Branching fraction measurement of J=Psi -> KSKL and search for J=Psi -> KSKS

This is the accepted manuscript made available via CHORUS. The article has been

published as:

Branching fraction measurement of J/ψ→K_{S}K_{L} and

search for J/ψ→K_{S}K_{S}

M. Ablikim et al. (BESIII Collaboration)

Phys. Rev. D 96, 112001 — Published 4 December 2017

DOI:

10.1103/PhysRevD.96.112001

M. Ablikim1, M. N. Achasov9,d, S. Ahmed14, M. Albrecht4, M. Alekseev53A,53C, A. Amoroso53A,53C, F. F. An1,

Q. An50,40, J. Z. Bai1, Y. Bai39, O. Bakina24, R. Baldini Ferroli20A, Y. Ban32, D. W. Bennett19, J. V. Bennett5,

N. Berger23_{, M. Bertani}20A_{, D. Bettoni}21A_{, J. M. Bian}47_{, F. Bianchi}53A,53C_{, E. Boger}24,b_{, I. Boyko}24_{, R. A. Briere}5_,

H. Cai55, X. Cai1,40, O. Cakir43A, A. Calcaterra20A, G. F. Cao1,44, S. A. Cetin43B, J. Chai53C, J. F. Chang1,40,

G. Chelkov24,b,c, G. Chen1, H. S. Chen1,44, J. C. Chen1, M. L. Chen1,40, S. J. Chen30, X. R. Chen27, Y. B. Chen1,40,

Z. X. Chen32_{, X. K. Chu}32_{, G. Cibinetto}21A_{, H. L. Dai}1,40_{, J. P. Dai}35,h_{, A. Dbeyssi}14_{, D. Dedovich}24_{, Z. Y. Deng}1_,

A. Denig23, I. Denysenko24, M. Destefanis53A,53C, F. De Mori53A,53C, Y. Ding28, C. Dong31, J. Dong1,40, L. Y. Dong1,44,

M. Y. Dong1,40,44, O. Dorjkhaidav22, Z. L. Dou30, S. X. Du57, P. F. Duan1, J. Fang1,40, S. S. Fang1,44, X. Fang50,40,

Y. Fang1_{, R. Farinelli}21A,21B_{, L. Fava}53B,53C_{, S. Fegan}23_{, F. Feldbauer}23_{, G. Felici}20A_{, C. Q. Feng}50,40_{, E. Fioravanti}21A_{, M.}

Fritsch23,14, C. D. Fu1, Q. Gao1, X. L. Gao50,40, Y. Gao42, Y. G. Gao6, Z. Gao50,40, B. Garillon23, I. Garzia21A,

K. Goetzen10, L. Gong31, W. X. Gong1,40, W. Gradl23, M. Greco53A,53C, M. H. Gu1,40, S. Gu15, Y. T. Gu12, A. Q. Guo1,

L. B. Guo29_{, R. P. Guo}1_{, Y. P. Guo}23_{, Z. Haddadi}26_{, S. Han}55_{, X. Q. Hao}15_{, F. A. Harris}45_{, K. L. He}1,44_{, X. Q. He}49_,

F. H. Heinsius4_{, T. Held}4_{, Y. K. Heng}1,40,44_{, T. Holtmann}4_{, Z. L. Hou}1_{, C. Hu}29_{, H. M. Hu}1,44_{, J. F. Hu}35,h_{, T. Hu}1,40,44_,

Y. Hu1, G. S. Huang50,40, J. S. Huang15, S. H. Huang41, X. T. Huang34, X. Z. Huang30, Z. L. Huang28, T. Hussain52,

W. Ikegami Andersson54, Q. Ji1, Q. P. Ji15, X. B. Ji1,44, X. L. Ji1,40, X. S. Jiang1,40,44, X. Y. Jiang31, J. B. Jiao34, Z. Jiao17,

D. P. Jin1,40,44_{, S. Jin}1,44_{, Y. Jin}46_{, T. Johansson}54_{, A. Julin}47_{, N. Kalantar-Nayestanaki}26_{, X. L. Kang}1_{, X. S. Kang}31_,

