Study of e^+e^- \rightarrow π^{0}X(3872)γ and search for Z_c(4020)^{0}\rightarrow X(3872)γ
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 Biernat, 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, et al. (420 additional authors not shown)
aa r X i v : . [ h e p - e x ] F e b Study of e + e − → π X (3872) γ and search for Z c (4020) → X (3872) γ 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 Biernat , 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 ,b ,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 , G. Y. Hou , , 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 , M. Q. Jing , ,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. 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 , 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 ,H. F. 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 , W. H. 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 , Zeng , Y. Zeng ,l , A. Q. Zhang ,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. 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 , , A. N. Zhu , , J. Zhu , K. Zhu , K. J. Zhu , , ,S. H. Zhu , T. J. Zhu , W. J. Zhu ,h , W. J. Zhu , 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, Staudinger Weg 18, 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
Using data samples collected with the BESIII detector operating at the BEPCII storage ringat center-of-mass energies from 4.178 to 4.600 GeV, we study the process e + e − → π X (3872) γ and search for Z c (4020) → X (3872) γ . We find no significant signal and set upper limits on σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) and σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) for each energy point at 90% confidence level, which is of theorder of several tenths pb.
I. INTRODUCTION
The recent discovery of several charmonium-like stateshas attracted great experimental and theoretical inter-ests [1]. The masses of these states are above the open-charm thresholds, and due to the unexpected resonanceparameters and decay channels, these states can not bedescribed by conventional quark models. Therefore, theyare good candidates for exotic states, such as hybrids,tetraquarks, molecules, etc. [2–4].The first charmonium-like state X (3872), which hasbeen recently renamed as χ c (3872) by the Particle DataGroup (PDG [1]), was observed by the Belle experimentin the process B ± → K ± X (3872) → K ± π + π − J/ψ [5].The X (3872) is a rather narrow state with a mass thatis consistent with D ¯ D ∗ threshold. It decays throughopen-charm, radiative and isospin-violating pion emis-sion decays, and is found to be an isospin singlet with J P C = 1 ++ [1]. Among these features, the extremelysmall mass difference between the X (3872) and D ¯ D ∗ threshold which we will denote as δ , is of particular in-terest. Taking the values for the D , D ∗ and X (3872)masses from the PDG [1], δ is calculated to be ( − ± c . Very recently, the LHCb reported a new mea-surement yielding δ = (70 ± c [6, 7]. Howeverthe improved precision is still insufficient to tell whetherthe X (3872) mass is above or below the D ¯ D ∗ threshold.Better knowledge of δ will be an important step towards adeeper understanding of the nature of the X (3872) [8, 9],and eventually of other related XY Z states. A complete-ly new method to measure the δ value by measuring the X (3872) γ line shape, which is sensitive to the δ valuedue to a triangle singularity, is proposed by Ref. [10–12]. Here, the X (3872) γ needs to be produced associ-ated with another positive C -parity neutral meson, e.g. e + e − → π X (3872) γ . In principle, this method could beapplied at the BESIII experiment, based on the sizabledata samples taken for XY Z studies.Recently, the BESIII Collaboration reported an en-hancement around 4.2 GeV for the e + e − → γX (3872)production cross sections [13], which suggests a connec-tion between Y and X states. BESIII also reported an-other connection, now between Y and Z states, withthe observation of a Y (4220) resonance in the process e + e − → π Z c (3900) [14]. Those observations may in-dicate some common nature among the XY Z states.Therefore, it is important to search for possible con-nections between Z and X states. Establishing connec-tions among XY Z states may be a clue that can facil-itate a better theoretical interpretation of these. Onesuch connection [15] could be a transition Z c (4020) → X (3872) γ in the scenario where the X (3872) is domi-nantly an S -wave D ¯ D ∗ molecule and the Z c (4020) is an isotopic triplet of near-threshold S -wave D ∗ ¯ D ∗ resonances. Therefore, the search for the transition Z c (4020) → X (3872) γ will help to quantitatively studythe molecular picture of the X (3872). The Z c (4020) isobserved in the e + e − → πZ c (4020) process, so the studyof e + e − → π X (3872) γ allows one to search for the tran-sition Z c (4020) → X (3872) γ .In this paper, we report the search for the reac-tion e + e − → π X (3872) γ and Z c (4020) → X (3872) γ based on the data of twenty-three energy points record-ed with the BESIII detector in the range of 4 . ≤√ s ≤ .
