Cross section measurement of e^+e^- \to p\bar{p}η and e^+e^- \to p\bar{p}ω at center-of-mass energies between 3.773 GeV and 4.6 GeV
M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, 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, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. G. Gao, I. Garzia, 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, X. Q. Hao, F. A. Harris, K. L. He, F. H. Heinsius, C. H. Heinz, et al. (394 additional authors not shown)
CCross section measurement of e + e − → p ¯ pη and e + e − → p ¯ pω at center-of-massenergies between 3.773 GeV and 4.6 GeV M. Ablikim , M. N. Achasov ,c , P. Adlarson , S. Ahmed , M. Albrecht , A. Amoroso A, C , Q. An , ,Anita , Y. Bai , O. Bakina , R. Baldini Ferroli A , I. Balossino A , Y. Ban ,k , K. Begzsuren , J. V. Bennett ,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 B ,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 , , J. P. Dai ,g , X. C. Dai , , A. Dbeyssi , R. B. 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 , , , S. X. Du , J. Fang , , S. S. Fang , , Y. Fang , R. Farinelli A , L. Fava B, C ,F. Feldbauer , G. Felici A , C. Q. Feng , , M. Fritsch , C. D. Fu , Y. Fu , X. L. Gao , , Y. Gao , Y. Gao ,k ,Y. G. Gao , I. Garzia A, B , 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 , Y. P. Guo , A. Guskov , S. Han , T. T. Han , T. Z. Han ,h ,X. Q. Hao , F. A. Harris , K. L. He , , F. H. Heinsius , T. Held , Y. K. Heng , , , M. Himmelreich ,f ,T. Holtmann , Y. R. Hou , Z. L. Hou , H. M. Hu , , J. F. Hu ,g , T. Hu , , , Y. Hu , G. S. Huang , ,L. Q. Huang , X. T. Huang , Y. P. Huang , Z. Huang ,k , N. Huesken , 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 , ,H. B. Jiang , X. S. Jiang , , , X. Y. 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 B,e , B. Kopf , M. Kuemmel , M. Kuessner ,A. Kupsc , M. G. Kurth , , W. K¨uhn , J. J. Lane , J. S. Lange , P. Larin , L. Lavezzi C , H. Leithoff ,M. Lellmann , T. Lenz , C. Li , C. H. Li , Cheng Li , , D. M. Li , F. Li , , G. Li , H. B. Li , , H. J. Li ,h ,J. L. Li , J. Q. Li , Ke Li , L. K. Li , Lei Li , P. L. Li , , P. R. Li , S. Y. Li , W. D. Li , , W. G. Li ,X. H. Li , , X. L. Li , Z. B. Li , Z. Y. Li , H. Liang , , H. Liang , , Y. F. Liang , Y. T. Liang ,L. Z. Liao , , J. Libby , C. X. Lin , B. Liu ,g , B. J. Liu , C. X. Liu , D. Liu , , D. Y. Liu ,g , F. H. Liu ,Fang Liu , Feng Liu , H. B. Liu , H. M. Liu , , Huanhuan Liu , Huihui Liu , J. B. Liu , , J. Y. Liu , ,K. Liu , K. Y. Liu , Ke Liu , L. Liu , , Q. Liu , S. B. Liu , , Shuai Liu , T. Liu , , X. Liu , Y. B. Liu ,Z. A. Liu , , , Z. Q. Liu , Y. F. Long ,k , X. C. Lou , , , 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. N. Ma , X. X. Ma , , X. Y. Ma , , Y. M. 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 , Y. Pan , A. Pathak , P. Patteri A ,M. Pelizaeus , H. P. Peng , , K. Peters ,f , J. Pettersson , J. L. Ping , R. G. Ping , , A. Pitka , R. Poling ,V. Prasad , , H. Qi , , H. R. Qi , M. 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 , A. Sarantsev ,d ,Y. Schelhaas , C. Schnier , K. Schoenning , D. C. Shan , W. Shan , X. Y. Shan , , 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 , Q. Q. Song , ,W. M. Song , Y. X. Song ,k , S. Sosio A, C , S. Spataro A, C , F. F. Sui , G. X. Sun , J. F. Sun , L. Sun ,S. S. Sun , , T. 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 , V. Thoren , B. Tsednee , I. Uman D ,B. Wang , B. L. Wang , C. W. Wang , D. Y. Wang ,k , H. P. Wang , , K. Wang , , L. L. Wang , M. Wang ,M. Z. Wang ,k , Meng 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 , 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 , Y. J. Xiao , , Z. J. Xiao , X. H. Xie ,k , Y. G. Xie , , Y. H. Xie , a r X i v : . [ h e p - e x ] F e b T. Y. Xing , , X. A. Xiong , , G. F. Xu , J. J. Xu , Q. J. Xu , W. Xu , , X. P. Xu , L. Yan A, C ,L. Yan ,h , W. B. Yan , , W. C. Yan , Xu Yan , H. J. Yang ,g , H. X. Yang , L. Yang , R. X. Yang , ,S. L. Yang , , Y. H. 