M. Kavatsyuk26, B. C. Ke5, T. Khan50,40, A. Khoukaz48, P. Kiese23, R. Kliemt10, L. Koch25, O. B. Kolcu43B,f, B. Kopf4,

M. Kornicer45, M. Kuemmel4, M. Kuhlmann4, A. Kupsc54, W. K¨uhn25, J. S. Lange25, M. Lara19, P. Larin14, L. Lavezzi53C,

H. Leithoff23_{, C. Leng}53C_{, C. Li}54_{, Cheng Li}50,40_{, D. M. Li}57_{, F. Li}1,40_{, F. Y. Li}32_{, G. Li}1_{, H. B. Li}1,44_{, H. J. Li}1_{, J. C. Li}1_,

Jin Li33, K. Li13, K. Li34, K. J. Li41, Lei Li3, P. L. Li50,40, P. R. Li44,7, Q. Y. Li34, T. Li34, W. D. Li1,44, W. G. Li1,

X. L. Li34, X. N. Li1,40, X. Q. Li31, Z. B. Li41, H. Liang50,40, Y. F. Liang37, Y. T. Liang25, G. R. Liao11, D. X. Lin14,

B. Liu35,h_{, B. J. Liu}1_{, C. X. Liu}1_{, D. Liu}50,40_{, F. H. Liu}36_{, Fang Liu}1_{, Feng Liu}6_{, H. B. Liu}12_{, H. H. Liu}1_{, H. H. Liu}16_,

H. M. Liu1,44, J. B. Liu50,40, J. Y. Liu1, K. Liu42, K. Y. Liu28, Ke Liu6, L. D. Liu32, P. L. Liu1,40, Q. Liu44, S. B. Liu50,40,

X. Liu27, Y. B. Liu31, Z. A. Liu1,40,44, Zhiqing Liu23, Y. F. Long32, X. C. Lou1,40,44, H. J. Lu17, J. G. Lu1,40, Y. Lu1,

Y. P. Lu1,40_{, C. L. Luo}29_{, M. X. Luo}56_{, X. L. Luo}1,40_{, X. R. Lyu}44_{, F. C. Ma}28_{, H. L. Ma}1_{, L. L. Ma}34_{, M. M. Ma}1_,

Q. M. Ma1_{, T. Ma}1_{, X. N. Ma}31_{, X. Y. Ma}1,40_{, Y. M. Ma}34_{, F. E. Maas}14_{, M. Maggiora}53A,53C_{, Q. A. Malik}52_,

Y. J. Mao32, Z. P. Mao1, S. Marcello53A,53C, Z. X. Meng46, J. G. Messchendorp26, G. Mezzadri21B, J. Min1,40, T. J. Min1,

R. E. Mitchell19_{, X. H. Mo}1,40,44_{, Y. J. Mo}6_{, C. Morales Morales}14_{, G. Morello}20A_{, N. Yu. Muchnoi}9,d_{, H. Muramatsu}47_,

A. Mustafa4_{, Y. Nefedov}24_{, F. Nerling}10_{, I. B. Nikolaev}9,d_{, Z. Ning}1,40_{, S. Nisar}8_{, S. L. Niu}1,40_{, X. Y. Niu}1_{, S. L. Olsen}33_,

Q. Ouyang1,40,44, S. Pacetti20B, Y. Pan50,40, M. Papenbrock54, P. Patteri20A, M. Pelizaeus4, J. Pellegrino53A,53C,

H. P. Peng50,40, K. Peters10,g, J. Pettersson54, J. L. Ping29, R. G. Ping1,44, A. Pitka23, R. Poling47, V. Prasad50,40, H. R. Qi2,

M. Qi30_{, T. .Y. Qi}2_{, S. Qian}1,40_{, C. F. Qiao}44_{, N. Qin}55_{, X. S. Qin}4_{, Z. H. Qin}1,40_{, J. F. Qiu}1_{, K. H. Rashid}52,i_,

C. F. Redmer23, M. Richter4, M. Ripka23, M. Rolo53C, G. Rong1,44, Ch. Rosner14, A. Sarantsev24,e, M. Savri´e21B,

C. Schnier4, K. Schoenning54, W. Shan32, M. Shao50,40, C. P. Shen2, P. X. Shen31, X. Y. Shen1,44, H. Y. Sheng1,

J. J. Song34_{, W. M. Song}34_{, X. Y. Song}1_{, S. Sosio}53A,53C_{, C. Sowa}4_{, S. Spataro}53A,53C_{, G. X. Sun}1_{, J. F. Sun}15_,

