Search for new decay modes of the ψ_2(3823) and the process e^+e^-\rightarrowπ^0π^0ψ_2(3823)
M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, Z. J Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, 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, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. G. Gao, I. Garzia, P. T. Ge, C. Geng, E. M. Gersabeck, A Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, C. Y Guan, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, T. T. Han, W. Y. Han, et al. (418 additional authors not shown)
aa r X i v : . [ h e p - e x ] F e b Search for new decay modes of the ψ (3823) and the process e + e − → π π ψ (3823) M. Ablikim , M. N. Achasov ,c , P. Adlarson , S. Ahmed , M. Albrecht , R. Aliberti , A. Amoroso A, C , M. R. An ,Q. An , , X. H. Bai , Y. Bai , O. Bakina , R. Baldini Ferroli A , I. Balossino A , Y. Ban ,k , K. Begzsuren ,N. Berger , M. Bertani A , D. Bettoni A , F. Bianchi A, C , J. Bloms , A. Bortone A, C , I. Boyko , R. A. Briere ,H. Cai , X. Cai , , A. Calcaterra A , G. F. Cao , , N. Cao , , S. A. Cetin A , J. F. Chang , , W. L. Chang , ,G. Chelkov ,b , D. Y. Chen , G. Chen , H. S. Chen , , M. L. Chen , , S. J. Chen , X. R. Chen , Y. B. Chen , ,Z. J Chen ,l , W. S. Cheng C , G. Cibinetto A , F. Cossio C , X. F. Cui , H. L. Dai , , X. C. Dai , , A. Dbeyssi ,R. E. de Boer , 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 , , , X. Dong , S. X. Du , Y. L. Fan , J. Fang , , S. S. Fang , ,Y. Fang , R. Farinelli A , L. Fava B, C , F. Feldbauer , G. Felici A , C. Q. Feng , , J. H. Feng , M. Fritsch , C. D. Fu ,Y. Gao ,k , Y. Gao , Y. Gao , , Y. G. Gao , I. Garzia A, B , P. T. Ge , C. Geng , E. M. Gersabeck , A Gilman ,K. Goetzen , L. Gong , W. X. Gong , , W. Gradl , M. Greco A, C , L. M. Gu , M. H. Gu , , S. Gu , Y. T. Gu ,C. Y Guan , , A. Q. Guo , L. B. Guo , R. P. Guo , Y. P. Guo ,h , A. Guskov , T. T. Han , W. Y. Han , X. Q. Hao ,F. A. Harris , N. H¨usken , , K. L. He , , F. H. Heinsius , C. H. Heinz , T. Held , Y. K. Heng , , , C. Herold ,M. Himmelreich ,f , T. Holtmann , Y. R. Hou , Z. L. Hou , H. M. Hu , , J. F. Hu ,m , T. Hu , , , Y. Hu ,G. S. Huang , , L. Q. Huang , X. T. Huang , Y. P. Huang , Z. Huang ,k , T. Hussain , W. Ikegami Andersson ,W. Imoehl , M. Irshad , , S. Jaeger , S. Janchiv ,j , Q. Ji , Q. P. Ji , X. B. Ji , , X. L. Ji , , Y. Y. Ji , H. B. Jiang ,X. S. Jiang , , , J. B. Jiao , Z. Jiao , S. Jin , Y. Jin , T. Johansson , N. Kalantar-Nayestanaki , X. S. Kang ,R. Kappert , M. Kavatsyuk , B. C. Ke , , I. K. Keshk , A. Khoukaz , P. Kiese , R. Kiuchi , R. Kliemt , L. Koch ,O. B. Kolcu A,e , B. Kopf , M. Kuemmel , M. Kuessner , A. Kupsc , M. G. Kurth , , W. K¨uhn , J. J. Lane ,J. S. Lange , P. Larin , A. Lavania , L. Lavezzi A, C , Z. H. Lei , , H. Leithoff , M. Lellmann , T. Lenz , C. Li ,C. H. Li , Cheng Li , , D. M. Li , F. Li , , G. Li , H. Li , , H. Li , H. B. Li , , H. J. Li , H. J. Li ,h , J. L. Li ,J. Q. Li , J. S. Li , Ke Li , L. K. Li , Lei Li , P. R. Li , S. Y. Li , W. D. Li , , W. G. Li , X. H. Li , , X. L. Li ,Xiaoyu Li , , Z. Y. Li , H. Liang , , H. Liang , , H. Liang , Y. F. Liang , Y. T. Liang , G. R. Liao , L. Z. Liao , ,J. Libby , C. X. Lin , B. J. Liu , C. X. Liu , D. Liu , , F. H. Liu , Fang Liu , Feng Liu , H. B. Liu , H. M. Liu , ,Huanhuan Liu , Huihui Liu , J. B. Liu , , J. L. Liu , J. Y. Liu , , K. Liu , K. Y. Liu , Ke Liu , L. Liu , ,M. H. Liu ,h , P. L. Liu , Q. Liu , Q. Liu , S. B. Liu , , Shuai Liu , T. Liu , , W. M. Liu , , X. Liu , Y. Liu ,Y. B. Liu , Z. A. Liu , , , Z. Q. Liu , X. C. Lou , , , F. X. Lu , F. X. Lu , H. J. Lu , J. D. Lu , , J. G. Lu , ,X. L. Lu , Y. Lu , Y. P. Lu , , C. L. Luo , M. X. Luo , P. W. Luo , T. Luo ,h , X. L. Luo , , S. Lusso C , X. R. Lyu ,F. C. Ma , H. L. Ma , L. L. Ma , M. M. Ma , , Q. M. Ma , R. Q. Ma , , R. T. Ma , X. X. Ma , , X. Y. Ma , ,F. E. Maas , M. Maggiora A, C , S. Maldaner , S. Malde , Q. A. Malik , A. Mangoni B , Y. J. Mao ,k , Z. P. Mao ,S. Marcello A, C , Z. X. Meng , J. G. Messchendorp , G. Mezzadri A , T. J. Min , R. E. Mitchell , X. H. Mo , , ,Y. J. Mo , N. Yu. Muchnoi ,c , H. Muramatsu , S. Nakhoul ,f , Y. Nefedov , F. Nerling ,f , I. B. Nikolaev ,c , Z. Ning , ,S. Nisar ,i , S. L. Olsen , Q. Ouyang , , , S. Pacetti B, C , X. Pan ,h , Y. Pan , A. Pathak , P. Patteri A , M. Pelizaeus ,H. P. Peng , , K. Peters ,f , J. Pettersson , J. L. Ping , R. G. Ping , , R. Poling , V. Prasad , , H. Qi , ,H. R. Qi , K. H. Qi , M. Qi , T. Y. Qi , T. Y. Qi , S. Qian , , W. B. Qian , Z. Qian , C. F. Qiao , L. Q. Qin ,X. P. Qin , X. S. Qin , Z. H. Qin , , J. F. Qiu , S. Q. Qu , K. H. Rashid , K. Ravindran , C. F. Redmer ,A. Rivetti C , V. Rodin , M. Rolo C , G. Rong , , Ch. Rosner , M. Rump , H. S. Sang , A. Sarantsev ,d ,Y. Schelhaas , C. Schnier , K. Schoenning , M. Scodeggio A, B , D. C. Shan , W. Shan , X. Y. Shan , ,J. F. Shangguan , M. Shao , , C. P. Shen , P. X. Shen , X. Y. Shen , , H. C. Shi , , R. S. Shi , , X. Shi , ,X. D Shi , , J. J. Song , W. M. Song , , Y. X. Song ,k , S. Sosio A, C , S. Spataro A, C , K. X. Su , P. P. Su , F. F.Sui , G. X. Sun , H. K. Sun , J. F. Sun , L. Sun , S. S. Sun , , T. Sun , , W. Y. Sun , W. Y. Sun , X Sun ,l ,Y. J. Sun , , Y. K. Sun , , Y. Z. Sun , Z. T. Sun , Y. H. Tan , Y. X. Tan , , C. J. Tang , G. Y. Tang , J. Tang ,J. X. Teng , , V. Thoren , Y. T. Tian , I. Uman B , B. Wang , C. W. Wang , D. Y. Wang ,k , H. J. Wang ,H. P. Wang , , K. Wang , , L. L. Wang , M. Wang , M. Z. Wang ,k , Meng Wang , , W. Wang , W. H. Wang ,W. P. Wang , , X. Wang ,k , X. F. Wang , X. L. Wang ,h , Y. Wang , Y. Wang , , Y. D. Wang , Y. F. Wang , , ,Y. Q. Wang , Y. Y. Wang , Z. Wang , , Z. Y. Wang , Ziyi Wang , Zongyuan Wang , , D. H. Wei , P. Weidenkaff ,F. Weidner , S. P. Wen , D. J. White , U. Wiedner , G. Wilkinson , M. Wolke , L. Wollenberg , J. F. Wu , , L. H. Wu ,L. J. Wu , , X. Wu ,h , Z. Wu , , L. Xia , , H. Xiao ,h , S. Y. Xiao , Z. J. Xiao , X. H. Xie ,k , Y. G. Xie , , Y. H. Xie ,T. Y. Xing , , G. F. Xu , Q. J. Xu , W. Xu , , X. P. Xu , Y. C. Xu , F. Yan ,h , L. Yan ,h , W. B. Yan , , W. C. Yan ,Xu Yan , H. J. Yang ,g , H. X. Yang , L. Yang , S. L. Yang , Y. X. Yang , Yifan Yang , , Zhi Yang , M. Ye , ,M. H. Ye , J. H. Yin , Z. Y. You , B. X. Yu , , , C. X. Yu , G. Yu , , J. S. Yu ,l , T. Yu , C. Z. Yuan , , L. Yuan ,X. Q. Yuan ,k , Y. Yuan , Z. Y. Yuan , C. X. Yue , A. Yuncu A,a , A. A. Zafar , Y. Zeng ,l , B. X. Zhang ,Guangyi Zhang , H. Zhang , H. H. Zhang , H. H. Zhang , H. Y. Zhang , , J. J. Zhang , J. L. Zhang , J. Q. Zhang ,J. W. Zhang , , , J. Y. Zhang , J. Z. Zhang , , Jianyu Zhang , , Jiawei Zhang , , L. M. Zhang , L. Q. Zhang ,Lei Zhang , S. Zhang , S. F. Zhang , Shulei Zhang ,l , X. D. Zhang , X. Y. Zhang , Y. Zhang , Y. H. Zhang , ,Y. T. Zhang , , Yan Zhang , , Yao Zhang , Yi Zhang ,h , Z. H. Zhang , Z. Y. Zhang , G. Zhao , J. Zhao ,J. Y. Zhao , , J. Z. Zhao , , Lei Zhao , , Ling Zhao , M. G. Zhao , Q. Zhao , S. J. Zhao , Y. B. Zhao , , Y. X. Zhao ,Z. G. Zhao , , A. Zhemchugov ,b , B. Zheng , J. P. Zheng , , Y. Zheng ,k , Y. H. Zheng , B. Zhong , C. Zhong ,L. P. Zhou , , Q. Zhou , , X. Zhou , X. K. Zhou , X. R. Zhou , , X. Y. Zhou , A. N. Zhu , , J. Zhu , K. Zhu ,K. J. Zhu , , , S. H. Zhu , T. J. Zhu , W. J. Zhu , W. J. Zhu ,h , Y. C. Zhu , , Z. A. Zhu , , B. S. Zou , J. H. Zou Typeset by REVTEX (BESIII Collaboration) Institute of High Energy Physics, Beijing 100049, People’s Republic of China Beihang University, Beijing 100191, People’s Republic of China Beijing Institute of Petrochemical Technology, Beijing 102617, 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 University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan Fudan University, Shanghai 200443, People’s Republic of China 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 Normal University, Changsha 410081, People’s Republic of China Hunan University, Changsha 410082, People’s Republic of China Indian Institute of Technology Madras, Chennai 600036, India Indiana University, Bloomington, Indiana 47405, USA INFN Laboratori Nazionali di Frascati , (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFNSezione di Perugia, I-06100, Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy INFN Sezione di Ferrara, (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara,Italy Institute of Modern Physics, Lanzhou 730000, People’s Republic of China Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia Jilin University, Changchun 130012, People’s Republic of China Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany Lanzhou University, Lanzhou 730000, People’s Republic of China Liaoning Normal University, Dalian 116029, 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 North China Electric Power University, Beijing 102206, People’s Republic of China Peking University, Beijing 100871, People’s Republic of China Qufu Normal University, Qufu 