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 , , W. Yuan A, C ,X. Q. Yuan ,k , Y. Yuan , Z. Y. Yuan , C. X. Yue , A. Yuncu B,a , A. A. Zafar , Y. Zeng ,l , B. X. Zhang ,Guangyi Zhang , H. H. Zhang , H. Y. Zhang , , J. L. Zhang , J. Q. Zhang , J. W. Zhang , , , J. Y. Zhang ,J. Z. Zhang , , Jianyu Zhang , , Jiawei Zhang , , L. Zhang , Lei Zhang , S. Zhang , S. F. Zhang ,T. J. Zhang ,g , 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 , W. J. Zhu , X. L. Zhu , Y. C. Zhu , , Z. A. Zhu , , 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 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 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN Sezionedi Perugia, I-06100, Perugia, Italy; (C)University of Perugia, I-06100, Perugia, Italy (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 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands 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 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 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 Tsinghua University, Beijing 100084, People’s Republic of China (A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul BilgiUniversity, 34060 Eyup, Istanbul, Turkey; (C)Uludag University, 16059 Bursa,Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 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 (A)University of Turin, I-10125, Turin, Italy; (B)University of EasternPiedmont, 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, Ministryof Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Instituteof 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 Instituteof Modern Physics, Fudan University, 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 of China l School of Physics and Electronics, Hunan University, Changsha 410082, China (Dated: February 9, 2021)Based on 14 . − of e + e − annihilation data collected with the BESIII detector at the BEPCIIcollider at 17 different center-of-mass energies between 3 . . e + e − → p ¯ pη and e + e − → p ¯ pω are measured for the first time. No indication of resonant production through a vector state V is observed, and upper limits on theBorn cross sections of e + e − → V → p ¯ pη and e + e − → V → p ¯ pω at the 90 % confidence level arecalculated for a large parameter space in resonance masses and widths. For the current world averageparameters of the ψ (4230) of m = 4 . /c and Γ = 44 MeV, we find upper limits on resonantproduction of the p ¯ pη and p ¯ pω final states of 7 . . I. INTRODUCTION
In recent years, several unexpected states have beendiscovered in the charmonium sector. Notable examplesare the χ c (3872) discovered by Belle [1], the chargedcharmonium-like Z c (3900) discovered by BESIII [2] andthe vector states ψ (4220) and ψ (4390), originally discov-ered by BaBar [3] as a single broad resonance named Y (4260) in the e + e − → γ ISR π + π − J/ψ process, andlater found to be two distinct states by BESIII [4].Charmonium-like vector states similar to the ψ (4220)and ψ (4390) were observed by BESIII in the processes e + e − → π + π − h c [5], π + π − ψ (3686) [6], D D ∗− π + [7], ωχ c [8] and ηJ/ψ [9–11]. However, so far no obser-vations have been made of decays into light mesons orbaryons for either the ψ (4220) or the ψ (4390). Crosssections have been determined for the processes e + e − → p ¯ pπ [12], φφφ , φφω [13], pK S ¯ nK − [14], K S K ± π ∓ [15], K S K ± π ∓ π and K S K ± π ∓ η [16] without significant de-tection of resonant production. Channels that include aproton anti-proton pair are especially interesting, sincethe partial width of decays of the type V → p ¯ ph , where V is a vector-state in the charmonium region and h is alight meson, can be related to the production cross sec-tion p ¯ p → V h [17]. In light of the upcoming PANDAexperiment at the FAIR