600 GeV. The X (3872) state is reconstructedvia X (3872) → π + π − J/ψ , J/ψ → ℓ + ℓ − ( ℓ = e or µ ). II. BESIII DETECTOR AND MONTE CARLOSIMULATION
The BESIII detector is a magnetic spectrometer [16]located at the Beijing Electron Positron Collider(BEPCII) [17]. The cylindrical core of the BESIIIdetector consists of a helium-based multilayer driftchamber (MDC), a plastic scintillator time-of-flight sys-tem (TOF), and a CsI(Tl) electromagnetic calorime-ter (EMC), which are all enclosed in a superconductingsolenoidal magnet, providing a 1.0 T magnetic field. Thesolenoid is supported by an octagonal flux-return yokewith resistive plate chamber muon identifier modules in-terleaved with steel. The acceptance of charged particlesand photons is 93% over the 4 π solid angle. The charged-particle momentum resolution at 1 GeV /c is 0 . E/ d x resolution is 6% for the electrons from Bhabhascattering. The EMC measures photon energies with aresolution of 2 .
5% (5%) at 1 GeV in the barrel (end cap)region. The time resolution of the TOF barrel section is68 ps, while that of the end cap section is 110 ps. Theend cap TOF system was upgraded in 2015 with multi-gap resistive plate chamber technology, providing a timeresolution of 60 ps [18]. About 70% of the data sampleused here was taken after this upgrade. Simulated data samples produced with the geant4 -based [19] Monte Carlo (MC) package, which includesthe geometric description of the BESIII detector andthe detector response, are used to determine the detec-tion efficiency and to estimate the background contribu-tions. The simulation includes the beam energy spreadand initial-state radiation (ISR) in the e + e − annihila-tions modeled with the generator kkmc [20]. The ISRproduction of vector charmonium(-like) states and thecontinuum processes are incorporated also in kkmc [20].The known decay modes are modeled with evtgen [21],using branching fractions summarized and averaged bythe PDG [1], and the remaining unknown decays from thecharmonium states are generated with lundcharm [22].Final state radiation from charged final state particles isincorporated with the photos package [23].Signal MC samples for e + e − → π X (3872) γ and e + e − → π Z c (4020) → π X (3872) γ are generated ac-cording to phase space at each center-of-mass energypoint, assuming that the cross section follows the func-tion fit for the e + e − → π + π − h c line shape in Ref. [24].The event selection criteria and the detection efficienciesare determined and studied based on signal MC samplesof 1 × signal events generated for each value of √ s .Detection efficiencies are determined by the ratio of thereconstructed event yields (after the selection criteria)and the number of generated events. Inclusive MC sam-ples consisting of open charm production processes areemployed to investigate potential backgrounds. III. EVENT SELECTION
For each charged track, the distance of closest ap-proach to the interaction point (IP) is required to bewithin 10 cm in the beam direction and within 1 cm inthe plane perpendicular to the beam direction. The po-lar angles ( θ ) of the tracks must be within the fiducialvolume of the MDC ( | cos θ | < . ◦ away from the nearest charged track. Thephoton energy is required to be at least 25 MeV in thebarrel region ( | cos θ | < .
80) or 50 MeV in the end capregion (0 . < | cos θ | < . ≤ t ≤
700 ns.Since the reaction e + e − → π X (3872) γ results in thefinal states γγγπ + π − ℓ + ℓ − , candidate events are requiredto have four tracks with zero net charge and at least threephotons. Tracks with momenta larger than 1.0 GeV/ c are assigned as leptons from the J/ψ decay; otherwise,they are regarded as pions. Leptons from the
J/ψ decaywith energy deposited in the EMC larger than 1.0 GeVare identified as electrons, while those with less than0.4 GeV as muons. The π candidates are reconstruct-ed from photons pairs with invariant mass in the range110 < M γγ <