273165, People’s Republic of China Shandong Normal University, Jinan 250014, People’s Republic of China Shandong University, Jinan 250100, People’s Republic of China Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China Shanxi Normal University, Linfen 041004, 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 South China Normal University, Guangzhou 510006, People’s Republic of China Southeast University, Nanjing 211100, People’s Republic of China State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China Suranaree University of Technology, University Avenue 111, Nakhon Ratchasima 30000, Thailand Tsinghua University, Beijing 100084, People’s Republic of China Turkish Accelerator Center Particle Factory Group, (A)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (B)NearEast University, Nicosia, North Cyprus, Mersin 10, Turkey University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China University of Groningen, NL-9747 AA Groningen, The Netherlands University of Hawaii, Honolulu, Hawaii 96822, USA University of Jinan, Jinan 250022, People’s Republic of China University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom University of Minnesota, Minneapolis, Minnesota 55455, USA University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany University of Oxford, Keble Rd, Oxford, UK OX13RH University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China 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 University of Turin and INFN, (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 Xinyang Normal University, Xinyang 464000, 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 Bogazici University, 34342 Istanbul, Turkey b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia c Also at the Novosibirsk State University, Novosibirsk, 630090, Russia d Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia e Also at Istanbul Arel University, 34295 Istanbul, Turkey f Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany g Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratoryfor Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China h Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, FudanUniversity, Shanghai 200443, People’s Republic of China i Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA j Currently at: Institute of Physics and Technology, Peace Ave.54B, Ulaanbaatar 13330, Mongolia k Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’s Republic ofChina l School of Physics and Electronics, Hunan University, Changsha 410082, China m Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China NormalUniversity, Guangzhou 510006, China
The decays ψ (3823) → γχ c , , , π + π − J/ψ, π π J/ψ, ηJ/ψ , and π J/ψ are searched for usingthe reaction e + e − → π + π − ψ (3823) in a 19 fb − data sample collected at center-of-mass energiesbetween 4.1 and 4.7 GeV with the BESIII detector. The process ψ (3823) → γχ c is observedin a 9 fb − data sample in the center-of-mass energy range 4.3 to 4.7 GeV, which confirms aprevious observation but with a higher significance of 11 . σ , and evidence for ψ (3823) → γχ c isfound with a significance of 3 . σ for the first time. The branching-fraction ratio B ( ψ (3823) → γχ c ) B ( ψ (3823) → γχ c ) is determined. No significant ψ (3823) signals are observed for any of the other decay channels.Upper limits of branching-fraction ratios for ψ (3823) → π + π − J/ψ, π π J/ψ, ηJ/ψ, π J/ψ, γχ c relative to ψ (3823) → γχ c are reported. The process e + e − → π π ψ (3823) is also searched for,and we find evidence for the process with a significance of 4 . σ . The average cross-section ratio σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) is also determined. Charmonium, the bound state of a charm quark andanticharm quark ( c ¯ c ), plays an important role in our un-derstanding of quantum chromodynamics (QCD), whichis the fundamental theory of the strong interaction. Lowenergy QCD remains a field of high interest both experi-mentally and theoretically. All charmonium states belowthe open-charm ( D ¯ D ) threshold have been observed ex-perimentally and can be well described by potential mod-els [1]. However, the understanding of the spectrum thatis above the D ¯ D threshold remains unsettled. During thepast decade, many new charmonium-like states have beendiscovered, such as the X (3872), Y (4260), Z c (3900), and Z cs (3985) [2–5]. These are good candidates for exotic states