L. Sun55, S. S. Sun1,44, X. H. Sun1, Y. J. Sun50,40, Y. K Sun50,40, Y. Z. Sun1, Z. J. Sun1,40, Z. T. Sun19, C. J. Tang37,

G. Y. Tang1, X. Tang1, I. Tapan43C, M. Tiemens26, B. T. Tsednee22, I. Uman43D, G. S. Varner45, B. Wang1, B. L. Wang44,

B. Q. Wang32_{, D. Wang}32_{, D. Y. Wang}32_{, Dan Wang}44_{, K. Wang}1,40_{, L. L. Wang}1_{, L. S. Wang}1_{, M. Wang}34_{, P. Wang}1_,

P. L. Wang1, W. P. Wang50,40, X. F. Wang42, Y. Wang38, Y. D. Wang14, Y. F. Wang1,40,44, Y. Q. Wang23, Z. Wang1,40,

Z. G. Wang1,40, Z. H. Wang50,40, Z. Y. Wang1, Zongyuan Wang1, T. Weber23, D. H. Wei11, J. H. Wei31, P. Weidenkaff23,

S. P. Wen1_{, U. Wiedner}4_{, M. Wolke}54_{, L. H. Wu}1_{, L. J. Wu}1_{, Z. Wu}1,40_{, L. Xia}50,40_{, Y. Xia}18_{, D. Xiao}1_{, H. Xiao}51_,

Y. J. Xiao1_{, Z. J. Xiao}29_{, X. H. Xie}41_{, Y. G. Xie}1,40_{, Y. H. Xie}6_{, X. A. Xiong}1_{, Q. L. Xiu}1,40_{, G. F. Xu}1_{, J. J. Xu}1_,

L. Xu1, Q. J. Xu13, Q. N. Xu44, X. P. Xu38, L. Yan53A,53C, W. B. Yan50,40, W. C. Yan2, Y. H. Yan18, H. J. Yang35,h,

H. X. Yang1, L. Yang55, Y. H. Yang30, Y. X. Yang11, M. Ye1,40, M. H. Ye7, J. H. Yin1, Z. Y. You41, B. X. Yu1,40,44,

C. X. Yu31_{, J. S. Yu}27_{, C. Z. Yuan}1,44_{, Y. Yuan}1_{, A. Yuncu}43B,a_{, A. A. Zafar}52_{, Y. Zeng}18_{, Z. Zeng}50,40_{, B. X. Zhang}1_,

B. Y. Zhang1,40, C. C. Zhang1, D. H. Zhang1, H. H. Zhang41, H. Y. Zhang1,40, J. Zhang1, J. L. Zhang1, J. Q. Zhang1,

J. W. Zhang1,40,44, J. Y. Zhang1, J. Z. Zhang1,44, K. Zhang1, L. Zhang42, S. Q. Zhang31, X. Y. Zhang34, Y. Zhang1,

Y. Zhang1_{, Y. H. Zhang}1,40_{, Y. T. Zhang}50,40_{, Yu Zhang}44_{, Z. H. Zhang}6_{, Z. P. Zhang}50_{, Z. Y. Zhang}55_{, G. Zhao}1_,

J. W. Zhao1,40, J. Y. Zhao1, J. Z. Zhao1,40, Lei Zhao50,40, Ling Zhao1, M. G. Zhao31, Q. Zhao1, S. J. Zhao57, T. C. Zhao1,

Y. B. Zhao1,40, Z. G. Zhao50,40, A. Zhemchugov24,b, B. Zheng51,14, J. P. Zheng1,40, W. J. Zheng34, Y. H. Zheng44,

B. Zhong29_{, L. Zhou}1,40_{, X. Zhou}55_{, X. K. Zhou}50,40_{, X. R. Zhou}50,40_{, X. Y. Zhou}1_{, J. Zhu}41_{, K. Zhu}1_{, K. J. Zhu}1,40,44_,

S. Zhu1, S. H. Zhu49, X. L. Zhu42, Y. C. Zhu50,40, Y. S. Zhu1,44, Z. A. Zhu1,44, J. Zhuang1,40, B. S. Zou1, J. H. Zou1

(BESIII Collaboration)

1 _{Institute of High Energy Physics, Beijing 100049, People’s Republic of China}