150 MeV /c .To reduce the background contributions and to im-prove the mass resolution, a five-constraint (5C) kine-matic fit is performed. Four constraints come from thetotal initial four momentum of the colliding beams; thelast one is from constraining the M γγ invariant mass tothe nominal π value [1]. If there is more than one com-bination in an event, the one with the smallest χ ischosen. Furthermore, the χ is required to be less than60. The J/ψ is reconstructed via ℓ + ℓ − decays, and theinvariant mass of lepton pairs is required to be in the J/ψ mass window [3 . , . /c . IV. BORN CROSS SECTION MEASUREMENTIV.I e + e − → π X (3872) γ After applying the above requirements, the remainingbackground is mainly coming from e + e − → γ ISR ηJ/ψ , η → π + π − π and e + e − → γωJ/ψ , ω → π + π − π events. In order to veto these events, the π + π − π in-variant mass is required to be outside the η and ω massregions [0 . , . /c and [0 . , . /c ,respectively. Besides the η and ω backgrounds, the π + π − ψ (3686), ψ (3686) → π π J/ψ background is re-moved by requiring the π + π − recoil mass to be outsidethe ψ (3686) mass region of [3 . , . /c .Figure 1 shows distributions of the π + π − J/ψ invari-ant mass M ( π + π − J/ψ ) for data and the MC samples of e + e − → π X (3872) γ . The X (3872) signal region is takenas [3.860, 3.885] GeV/ c , while the sideband regions areset to be [3.825, 3.850] GeV/ c and [3.895, 3.920] GeV/ c .No significant X (3872) signals are seen at any energies.The signal yield is determined from the event yields inthe X (3872) signal and sideband regions. The sidebandyields are scaled by the ratio of the relevant mass-windowwidths in order to predict the background expected in thesignal region. Upper limits on the number of signal eventsat the 90% C.L. are calculated by using a frequentistmethod [25] with unbounded profile likelihood treatmentof systematic uncertainties, which is implemented by thepackage trolke [26] in the root framework [27], wherethe signal and background obey Poisson statistics, andthe efficiencies are Gaussian-distributed. The numericalresults are summarized in Table I.The Born cross section multiplied by the branch-ing fraction σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) is calculated as: σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) = N X (3872) ǫ L int (1 + δ ( s )) | − Π | B ( J/ψ → ℓ + ℓ − ) B ( π → γγ ) , (1) where N X (3872) is the number of X (3872) signal events, ǫ is the detection efficiency (excluding intermediatebranching fractions), L int is the integrated luminosi-ty [28], 1+ δ ( s ) is the ISR correction factor obtained froma quantum electrodynamics calculations [20, 29], | − Π | isvacuum polarization factor [30]. The corresponding up-per limits for this cross section at the 90% C.L. for eachenergy point are listed in Table I and shown in Fig. 2 (a). IV.II Z c (4020) → X (3872) γ The possible connection between X and Z charmonium-like states can be studied via the de-cay Z c (4020) → X (3872) γ . In order to search forthe process, the X (3872) signal region is set to be[3.860, 3.885] GeV/ c , which is the same as for the e + e − → π X (3872) γ study. After the requirementof the X (3872) mass window no significant η , ω and ψ (3686) background remain. Figure 3 shows the X (3872) γ invariant mass distributions for data andMC samples of e + e − → π Z c (4020) → π X (3872) γ .No Z c (4020) candidates are found. Therefore, thesame method as before is employed to calculate theupper limits for this process. For data samples takenabove √ s = 4 .
280 GeV, the Z c (4020) signal regionis set to be [3.995, 4.055] GeV/ c , and the side-band regions are set to be [3 . , . /c and[4 . , . /c . At lower energies, kinematicsdictates that Z c (4020) candidates cannot have a massabove 4 . − M π = 4 .