that lie outside the conventional quark model asdiscussed in Refs. [6–9]. On the other hand, there arestill excited charmonium states above the D ¯ D thresholdpredicted by potential models, which have not yet beenobserved. Thus, a more complete understanding of thecharmonium(-like) spectrum is necessary to identify con-ventional and exotic states.The lightest charmonium resonance above the D ¯ D threshold is the ψ (3770), which is identified as the ψ (1 D ) state, the J = 1 member of the D -wave spin-triplet [10]. Recently, two more states have been ob-served, which are considered to be good candidates formembers of this spin-triplet. The ψ (3823), for whichfirst evidence was found by the Belle Collaboration andwhich was later observed by the BESIII Collaborationin ψ (3823) → γχ c , is considered to be the ψ (1 D )state [11, 12]. The LHCb Collaboration also observedthe ψ (3823) in its decay to π + π − J/ψ [13]. The othernewly observed resonance is the ψ (3842) seen by LHCbCollaboration in ψ (3842) → D ¯ D [14]. It is suggested tobe the ψ (1 D ) state.The motivation of this Letter is to provide addition-al experimental evidence for the correct assignment ofthe ψ (3823) to be the J = 2 spin-triplet partner,by comparing its decay channels to the theory predic-tions of Refs. [15–24]. Experimental information onthe ψ (3823) is still sparse. The partial widths fordecays of the ψ (1 D ) state to several channels havebeen predicted by various different models. These mod-els agree that the dominant decay of the ψ (1 D ) isto γχ c , with the next most probable decays being to γχ c and to π + π − J/ψ . The branching-fraction ratios B ( ψ (1 D ) → γχ c ) B ( ψ (1 D ) → γχ c ) and B ( ψ (1 D ) → π + π − J/ψ ) B ( ψ (1 D ) → γχ c ) are predictedto be 0 . ∼ .
32 and 0 . ∼ .
39, respectively [15–24].In this Letter, a search for ψ (3823) → γχ c , , , π + π − J/ψ , π π J/ψ , ηJ/ψ , and π J/ψ is reported, us-ing e + e − → π + π − ψ (3823) events from a 19 fb − data sample collected at center-of-mass energy in therange 4 . < √ s < . e + e − → π π ψ (3823) with ψ (3823) → γχ c .The BESIII detector is a magnetic spectrometer locat-ed at the Beijing Electron Positron Collider (BEPCII).For more details on the detector or the accelerator, werefer to Refs. [25–27]. Simulated samples producedwith the Geant4 -based [28] Monte Carlo (MC) package,which includes the geometric description of the BESIIIdetector and the detector response, are used to deter-mine the detection efficiency and to estimate backgroundcontributions. The simulation includes the beam energyspread and initial-state radiation (ISR) in e + e − annihi-lations modeled with the generator kkmc [29]. SignalMC samples for e + e − → ππψ (3823) are generated us-ing isotropic phase space populations, assuming that thecross section follows a coherent sum of ψ (4360) and the ψ (4660) Breit-Wigner (BW) distributions, whose magni-tude and phase parameters we obtain from a fit to theobserved cross section, with the ψ (3823) mass fixed tothe Particle Data Group (PDG) value [10] and widthfixed to zero. The subsequent ψ (3823) decays are gen-erated uniformly in the phase space, and the effects fromthe angular distributions of ψ (3823) decays are studiedand found to be small. Inclusive MC samples consist ofthe production of open charm processes, the ISR produc-tion of vector charmonium(-like) states, and the contin-uum processes incorporated in kkmc [29]. Known de-cay modes are modeled with evtgen [30] using branch-ing fractions summarized and averaged by the PDG [10]. The remaining unknown decays from the charmoniumstates are generated with lundcharm [31]. Final stateradiation from charged final-state particles is incorporat-ed with the photos package [32].The χ c , are reconstructed via χ c , → γJ/ψ decays,the J/ψ is reconstructed in its decay to an e + e − or µ + µ − pair, the π and η are reconstructed via π /η → γγ de-cays, and the χ c is reconstructed in its decay to a π + π − or K + K − pair. For each charged track, the distance ofclosest approach to the interaction point is required tobe within ±
10 cm in the beam direction and within 1 cmin the plane perpendicular to the beam direction. Thepolar angle ( θ ) of the tracks must be within the fiducialvolume of the multilayer drift chamber ( | cos θ | < . ◦ away from the nearest charged track. The photonenergy is required to be at least 25 MeV in the barrelregion ( | cos θ | < .