2 _{Beihang University, Beijing 100191, People’s Republic of China}

3

Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China 4

Bochum Ruhr-University, D-44780 Bochum, Germany

5 _{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA}

6

Central China Normal University, Wuhan 430079, People’s Republic of China 7

2

8

COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan

9 _{G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia}

10 _{GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany}

11

Guangxi Normal University, Guilin 541004, People’s Republic of China

12 _{Guangxi University, Nanning 530004, People’s Republic of China}

13 _{Hangzhou Normal University, Hangzhou 310036, People’s Republic of China}

14

Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 15

Henan Normal University, Xinxiang 453007, People’s Republic of China

16 _{Henan University of Science and Technology, Luoyang 471003, People’s Republic of China}

17

Huangshan College, Huangshan 245000, People’s Republic of China 18

Hunan University, Changsha 410082, People’s Republic of China

19 _{Indiana University, Bloomington, Indiana 47405, USA}

20

(A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy

21 _{(A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy}

22

Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia 23

Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

24 _{Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia}

25 _{Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany}

26

KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands 27

Lanzhou University, Lanzhou 730000, People’s Republic of China

28 _{Liaoning University, Shenyang 110036, People’s Republic of China}

29

Nanjing Normal University, Nanjing 210023, People’s Republic of China 30

Nanjing University, Nanjing 210093, People’s Republic of China

31 _{Nankai University, Tianjin 300071, People’s Republic of China}

32

Peking University, Beijing 100871, People’s Republic of China 33

Seoul National University, Seoul, 151-747 Korea

34 _{Shandong University, Jinan 250100, People’s Republic of China}

35

Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China 36

Shanxi University, Taiyuan 030006, People’s Republic of China

37 _{Sichuan University, Chengdu 610064, People’s Republic of China}

38 _{Soochow University, Suzhou 215006, People’s Republic of China}

39

Southeast University, Nanjing 211100, People’s Republic of China 40

State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China

41 _{Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China}

42

Tsinghua University, Beijing 100084, People’s Republic of China 43

(A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

44

University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 45

University of Hawaii, Honolulu, Hawaii 96822, USA

46 _{University of Jinan, Jinan 250022, People’s Republic of China}

47

University of Minnesota, Minneapolis, Minnesota 55455, USA 48

University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany

49 _{University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China}

50 _{University of Science and Technology of China, Hefei 230026, People’s Republic of China}

51

University of South China, Hengyang 421001, People’s Republic of China 52

University of the Punjab, Lahore-54590, Pakistan

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

Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy 54

Uppsala University, Box 516, SE-75120 Uppsala, Sweden

55 _{Wuhan University, Wuhan 430072, People’s Republic of China}

56

Zhejiang University, Hangzhou 310027, People’s Republic of China 57

Zhengzhou University, Zhengzhou 450001, People’s Republic of China a

Also at Bogazici University, 34342 Istanbul, Turkey b

Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia

c _{Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia}

d

Also at the Novosibirsk State University, Novosibirsk, 630090, Russia e

Also at the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia

f _{Also at Istanbul Arel University, 34295 Istanbul, Turkey}

g

Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany h

Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China

i

Using a sample of 1.31×109J/ψ events collected with the BESIII detector at the BEPCII collider,

we study the decays of J/ψ → KSKL and KSKS. The branching fraction of J/ψ → KSKL is

determined to be B(J/ψ → KSKL) = (1.93 ± 0.01 (stat.) ± 0.05 (syst.)) × 10−4, which significantly

improves on previous measurements. No clear signal is observed for the J/ψ → KSKS process,

and the upper limit at the 95% confidence level for its branching fraction is determined to be

B(J/ψ → KSKS) < 1.4×10−8

, which improves on the previous searches by two orders in magnitude and reaches the order of the Einstein-Podolsky-Rosen expectation.

PACS numbers: 13.66.Bc, 13.25.Gv, 03.65.Vf

I. INTRODUCTION

The charmonium state J/ψ with a mass below the open charm threshold decays to light hadrons through the annihilation of c¯c into one virtual photon, three gluons or one photon and two gluons. The J/ψ decaying to KSKL

proceeds via the first two processes, thereby providing valuable information to understand the nature of J/ψ decays. The available measurements of its branching fraction, B(J/ψ → KSKL), based on 57.7 million J/ψ

events collected at BESII [1] and 24.5 million ψ(3686) events at CLEO [2], are given by (1.82±0.04±0.13)×10−4 and (2.62 ± 0.15 ± 0.14) × 10−4 respectively. Due to the discrepancy between these two measurements, the world average value in the particle data group (PDG) [3] has quoted a relative precision of 19%, which limits the precise understanding of J/ψ decay mechanisms.

