Search for C-parity violation in J/ψ→γγ and γϕ
BESIII Collaboration, M. Ablikim, M. N. Achasov, X. C. Ai, O. Albayrak, M. Albrecht, D. J. Ambrose, A. Amoroso, F. F. An, Q. An, J. Z. Bai, R. Baldini Ferroli, Y. Ban, D. W. Bennett, J. V. Bennett, M. Bertani, D. Bettoni, J. M. Bian, F. Bianchi, E. Boger, O. Bondarenko, I. Boyko, S. Braun, R. A. Briere, H. Cai, X. Cai, O. Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. F. Chang, G. Chelkov, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, S. J. Chen, X. Chen, X. R. Chen, Y. B. Chen, H. P. Cheng, X. K. Chu, Y. P. Chu, G. Cibinetto, D. Cronin-Hennessy, H. L. Dai, J. P. Dai, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, S. X. Du, J. Z. Fan, J. Fang, S. S. Fang, Y. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, E. Fioravanti, C. D. Fu, Q. Gao, Y. Gao, I. Garzia, C. Geng, K. Goetzen, W. X. Gong, W. Gradl, M. Greco, M. H. Gu, Y. T. Gu, Y. H. Guan, A. Q. Guo, L. B. Guo, T. Guo, Y. P. Guo, Z. Haddadi, S. Han, Y. L. Han, F. A. Harris, K. L. He, Z. Y. He, T. Held, Y. K. Heng, Z. L. Hou, C. Hu, H. M. Hu, J. F. Hu, T. Hu, G. M. Huang, G. S. Huang, H. P. Huang, et al. (295 additional authors not shown)
aa r X i v : . [ h e p - e x ] O c t Search for C-parity violation in
J/ψ → γγ and γφ M. Ablikim , M. N. Achasov ,a , X. C. Ai , O. Albayrak , M. Albrecht , D. J. Ambrose , A. Amoroso A, C , F. F. An ,Q. An , J. Z. Bai , R. Baldini Ferroli A , Y. Ban , D. W. Bennett , J. V. Bennett , M. Bertani A , D. Bettoni A ,J. M. Bian , F. Bianchi A, C , E. Boger ,g , O. Bondarenko , I. Boyko , S. Braun , R. A. Briere , H. Cai , X. Cai , O.Cakir A , A. Calcaterra A , G. F. Cao , S. A. Cetin B , J. F. Chang , G. Chelkov ,b , G. Chen , H. S. Chen , J. C. Chen ,M. L. Chen , S. J. Chen , X. Chen , X. R. Chen , Y. B. Chen , H. P. Cheng , X. K. Chu , Y. P. Chu , G. Cibinetto A ,D. Cronin-Hennessy , H. L. Dai , J. P. Dai , D. Dedovich , Z. Y. Deng , A. Denig , I. Denysenko , M. Destefanis A, C ,F. De Mori A, C , Y. Ding , C. Dong , J. Dong , L. Y. Dong , M. Y. Dong , S. X. Du , J. Z. Fan , J. Fang ,S. S. Fang , Y. Fang , L. Fava B, C , F. Feldbauer , G. Felici A , C. Q. Feng , E. Fioravanti A , C. D. Fu , Q. Gao ,Y. Gao , I. Garzia A , C. Geng , K. Goetzen , W. X. Gong , W. Gradl , M. Greco A, C , M. H. Gu , Y. T. Gu ,Y. H. Guan , A. Q. Guo , L. B. Guo , T. Guo , Y. P. Guo , Z. Haddadi , S. Han , Y. L. Han , F. A. Harris ,K. L. He , Z. Y. He , T. Held , Y. K. Heng , Z. L. Hou , C. Hu , H. M. Hu , J. F. Hu A , T. Hu , G. M. Huang ,G. S. Huang , H. P. Huang , J. S. Huang , X. T. Huang , Y. Huang , T. Hussain , Q. Ji , Q. P. Ji , X. B. Ji ,X. L. Ji , L. L. Jiang , L. W. Jiang , X. S. Jiang , J. B. Jiao , Z. Jiao , D. P. Jin , S. Jin , T. Johansson , A. Julin ,N. Kalantar-Nayestanaki , X. L. Kang , X. S. Kang , M. Kavatsyuk , B. C. Ke , B. Kloss , O. B. Kolcu B,c , B. Kopf ,M. Kornicer , W. Kuehn , A. Kupsc , W. Lai , J. S. Lange , M. Lara , P. Larin , M. Leyhe , Cheng Li , Cui Li ,D. M. Li , F. Li , G. Li , H. B. Li , J. C. Li , Jin Li , K. Li , K. Li , Q. J. Li , T. Li , W. D. Li , W. G. Li , X. H. Li ,X. L. Li , X. N. Li , X. Q. Li , Z. B. Li , H. Liang , Y. F. Liang , Y. T. Liang , D. X. Lin , B. J. Liu , C. L. Liu ,C. X. Liu , F. H. Liu , Fang Liu , Feng Liu , H. B. Liu , H. H. Liu , H. M. Liu , J. Liu , J. P. Liu , K. Liu ,K. Y. Liu , Q. Liu , S. B. Liu , X. Liu , X. X. Liu , Y. B. Liu , Z. A. Liu , Zhiqiang Liu , Zhiqing Liu , H. Loehner ,X. C. Lou ,d , H. J. Lu , J. G. Lu , R. Q. Lu , Y. Lu , Y. P. Lu , C. L. Luo , M. X. Luo , T. Luo , X. L. Luo , M. Lv ,X. R. Lyu , F. C. Ma , H. L. Ma , Q. M. Ma , S. Ma , T. Ma , X. Y. Ma , F. E. Maas , M. Maggiora A, C ,Q. A. Malik , Y. J. Mao , Z. P. Mao , S. Marcello A, C , J. G. Messchendorp , J. Min , T. J. Min , R. E. Mitchell ,X. H. Mo , Y. J. Mo , H. Moeini , C. Morales Morales , K. Moriya , N. Yu. Muchnoi ,a , H. Muramatsu , Y. Nefedov ,F. Nerling , I. B. Nikolaev ,a , Z. Ning , S. Nisar , S. L. Niu , X. Y. Niu , S. L. Olsen , Q. Ouyang , S. Pacetti B ,P. Patteri A , M. Pelizaeus , H. P. Peng , K. Peters , J. L. Ping , R. G. Ping , R. Poling , Y. N. Pu , M. Qi , S. Qian ,C. F. Qiao , L. Q. Qin , N. Qin , X. S. Qin , Y. Qin , Z. H. Qin , J. F. Qiu , K. H. Rashid , C. F. Redmer ,H. L. Ren , M. Ripka , G. Rong , X. D. Ruan , V. Santoro A , A. Sarantsev ,e , M. Savri´e B , K. Schoenning ,S. Schumann , W. Shan , M. Shao , C. P. Shen , X. Y. Shen , H. Y. Sheng , M. R. Shepherd , W. M. Song ,X. Y. Song , S. Sosio A, C , S. Spataro A, C , B. Spruck , G. X. Sun , J. F. Sun , S. S. Sun , Y. J. Sun , Y. Z. Sun ,Z. J. Sun , Z. T. Sun , C. J. Tang , X. Tang , I. Tapan C , E. H. Thorndike , M. Tiemens , D. Toth , M. Ullrich ,I. Uman B , G. S. Varner , B. Wang , B. L. Wang , D. Wang , D. Y. Wang , K. Wang , L. L. Wang , L. S. Wang ,M. Wang , P. Wang , P. L. Wang , Q. J. Wang , S. G. Wang , W. Wang , X. F. Wang , Y. D. Wang A , Y. F. Wang ,Y. Q. Wang , Z. Wang , Z. G. Wang , Z. H. Wang , Z. Y. Wang , D. H. Wei , J. B. Wei , P. Weidenkaff , S. P. Wen ,M. Werner , U. Wiedner , M. Wolke , L. H. Wu , Z. Wu , L. G. Xia , Y. Xia , D. Xiao , Z. J. Xiao , Y. G. Xie ,Q. L. Xiu , G. F. Xu , L. Xu , Q. J. Xu , Q. N. Xu , X. P. Xu , Z. Xue , L. Yan , W. B. Yan , W. C. Yan ,Y. H. Yan , H. X. Yang , L. Yang , Y. Yang , Y. X. Yang , H. Ye , M. Ye , M. H. Ye , B. X. Yu , C. X. Yu ,H. W. Yu , J. S. Yu , C. Z. Yuan , W. L. Yuan , Y. Yuan , A. Yuncu B,f , A. A. Zafar , A. Zallo A , S. L. Zang ,Y. Zeng , B. X. Zhang , B. Y. Zhang , C. Zhang , C. C. Zhang , D. H. Zhang , H. H. Zhang , H. Y. Zhang , J. J. Zhang ,J. Q. Zhang , J. W. Zhang , J. Y. Zhang , J. Z. Zhang , L. Zhang , S. H. Zhang , X. J. Zhang , X. Y. Zhang , Y. Zhang ,Y. H. Zhang , Z. H. Zhang , Z. P. Zhang , Z. Y. Zhang , G. Zhao , J. W. Zhao , J. Z. Zhao , Lei Zhao , Ling Zhao ,M. G. Zhao , Q. Zhao , Q. W. Zhao , S. J. Zhao , T. C. Zhao , Y. B. Zhao , Z. G. Zhao , A. Zhemchugov ,g , B. Zheng ,J. P. Zheng , Y. H. Zheng , B. Zhong , L. Zhou , Li Zhou , X. Zhou , X. R. Zhou , X. Y. Zhou , K. Zhu , K. J. Zhu ,X. L. Zhu , Y. C. Zhu , Y. S. Zhu , Z. A. Zhu , J. Zhuang , B. S. Zou , J. H. Zou (BESIII Collaboration) Institute of High Energy Physics, Beijing 100049, People’s Republic of China Beihang University, Beijing 100191, People’s Republic of China Bochum Ruhr-University, D-44780 Bochum, Germany Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA Central China Normal University, Wuhan 430079, People’s Republic of China China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany Guangxi Normal University, Guilin 541004, People’s Republic of China GuangXi University, Nanning 530004, People’s Republic of China Hangzhou Normal University, Hangzhou 310036, People’s Republic of China Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany Henan Normal University, Xinxiang 453007, People’s Republic of China Henan University of Science and Technology, Luoyang 471003, People’s Republic of China Huangshan College, Huangshan 245000, People’s Republic of China Hunan University, Changsha 410082, People’s Republic of China Indiana University, Bloomington, Indiana 47405, USA (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia,Italy (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands Lanzhou University, Lanzhou 730000, People’s Republic of China Liaoning