8) or 50 MeV in the end-cap region(0 . < | cos θ | < . c are assigned to be leptonsfrom the decay of a J/ψ or to be π/K from the decay ofa χ c . Otherwise, tracks are considered pions. Leptonsfrom the J/ψ decay with an energy deposit in the EMClarger than 1.0 GeV are identified as electrons, and thosewith less than 0.4 GeV as muons. To reduce backgroundcontributions and to improve the mass resolution, a four-constraint kinematic fit is performed to constrain the to-tal four-momentum of the final state particles to the four-momentum of the colliding beams. Additionally, for the ψ (3823) → π π J/ψ and e + e − → π π ψ (3823) chan-nels the invariant masses of the two pairs of photons areconstrained to the nominal mass of the π meson [10].The two track candidates from the decay of χ c mesonsare considered to be either a π + π − or a K + K − pair de-pending on the χ of the four-constraint kinematic fit.If χ ( π + π − ) < χ ( K + K − ), the two tracks are identifiedas a π + π − pair, otherwise, as a K + K − pair. For allthese channels, if there is more than one combination ofphotons in an event, the one with the smallest χ of thekinematic fit is selected. The χ of the candidate processis required to be less than 60 in all cases.Besides the requirements described above, further se-lection criteria are applied. To suppress the back-ground from π /η → γγ in ψ (3823) → γχ c , de-cays, regions around the π and η masses, namely[0 . , .
16] GeV/ c and [0 . , .
58] GeV/ c , in the in-variant mass M ( γγ ) are excluded. In order to removebackground from ψ (3686) → π + π − J/ψ in ψ (3823) → π + π − J/ψ, π π J/ψ, ηJ/ψ, π J/ψ decays, all possible in-variant mass M ( π + π − J/ψ ) combinations are requiredto be outside the region [3 . , . c . Toeliminate background from η ′ → ηπ + π − and χ c → γJ/ψ in ψ (3823) → ηJ/ψ decays, the invariant masses M ( γγπ + π − ) and M ( γ H J/ψ ) are required to be outsidethe regions [0 . , .
97] GeV/ c and [3 . , .
53] GeV/ c respectively, where γ H is the highest energy photon.This condition removes almost all of the η ′ /χ c back-ground. To remove background from η → π π + π − in ψ (3823) → π J/ψ decays, candidates are excluded thathave an invariant mass M ( γγπ + π − ) around the nominal η mass in the region [0 . , .
58] GeV/ c . Finally, to rejectbackground from photon conversion in ψ (3823) → γχ c decays, the cosine of the angle between any two chargedtracks is required to be less than 0.9.The J/ψ signal region is defined by the mass range[3.075, 3.125] GeV/ c in M ( e + e − /µ + µ − ), apart from inthe decay channel ψ (3823) → π + π − J/ψ where the
J/ψ signal region is narrowed to the range [3.09, 3.11] GeV/ c due to the better resolution for the four charged-track fi-nal states. The χ c and χ c signal regions are chosen asthe ranges [3 . , .
53] GeV /c and [3 . , .
57] GeV /c in M ( γ H J/ψ ), respectively, and sideband regions, definedas the ranges [3 . , .
48] GeV /c and [3 . , .
63] GeV /c ,are used to study the non-resonant background. The η , π and χ c signal regions are chosen to be [0.52,0.57] GeV /c and [0.12, 0.15] GeV /c in M ( γγ ), and[3 . , .