In the CP-violating decay of J/ψ to KSKS, the two

identical bosons from the decay would need to form an antisymmetric state, and the process would be ruled out according to Bose-Einstein statistics. However, according to the Einstein-Podolsky-Rosen (EPR) [4] paradox, the quantum state of a two-particle system can not always be decomposed into the joint state of the two particles. Thus the space-like separated coherent quantum system may also yield a sizable decay branching fraction of J/ψ → KSKSat the 10−8level [5]. In this way, the KSKSsystem

can be used to test the EPR paradox versus quantum theory. There also might be a small possibility to have a KSKS final state due to CP violation. In the K0K¯0

oscillation model [6], the CP violating branching fraction of J/ψ → KSKS is calculated to be (1.94 ± 0.20) × 10−9.

The MARKIII experiment searched for the decay J/ψ → KSKS with 2.7 million events, and the upper limit was

determined to be B(J/ψ → KSKS) < 5.2 × 10−6 at the

90% confidence level (C.L.) [7]. Based on 57.7 million J/ψ events collected at the BESII detector, the upper limit on the branching fraction was improved to be 1.0 × 10−6 at the 95% C.L. [8], which is still far from the expectations from K0_{− ¯K}0 _{oscillation and EPR.}

The world’s largest J/ψ sample with 1.31 × 109_events

was accumulated at BESIII during 2009 and 2012 [9]. In this paper, we measure the branching fraction of J/ψ → KSKL, and also search for the CP violating decay J/ψ →

KSKS.

II. APPARATUS AND MONTE CARLO

SIMULATION

The Beijing Spectrometer III (BESIII), located at the double-ring e+e− Beijing Electron Positron Collider (BEPCII), is a general purpose detector as described in Ref. [10]. It covers 93% of 4π in geometrical acceptance and consists of four main detectors. A 43-layer small-cell, helium gas based main drift chamber, operating in a 1.0 (0.9) T solenoidal magnetic field in 2009 (2012), provides an average single-hit resolution of 135 µm. A time-of-flight system, composed of 5 cm thick plastic scintillators with 176 bars of 2.4 m length, arranged in two layers in the barrel and 96 fan-shaped counters in the end-caps, has a time resolution of 80 ps (100 ps) in the barrel (end-caps) region providing 2σ K/π separation for momenta up to 1.0 GeV/c. An electromagnetic calorimeter, which consists of 5280 CsI(Tl) crystals arranged in a cylindrical structure in the barrel and 480 crystals in each of the two end-caps, provides an energy resolution for a 1.0 GeV/c photon of 2.5% in the barrel region and 5% in the end-caps. The position resolution is 6 mm (9 mm) in the barrel (end-caps). A muon counter system, which consists of resistive plate chambers arranged in nine barrel and eight end-cap layers, provides 2.0 cm position resolution.

The optimization of event selection criteria, the de-termination of detection efficiencies, and the estimation of background are performed by means of Monte Carlo (MC) simulations. The KKMC [11] generator is used to simulate the J/ψ → K0K¯0 _{process. The angular}

distribution of the K0 or K¯0 _{is generated to be}

proportional to sin2θ, where θ is the polar angle in the laboratory system. In the MC simulation, the interference between the J/ψ resonance decay and the continuum process is ignored. A GEANT4-based [12, 13] detector simulation software, which includes the geometric and material description of the BESIII spectrometer, and the detector response, is used to generate the MC samples. The background is studied with a MC sample of 1.23×109

inclusive J/ψ decays, in which the known decays are generated with the EvtGen [14, 15] generator by setting the branching fraction to the values in the PDG [3] and the remaining unknown decays are generated with the LUNDCHARM [16].

