the Λ¯Λ pair are subjected

to a 4C kinematic fit under the hypothesis of ψ′ _{→ γγγΛ¯Λ to reduce background and}

combinations are looped over, the one with the smallest χ2

4C is kept, and χ24C < 35 is

required to suppress the dominant background from ψ′ _{→ Σ}0_Σ¯0_{. Figure 1 (c) shows the}

comparison of χ2

4C between data and MC simulation, which is normalized with the number

of events satisfying the χ2 _{requirement. The Σ}0_Σ¯0 _{candidates are chosen by minimizing}

p(MγΛ− MΣ0)2 + (M_{γ ¯Λ}− M_Σ¯0)2. Figure 1 (d) shows the scatter plot of M_γΛ versus M_{γ ¯Λ}

from the data. Clear Σ0_Σ¯0 _{signals can be seen. The square around the Σ}0 _{nominal mass}

with a width of 32 MeV/c2 _{represents the signal region.}

C. χcJ →Σ+Σ¯−

Candidate events contain at least one positively-charged, one negatively-charged tracks and five photons. We impose a 4C kinematic fit to the selected tracks and photons under

the ψ′ _{→ 5γp¯p hypothesis and keep the one with the smallest χ}2

4C, and χ24C < 50 is required

to suppress the dominant background from ψ′ _{→ Σ}+_Σ¯−_{. Figure 1 (e) shows the comparison}

of χ2

4C between data and MC simulation, which is normalized with the number of events

satisfying the χ2 _{requirement. The π}0 _{candidates are reconstructed by selecting the}

com-bination which minimizes q

(Mγγ(1)− Mπ0)2+ (M_γγ(2) − M_π0)2. The Σ+Σ¯− pair is selected by

minimizingp(Mpπ0 − M_Σ+)2+ (M_pπ¯ 0 − M_Σ¯−)2. Figure 1 (f) shows the scatter plot of Mpπ0

versus Mpπ¯ 0 from the data. Clear Σ+Σ¯− signals can be seen. The square of 1.17 GeV/c2

< Mpπ0 < 1.20 GeV/c2 and 1.17 GeV/c2< M_pπ¯ 0 < 1.20 GeV/c2 denotes the signal region.

IV. BACKGROUND STUDY

A. Continuum backgrounds

The events collected at Ecm = 3.65 GeV, whose integrated luminosity is more than 1/4

of ψ′ _{samples, are analyzed to estimate the contribution from the continuum process. No}

events are survived in the Λ¯Λ, Σ0_Σ¯0 _{and Σ}+_Σ¯− _{signal regions. Therefore, backgrounds from}

2 χ 0 20 40 60 80 100 120 140 160 180 200 Events 0 20 40 60 80 100 120 140 160 180 200 220 (a) ) 2 (GeV/c -π p M 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 ) 2 (GeV/c₊ π p M 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 _(b) 2 χ 0 20 40 60 80 100 120 140 160 180 200 Events 0 10 20 30 40 50 60 70 80 90 (c) ) 2 (GeV/c Λ γ M 1.14 1.16 1.18 1.20 1.22 1.24 1.26 ) 2 (GeV/c Λγ M 1.14 1.16 1.18 1.20 1.22 1.24 1.26 (d) 2 χ 0 20 40 60 80 100 120 140 160 180 200 Events 0 10 20 30 40 50 (e) ) 2 (GeV/c 0 π p M 1.14 1.16 1.18 1.20 1.22 1.24 ) 2 (GeV/c0_π p M 1.14 1.16 1.18 1.20 1.22 1.24 _(f)

FIG. 1. (a) the χ2_4C distribution and (b) Mpπ− versus M_pπ¯ + (data) for the ψ′ → γχ_cJ, χ_cJ → Λ¯Λ

candidates; (c) the χ2_4C distribution and (d) MγΛversus Mγ ¯Λ(data) for the ψ′→ γχcJ, χcJ → Σ0Σ¯0

candidates; (e) the χ2

4C distribution and (f) Mpπ0 versus M_pπ¯ 0 (data) for the ψ′ → γχ_cJ, χ_cJ →

Σ+Σ¯− _candidates.