facility [18], it is important toobtain the production cross sections of potentially exoticresonances in the charmonium sector.Multiple theoretical explanations have been offeredconcerning the nature of the ψ (4220) and ψ (4390) states.Possible interpretations include D ¯ D molecules, hybridcharmonia or baryonium states, and their compatibilitywith experimental data has recently been discussed in de-tail in Ref. [19]. Additional information is needed fromexperiments in order to discriminate between the differ-ent hypotheses. Thus, the search for new decay modesof the ψ (4220) and ψ (4390) is important.In this work, we report measurements of the Born crosssections of the processes e + e − → p ¯ pη and e + e − → p ¯ pω for data collected at 17 different center-of-mass energiesbetween √ s = 3 . V → p ¯ pη and V → p ¯ pω . II. BESIII DETECTOR AND MONTE CARLOSIMULATIONS
The BESIII detector is a magnetic spectrome-ter [20] located at the Beijing Electron Positron Col- lider (BEPCII) [21]. The cylindrical core of the BE-SIII detector 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 counter 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 . dE/dx 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 part is68 ps, while that of the end cap part is 110 ps. The endcap TOF system was upgraded in 2015 with multi-gapresistive plate chamber technology, providing a time res-olution of 60 ps [22]. This improvement affects data at11 of the 17 center-of-mass energy points.A Monte Carlo (MC) simulation of the full BESIII de-tector, based on geant [23], is used to optimize se-lection requirements, determine the product of detectoracceptance and reconstruction efficiency and study andestimate possible background contributions. These simu-lations also account for the observed beam energy spread.Dedicated simulations with 10 events per center-of-mass energy of the signal processes e + e − → p ¯ pη and e + e − → p ¯ pω with subsequent decays η → γγ , η → π + π − π , ω → π + π − π and π → γγ are generated withthe ConExc [24] generator, accounting for initial stateradiation (ISR) and vacuum polarization (VP). The threedifferent decay modes of the η meson are weighted ac-cording to the respective branching fraction as given bythe Particle Data Group (PDG) Ref. [25].In addition, an inclusive MC sample at a center-of-mass energy of √ s = 4 . q ¯ q (where q is a u, d, s quark) processes.Known decay modes are modeled with evtgen [26] usingbranching fractions taken from the PDG [25], whereasunknown processes are modeled by the lundcharm model [27]. Final state radiation (FSR) from charged fi-nal state particles is incorporated with the photos pack-age [28]. The inclusive MC sample at √ s = 4 . III. EVENT SELECTION
Two different final states are studied in this work,namely p ¯ pγγ (for e + e − → p ¯ pη with η → γγ ) and p ¯ pπ + π − γγ (for e + e − → p ¯ pη with η → π + π − π and e + e − → p ¯ pω with ω → π + π − π , both with a subse-quent π → γγ decay). In the analysis, the invariantmass distributions m ( γγ ) and m ( π + π − π ) will be usedto identify and quantify η and ω contributions. The po-lar angle θ of each charged track detected in the MDChas to satisfy | cos θ | < .
93, and its point of closest ap-proach to the interaction point must be within ±
10 cm inthe beam direction and within 1 cm in the plane perpen-dicular to the beam direction. For particle identification(PID), the TOF information and the specific energy de-posit dE/dx in the MDC are combined to calculate alikelihood P ( h ) for the particle hypotheses h = π, K, p .The particle type with the largest likelihood is assignedto each track. In addition, we require a minimum likeli-hood of P ( h ) > − to suppress background.For photons, a minimum energy deposit in thecalorimeter of 25 MeV in the barrel region ( | cos θ | < .
80) or of 50 MeV in the end-cap regions (0 . < | cos θ | < .