4

III. BRANCHING FRACTION

MEASUREMENT OF J/ψ → KSKL

The KS candidate is reconstructed from its charged

π+_π− _{final state, while the K}

L is assumed not to decay

in the detector leaving only the signature of missing energy. The KScandidates are reconstructed with

vertex-constrained fits to pairs of oppositely charged tracks, assumed to be pions, whose polar angles satisfy the condition | cos θ| < 0.93. Only one KS candidate is

accepted in each event. The KS candidates are required

to satisfy L >1 cm and L/σL> 2, where L is the distance

between the common vertex of the π+π− pair and the interaction point and σLis its uncertainty. The invariant

mass of the π+_π− _{pair, M}

π+_π−, shown in Fig. 1, is

required to satisfy |Mπ+_π−− M_KS| < 18 MeV/c2, where

MKS is the KS nominal mass [3]. There should be no

extra tracks satisfying | cos θ| < 0.93, within 1 cm of the interaction point in the transverse direction to the beam line and 10 cm of the interaction point along the beam axis. In order to suppress γ conversion background, the angle between the two charged tracks, θch, is required to

satisfy θch> 15◦.

The same event selection criteria are applied to the inclusive MC sample. The major potential backgrounds are J/ψ → π0_K

SKLand J/ψ → γKSKS events, but the

leakage of their KS momentum (PKS) spectra into the

signal region is smooth and tiny.

)

(GeV/c

M

)

Events/(2MeV/c

FIG. 1: (color online) The distribution of Mπ+π−. The (black)

crosses are from data, and the (red) histogram represents the signal MC sample.

The J/ψ → KSKL signal yield is determined from

a maximum likelihood fit to the PKS distribution, as

shown in Fig.2. In the fit, the signal shape is described by a double Gaussian function with a common mean value and two different widths. The background shape is represented by a second-order Chebychev polynomial function.

The continuum process e+e−→ KSKLis studied with

a data set of 30.0 pb−1 taken at 3.080 GeV. The same selection criteria are applied. The result of the maximum

(GeV/c)

P

Events/(1MeV/c)

(GeV/c)

P

Events/(1MeV/c)

FIG. 2: (color online) The momentum distribution of KS in

the e+_e−

rest frame. The (black) crosses are from data, and the (blue) solid line is the fit result. The (red) long-dashed line is the signal, and the (green) short-dashed line is background.

likelihood fit to the PKS distribution is shown in Fig.3.

In the fit, the signal function is the same as that used in the fit of J/ψ data. The background shape is represented by a first-order Chebychev polynomial function.

(GeV/c)

P

Events(3MeV/c)

(GeV/c)

P

Events(3MeV/c)

FIG. 3: (color online) The KS momentum distribution for

data taken at√s = 3.080 GeV. The (black) crosses are data,

and the (blue) solid line is the fitting result. The (red) long-dashed line corresponds to the signal, and the (green) short-dashed line represents the background.

The event selection efficiencies are assumed to be the same at 3.080 GeV and the J/ψ resonance. The continuum contribution to the J/ψ resonance region is estimated from

N_contJ/ψ = N_obs3.080·L · s

03

L0_{· s}3, (1)

where N3.080

obs is the signal yield at 3.080 GeV, L and

L0 _{are the luminosities collected at the J/ψ and at}

3.080 GeV, determined with e+e−→ γγ events [9], while s and s0 correspond to the squares of center-of-mass energies of J/ψ and 3.080 GeV. The power law of the

center-of-mass energy follows the K+K− cross section slope measured by BaBar [17].

Assuming no interference between the J/ψ decay and the continuum process, the branching fraction is determined from B(J/ψ → KSKL) = N_obsJ/ψ− NcontJ/ψ  · NJ/ψ_{· B(K} S → π+π−) , (2)

where N_obsJ/ψ is the number of signal events obtained in the J/ψ sample,  is the event selection efficiency, NJ/ψ_is

the number of J/ψ events [9] and B(KS → π+π−) is the

branching fraction of KS → π+π−. Table I summarizes

the values used in the calculation, and B(J/ψ → KSKL)

is determined to be (1.93±0.01)×10−4, where the quoted uncertainty is purely statistical.

TABLE I: Numbers used in the branching fraction calculation

for the KSKLchannel, where the uncertainties are statistical

only. 3.097 GeV (J/ψ) 3.080 GeV Nobs 110203 ± 504 13 ± 5  (%) 62.9 62.9 L (pb−1) 394.7 30.9 B(KS → π+π−) [3] 0.692 0.692

The systematic uncertainties for the B(J/ψ → KSKL)

measurement include those due to KS reconstruction,

the requirement on θch, the fit to the PKS spectrum, the

branching fraction of the KS decay, and the number of

J/ψ events.