145 GeV /c , where M π is π nominal mass. Accordingly, we use a single sidebandregion of [3.900, 3.960] GeV/ c .The Born cross section multiplied by branchingfractions σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) is calculated withthe following formula: σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) = N Z c (4020) ǫ L int (1 + δ ( s )) | − Π | B ( J/ψ → ℓ + ℓ − ) B ( π → γγ ) , (2)where N Z c (4020) is the number of Z c (4020) signalevents. The corresponding upper limits at the 90% C.L.for each energy are listed in Table I and shown in Fig. 2(b). V. SYSTEMATIC UNCERTAINTY ESTIMATION
The systematic uncertainties of σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) and σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) originate from the luminosity measurement, h1 Entries 9Mean 3.849RMS 0.04087 h2 Entries 15162Mean 3.873RMS 0.007055 h1 Entries 9Mean 3.849RMS 0.04087 h1 Entries 9Mean 3.849RMS 0.04087 h1 Entries 16Mean 3.904RMS 0.02948 h2 Entries 15041Mean 3.873RMS 0.00707 h1 Entries 16Mean 3.904RMS 0.02948 h1 Entries 16Mean 3.904RMS 0.02948 h1 Entries 13Mean 3.89RMS 0.000868 h2 Entries 14468Mean 3.873RMS 0.007315 h1 Entries 13Mean 3.89RMS 0.000868 h1 Entries 13Mean 3.89RMS 0.000868 h1 Entries 27Mean 3.853RMS 0 h2 Entries 14697Mean 3.873RMS 0.007275 h1 Entries 27Mean 3.853RMS 0 h1 Entries 27Mean 3.853RMS 0 h1 Entries 1Mean 0RMS 0 h2 Entries 9904Mean 3.873RMS 0.007109 h1 Entries 1Mean 0RMS 0 h1 Entries 1Mean 0RMS 0 h1 Entries 5Mean 0RMS 0 h2 Entries 15198Mean 3.873RMS 0.006965 h1 Entries 5Mean 0RMS 0 h1 Entries 5Mean 0RMS 0 h1 Entries 18Mean 0RMS 0 h2 Entries 15669Mean 3.873RMS 0.007221 h1 Entries 18Mean 0RMS 0 h1 Entries 18Mean 0RMS 0 h1 Entries 9Mean 0RMS 0 h2 Entries 14851Mean 3.873RMS 0.007158 h1 Entries 9Mean 0RMS 0 h1 Entries 9Mean 0RMS 0 h1 Entries 17Mean 0RMS 0 h2 Entries 14897Mean 3.873RMS 0.007248 h1 Entries 17Mean 0RMS 0 h1 Entries 17Mean 0RMS 0 h1 Entries 41Mean 3.824RMS 0.01678 h2 Entries 14151Mean 3.873RMS 0.007487 h1 Entries 41Mean 3.824RMS 0.01678 h1 Entries 41Mean 3.824RMS 0.01678 h1 Entries 4Mean 0RMS 0 h2 Entries 8822Mean 3.873RMS 0.007531 h1 Entries 4Mean 0RMS 0 h1 Entries 4Mean 0RMS 0 h1 Entries 9Mean 3.815RMS 0 h2 Entries 15290Mean 3.873RMS 0.007096 h1 Entries 9Mean 3.815RMS 0 h1 Entries 9Mean 3.815RMS 0 h1 Entries 9Mean 0RMS 0 h2 Entries 15658Mean 3.873RMS 0.007184 h1 Entries 9Mean 0RMS 0 h1 Entries 9Mean 0RMS 0 h1 Entries 8Mean 0RMS 0 h2 Entries 14538Mean 3.873RMS 0.00729 h1 Entries 8Mean 0RMS 0 h1 Entries 8Mean 0RMS 0 h1 Entries 23Mean 3.847RMS 0 h2 Entries 15286Mean 3.873RMS 0.007423 h1 Entries 23Mean 3.847RMS 0 h1 Entries 23Mean 3.847RMS 0 h1 Entries 24Mean 3.899RMS 0.03263 h2 Entries 10801Mean 3.874RMS 0.007625 h1 Entries 24Mean 3.899RMS 0.03263 h1 Entries 24Mean 3.899RMS 0.03263 h1 Entries 25Mean 3.915RMS 0.007453 h2 Entries 8356Mean 3.873RMS 0.007504 h1 Entries 25Mean 3.915RMS 0.007453 h1 Entries 25Mean 3.915RMS 0.007453 h1 Entries 7Mean 0RMS 0 h2 Entries 15406Mean 3.873RMS 0.007059 h1 Entries 7Mean 0RMS 0 h1 Entries 7Mean 0RMS 0 h1 Entries 12Mean 0RMS 0 h2 Entries 15119Mean 3.873RMS 0.007156 h1 Entries 12Mean 0RMS 0 h1 Entries 12Mean 0RMS 0 h1 Entries 10Mean 0RMS 0 h2 Entries 14409Mean 3.873RMS 0.007299 h1 Entries 10Mean 0RMS 0 h1 Entries 10Mean 0RMS 0 h1 Entries 23Mean 3.843RMS 0.003766 h2 Entries 15261Mean 3.873RMS 0.007488 h1 Entries 23Mean 3.843RMS 0.003766 h1 Entries 23Mean 3.843RMS 0.003766 h1 Entries 1Mean 0RMS 0 h2 Entries 5934Mean 3.873RMS 0.009201 h1 Entries 1Mean 0RMS 0 h1 Entries 1Mean 0RMS 0 h1 Entries 345Mean 3.866RMS 0.0398 h2 Entries 314048Mean 3.873RMS 0.007285 h1 Entries 345Mean 3.866RMS 0.0398 h1 Entries 345Mean 3.866RMS 0.0398 ) c ) (GeV/ ψ J/ - π + π M( c E v e n t s / M e V / √ s = 4 .