B. Dominant backgrounds in Λ ¯Λ, Σ0_Σ¯0 _{and Σ}+_Σ¯− _{final states}

By using 106 million inclusive MC events, we find that the dominant background for

χcJ → Λ¯Λ comes from the decay ψ′ → Σ0Σ¯0 in which one photon is missing. The

non-Λ¯Λ background from the decay χcJ → π+π−p¯p is negligibly small due to the low efficiency

near the mass threshold. For χcJ → Σ0Σ¯0, the dominant background is also found to arise

the Σ0_Σ¯0 _{invariant mass. In addition, a few background events come from ψ}′ _{→ π}0_π0_J/ψ

and ψ′ _{→ Ξ}0_Ξ¯0_{. For χ}

cJ → Σ+Σ¯−, the backgrounds are small, they are from the decay

ψ′ _{→ Σ}+_Σ¯−_{, ψ}′ _{→ π}0_π0_{J/ψ and J/ψ → p¯p (or γp¯p). The contributions of all backgrounds}

mentioned above are estimated by MC simulation according to their branching fractions.

V. FIT TO THE SIGNAL OF χcJ

The invariant mass of the baryon pairs MB ¯B for all selected events are shown in Figs. 2

(a), (b), and (c) for χcJ → Λ¯Λ, Σ0Σ¯0 and Σ+Σ¯−, respectively. Clear χc0,1,2 signals can be

seen in Λ¯Λ final state, and a clear χc0 signal is seen in both Σ0Σ¯0 and Σ+Σ¯− final state,

while the χc1,2 signals are not significant in Σ0Σ¯0 and Σ+Σ¯− final state. We fit the invariant

mass spectra of baryon pairs, MB ¯B, to extract the numbers of χcJ signal events, where

the signals are represented by Breit-Wigner functions convolved with a Crystal Ball (CB) function to account for the detector resolution, a second order Chebychev polynomial is used to describe non-peaking backgrounds, and the dominant background events, estimated by MC simulation, have been directly subtracted from the data. The widths of the Breit-Wigner functions were fixed according to the known values [4], the parameters of the CB function are fixed based on MC simulation, and these parameters are varied by ± σ for the determination of systematic uncertainties. To determine the goodness of fit, we bin the data

so that the number of events in each bin is at least ten. The calculated χ2_{/d.o.f is 1.03, 1.53}

and 1.71 for the Λ¯Λ, Σ0_Σ¯0 _{and Σ}+_Σ¯− _{final states, respectively. The numbers of χ}

c0,1,2signal

events from the fits are listed in Table I. For the decay χc1,2 → Σ0Σ¯0, Σ+Σ¯−, the upper limits

of the branching fractions at the 90% C.L. are also determined with a Bayesian method [16].

The statistical significances of the signals are calculated as √_{−2∆ ln L, where ∆ ln L is the}

difference between the logarithmic maximum likelihood (ML) values of the fit with and

without the corresponding signal function. They are 4.3σ and 4.6σ for χc1,2 → Σ0Σ¯0, and

4.4σ and 3.0σ for χc1,2 → Σ+Σ¯−, respectively. The signal efficiencies determined from MC

simulation are also listed in Table I, where the proper angular distributions for photons

emitted in ψ′ _{→ γχ}

cJ are used [17]. The decay of χcJ → B ¯B and the decay of baryons are

mes 0 20 40 60 mes 0 20 40 60

Λ

Λ

Events/3.0 MeV/c

Events/3.0 MeV/c

0

Σ

0

Σ

-Σ

+

Σ

M

(GeV/c

)

FIG. 2. The fit to the invariant mass M_{B ¯B}. Dots with error bars are for data. Solid line is the fit results. Dashed-line is other background. The parameters of signal function are fixed to those obtained from MC simulation.

TABLE I. Efficiencies (ǫ in %) obtained from MC simulation, and the signal yields Nobs_determined

from fit.

Mode χc0 χc1 χc2

Nobs _{ǫ N}obs _{ǫ N}obs _ǫ

Λ¯Λ _{368.9 ± 22.1 26.6 ± 0.2 135.6 ± 12.6 27.9 ± 0.2 207.1±15.7 26.3 ± 0.2} Σ0_Σ¯0 _{242.8 ± 17.1 12.2 ± 0.1 20.0 ± 5.3 13.2 ± 0.1 18.9 ± 5.3 12.7 ± 0.1}

VI. SYSTEMATIC ERROR

The systematic errors mainly originate from the uncertainties of the tracking efficiency,

Λ(¯Λ) reconstruction efficiency, the photon efficiency, 4C kinematic fit, the branching fractions

of the intermediate states, fit range, the angular distribution of χc1,2 → B ¯B, background

shape, signal lineshape, MC resolution and the total number of ψ′ _events.