The KS reconstruction involves the charged track

reconstruction of the π+_π− _{pair, the vertex fit and the}

KS mass window requirement. The corresponding

sys-tematic uncertainty is estimated using a control sample of J/ψ → K∗±(892)K∓ events, where K∗±(892) → KSπ±.

The momentum of the KS, PKS in J/ψ → KSKL

decay is around 1.46 GeV/c, thus only KS candidates

with momentum larger than 1 GeV/c in the control sample are considered. The ratio of the reconstruction efficiency of the data over that in the MC is taken as a correction factor to the KSKL selection efficiency,

while the uncertainty of the ratio, 1.4%, is taken as the systematic uncertainty.

The uncertainty from the θchrequirement is estimated

by varying the selection range. The range is expanded and contracted by 5◦, and the largest change in the branching fraction with respect to the nominal value is taken as the systematic uncertainty.

The systematic uncertainty related to the fit method is estimated by varying the fit range and the background shape simultaneously. The fit range is expanded and contracted by 8 MeV/c. For the J/ψ data sample, the background shape is varied from a second-order Cheby-shev polynomial function to a third-order ChebyCheby-shev polynomial function and an exponential function. For the continuum data sample, the background is replaced

TABLE II: Systematic uncertainties for the measurement of

branching fraction of the KSKLchannel.

Source Uncertainty (%) KS reconstruction 1.4 θch 1.0 Fit to PKS 1.9 B(KS→ π+π−) 0.1 NJ/ψ 0.6 Total 2.6

by a second-order Chebychev polynomial function. The largest change in the branching fraction is treated as the systematic uncertainty.

The branching fraction of KS → π+π− is taken from

the PDG [3] and its uncertainty is 0.1%. The number of J/ψ events and its uncertainty are determined with J/ψ inclusive decays [9].

The summary of all individual systematic uncertainties is shown in Table II, where the total uncertainty is obtained by adding the individual contributions in quadrature.

IV. SEARCH FOR J/ψ → KSKS

For J/ψ → KSKS with KS → π+π−, the final state is

π+_π−_π+_π−_{. The candidate events are required to have}

at least four charged tracks whose polar angles satisfy | cos θ| < 0.93. The KS candidates are reconstructed by

secondary vertex fits to all oppositely charged track pairs assuming them to be pions, and the π+_π−_{invariant mass}

must be within 18 MeV/c2 _{from the K}

S nominal mass.

The KS candidates must have a momentum within the

range of [1.40, 1.60] GeV/c. In order to suppress the non-KS backgrounds, the decay length over its uncertainty

(L/σL) has to be larger than 2.0. Each event must have

at least two KS candidates. If there are more than two

KS candidates, the combination with the smallest sum

of χ2 _{of the secondary vertex fits is selected.}

The KSKS candidates are then combined in a 4C

kinematic fit, where the constraints are provided by energy and momentum conservation. Only events with χ2 _{< 40 are retained. The distribution of the K}

S

momentum in the J/ψ rest frame is shown in Fig.4. The KS momentum resolution is determined from the signal

MC sample as σw = 1.3 MeV/c, which is the weighted

average of the standard deviations of two Gaussians with common mean. The number of signal events is obtained by counting the remaining events within 5 × σw of the

expected momentum. After all requirements have been imposed, two events remain in this region.

The same selection criteria are applied to the inclusive MC sample, which shows that the background mainly comes from the processes J/ψ → π+π−π+π− and J/ψ → KSKL. Their contributions are estimated from

6

(GeV/c)

P

Events/(0.3MeV/c)

FIG. 4: (color online) The distribution of KS momentum in

the J/ψ rest frame. The (black) crosses are from data, and the (red) solid line is from the signal MC sample. The arrows

indicate the 5×σwselection region.

the corresponding MC samples using

N_expX = NJ/ψ· B(J/ψ → X) · XKSKS, (3)

where X represents the corresponding channels J/ψ → π+π−π+π−or J/ψ → KSKL(KS → π+π−), and NexpX is

the expected number of events from channel X. B(J/ψ → X) is the product branching fractions of the cascade decay, where B(J/ψ → π+_π−_π+_π−_{) is taken from the}