University, Shenyang 110036, People’s Republic of China Nanjing Normal University, Nanjing 210023, People’s Republic of China Nanjing University, Nanjing 210093, People’s Republic of China Nankai University, Tianjin 300071, People’s Republic of China Peking University, Beijing 100871, People’s Republic of China Seoul National University, Seoul, 151-747 Korea Shandong University, Jinan 250100, People’s Republic of China Shanxi University, Taiyuan 030006, People’s Republic of China Sichuan University, Chengdu 610064, People’s Republic of China Soochow University, Suzhou 215006, People’s Republic of China Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China Tsinghua University, Beijing 100084, People’s Republic of China (A)Ankara University, Dogol Caddesi, 06100 Tandogan, Ankara, Turkey; (B)Dogus University, 34722 Istanbul, Turkey;(C)Uludag University, 16059 Bursa, Turkey Universitaet Giessen, D-35392 Giessen, Germany University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China University of Hawaii, Honolulu, Hawaii 96822, USA University of Minnesota, Minneapolis, Minnesota 55455, USA University of Rochester, Rochester, New York 14627, USA University of Science and Technology of China, Hefei 230026, People’s Republic of China University of South China, Hengyang 421001, People’s Republic of China University of the Punjab, Lahore-54590, Pakistan (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN,I-10125, Turin, Italy Uppsala University, Box 516, SE-75120 Uppsala, Sweden Wuhan University, Wuhan 430072, People’s Republic of China Zhejiang University, Hangzhou 310027, People’s Republic of China Zhengzhou University, Zhengzhou 450001, People’s Republic of China a Also at the Novosibirsk State University, Novosibirsk, 630090, Russia b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia and at the Functional ElectronicsLaboratory, Tomsk State University, Tomsk, 634050, Russia c Currently at Istanbul Arel University, Kucukcekmece, Istanbul, Turkey d Also at University of Texas at Dallas, Richardson, Texas 75083, USA e Also at the PNPI, Gatchina 188300, Russia f Also at Bogazici University, 34342 Istanbul, Turkey g Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
Using 1 . × ψ (3686) events recorded in e + e − collisions at √ s = 3.686 GeV with the BESIIIat the BEPCII collider, we present searches for C-parity violation in J/ψ → γγ and γφ decays via ψ (3686) → J/ψπ + π − . No significant signals are observed in either channel. Upper limits on thebranching fractions are set to be B ( J/ψ → γγ ) < . × − and B ( J/ψ → γφ ) < . × − at the90% confidence level. The former is one order of magnitude more stringent than the previous upperlimit, and the latter represents the first limit on this decay channel. PACS numbers: 11.30.Er, 13.25.Gv, 12.38.Qk
I. INTRODUCTION
The charge conjugation (C) operation transforms aparticle into its antiparticle and vice versa. In the Stan- dard Model (SM), C invariance is held in strong andelectromagnetic (EM) interactions. Until now, no C-violating processes have been observed in EM interac-tions [1]. While both C-parity and P-parity can be vio-lated in the weak sector of the electroweak interactions inthe SM, evidence for C violation in the EM sector wouldimmediately indicate physics beyond the SM.Tests of C invariance in EM interactions have been car-ried out by many experiments [1]. In
J/ψ decays, how-ever, only the channel