178 GeV √ s = 4 .
189 GeV √ s = 4 .
199 GeV √ s = 4 .
209 GeV √ s = 4 .
219 GeV √ s = 4 .
226 GeV √ s = 4 .
236 GeV √ s = 4 .
244 GeV √ s = 4 .
258 GeV √ s = 4 .
267 GeV √ s = 4 .
278 GeV √ s = 4 .
288 GeV √ s = 4 .
312 GeV √ s = 4 .
338 GeV √ s = 4 .
358 GeV √ s = 4 .
378 GeV √ s = 4 .
397 GeV √ s = 4 .
416 GeV √ s = 4 .
437 GeV √ s = 4 .
467 GeV √ s = 4 .
527 GeV √ s = 4 .
574 GeV √ s = 4 .
600 GeV all
FIG. 1. The distribution of M ( π + π − J/ψ ) for each energy point and the sum (all). Dots with error bars denote data, and thered histogram denotes the MC simulation of e + e − → π X (3872) γ . The blue solid lines mark the signal region of X (3872), andthe pink dashed lines mark the sideband regions of X (3872). TABLE I. The upper limits (calculated including the systematic uncertainties) on σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) and σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) at the 90% C.L. for each energypoint, together with integrated luminosities L int , the number of events in signal region N obs , the number of events in sidebandregion N sb , the number of signal events N at the 90% C.L., radiative correction factors 1+ δ (s), vacuum polarization factors | − Π | , and efficiencies without intermediate branching fractions ǫ . Here, σ ·B represents σ ( e + e − → π X (3872) γ ) ·B ( X (3872) → π + π − J/ψ ) or σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ). The first values in brackets arefor the process e + e − → π X (3872) γ , and the second for the process e + e − → π Z c (4020) → π X (3872) γ . The low efficiencyat 4.467 GeV is caused by the cut on the π + π − recoil mass. √ s (GeV) L int (pb − ) N obs N sb N δ (s) | − Π | ǫ (%) σ · B (pb)4.178 3195 (1, 0) (1, 1) ( < . , < .
26) (0.70, 0.69) 1.055 (14.02, 13.97) ( < . , < . < . , < .
52) (0.70, 0.70) 1.056 (14.12, 14.02) ( < . , < . < . , < .
00) (0.70, 0.70) 1.057 (14.13, 14.24) ( < . , < . < . , < .
00) (0.71, 0.71) 1.057 (14.29, 13.75) ( < . , < . < . , < .
00) (0.72, 0.72) 1.057 (14.07, 13.74) ( < . , < . < . , < .
00) (0.74, 0.74) 1.057 (14.51, 14.11) ( < . , < . < . , < .
00) (0.76, 0.76) 1.056 (14.50, 13.43) ( < . , < . < . , < .
00) (0.78, 0.78) 1.056 (14.03, 13.20) ( < . , < . < . , < .
01) (0.81, 0.81) 1.054 (14.00, 12.99) ( < . , < . < . , < .
01) (0.83, 0.83) 1.053 (13.78, 12.23) ( < . , < . < . , < .
02) (0.84, 0.84) 1.053 (13.44, 11.89) ( < . , < . < . , < .
01) (0.84, 0.84) 1.053 (13.29, 11.74) ( < . , < . < . , < .
02) (0.84, 0.84) 1.052 (13.35, 11.68) ( < . , < . < . , < .
02) (0.83, 0.83) 1.051 (13.76, 12.03) ( < . , < . < . , < .
02) (0.83, 0.83) 1.051 (14.11, 12.42) ( < . , < . < . , < .
02) (0.84, 0.84) 1.052 (14.06, 12.47) ( < . , < . < . , < .
02) (0.86, 0.86) 1.052 (13.60, 12.34) ( < . , < . < . , < .
03) (0.90, 0.90) 1.053 (13.04, 12.10) ( < . , < . < . , < .
57) (0.97, 0.97) 1.054 (9.94, 11.47) ( < . , < . < . , < .
03) (1.09, 1.09) 1.055 (5.25, 10.39) ( < . , < . < . , < .
02) (1.38, 1.38) 1.055 (9.19, 8.56) ( < . , < . < . , < .
03) (1.62, 1.62) 1.055 (8.11, 7.31) ( < . , < . < . , < .
02) (1.76, 1.75) 1.055 (7.71, 7.06) ( < . , < . (GeV)s4.2 4.3 4.4 4.5 4.6 ( pb ) B ⋅ σ (a) (GeV)s4.2 4.3 4.4 4.5 4.6 ( pb ) B ⋅ σ (b) FIG. 2. The upper limits at the 90% C.L. on σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) (a) and σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) (b) for each energy point. the tracking efficiency, the photon detection efficiency,the kinematic fit, the
J/ψ mass window, the X (3872)mass window, the Z c (4020) parameters, the line shape,the generator model, the ISR correction, and the inputbranching fractions.The integrated luminosity at each point has been mea- sured with a precision of 1 .
0% using the Bhabha pro-cess [28].The uncertainty from the tracking efficiency is 1 . .