1. The decay ψ′ _{→ Λ¯Λ with Λ → pπ}− _{and Λ → ¯pπ}− _{is employed to study the Λ(¯Λ)}

re-construction efficiency. The selection criteria of charged tracks are the same as before except we use particle identification information to suppress background. Candidate events have at least one positively-charged and one negatively-charged tracks, which

are required to be identified as a π+_(π−_{) track and an ¯p(p) track, respectively. Also,}

the invariant mass of π+_p(π¯ −_{p) must be within 10 MeV/c}2 _{of the nominal ¯Λ mass.}

Furthermore, the momentum of ¯Λ(Λ) candidates is required to be within 20 MeV/c

of its nominal value in two-body decay of ψ′ _{→ Λ¯Λ. The number of Λ signal events,}

N0

Λ, is extracted by fitting the recoiling mass spectrum of ¯Λ, M

¯ Λ

recoil. Then two

addi-tional oppositive charged tracks, a π−_(π+_{) and a p(¯p), are required to reconstruct Λ}

and are constrained to the secondary vertex. The number of Λ signal events, N1

Λ, is

extracted by fitting MΛ¯

recoil after requiring a Λ secondary vertex constraint. The Λ(¯Λ)

reconstruction efficiency is determined as ǫΛ =

N1 Λ

N0

Λ. The difference of the efficiencies

between data and MC simulation is found to be 2.0% for a Λ and 5.0% for a ¯Λ, which

are taken as the systematic error due to Λ(¯Λ) reconstruction efficiency.

2. Since the decay length for Σ+_{( ¯Σ}−_{) is small, the decay J/ψ → π}+_π−_{p¯p is used to study}

the MDC tracking efficiency for the proton and anti-proton of the Σ+_Σ¯− _{final state.}

It is found that the efficiency for MC simulated events agrees with that determined from data within 1.0% for each charged track. Hence, 2.0% is taken as the systematic

error for the proton and anti-proton of the Σ+_Σ¯− _{final state.}

3. The uncertainty due to photon detection efficiency is 1% per photon, which is deter-mined from the decay J/ψ → ρπ [18].

4. Five decays, J/ψ → Λ¯Λ, J/ψ → Σ0_Σ¯0_{, J/ψ → Ξ}0_Ξ¯0_{, ψ}′ _{→ π}0_π0_{J/ψ (J/ψ → p¯p) and}

fits. The signal events are selected from data and inclusive MC events without the 4C fit information. The remaining background is found to be negligible according to the studies of the inclusive MC events. The efficiency of the 4C kinematic fit is

defined as N1

N0, where N0 is the the number of signal events, N1 is the number of events

survived the. For the χcJ → Λ¯Λ, where the final state is ψ′ → γΛ¯Λ, two decays,

J/ψ → Λ¯Λ, and J/ψ → Σ0_Σ¯0_{, are used to investigate the systematic error due to the}

4C kinematic fit. The final states of these two control samples contain one photon less or more than the signal channel. Conservatively, the larger difference observed in the two control samples, 2.4%, is taken as the systematic error. Similarly, the larger

difference in J/ψ → Σ0_Σ¯0 _{and J/ψ → Ξ}0_Ξ¯0_{, 2.9%, is taken as the systematic error of}

the χcJ → Σ0Σ¯0 channel, and the larger difference in ψ′ → π0π0J/ψ (J/ψ → p¯p) and

ψ′ _{→ π}0_π0_{J/ψ (J/ψ → p¯pπ}0_{), 1.3%, is taken as the error of χ}

cJ → Σ+Σ¯−.

5. When changing mass ranges in fitting MB ¯B signals to 3.30-3.62 GeV/c2 or to 3.25-3.62

GeV/c2_{, the fitted numbers of χ}

c0,1,2 have some changes for data and MC simulation.

Taking the Λ¯Λ channel as an example, the results in the range of 3.30 GeV/c2 _{to 3.60}

GeV/c2 _{are taken as central values, when the fit range is changed to 3.32-3.60 GeV/c}2_,

the changes relative to central values are found to be 2.7%, 3.6% and 2.2% for the χc0,1,2 decays, respectively, while in the range 3.25-3.62 GeV/c2, the changes are found to be 2.2%, 0.9%, 4.3%. Conservatively, we take the larger ones, 2.7%, 3.6% and 4.3%,

as the systematic errors for the Λ¯Λ final state. With the same method, the systematic

errors for the other two channels are determined to be 1.4%, 6.7%, 4.3% for the Σ0_Σ¯0

final state, and 1.4%, 3.0%, 7.2% for the Σ+_Σ¯− _{final state.}

6. In the fits to the MB ¯B invariant mass, the signals are described by a parameterized

shape obtained from MC simulation in which the widths of χcJ are fixed since we only

observe a small number of signal events in χc1,2 → Σ0Σ¯0 and Σ+Σ¯−. When changing

the parameters of χcJ widths in this MC simulation by ± σ, it is found that the

difference of the numbers of fitted χc1,2 events between data and MC is 1.2%, 0.0%,