J/ψ → γγ has been studied [2–5],and the corresponding best upper limit on the branch-ing fraction is 5 × − , measured by the CLEO Col-laboration. In this paper, we report on searches for thedecays of J/ψ → γγ and γφ via ψ (3686) → J/ψπ + π − .The analysis is based on a data sample correspondingto 1 . × ψ (3686) events collected at √ s = 3.686GeV (referred to as on-resonance data) [6] and a data setof 44.5 pb − collected at 3.650 GeV (referred to as off-resonance data) [7] with the Beijing Spectrometer (BE-SIII). II. BESIII AND BEPCII
The BESIII detector at the BEPCII [8] double-ring e + e − collider is a major upgrade of the BESII experimentat the Beijing Electron-Positron Collider (BEPC) [9] forstudies of physics in the τ -charm energy region [10]. Thedesign peak luminosity of BEPCII is 10 cm − s − ata beam current of 0.93 A. Until now, the achieved peakluminosity is 7 . × cm − s − at 3773 MeV. TheBESIII detector, with a geometrical acceptance of 93%of 4 π , consists of the following main components. (1) Asmall-celled main drift chamber (MDC) with 43 layersis used to track charged particles. The average single-wire resolution is 135 µ m, and the momentum resolutionfor 1 GeV/ c charged particles in a 1 T magnetic field is0.5%. (2) An EM calorimeter (EMC) is used to measurephoton energies. The EMC is made of 6240 CsI (Tl)crystals arranged in a cylindrical shape (barrel) plus twoend caps. For 1.0 GeV photons, the energy resolutionis 2.5% in the barrel and 5% in the end-caps, and theposition resolution is 6 mm in the barrel and 9 mm inthe end caps. (3) A time-of-flight system (TOF) is usedfor particle identification. It is composed of a barrel madeof two layers, each consisting of 88 pieces of 5 cm thickand 2.4 m long plastic scintillators, as well as two end-caps with 96 fan-shaped, 5 cm thick, plastic scintillatorsin each end cap. The time resolution is 80 ps in the barreland 110 ps in the end caps, providing a K/π separationof more than 2 σ for momenta up to about 1.0 GeV/ c .(4) The muon chamber system is made of resistive platechambers arranged in 9 layers in the barrel and 8 layers inthe end-caps and is incorporated into the return iron yokeof the superconducting magnet. The position resolutionis about 2 cm.The optimization of the event selection and the esti-mation of background contributions from ψ (3686) decaysare performed through Monte Carlo (MC) simulations.The GEANT4 -based simulation software
BOOST [11]includes the geometric and material description of theBESIII detectors, the detector response and digitiza- tion models, as well as a record of the detector run-ning conditions and performances. The production of the ψ (3686) resonance is simulated by the MC event genera-tor KKMC [12], while the decays are generated by
EVT-GEN [13] for known decay modes with branching ratiosbeing set to the PDG [14] world average values, and by
LUNDCHARM [15] for the remaining unknown decays.The process of ψ (3686) → J/ψπ + π − is generated accord-ing to the formulas and measured results in Ref. [16],which takes the small D-wave contribution into account.The signal channels, J/ψ → γγ and γφ , are generated ac-cording to phase space. The process φ → K + K − is gen-erated using a sin θ distribution, where θ is the helicityangle of the kaon defined in the φ center-of-mass system.To obtain upper limits from the measured distributions,we test both the Bayesian method [17] and the Feldman-Cousins construction [18] and choose for each channel themethod resulting in the most stringent upper limit. III. SEARCH FOR
J/ψ → γγ To search for
J/ψ → γγ via ψ (3686) → J/ψπ + π − ,candidate events with the topology γγπ + π − are selectedusing the following criteria. For each candidate event,we require that at least two charged tracks are recon-structed in the MDC and that the polar angles of thetracks satisfy | cos θ | < .