PDG [3], B(J/ψ → KSKL) is set to the value obtained

in this paper, and X_KSKS is the KSKS selection efficiency

for a sample of X events. The efficiencies of J/ψ → π+_π−_π+_π−_{and K}

SKLchannels are (1.9±0.6)×10−7and

(8.5 ± 3.4) × 10−6, respectively. The expected background numbers are calculated to be Nπ+_π−_π+_π−

exp = 0.9 ± 0.3

and NKSKL

exp = 1.5 ± 0.6, where the uncertainties are

from propagation of the items in equation3. Some other exclusive processes, such as J/ψ → γKSKS, are also

studied with high statistics MC samples, but none of them survive the event selection.

Table III summarizes the systematic uncertainties in the search for J/ψ → KSKS. Common uncertainties

including those from the number of J/ψ decays and the KS → π+π− branching fraction are the same

as described in Section III. The uncertainty from KS

reconstruction is evaluated according to the KS selection

criteria used in this channel, with a method similar to that in SectionIII, and is determined to be 1.5% per KS.

The uncertainty from the 4C kinematic fit is investigated using the control sample of J/ψ → γKSKS, and the

difference of the efficiency between the data and MC samples is taken as the systematic uncertainty associated

with the kinematic fit.

TABLE III: The systematic uncertainties related to the search for J/ψ → KSKS. Source Uncertainty (%) KS reconstruction 3.0 4C kinematic fit 1.1 B(KS → π+π−) 0.2 NJ/ψ 0.6 Total 3.2

Since we have not observed a significant signal, an upper limit for B(J/ψ → KSKS) is set at the 95% C.L.

The upper limit is calculated using the relation B(J/ψ → KSKS) <

NUL

MC· NJ/ψ

. (4)

where NUL _{is upper limit on the number of signal}

events estimated with Nobs and Nbkg using a frequentist

approach with the profile likelihood method, as imple-mented in the ROOT framework [18], and MC is the

detection efficiency. The calculation includes statistical fluctuations and systematic uncertainties. The signal and background fluctuations are assumed to follow Poisson distributions, while the systematic uncertainty is taken to be a Gaussian distribution. The branching fraction of KS → π+π− is included in the event selection efficiency

MC. The values of variables used to calculate the upper

limit on the branching fraction and the final result are summarized in TableIV, where the Nbkg is the sum of

Nπ+π−π+π−

exp and NexpKSKL.

TABLE IV: Numbers used in the B(J/ψ → KSKS)

calculation of the upper limit on the signal yield at the 95% C.L. Nobs 2 Nbkg 2.4 NUL _4.7 MC(%) 25.7 B(J/ψ → KSKS) (95% C.L.) < 1.4 × 10−8 V. SUMMARY

Based on a data sample of 1.31 × 109 J/ψ events collected with the BESIII detector, the measurements of J/ψ → KSKL and KSKS have been performed. The

branching fraction of J/ψ → KSKL is determined to be

B(J/ψ → KSKL) = (1.93 ± 0.01 (stat.) ± 0.05 (syst.)) ×

10−4, which agrees with the BESII measurement [1] while discrepancy with the CLEO data [2] persists. Compared with the world average value listed in the PDG [3], the

relative precision is greatly improved, while the central value is consistent. With regard to the search for the CP and Bose-Einstein statistics violating process J/ψ → KSKS, an upper limit on its branching fraction is set

at the 95% C.L. to be B(J/ψ → KSKS) < 1.4 × 10−8,

which is an improvement by two orders in magnitude compared to the best previous searches [7,8]. The upper limit reaches the order of the EPR expectations[5].

VI. ACKNOWLEDGEMENT

The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11235011, 11335008, 11425524, 11625523, 11635010; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts

Nos. U1232105, U1332201, U1532257, U1532258; CAS under Contracts Nos. N29, KJCX2-YW-N45, QYZDJ-SSW-SLH003; 100 Talents Program of CAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contracts Nos. Collaborative Research Center CRC 1044, FOR 2359; Istituto Nazionale di Fisica Nucleare, Italy; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Natural Science Foundation of China (NSFC) under Contract No. 11505010; National Science and Technology fund; The Swedish Resarch Council; U. S. Department of Energy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0010504, DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum f¨ur Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.

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