0.0% for the Λ¯Λ final state; 1.9%, 0.0%, 3.7% for the Σ0_Σ¯0 _{final state and 1.0%, 0.5%,}

2.0% for the Σ+_Σ¯− _{final state. Hence, we take the difference as the systematic error}

due to the χcJ widths.

the radiative photon energy (E3

γ), which leads to a diverging tail in the lower mass

region. Two damping factors have been proposed by the KEDR [19] and the CLEO [20] collaborations and have been included to describe the signal lineshape. Differences in the signal yields with respect to the fit not taking into account this damping factor

are observed, and the greater differences are 0.7%, 2.1%, 2.7% for the Λ¯Λ final state;

1.4%, 1.0%, 2.2% for the Σ0_Σ¯0 _{final state and 0.0%, 2.7%, 5.5% for the Σ}+_Σ¯− _final

state, which are taken as the systematic error associated with the signal lineshape.

8. From the decay J/ψ → Λ¯Λ, it is found that the average resolution is 7.90 ± 0.09

MeV/c2 _{for the data, and 7.08 ± 0.04 MeV/c}2 _{for MC. Differences in fitting the χ}

cJ signal with and without fixing the MC parameters are found to be 1.5%, 0.5% and

2.4% for the Λ¯Λ final states, which are taken as the systematic error of the resolution.

However, from the decays J/ψ → Σ0_Σ¯0 _{and J/ψ → Σ}+_Σ¯−_{, one can found that the}

resolutions between data and MC are consistent. Therefore, the systematic errors of

the resolution for the Σ0_Σ¯0 _{and Σ}+_Σ¯− _{final state are neglected.}

9. To estimate the uncertainty of the angular distribution, we use another model in which

the angular distribution of χc1,2 → B ¯B is taken into account according to the helicity

amplitude [21]. When the two independent helicity amplitudes, B1

2,− 1 2 and B− 1 2, 1 2, are

set to be 1.0, the efficiencies are found to be (28.8 ± 0.2)% and (27.9 ± 0.2)% for the

χc1,2 → Λ¯Λ final state, respectively. The differences from phase space are 3.2% and

6.0%. Similar comparisons are also done for the Σ0_Σ¯0 _{and Σ}+_Σ¯− _{final states, and the}

differences are smaller. Conservatively, we take the difference of the Λ¯Λ final state as

the systematic error of the angular distribution for all B ¯B final states.

10. In Fig. 2, the combinatorial background curves are fitted with a second order Cheby-chev polynomial. The background function is changed to first and third order polyno-mials, and the largest difference is taken as the systematic error due to the uncertainty in the description of the background shape.

11. The total number of ψ′ _{events are obtained by studying inclusive hadronic ψ}′ _decays

with uncertainty of 0.81% [9].

Table II lists all systematic error contributions, and the total systematic error is obtained by adding the individual contributions in quadrature.

TABLE II. Systematic errors in the branching fraction measurements (%) .

χcJ → Λ¯Λ χcJ → Σ0Σ¯0 χcJ → Σ+Σ¯−

Source χc0 χc1 χc2 χc0 χc1 χc2 χc0 χc1 χc2

The total number of ψ′ _{0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81 0.81}

MDC tracking (p, ¯p) – – – – – – 2.0 2.0 2.0 Photon efficiency 1.0 1.0 1.0 3.0 3.0 3.0 5.0 5.0 5.0 Λ reconstruction 2.0 2.0 2.0 2.0 2.0 2.0 – – – ¯ Λ reconstruction 5.0 5.0 5.0 5.0 5.0 5.0 – – – Kinematic fit 2.4 2.4 2.4 2.9 2.9 2.9 1.3 1.3 1.3 Fitting range 2.7 3.6 4.3 1.4 6.7 4.3 1.4 3.0 7.2 χcJ width 1.2 0.0 0.0 1.9 0.0 3.7 1.0 0.5 2.0 Angular distribution 0.0 3.2 6.0 0.0 3.2 6.0 0.0 3.2 6.0 Background shape 0.5 1.3 1.3 1.7 7.8 6.0 1.8 2.5 3.0 Signal lineshape 0.7 2.1 2.7 1.4 1.0 2.2 0.0 2.7 5.5 MC resolution 1.5 0.5 2.4 0.0 0.0 0.0 0.0 0.0 0.0 B(ψ′_{→ γχcJ) 3.2 4.3 4.0 3.2 4.3 4.0 3.2 4.3 4.0} B(Σ → pπ) – – – – – – 0.82 0.82 0.82 B(Λ → pπ) 1.1 1.1 1.1 1.1 1.1 1.1 – – – Total systematic error 7.7 9.3 11.1 8.3 13.6 13.2 7.0 9.1 13.4