93. The tracks are requiredto pass within ±
10 cm of the interaction point along thebeam direction and within ± | cos θ | < .
80) or 50 MeV in the end-cap region(0 . < | cos θ | < . ≤ t ≤
14 in units of50 ns) are used to suppress electronic noise and energydeposits unrelated to the event. Only events with exactlytwo photon candidates are retained for further analysis.In addition, the energies of both photons are required tobe greater than 1.0 GeV.Two oppositely charged tracks, with momentum lessthan 0.45 GeV/ c , are selected and assumed to be pionswithout particle identification. We impose | cos θ π + π − | < .
95 to exclude random combinations and reject back-grounds from e + e − → γγe + e − events, where θ π + π − isthe angle between the two oppositely charged tracks.A kinematic fit enforcing energy-momentum conserva-tion is performed under the γγπ + π − hypothesis, and theobtained χ value of the fit is required to be χ < π + π − , M rec π + π − , whichis calculated using the momentum vectors of the corre-sponding tracks measured in the MDC. Figure 1 showsthe resulting distribution of M rec π + π − from the candidatesfor ψ (3686) → J/ψπ + π − , J/ψ → γγ from on-resonancedata. A J/ψ signal is clearly observed, which, as in-dicated by the studies described later, is dominated bybackgrounds. The M rec π + π − spectrum is fitted using anunbinned maximum likelihood fit. The J/ψ signal lineshape is extracted from a control sample, ψ (3686) → J/ψπ + π − , J/ψ → µ + µ − , selected from the on-resonancedata. A first-order Chebychev polynomial is used to de-scribe the non-peaking background. The fit determinesthe number of observed events to be N obs = 29 . ± . ) (GeV/c - π + π rec M ) E v e n t s / ( . G e V / c Figure 1. The M rec π + π − (calculated from MDC measurements)distribution for ψ (3686) → J/ψπ + π − , J/ψ → γγ candidateevents from on-resonance data. The solid curve shows theglobal fit results and the dashed line indicates the non-peakingbackgrounds. The main peaking backgrounds come from ψ (3686) → J/ψπ + π − , J/ψ → γπ , γη, γη c and 3 γ ( π /η/η c → γγ ).Large exclusive MC samples are generated to study thepeaking backgrounds, where J/ψ → γπ and γη are gen-erated by the HELAMP generator of EVTGEN [13] tomodel the angular distribution; the other exclusive MCsamples are generated according to phase space. Thesame signal extraction procedure is performed on eachexclusive MC sample. Then the contribution of each indi-vidual process is estimated by normalizing the yields sep-arately according to the equivalent generated luminosi-ties and the branching fractions taken from the PDG [1].The normalized number of background events for thepeaking backgrounds are summarized in Table I. Contri-butions from other background channels such as J/ψ → γf , f → π π and J/ψ → γη ′ , η ′ → π π η, η → γγ are negligible. The backgrounds from continuum pro-cesses are studied with the off-resonance data. No peak-ing background is identified from those. Summing up thecontributions of the individual channels, we obtain a to-tal of 45 . ± . J/ψ → γπ and J/ψ → γη are expected to yield the dominant contribution tothe peaking background, we perform further studies onthese channels. We examine the branching fractions with106 M simulated inclusive ψ (3686) events and find goodagreement between the branching fractions used as inputto the simulation and the one measured on this MC sam-ple. We also roughly measure the branching fractions ofboth channels with the same data set and find resultsconsistent with those listed at PDG [1]. The smoothbackgrounds visible in Fig. 1 are also reasonably welldescribed by the background sources mentioned above.These studies indicate that the above background esti-mation is reliable. Table I. The expected number of peaking background events( N bkg ) for J/ψ → γγ . The uncertainties include the statisti-cal uncertainty and uncertainty of all intermediate resonancedecay branching fractions.Background channel Expected counts ( N bkg ) J/ψ → γπ , π → γ . ± . J/ψ → γη, η → γ . ± . J/ψ → γη c , η c → γ . ± . J/ψ → γ . ± . . ± . After subtracting the background events from the to-tal yields, we obtain the net number of events as N net = − . ± .