92) is required. In addition, the time in-formation from the shower in the calorimeter relative tothe event start time has to be less than 700 ns. Showerswithin 10 ◦ of the impact point of any charged track arediscarded.Only events containing exactly one good proton andone good anti-proton candidate (and exactly one good π + and one good π − candidate in case of the p ¯ pπ + π − γγ final state) and at least two good photon candidates areretained. A four- (five-)constraint kinematic fit is per-formed to the p ¯ pγγ ( p ¯ pπ + π − π with π → γγ ) hypoth-esis requiring four-momentum conservation between ini-tial and final states and, if relevant, an additional massconstraint for the π → γγ decay. If more than one γγ combination in an event satisfies the above requirements,only the combination with the lowest kinematic fit χ iskept for further analysis. The resulting invariant massspectra for the decays η → γγ , η → π + π − π and ω → π + π − π are displayed for the data at √ s = 4 . p ¯ pγγ final state, the main background chan-nels are the processes e + e − → p ¯ p , p ¯ pπ , p ¯ pω with asubsequent ω → π γ decay and e + e − → γ ISR
J/ψ witha subsequent
J/ψ → p ¯ p decay. For the p ¯ pπ + π − γγ finalstate, the main background channels are e + e − → ∆ ¯∆ π , e + e − → p ¯∆ ρ , e + e − → p ¯∆ ππ and e + e − → p ¯ pρπ (thevarious possible charges of the ∆, ¯∆, ρ and π and overallcharge conjugation are taken into account), which can alllead to the signal final state. No peaking backgrounds inthe invariant mass distributions m ( γγ ) and m ( π + π − π )are found.The selection criteria with respect to the kinematic fitare optimized according to s √ s + b , where s and b are the number of signal and background events in the inclusiveMC sample, that has been scaled to data, after requir-ing χ < χ . In case of the p ¯ pγγ final state, χ < p ¯ pπ + π − π system so thatno requirement is made on the χ of the kinematic fit.This procedure is repeated with s (cid:48) and b (cid:48) being signaland background contributions determined directly fromdata using the η ( ω ) signal- and sidebands. The result-ing selection condition agrees with the one determinedfrom the inclusive MC sample within statistical uncer-tainties. As both the data and the inclusive MC sam-ples at the other center-of-mass energies are significantlysmaller than those at √ s = 4 . χ <
30 for the p ¯ pγγ final state is applied for all center-of-mass energies.The number of signal events is determined from a fitto the invariant mass spectra (see Fig. 1). In the fit, thesignal is described by a shape determined from signal MCsimulations convolved with a Gaussian function in orderto account for a possible underestimation of the mass res-olution in MC simulation. The background is describedby first- and second-order polynomial functions in the η → γγ and η ( ω ) → π + π − π channels, respectively. Inthe first step, we perform a global binned maximum like-lihood fit to the sum of the data at all center-of-massenergies, determining a width of the Gaussian smearingfunctions as well as a background shape for each of thethree channels. A binned maximum likelihood fit is thenperformed to each dataset and channel individually, withonly the signal and background yields as free parame-ters. The signal and background shape are fixed to theresult of the global fit in order to obtain reliable resultsfrom all sample sizes. The number of signal events inchannel i at center-of-mass energy √ s is then defined as N i sig ( s ) = n sr − n bg,sr , where n sr is the number of events inthe signal region (defined as the symmetric region aroundthe nominal η ( ω ) meson mass containing 95% of all sig-nal events according to the signal shape) and n bg,sr is thenumber of background events in the signal region accord-ing to the polynomial background function (see Fig. 1). IV. EFFICIENCY DETERMINATION