VII. RESULTS

The branching fraction of χcJ → B ¯B is determined by

B(χcJ → B ¯B) = Nobs_[χ cJ] Nψ′ · ǫ · Q iBi ,

and if the signal is not significant, the corresponding upper limit of branching fraction is set with B(χcJ → B ¯B) < Nobs U L[χcJ] Nψ′ · ǫ ·Q_iB_i· (1.0 − σ_sys.) ,

where, Nobs _{is the number of observed signal events and N}obs

U Lis the upper limit of the number

of events, ǫ is the detection efficiency shown in Table I, σsys. is the relative the systematic

error, Nψ′ is the total number of ψ′ events [9], and Q_iB_i is the product of the branching

fractions taken from the world average [4] for the ψ′ _{→ γχ}

cJ and the other decays that are

involved. With the numbers listed in Table I and the branching fractions for the relevant

baryon decays, the branching fractions or the upper limits at the 90% C.L. for χcJ decays

are determined, as listed in Table III.

TABLE III. Branching fractions (or their upper limits) of χcJ → Λ¯Λ, Σ0Σ¯0 and Σ+Σ¯−(in units of

10−5_{). The first error is statistical and the second is systematic.}

Mode χc0 χc1 χc2 This work 33.3 ± 2.0 ± 2.6 12.2 ± 1.1 ± 1.1 20.8 ± 1.6 ± 2.3 PDG 33.0 ± 4.0 11.8 ± 1.9 18.6 ± 2.7 Λ ¯Λ CLEO 33.8 ± 3.6 ± 2.2 ± 1.7 11.6 ± 1.8 ± 0.7 ± 0.7 17.0 ± 2.2 ± 1.1 ± 1.1 Theory (93.5 ± 20.5a , 22.1 ± 6.1b )[2] _{– (15.2 ± 1.7}a , 4.3 ± 0.6b )[2] 11.9 ∼ 15.1[3] _3.9[22] _3.5[22] This work 47.8 ± 3.4 ± 3.9 3.8 ± 1.0 ± 0.5 (< 6.2) 4.0 ± 1.1 ± 0.5 (< 6.5) PDG 42.0 ± 7.0 <4.0 <8.0 Σ0_Σ¯0 _CLEO 44.1 ± 5.6 ± 4.2 ± 2.2 <4.4 <7.5 Theory (25.1 ± 3.4a , 18.7 ± 4.5b )[2] _{– (38.9 ± 8.8}a , 4.2 ± 0.5b )[2] – 3.3[22] _5.0[22] This work 45.4 ± 4.2 ± 3.0 5.4 ± 1.5 ± 0.5 (< 8.7) 4.9 ± 1.9 ± 0.7 (< 8.8) PDG 31.0 ± 7.0 <6.0 <7.0 Σ+_Σ¯_{− CLEO} 32.5 ± 5.7 ± 4.0 ± 1.7 <6.5 <6.7 Theory 5.5 ∼ 6.9[3] 3.3[22] 5.0[22] VIII. SUMMARY

Three χcJ decays to the baryon pairs are observed, and their branching fractions are

the decay of χcJ → Λ¯Λ, the experimental results are still inconsistent with theoretical

predictions [2, 3, 22], which are helpful to check the theoretical model of decays of χcJ → Λ¯Λ.

For the decays of χc1,2 → Σ0Σ¯0 and Σ+Σ¯−, the significances are improved relative to the

previous measurments, but the comparisons of their branching fractions between experiments and theoretical predictions are inconclusive due to the limited experimental precision.

IX. ACKNOWLEDGEMENT

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, 2009CB825206; National Natural Science Foun-dation of China (NSFC) under Contracts Nos. 10625524, 10821063, 10825524, 10835001, 10935007, 10975143, 10975047, 10979008, 11125525, 11275057; Joint Funds of the National Natural Science Foundation of China under Contracts Nos. 11079008, 11079027, 11179007; 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; Ministry of Development of Turkey under Contract No. DPT2006K-120470; U. S. Department of Energy under Contracts Nos. DE-FG02-04ER41291, DE-FG02-91ER40682, DE-FG02-94ER40823; U.S. National Science Founda-tion; 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.

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