5. Both methods to obtain upper limits aretested, and the Feldman-Cousins method, the one result-ing in a more stringent upper limit, is chosen. Accordingto the Feldman-Cousins method, assuming a Gaussiandistribution and constraining the net number to be non-negative, the upper limit on the number of
J/ψ → γγ events is estimated to be N upsig = 2 . IV. SEARCH FOR
J/ψ → γφ To search for
J/ψ → γφ via ψ (3686) → J/ψπ + π − ,candidate events with the topology γK + K − π + π − areselected using the following criteria. The selection cri-teria for charged tracks and photons are the same asthose listed in Section III. Candidate events must havefour charged tracks with zero net charge and at least onephoton with energy greater than 1.0 GeV. The selectioncriteria for π + π − are the same as before except that werequire cos θ π + π − < .
95 in this case to exclude randomcombinations.For other charged particles, the particle identification(PID) confidence levels are calculated from the dE/dx and time-of-flight measurements under a pion, kaon orproton hypothesis. For kaon candidates, we require thatthe confidence level for the kaon hypothesis is larger thanthe corresponding confidence levels for the pion and pro-ton hypotheses. Two kaons with opposite charge are re-quired in each candidate event.All combinations of the four charged tracks with onehigh energetic photon are subjected to a kinematic fitimposing energy-momentum conservation. Candidateswith χ <
40 are accepted. If more than one com-bination from photons satisfies the selection criteria inan event, only the combination with the minimum χ is retained. Finally, only events are retained in whichthe mass recoiling against the di-pion system satisfies3 . < M rec π + π − < .
112 GeV/ c .The candidate signal events are studied by examiningthe invariant K + K − mass, M K + K − , where the momentaobtained from the kinematic fit are used to improve themass resolution. Figure 2 shows the resulting M K + K − spectrum for ψ (3686) → J/ψπ + π − , J/ψ → γφ, φ → K + K − candidates selected from on-resonance data.An unbinned maximum likelihood fit is performed toextract the number of reconstructed candidate eventsfrom the K + K − invariant-mass spectrum. The φ sig-nal line shape is extracted from a MC simulation. A firstorder Chebychev polynomial is used to describe the back-ground, which is shown in Fig. 2. The fit yields 0 . ± . ψ (3686) → J/ψπ + π − , J/ψ → γf (1270) , π K + K − and π a . There are no candidatesfrom the off-resonance data observed; we therefore ne-glect the contribution from continuum processes.To obtain the upper limit, both methods are tested andin this case the Bayesian method is chosen. We determinethe upper limit on the observed number of events ( N upsig )with the Bayesian method at the 90% C.L. as R N upsig L dN sig R ∞ L dN sig = 0 . , where L is the value of likelihood as a function of N sig .The upper limit on the number of J/ψ → γφ is deter-mined to be 6.9. V. SYSTEMATIC UNCERTAINTIES
The systematic uncertainties in the measurements aresummarized in Table II.The uncertainties in the tracking efficiency and kaonidentification have been studied in Ref. [19], which are2.0% per track and 2.0% per kaon, respectively.The energies of the photons in both channels aregreater than 1.0 GeV. The uncertainty due to the detec-tion efficiency of high energy photons is estimated to beless than 0.25% using
J/ψ → γη ′ , described in Ref. [20].We therefore assign 0.25% per photon as the systematicuncertainty for photon detection. ) (GeV/c - K + K M ) E v e n t s / ( . G e V / c Figure 2. The M K + K − distribution for ψ (3686) → J/ψπ + π − , J/ψ → γφ, φ → K + K − candidate events from on-resonance data. The solid line shows the global fit results andthe dashed line shows the background, and they are overlapeach other. The region between the arrows contains about90% of the signal according to MC simulation. The uncertainty of the kinematic fit for the