0% per photon [32].The uncertainty due to the kinematic fit requirements h1 Entries 1Mean 3.893RMS 0 h2 Entries 15878Mean 4.02RMS 0.02476 h1 Entries 1Mean 3.893RMS 0 h1 Entries 1Mean 3.893RMS 0 h1 Entries 1Mean 3.887RMS 0 h2 Entries 15139Mean 4.025RMS 0.02467 h1 Entries 1Mean 3.887RMS 0 h1 Entries 1Mean 3.887RMS 0 h1Entries 0Mean 0RMS 0h2
Entries 14014Mean 4.029RMS 0.03042 h1Entries 0Mean 0RMS 0h1Entries 0Mean 0RMS 0 h1Entries 0Mean 0RMS 0h2
Entries 14670Mean 4.028RMS 0.02936 h1Entries 0Mean 0RMS 0h1Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 10188Mean 4.026RMS 0.02622 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 2Mean 3.913RMS 0.003891 h2 Entries 16349Mean 4.015RMS 0.02575 h1 Entries 2Mean 3.913RMS 0.003891 h1 Entries 2Mean 3.913RMS 0.003891 h1 Entries 2Mean 3.988RMS 0.08874 h2 Entries 16276Mean 4.022RMS 0.02434 h1 Entries 2Mean 3.988RMS 0.08874 h1 Entries 2Mean 3.988RMS 0.08874 h1 Entries 0Mean 0RMS 0 h2 Entries 14398Mean 4.026RMS 0.02571 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 14451Mean 4.029RMS 0.03235 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 14506Mean 4.027RMS 0.02884 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 8762Mean 4.026RMS 0.02724 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 16527Mean 4.017RMS 0.02531 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 15573Mean 4.022RMS 0.0245 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 14111Mean 4.026RMS 0.02686 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 14817Mean 4.029RMS 0.0321 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 3Mean 4.125RMS 0.02901 h2 Entries 13698Mean 4.027RMS 0.02796 h1 Entries 3Mean 4.125RMS 0.02901 h1 Entries 3Mean 4.125RMS 0.02901 h1 Entries 0Mean 0RMS 0 h2 Entries 8367Mean 4.027RMS 0.02583 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 1Mean 3.881RMS 0 h2 Entries 15922Mean 4.019RMS 0.02468 h1 Entries 1Mean 3.881RMS 0 h1 Entries 1Mean 3.881RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 15327Mean 4.023RMS 0.0247 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 13954Mean 4.026RMS 0.02769 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h2 Entries 14835Mean 4.028RMS 0.03079 h1 Entries 0Mean 0RMS 0 h1 Entries 0Mean 0RMS 0 h1 Entries 1Mean 0RMS 0 h2 Entries 12434Mean 4.027RMS 0.02745 h1 Entries 1Mean 0RMS 0 h1 Entries 1Mean 0RMS 0 h1 Entries 13Mean 3.971RMS 0.1025 h2 Entries 326545Mean 4.024RMS 0.02751 h1 Entries 13Mean 3.971RMS 0.1025 h1 Entries 13Mean 3.971RMS 0.1025 ) c ) (GeV/ γ M(X(3872) c E v e n t s / M e V / √ s = 4 .
178 GeV √ s = 4 .
189 GeV √ s = 4 .
199 GeV √ s = 4 .
209 GeV √ s = 4 .
219 GeV √ s = 4 .
226 GeV √ s = 4 .
236 GeV √ s = 4 .
244 GeV √ s = 4 .
258 GeV √ s = 4 .
267 GeV √ s = 4 .
278 GeV √ s = 4 .
288 GeV √ s = 4 .
312 GeV √ s = 4 .
338 GeV √ s = 4 .
358 GeV √ s = 4 .
378 GeV √ s = 4 .
397 GeV √ s = 4 .
416 GeV √ s = 4 .
437 GeV √ s = 4 .
467 GeV √ s = 4 .
527 GeV √ s = 4 .
574 GeV √ s = 4 .
600 GeV all
FIG. 3. The distribution of M ( X (3872) γ ) for each energy point and the sum (all). Dots with error bars denote data, and thered histogram denotes the MC simulation of e + e − → π Z c (4020) → π X (3872) γ . The blue solid lines mark the signal regionof Z c (4020) , and the pink dashed lines mark the sideband regions of Z c (4020) . is estimated by correcting the helix parameters of chargedtracks according to the method described in Ref. [33].The difference between detection efficiencies obtainedfrom MC samples with and without this correction istaken as the uncertainty.The uncertainty for the J/ψ mass window isestimated using the control sample of e + e − → γ ISR ψ (3686) , ψ (3686) → π + π − J/ψ . The difference of theefficiency between data and MC simulation is found to be1.6% [34], which is taken as the uncertainty.The uncertainty from the X (3872) mass window is es-timated by changing the window range by ± Z c (4020) mass andwidth are estimated by changing them by one standarddeviation values [1] while generating the signal MC. Thelargest efficiency difference relative to the nominal one istaken as the uncertainty.The line shape affects the ISR correction factor and theefficiency. No obvious signal was found for our Z c (4020) search, so we use the line shape from e + e − → π + π − h c in Ref. [24] as the input line shape to get the nominalresults. To get the uncertainty introduced by the lineshape, we change it to a Breit-Wigner function describingthe ψ (4230) or ψ (4415), with the masses and widths fixedto the values from PDG [1]. The largest difference of thefinal result is taken as a systematic uncertainty.For the systematic uncertainty from the MC simulationdescribing the process e + e − → π X (3872) γ , we use thethree-body phase space MC simulation to get the nomi-nal efficiency, then change to the e + e − → π Z c (4020) → π X (3872) γ . The difference on the detection efficiencywith and without the intermediate resonant state is takenas the uncertainty due to the MC model.The systematic uncertainty from the MC simula-tion describing the process e + e − → π Z c (4020) → π X (3872) γ is estimated by varying the distribution ofthe π polar angle θ . The nominal efficiency is deter-mined assuming a flat distribution in cos θ . A conserva-tive estimate of the systematic uncertainty is obtainedusing alternative MC samples with angular distributionsof 1 ± cos θ . The largest change of efficiency is taken asthe uncertainty due to the MC model.The ISR correction factor is obtained from quantumelectrodynamics calculations [20, 29]. We also analyzeMC samples with and without ISR effects considered toget the ISR correction factor, the difference of the tworesults is taken as the systematic uncertainty on the ISRcorrection factor.As uncertainties introduced by the branching fractionsof J/ψ → ℓ + ℓ − and π → γγ we use those quoted by thePDG [1].Table II summarizes all the systematic uncertain-ties related to σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) and σ ( e + e − → π Z c (4020) ) ·B ( Z c (4020) → X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) for each center-of- mass energy. The total systematic uncertainty for eachenergy point is calculated as the quadratic sum of theindividual uncertainties, assuming them to be uncorre-lated.