We define the efficiency, (cid:15) i ( s ), according to (cid:15) i ( s ) = N i acc ( s ) N i gen ( s ) , (1)where N i acc ( s ) is the number of reconstructed signalevents and N i gen ( s ) is the total size of the signal MCsample in channel i for a center-of-mass energy √ s . Ifthe efficiency is not constant over the full n -particlephase-space, Eq. 1 only holds if the signal MC sampleproperly reflects data in all relevant coordinates (cid:126)x = ) ) (GeV/c gg m( ) E v en t s / ( . G e V / c data (4.1784 GeV)fit result-2lnL / ndf = 96.2 / 1481st order polynomial (a) ) ) (GeV/c p - p + p m( ) E v en t s / ( . G e V / c data (4.1784 GeV)fit result-2lnL / ndf = 78.8 / 1482nd order polynomial (b) ) ) (GeV/c p - p + p m( ) E v en t s / ( . G e V / c data (4.1784 GeV)fit result-2lnL / ndf = 159 / 2482nd order polynomial (c)Figure 1. (Color online) Fits to the invariant mass of the(a) η → γγ , (b) η → π + π − π and (c) ω → π + π − π systems.Black points represent data at the center-of-mass energy of √ s = 4 . { p p , θ p , φ p , p ¯ p , θ ¯ p , φ ¯ p , ... } . Since the data distribution isa priori unknown, we will perform a partial wave analy-sis of the data in order to re-weight our MC sample.The isobar model [29] is used in the partial wave anal-ysis by decomposing the full e + e − → γ ∗ → p ¯ pη and e + e − → γ ∗ → p ¯ pω processes into a sequence of two-bodydecays. Each two-body decay is described in the helicityformalism [30]. The η meson is treated as a stable par-ticle in the amplitude analysis, whereas the three-bodydecay of the ω meson is described by a three-body am- plitude according to Ref. [31]. Blatt-Weisskopf barrierfactors [30] are used for both the production γ ∗ → ad and the two-body decay a → bc according to Ref. [31] .The dynamical part of the amplitude is described by rel-ativistic Breit-Wigner amplitudes. Only the line-shapeof the η and ω mesons is not described in this way. Herewe employ the signal MC simulations that are used fornormalization in the partial wave analysis for the line-shapes. For the two e + e − → p ¯ pη channels, we include asintermediate p ¯ p resonances the J/ψ (using a Voigt distri-bution) and possible contributions of a J P C = 1 −− and a J P C = 3 −− resonance. We also include one J P = − (+) and one J P =
32 +( − ) resonance contribution for the ηp (¯ p ) system. For of the e + e − → p ¯ pω channel, onlyintermediate states that decay to the p ¯ p system are in-cluded. For each of the three possible quantum numbers J P C = 0 − + , ++ , ++ we include a phase-space con-tribution that is constant as a function of m ( p ¯ p ) as wellas two resonant contributions. All masses and widths ofintermediate states are free parameters in the fit, apartfrom the J/ψ contribution, where mass and width arefixed to the values given in the PDG [25]. Note that theaim of this partial wave analysis is only to describe thedata accurately enough to enable an accurate determina-tion of the efficiency.The partial wave analysis is performed as an unbinnedmaximum likelihood fit using the software package
PAW-IAN [32]. Details on likelihood construction in
PAW-IAN can be found in Refs. [31–33]. The remaining back-ground events underneath the η ( ω ) peaks are accountedfor in the partial wave analysis by adding the sidebandsdefined in Fig. 1 to the likelihood with negative weightsin such a way that the combined sideband weight is equalto the integral of the background function in the signalregion.The data for the two decay channels η → γγ and η → π + π − π are fitted simultaneously with all ampli-tudes fully constrained between the two channels apartfrom an overall scaling factor. The results of the partialwave analysis for the different channels are displayed inFig. 