J/ψ → γγ channel is estimated from a control sample of ψ (3686) → γη ′ , η ′ → γρ , ρ → π + π − . The efficiency is obtainedfrom the change in the yield of η ′ signal by a fit to the γπ + π − invariant-mass spectrum with or without the re-quirement of χ <
40 of the kinematic fit. The sys-tematic uncertainty is determined to be 1.9%. The un-certainty of the kinematic fit for the
J/ψ → γφ channelis estimated to be 3.5% from ψ (3686) → γχ cJ , χ cJ → K + K − π + π − .The uncertainty associated with the requirement onthe number of good photons ( N γ ) for the J/ψ → γγ chan-nel is estimated by using a control sample of ψ (3686) → J/ψπ + π − , J/ψ → γη, η → γγ events. The differencesof selection efficiencies with and without the N γ require-ment ( N γ = 3 for the control sample) between data andMC is 3.0%, which is taken as the systematic uncertaintydue to the N γ requirement.By comparing the differences of selection efficiencieswith and without the cos θ π + π − requirement betweendata and MC, the uncertainties due to this requirementfor both channels are estimated to be 0.9% and 0.8%,respectively.The uncertainty due to the requirement of M rec π + π − tobe within the J/ψ signal region for
J/ψ → γφ is es-timated as 1.4% by comparing the selection efficienciesbetween data and MC.The uncertainties due to the details of the fit proce-dure are estimated by repeating the fit with appropriatemodifications. Different fit ranges (4 ranges) and differ-ent orders of the polynomial (1 st and 2 nd orders) are usedin the fits. For J/ψ → γγ , the uncertainty is estimatedby averaging the differences of the obtained yields withrespect to the values derived from the standard fit. For J/ψ → γφ , the uncertainty is estimated as the maximumdifference between the obtained upper limits and the up-per limit derived from the standard fit. The uncertaintiesfrom fitting are estimated as 2.7% and 1.5%, respectively.The branching fractions for ψ (3686) → J/ψπ + π − and φ → K + K − decays are taken from the PDG [1]. The un-certainties of the branching fractions are taken as system-atic uncertainties in the measurements, which are 1.2%and 1.0%, respectively.The uncertainty in the number of ψ (3686) eventsis 0.81%, which is measured by inclusive hadronic de-cays [6].Adding the uncertainties in quadrature yields total sys-tematic uncertainties of 6.3% and 10.0% for J/ψ → γγ and J/ψ → γφ , respectively. Table II. Summary of the systematic uncertainties (%).Sources
J/ψ → γγ J/ψ → γφ Tracking 4.0 8.0Kaon identification - 4.0Photon detection 0.5 0.3Kinematic fit 1.9 3.5Number of photons 3.0 -cos θ π + π − requirement 0.9 0.8 M rec π + π − requirement - 1.4Fitting 2.7 1.5 B ( ψ (3686) → J/ψπ + π − ) 1.2 1.2 B ( φ → K + K − ) - 1.0Number of ψ (3686) 0.8 0.8Total 6.3 10.0 VI. RESULTS
Since no significant signals are observed, the upper lim-its on the branching fractions are determined by B ( J/ψ → f ) < N upsig N tot ψ (3686) × ǫ × B i × (1 − ∆ sys ) , (1)where N upsig is the upper limit on the number of observedevents for the signal channel; f represents γγ or γφ ; ǫ is the detection efficiency determined by MC simulation; N tot ψ (3686) is the total number of ψ (3686) events, (106 . ± . × ; B i denotes the branching fractions involved(such as B ( ψ (3686) → J/ψπ + π − ) = (34 . ± . B ( φ → K + K − ) = (48 . ± . sys is the totalsystematic uncertainty, and 1 / (1 − ∆ sys ) is introducedto estimate a conservative upper limit on the branchingfraction. The individual values are summarized in Ta-ble III.Inserting N upsig , N tot ψ (3686) , ǫ , B i and ∆ sys into Eq.(1), weobtain B ( J/ψ → γγ ) < . × − and B ( J/ψ → γφ ) < . × − . Table III. Results for both channels. γγ γφN obs . ± . . ± . N bkg . ± . N upsig (90% C.L.) 2.8 6.9 ǫ (%) 30 . ± .