VI. SUMMARY
Using data samples collected at the center-of-massenergies between 4.178 and 4.600 GeV, the processes e + e − → π X (3872) γ and Z c (4020) → X (3872) γ areinvestigated. In neither of the two processes are signifi-cant signals observed. Upper limits at the 90% C.L. onthe cross section multiplied by the branching fraction, σ ( e + e − → π X (3872) γ ) · B ( X (3872) → π + π − J/ψ ) and σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → X (3872) γ ) ·B ( X (3872) → π + π − J/ψ ), are reported for each ener-gy point. The measured results of the process e + e − → π X (3872) γ are not in conflict with the theoretical expec-tation of about 0.1 fb [12]. A three orders of magnitudeincrease in statistics is needed to test these models.Using the experimental results on the σ ( e + e − → π Z c (4020) ) · B ( Z c (4020) → ( D ∗ ¯ D ∗ ) ) at √ s = 4 .
226 and 4 .
258 GeV [35], the ratio B ( Z c (4020) → X (3872) γ ) ·B ( X (3872) → π + π − J/ψ ) B ( Z c (4020) → ( D ∗ ¯ D ∗ ) ) is determinedto be less than 0.24% at √ s = 4 .
226 GeV and less than0.42% at √ s = 4 .
258 GeV at the 90% C.L. These ratiosdo not contradict the prediction reported in Ref. [15]based on the molecular picture. Since no significant e + e − → π X (3872) γ signals are observed, we cannotstudy the lineshape as proposed in Ref. [10, 11]; this maybe achieved at future super tau-charm facilities [36, 37]. ACKNOWLEDGMENTS
The BESIII collaboration thanks the staff of BEPCIIand the IHEP computing center for their strong sup-port. This work is supported in part by National NaturalScience Foundation of China (NSFC) under ContractsNos. 11905179, 11625523, 11635010, 11735014,11822506, 11835012, 11935015, 11935016, 11935018,11961141012; the Chinese Academy of Sciences (CAS)Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CASunder Contracts Nos. U1732263, U1832207; CAS KeyResearch Program of Frontier Sciences under ContractsNos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100Talents Program of CAS; INPAC and Shanghai KeyLaboratory for Particle Physics and Cosmology; ERC un-der Contract No. 758462; 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.0
TABLE II. Summary of relative systematic uncertainties (%) associated with luminosity( L int ), tracking efficiency (Tracks),photon detection efficiency (Photons), kinematic fitting ( χ C ), J/ψ mass window (