44] GeV /c in M ( π + π − /K + K − ), respectively.Figure 1 shows the π + π − recoil-mass distribution RM ( π + π − ) for the γχ c channel. A clear ψ (3823) sig-nal is observed for 9 fb − of data at 4 . < √ s < . ψ (3823) signal is seen for the 10 fb − sample at 4 . < √ s < . χ c sideband region. Thus, only data at 4 . < √ s < . ψ (3823) decay chan-nels. ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c DataSideband c1 χγ (a) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c DataSideband c1 χγ (b) FIG. 1. π + π − recoil-mass distribution RM ( π + π − ) for γχ c channel for the data at 4 . < √ s < . . < √ s < . χ c sidebandregion. Figure 2 shows the distributions of RM ( π + π − ) forthe decays ψ (3823) → γχ c , γχ c , π + π − J/ψ , π π J/ψ , ηJ/ψ , π J/ψ , γχ c and a scatter plot of M ( γ H J/ψ ) ver-sus RM ( π + π − ) for the decays ψ (3823) → γχ c , for ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c c1 χγ (a) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c c2 χγ (b) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c ψ J/ - π + π (c) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c ψ J/ π π (d) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c ψ J/ η (e) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c ψ J/ π (f) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c c0 χγ (g) ) ) (GeV/c - π + π RM(3.78 3.8 3.82 3.84 3.86 3.88 ) ) ( G e V / c ψ J / H γ M ( c1,2 χγ (h) FIG. 2. Results of the simultaneous fits to the seven distri-butions of RM ( π + π − ) for the decays ψ (3823) → γχ c (a), γχ c (b), π + π − J/ψ (c), π π J/ψ (d), ηJ/ψ (e), π J/ψ (f), γχ c (g), and a scatter plot of M ( γ H J/ψ ) versus RM ( π + π − )for the decays ψ (3823) → γχ c , (h) for data at 4 . < √ s < . data at 4 . < √ s < . RM ( π + π − )combinations of the π + π − J/ψ decay are retained. In ad-dition to the ψ (3823) signal observed in the ψ (3823) → γχ c channel, there are also events clustered in the sig-nal region for the mode ψ (3823) → γχ c . No signif-icant ψ (3823) signals are observed for the other chan-nels. Furthermore, in any of these channels, no significant e + e − → π + π − ψ (3842) signals are found. A detailedstudy of the inclusive MC samples indicates that thereare no peaking background contributions in the ψ (3823)signal region [33]. In order to extract the ψ (3823) sig-nal yield, a simultaneous unbinned maximum-likelihoodfit is performed to the seven decay channels. The ex-pected shape of RM ( π + π − ) from the signal process ismodeled by the shape from the MC simulation convolvedwith a Gaussian function. The parameters of mean andwidth are free parameters in the fit, but are constrainedto be the same in all channels. The background is de-scribed by a constant. The solid curves in Fig. 2 showthe fit results. The significances with systematic un-certainty included for the decays ψ (3823) → γχ c and ψ (3823) → γχ c are 11 . σ and 3 . σ , respectively. Forthe other decays, where there are no significant signals,upper limits of the relative branching ratio compared tothe decay ψ (3823) → γχ c at the 90% confidence level(C.L.) are determined. These upper limits are calculatedfrom the likelihood curve of the fits as a function of signalyield after being convolved with a Gaussian distribution,where the width of Gaussian distribution is the quadraticsum of the systematic uncertainty and statistical uncer-tainty of the ψ (3823) → γχ c signal yield. Those limitstogether with the corresponding limits on the number ofsignal events are summarized in Table I. TABLE I. The number of ψ (3823) signal events N ψ (3823) and branching-fraction ratios B ( ψ (3823) → ... ) B ( ψ (3823) → γχ c ) for different ψ (3823) decay channels. For N ψ (3823) only the statisticaluncertainty is shown. For the ratios the first uncertainty isstatistical and the second uncertainty is systematic. The up-per limits at the 90% C.L. are calculated taking into accountboth contributions. Dash means that the result is not appli-cable.Channel N ψ (3823) B ( ψ (3823) → ... ) B ( ψ (3823) → γχ c ) γχ c . ± . − γχ c . +4 . − . . +0 . − . ± . π + π − J/ψ < . < . π π J/ψ < . < . ηJ/ψ < . < . π J/ψ < . < . γχ c < . < . The values of the branching-fraction ratio B ( ψ (3823) → γχ c ) B ( ψ (3823) → γχ c ) and the upper limits of the branching-fraction ratios for ψ (3823) → π + π − J/ψ , π π J/ψ , ηJ/ψ , π J/ψ and γχ c relative to the decay ψ (3823) → γχ c shown in Table I are calculatedusing the definition in Table II, where N is the yieldof signal events, L is the integrated luminosity [34], σ is the cross section, 1 + δ is the radiative correctionfactor [29, 35], ǫ is the efficiency, B is the branchingfraction [10], and i denotes each energy point.Figure 3 shows the π π recoil-mass distribution RM ( π π ) for the decay ψ (3823) → γχ c for dataat 4 . < √ s < . e + e − → π π ψ (3823) can be seen.In order to determine the signal yield, an unbinnedmaximum-likelihood fit is performed. The ψ (3823) sig-nal is modeled by the MC-determined shape convolvedwith a Gaussian function, whose mean value and width are fixed to be the values obtained from the same final-state process e + e − → π π ψ (3686). The background isdescribed with a constant. The