07 30 . ± . B ( J/ψ → ) (this work) < . × − < . × − B ( J/ψ → ) (PDG [1]) < × − - VII. SUMMARY
In this paper, we report on searches for
J/ψ → γγ and J/ψ → γφ . No significant signal is observed. Weset the upper limits B ( J/ψ → γγ ) < . × − and B ( J/ψ → γφ ) < . × − at the 90% C.L. for thebranching fractions of J/ψ decays into γγ and γφ , respec-tively. The upper limit on B ( J/ψ → γγ ) is one order ofmagnitude more stringent than the previous upper limit,and B ( J/ψ → γφ ) is the first upper limit for this channel.Our results are consistent with C-parity conservation ofthe EM interaction. VIII. ACKNOWLEDGEMENTS
The BESIII collaboration thanks the staff of BEPCIIand the IHEP computing center for their strong sup-port. This work is supported in part by NationalKey Basic Research Program of China under ContractNo. 2015CB856700; National Natural Science Founda-tion of China (NSFC) under Contracts Nos. 10935007,11121092, 11125525, 11235011, 11322544, 11335008;Joint Funds of the National Natural Science Founda-tion of China under Contracts Nos. 11079008, 11179007,U1232201, U1332201; the Chinese Academy of Sciences(CAS) Large-Scale Scientific Facility Program; CAS un-der Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45;100 Talents Program of CAS; German Research Foun-dation DFG under Contract No. Collaborative Re-search Center CRC-1044; Istituto Nazionale di FisicaNucleare, Italy; Ministry of Development of Turkey un-der Contract No. DPT2006K-120470; Russian Foun-dation for Basic Research under Contract No. 14-07-91152; U. S. Department of Energy under ContractsNos. DE-FG02-04ER41291, DE-FG02-05ER41374, DE-FG02-94ER40823, DESC0010118; U.S. National Sci-ence Foundation; University of Groningen (RuG) andthe Helmholtzzentrum fuer Schwerionenforschung GmbH(GSI), Darmstadt; WCU Program of National ResearchFoundation of Korea under Contract No. R32-2008-000- 10155-0 [1] J. Beringer et al. [Particle Data Group], Phys. Rev. D , 010001 (2012), and 2013 partial update for the 2014edition.[2] W. Bartel et al. , Phys. Lett. B , 489 (1977).[3] M. Ablikim et al. [BES Collaboration], Phys. Rev. D ,117101 (2007).[4] K. Abe et al. , [Belle Collaboration], Phys. Lett. B ,323 (2008).[5] G. S. Adams et al. [CLEO Collaboration], Phys. Rev.Lett. , 101801 (2008).[6] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 063001 (2013).[7] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 123001 (2013).[8] M. Ablikim et al. [BES Collaboration], Nucl. Instrum.Meth. Phys. Res. A , 345 (2010).[9] J. Z. Bai et al. [BES Collaboration], Nucl. Instrum. Meth.Phys. Res. A , 319 (1994); , 627 (2001).[10] Special issue on Physics at BES-III, edited by K. T. Chaoand Y. F. Wang, Int. J. Mod. Phys. A Supp. (2009). [11] Z. Y. Deng et al. , High Energy Physics & Nuclear Physics , 371 (2006).[12] S. Jadach, B. F. L. Ward, and Z. Was, Comput. Phys.Commun. , 260 (2000); Phys. Rev. D , 113009(2001).[13] R. G. Ping, Chin. Phys. C , 599 (2008); D. J. Lange,Nucl. Instr. Meth. A , 152 (2001).[14] K. Nakamura et al. [Particle Data Group], J. Phys. G ,075021 (2010).[15] J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang andY. S. Zhu, Phys. Rev. D , 034003 (2000).[16] J. Z. Bai et al. [BES Collaboration], Phys. Rev. D ,032002 (2000).[17] Y. S. Zhu, Chin. Phys. C , 363 (2008).[18] G. J. Feldman and R. D. Cousins, Phys. Rev. D , 3873(1998).[19] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D , 112005 (2011).[20] M. Ablikim et al. [BESIII Collaboration], Phys. Rev.Lett.105