J/ψ ), X (3872) mass window ( X (3872)), Z c (4020) parameters ( Z c (4020) ), line shape (Line shape), generator model (Generator), ISR correction factor (ISR) andbranching fraction ( B ). The first values in brackets are for the process e + e − → π X (3872) γ , and the second for the process e + e − → π Z c (4020) → π X (3872) γ . A dash indicates that a systematic effect is not applicable. √ s (GeV) L int Tracks Photons χ C J/ψ X (3872) Z c (4020) Line shape Generator ISR B Sum4.178 1.0 4.0 3.0 (2.6, 2.0) 1.6 1.3 (-, 4.2) (5.6, 6.0) (7.4, 2.4) (0.7, 0.7) 0.4 (11.1, 9.7)4.189 1.0 4.0 3.0 (2.8, 2.1) 1.6 1.3 (-, 3.5) (6.4, 6.8) (5.7, 3.9) (0.7, 0.6) 0.4 (10.6, 10.4)4.199 1.0 4.0 3.0 (2.1, 2.2) 1.6 1.3 (-, 4.3) (6.7, 4.7) (7.5, 3.9) (0.5, 0.5) 0.4 (11.7, 9.6)4.209 1.0 4.0 3.0 (2.0, 2.1) 1.6 1.4 (-, 4.1) (4.9, 6.3) (3.5, 6.6) (0.2, 0.3) 0.4 (8.4, 11.6)4.219 1.0 4.0 3.0 (2.4, 2.6) 1.6 1.5 (-, 5.7) (4.3, 3.5) (5.2, 7.7) (0.1, 0.1) 0.4 (9.1, 11.9)4.226 1.0 4.0 3.0 (2.3, 2.1) 1.6 1.5 (-, 5.6) (1.5, 2.3) (5.1, 7.1) (0.1, 0.1) 0.4 (8.0, 11.1)4.236 1.0 4.0 3.0 (2.3, 2.1) 1.6 1.5 (-, 6.3) (2.1, 2.2) (1.3, 9.2) (0.1, 0.1) 0.4 (6.5, 12.8)4.244 1.0 4.0 3.0 (2.1, 2.3) 1.6 1.3 (-, 4.6) (4.4, 1.3) (3.3, 9.7) (0.2, 0.1) 0.4 (8.1, 12.4)4.258 1.0 4.0 3.0 (2.3, 2.6) 1.6 1.6 (-, 5.8) (6.4, 4.4) (3.3, 9.5) (0.2, 0.3) 0.4 (9.4, 13.5)4.267 1.0 4.0 3.0 (2.0, 2.0) 1.6 1.3 (-, 5.9) (5.7, 6.8) (0.2, 12.9) (0.2, 0.1) 0.4 (8.2, 16.8)4.278 1.0 4.0 3.0 (2.4, 2.1) 1.6 1.5 (-, 5.6) (6.9, 7.2) (1.0, 13.6) (0.2, 0.1) 0.4 (9.2, 17.4)4.288 1.0 4.0 3.0 (2.1, 2.2) 1.6 1.4 (-, 5.9) (7.9, 6.0) (1.3, 13.5) (0.2, 0.1) 0.4 (10.0, 17.0)4.312 1.0 4.0 3.0 (2.8, 2.1) 1.6 1.3 (-, 6.6) (5.8, 5.9) (2.2, 15.4) (0.1, 0.2) 0.4 (8.8, 18.7)4.338 1.0 4.0 3.0 (2.1, 2.2) 1.6 1.5 (-, 5.4) (7.0, 5.6) (2.9, 16.0) (0.1, 0.1) 0.4 (9.6, 18.8)4.358 1.0 4.0 3.0 (2.0, 1.8) 1.6 1.2 (-, 5.6) (7.6, 6.1) (2.8, 15.5) (0.1, 0.1) 0.4 (10.0, 18.5)4.378 1.0 4.0 3.0 (2.1, 1.8) 1.6 1.5 (-, 6.0) (7.0, 3.9) (3.5, 14.9) (0.1, 0.1) 0.4 (9.8, 17.5)4.397 1.0 4.0 3.0 (2.1, 1.8) 1.6 1.3 (-, 7.4) (5.3, 5.5) (5.3, 16.4) (0.1, 0.1) 0.4 (9.5, 19.7)4.416 1.0 4.0 3.0 (1.8, 1.7) 1.6 1.3 (-, 7.1) (4.4, 5.5) (4.3, 19.0) (0.1, 0.1) 0.4 (8.5, 21.8)4.437 1.0 4.0 3.0 (2.1, 2.0) 1.6 1.4 (-, 7.1) (3.1, 1.2) (5.9, 17.4) (0.1, 0.2) 0.4 (8.9, 19.7)4.467 1.0 4.0 3.0 (2.4, 2.2) 1.6 1.5 (-, 7.3) (3.7, 5.5) (9.8, 18.2) (0.1, 0.1) 0.4 (12.1, 21.2)4.527 1.0 4.0 3.0 (2.6, 1.5) 1.6 1.5 (-, 7.4) (5.8, 2.1) (5.5, 17.8) (0.2, 0.3) 0.4 (10.1, 20.2)4.575 1.0 4.0 3.0 (2.3, 1.5) 1.6 1.4 (-, 7.2) (4.1, 3.0) (7.4, 20.1) (0.5, 0.5) 0.4 (10.4, 22.3)4.600 1.0 4.0 3.0 (2.3, 1.9) 1.6 1.4 (-, 6.6) (0.4, 1.1) (8.1, 16.2) (0.5, 0.6) 0.4 (10.1, 18.5)
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