solid curve in Fig. 3 showsthe fit results. The number of signal events is deter-mined to be 15 . +5 . − . , and the significance for the process e + e − → π π ψ (3823) with systematic uncertainties in-cluded is found to be 4 . σ . The average cross-section ra-tio σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) for the γχ c channel for data at4 . < √ s < . . +0 . − . ± . ) ) (GeV/c π π RM(3.78 3.8 3.82 3.84 3.86 3.88 E v en t s / M e V / c DataFit resultBackgroundSideband c1 χγ FIG. 3. Results of the fit to the invariant-mass distributionof RM ( π π ) for decay ψ (3823) → γχ c for data at 4 . < √ s < . χ c sideband region. The considered sources of systematic uncertainties re-lated to the branching-fraction ratios and average cross-section ratio are summarized in Table III, where thosethat are common to the numerator and denominator can-cel. The uncertainty in the tracking efficiency and pho-ton efficiency is 1% per track or per photon [36]. Theuncertainty from the branching fractions is taken fromthe PDG [10]. The uncertainty due to the kinematicfit is estimated by correcting the helix parameters ofcharged tracks, and the difference between the resultswith and without this correction is taken as the uncer-tainty [37]. To estimate the uncertainty related to theinput line-shape of the process e + e − → ππψ (3823),we change the input line-shape to a coherent sum ofBW functions of ψ (4415) and ψ (4660) with the parame-ters fixed to PDG values, where magnitude and phaseparameters are obtained from a fit to the cross sec-tion of e + e − → π + π − ψ (3823). The process e + e − → ππψ (3823) is generated by the three-body phase-spacemodel, the uncertainty of the MC decay model is ob-tained by changing the phase-space model to the model e + e − → f (500) ψ (3823) with a D -wave in the MC sim-ulation. The angular distribution of the angle betweenthe two low-momentum pions in the lab frame is sensi- TABLE II. Definitions of the ratios B ( ψ (3823) → ... ) B ( ψ (3823) → γχ c ) and σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) , where B ( ψ (3823) → ... ) represents the branch-ing fraction of ψ (3823) decays into a certain channel, and B ( ... ) represents the branching fraction of subsequent decays.Ratio Definition B ( ψ (3823) → ... ) B ( ψ (3823) → γχ c ) N ψ → ... N ψ → γχc P i L i σ i (1+ δ ) i ǫ ψ → γχc i P i L i σ i (1+ δ ) i ǫ ψ → ...i B ( χ c → γJ/ψ → γl + l − ) B ( ... ) σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) N π π ψ N π + π − ψ P i L i (1+ δ ) i ǫ π + π − ψ i P i L i (1+ δ ) i ǫ π π ψ i B ( π → γγ ) TABLE III. Relative systematic uncertainties (in %) from the different sources for average cross-section ratio σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) (first column) and branching-fraction ratios B ( ψ (3823) → ... ) B ( ψ (3823) → γχ c ) (second to sixth columns) for each decaychannel. Dashes mean that the results are not applicable or cancel in the ratio.Source γχ c γχ c π + π − J/ψ π π J/ψ ηJ/ψ π J/ψ γχ c Tracking efficiency 2.0 − − − − − Photon efficiency 4.0 − − − − − − − − Mass window − − tive to the MC model for the ψ (3823) → γχ c decay,which leads to the dominant systematic uncertainty con-tribution for this mode. The uncertainty from the fitrange is obtained by varying the limits of the fit rangeby ± /c , and the uncertainty associated with thebackground shape is estimated by changing the constantbackground to a linear background. The influence fromthe possible presence of a ψ (3842) state is accounted forby including this component in the fit. In each case, thedifference to the nominal result is taken as the system-atic uncertainty. The uncertainties from the J/ψ , π /η , χ c , and χ c mass-window requirements are 1 . . . . ψ (3823) → γχ c , , , π + π − J/ψ, π π J/ψ, ηJ/ψ , and π J/ψ are searched forusing the process e + e − → π + π − ψ (3823) in a 19fb − data sample collected at center-of-mass energybetween 4.1 and 4 . ψ (3823) → γχ c is observed in a 9fb − data sample in the center-of-mass energy range4.3 to 4 . . σ , and evidence for the process ψ (3823) → γχ c is foundfor the first time with a significance of 3 . σ . Thebranching-fraction ratio B ( ψ (3823) → γχ c ) B ( ψ (3823) → γχ c ) is measured tobe 0 . +0 . − . ± .
02, which is consistent with the theo-retical predictions for B ( ψ (1 D ) → γχ c ) B ( ψ (1 D ) → γχ c ) [15–24]. No sig-nificant ψ (3823) signals are observed for other chan-nels. The upper limits of branching-fraction ratios for ψ (3823) → π + π − J/ψ, π π J/ψ, ηJ/ψ, π J/ψ and γχ c relative to ψ (3823) → γχ c are reported, and the re-sults can be found in Table I. The upper limit at the 90%C.L. of the branching-fraction ratio B ( ψ (3823) → π + π − J/ψ ) B ( ψ (3823) → γχ c ) is determined to be 0.06, which is lower than the theo-retical predictions given in Refs. [15–24]. No significant e + e − → π + π − ψ (3842) signals are seen in any of thechannels we studied. The process e + e − → π π ψ (3823)with ψ (3823) → γχ c is also searched for, and evidencefor the process is found with a significance of 4 . σ . Theaverage cross-section ratio σ ( e + e − → π π ψ (3823)) σ ( e + e − → π + π − ψ (3823)) is deter-mined to be 0 . +0 . − . ± .