2 for the high statistics data at a center-of-mass en-ergy of √ s = 4 . w ( (cid:126)x ), from thepartial wave analysis as a function of the coordinates inthe n -particle phase-space, and they are used to deter-mine the efficiency (cid:15) i ( s ) as (cid:15) i ( s ) = N i acc ( s ) (cid:80) j =0 w ( (cid:126)x j ) N i gen ( s ) (cid:80) j =0 w ( (cid:126)x j ) . (2)The efficiencies obtained in this way are summarized inTables I and II. ) ) (GeV/cpm(p ) E v en t s / ( . G e V / c (a) ) ) (GeV/c h p/ h m(p ) E v en t s / ( . G e V / c (b) ) ) (GeV/cpm(p ) E v en t s / ( . G e V / c (c) ) ) (GeV/c h p/ h m(p ) E v en t s / ( . G e V / c (d) ) ) (GeV/cpm(p ) E v en t s / ( . G e V / c (e) ) ) (GeV/c w p/ w m(p ) E v en t s / ( . G e V / c (f)Figure 2. (Color online) Results of the partial wave analysis of the e + e − → p ¯ pη channel with subsequent η → γγ (a - b) and η → π + π − π decays (c - d) and the e + e − → p ¯ pω process (e - f) for the data at a center-of-mass energy of √ s = 4 . p ¯ p system, the right column the invariant mass of the pη ( pω ) system. Blackpoints correspond to data, full (red) lines show the result of the amplitude analysis. V. DETERMINATION OF BORN CROSSSECTIONS
The Born cross section of the process e + e − → p ¯ pη ( e + e − → p ¯ pω ) is given by σ B ( s ) = N ( s ) L ( s ) · (1 + δ r ( s )) · | − Π | · (cid:15) ( s ) · B , (3) where N ( s ) is the number of signal events observed inthe data sample at center-of-mass energy √ s , L ( s ) isthe corresponding integrated luminosity determined us-ing Bhabha scattering [34], δ r ( s ) and | − Π | are correc-tions accounting for initial state radiation and vacuumpolarization, (cid:15) ( s ) is the efficiency and B is the prod-uct of branching ratios involved in the decay. The cor-rection | − Π | is calculated with the alphaQED soft-ware package [35] with an accuracy of 0 . σ B ( s ). We consider two successive iterations con-verged if κ i /κ i − = 1 within statistical uncertainties,where κ ( s ) = (cid:15) ( s ) · (1 + δ r ( s )) is the product of the ef- ficiency and a radiative correction factor 1 + δ r ( s ) ob-tained from the ConExc
MC generator. The product ofbranching fractions is given by B = Br ( η → γγ ) for the e + e − → p ¯ pη ( → γγ ) channel, B = Br ( η → π + π − π ) · Br ( π → γγ ) for the e + e − → p ¯ pη ( → π + π − π ) chan-nel and B = Br ( ω → π + π − π ) · Br ( π → γγ ) for the e + e − → p ¯ pω ( → π + π − π ) channel. A combined Borncross section σ B is determined for the two different η de-cay modes by using a weighted least squares method [36].The resulting cross sections are displayed in Fig. 3 andall necessary values for their calculation are summarizedin Tables I and II. Table I. Summary of the Born cross sections σ B of the process e + e − → p ¯ pη for the datasets at different center-of-mass energies √ s , integrated luminosity L , radiative corrections 1 + δ r , vacuum polarization correction | − Π | , number of observed events N i , efficiency (cid:15) i , and cross section σ i in the two channels (1) η → γγ and (2) η → π + π − π . √ s (GeV) L (pb − ) (1 + δ r ) | − Π | N ε (%) σ (pb) N ε (%) σ (pb) σ B (pb)3.7730 2931 . . +39 . − . . ± . . +0 . − . . +28 . − . . ± . . +0 . − . . +0 . − . ± . . . +11 . − . . ± . . +0 . − . . + 7 . − . . ± . . +0 . − . . +0 . − . ± . . . +14 . − . . ± . . +0 . − . . +10 . − . . ± . . +0 . − . . +0 . − . ± . . . +29 . − . . ± . . +0 . − . . +18 . − . . ± . . +0 . − . . +0 . − . ± . . . +13 . − . . ± . . +0 . − . . + 9 . − . . ± . . +0 . − . . +0 . − . ± . . . +12 . − . . ± . . +0 . − . . + 8 . − . . ± . . +0 . − . . +0 . − . ± . . . +12 . − . . ± . . +0 . − . . + 8 . − . . ± . . +0 . − . . +0 . − . ± . . . +11 . − . . ± . . +0 . − . . + 7 . − . . ± . . +0 . − . . +0 . − . ± . . . +16 . − . . ± . . +0 . − . . +11 . − . . ± . . +0 . − . . +0 . − . ± . . . +12 . − . . ± . . +0 . − . . + 7 . − . . ± . . +0 . − . . +0 . − . ± . . . +11 . − . . ± . . +0 . − . . + 8 . − . . ± . . +0 . − . . +0 . − . ± . . . +14 . − . . ± . . +0 . − . . + 9 . − . . ± . . +0 . − . . +0 . − . ± . . . +12 . − . . ± . . +0 . − . . + 7 . − . . ± . . +0 . − . . +0 . − . ± . . . + 7 . − . . ± . . +0 . − . . + 4 . − . . ± . . +0 . − . . +0 . − . ± . . . + 9 . − . . ± . . +0 . − . . + 6 . − . . ± . . +0 . − . . +0 . − . ± . . . +14 . − . . ± . . +0 . − . . + 9 . − . . ± . . +0 . − . . +0 . − . ± . . . + 9 . − . . ± . . +0 . − . . + 5 . − . . ± . . +0 . − . . +0 . − . ± . VI. SYSTEMATIC UNCERTAINTIES