05, which is consistent with theexpectation of isospin symmetry.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 Research and Development Program of China un-der Contracts Nos. 2020YFA0406300, 2020YFA0406400;National Natural Science Foundation of China (NSFC)under Contracts Nos. 11905179, 11625523, 11635010,11735014, 11822506, 11835012, 11935015, 11935016,11935018, 11961141012; the Chinese Academy ofSciences (CAS) Large-Scale Scientific Facility Program;Joint Large-Scale Scientific Facility Funds of the NSFCand CAS under Contracts Nos. U1732263, U1832207;CAS Key Research Program of Frontier Sciences un-der Contracts Nos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPACand Shanghai Key Laboratory for Particle Physics andCosmology; ERC under Contract No. 758462; EuropeanUnion Horizon 2020 research and innovation programmeunder Contract No. Marie Sklodowska-Curie grantagreement No 894790; German Research FoundationDFG under Contracts Nos. 443159800, CollaborativeResearch Center CRC 1044, FOR 2359, FOR 2359,GRK 214; Istituto Nazionale di Fisica Nucleare, Italy;Ministry of Development of Turkey under Contract No.DPT2006K-120470; National Science and Technologyfund; Olle Engkvist Foundation under Contract No. 200-0605; STFC (United Kingdom); The Knut and AliceWallenberg Foundation (Sweden) under Contract No.2016.0157; The Royal Society, UK under Contracts Nos.DH140054, DH160214; The Swedish Research Council;U. S. Department of Energy under Contracts Nos. DE-FG02-05ER41374, DE-SC-0012069. [1] S. Godfrey and N. Isgur, Phys. Rev. D , 189 (1985).[2] S. K. Choi et al. [Belle Collaboration], Phys. Rev. Lett. , 262001 (2003).[3] B. Aubert et al. [BaBar Collaboration], Phys. Rev. Lett. , 142001 (2005).[4] M. Ablikim et al. [BESIII Collaboration], Phys. Rev.Lett. , 252001 (2013).[5] M. Ablikim et al. [BESIII Collaboration], arXiv:2011.07855.[6] N. Brambilla et al. , Eur. Phys. J. C , 1534 (2011).[7] H. X. Chen, W. Chen, X. Liu and S. L. Zhu, Phys. Rept. , 1-121 (2016).[8] Y. R. Liu, H. X. Chen, W. Chen, X. Liu and S. L. Zhu,Prog. Part. Nucl. Phys. , 237 (2019).[9] N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev,C. P. Shen, C. E. Thomas, A. Vairo and C. Z. Yuan,Phys. Rept. , 1-154 (2020).[10] P. A. Zyla et al. [Particle Data Group], PTEP ,083C01 (2020).[11] V. Bhardwaj et al. [Belle Collaboration], Phys. Rev. Lett. , 032001 (2013).[12] M. Ablikim et al. [BESIII Collaboration], Phys. Rev.Lett. , 011803 (2015).[13] R. Aaij et al. [LHCb Collaboration], JHEP , 123 (2020).[14] R. Aaij et al. [LHCb Collaboration], JHEP , 035(2019).[15] C. F. Qiao, F. Yuan and K. T. Chao, Phys. Rev. D ,4001 (1997).[16] E. J. Eichten, K. Lane and C. Quigg, Phys. Rev. Lett. , 162002 (2002).[17] D. Ebert, R. N. Faustov and V. O. Galkin, Phys. Rev. D , 014027 (2003).[18] T. Barnes and S. Godfrey, Phys. Rev. D , 054008(2004).[19] T. Barnes, S. Godfrey and E. S. Swanson, Phys. Rev. D , 054026 (2005).[20] B. Q. Li and K. T. Chao, Phys. Rev. D , 094004 (2009).[21] W. J. Deng, L. Y. Xiao, L. C. Gui and X. H. Zhong,arXiv:1510.08269.[22] B. Wang, H. Xu, X. Liu, D. Y. Chen, S. Coito andE. Eichten, Front. Phys. , 111402 (2016).[23] W. J. Deng, H. Liu, L. C. Gui and X. H. Zhong, Phys.Rev. D , 034026 (2017).[24] T. Wang, H. F. Fu, Y. Jiang, Q. Li and G. L. Wang, Int.J. Mod. Phys. A , 1750035 (2017).[25] M. Ablikim et al. [BESIII Collaboration], Nucl. Instrum.Meth. A , 345 (2010).[26] C. H. Yu et al. , Proceedings of IPAC2016, Busan, Korea,2016, doi:10.18429/JACoW-IPAC2016-TUYA01.[27] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 040001 (2020).[28] S. Agostinelli et al. [GEANT4 Collaboration], Nucl.Instrum. Meth. A , 250 (2003).[29] S. Jadach, B. F. L. Ward and Z. Was, Phys. Rev. D , 113009 (2001); Comput. Phys. Commun. , 260(2000).[30] D. J. Lange, Nucl. Instrum. Meth. A , 152 (2001);R. G. Ping, Chin. Phys. C , 599 (2008).[31] J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang andY. S. Zhu, Phys. Rev. D , 034003 (2000); R. L. Yang,R. G. Ping and H. Chen, Chin. Phys. Lett. , 061301(2014).[32] E. Richter-Was, Phys. Lett. B , 163 (1993).[33] X. Zhou, S. Du, G. Li and C. Shen, Comput. Phys.Commun. , 107540 (2021).[34] M. Ablikim et al. [BESIII Collaboration], Chin. Phys. C , 093001 (2015).[35] E. A. Kuraev and V. S. Fadin, Sov. J. Nucl. Phys. ,466 (1985).[36] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D , 091103 (2019).[37] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D , 012002 (2013).[38] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D , 012008 (2020).[39] M. Ablikim et al. [BESIII Collaboration], Phys. Rev.Lett.116