Various sources of systematic uncertainties contribut-ing to the measurement of the e + e − → p ¯ pη and e + e − → p ¯ pω Born cross sections have been considered.The uncertainty of the integrated luminosity deter-mined using Bhabha scattering is 1% [34]. The sys-tematic uncertainty of the tracking efficiency has beendetermined using a
J/ψ → p ¯ pπ + π − control sample inRef. [37] as 1% per track. Similarly, systematic uncer-tainties of photon detection efficiencies have been stud-ied using a J/ψ → ρπ control sample [38] and were found to be 1% per photon. For PID efficiency, a system-atic uncertainty of 1% per proton and 1% per pion aretaken from Ref. [12, 39]. For multiple particles, each ofthe track-finding, PID, and photon efficiency uncertain-ties are added linearly [12, 37–39]. Uncertainties on thebranching fractions are taken from the PDG [25]. Withregard to the kinematic fit, where a selection conditionof χ <
30 is applied in case of the e + e − → p ¯ pη ( → γγ )mode, the selection condition is varied between χ < χ <
55 in steps of δχ = 5 and the resulting Borncross section is determined and compared with the nomi-nal value R = σ step σ nom . We take the standard deviation of a Table II. Summary of the Born cross sections σ B of the process e + e − → p ¯ pω for the datasets at different center-of-massenergies √ s , integrated luminosity L , radiative corrections 1 + δ r , vacuum polarization correction | − Π | , number of observedevents N , and the efficiency (cid:15) . √ s (GeV) L ( pb − ) (1 + δ r ) | − Π | N ε (%) σ B (pb)3.7730 2931 . . +79 . − . . ± . . +0 . − . ± . . . +19 . − . . ± . . +0 . − . ± . . . +25 . − . . ± . . +0 . − . ± . . . +53 . − . . ± . . +0 . − . ± . . . +22 . − . . ± . . +0 . − . ± . . . +22 . − . . ± . . +0 . − . ± . . . +21 . − . . ± . . +0 . − . ± . . . +20 . − . . ± . . +0 . − . ± . . . +30 . − . . ± . . +0 . − . ± . . . +22 . − . . ± . . +0 . − . ± . . . +21 . − . . ± . . +0 . − . ± . . . +26 . − . . ± . . +0 . − . ± . . . +21 . − . . ± . . +0 . − . ± . . . +12 . − . . ± . . +0 . − . ± . . . +19 . − . . ± . . +0 . − . ± . . . +26 . − . . ± . . +0 . − . ± . . . +16 . − . . ± . . +0 . − . ± . weighted sample of the ratio R as the systematic uncer-tainty due to potential differences in the χ distributionsbetween data and MC simulation. Here, 1 /δR is usedas the weight, where δR is the uncertainty taking intoaccount the sizable correlation between the event sam-ples. The nominal symmetric signal region containing95% of the total signal is altered to a set of both smallerand larger signal regions and we determine the resultingBorn cross sections. As outlined above, we take the stan-dard deviation of a sample of ratios R weighted by theinverse of the statistical uncertainty as the systematicuncertainty resulting from the choice of signal region.For the background description, the polynomial shapeswere increased by one order from the nominal first orderpolynomial used for the η → γγ invariant mass spec-trum, and the second order polynomial in the case of the η → π + π − π and ω → π + π − π invariant mass spectra.The fits are then repeated and the difference to the nom-inal results is taken as a systematic uncertainty. For theradiative correction factor, we performed five additionaliterations and found no difference beyond the statisticaluncertainty. This contribution to the systematic uncer-tainty is therefore neglected.The systematic uncertainties are summarized in Ta-ble III for the data at a center-of-mass energy of √ s =4 . e + e − → p ¯ pη chan-nels are accounted for in the calculation of the combinedBorn cross section following Ref. [36]. Table III. Summary of systematic uncertainties in percentfor the data at √ s = 4 . η → γγ η → π + π − π ω → π + π − π Luminosity 1.0 1.0 1.0Tracking efficiency 2.0 4.0 4.0Photon detection 2.0 2.0 2.0Particle Identification 2.0 4.0 4.0Branching fraction 0.5 1.2 0.8 χ cut 1.9Signal region 0.6 0.8 0.8Background description 0.7 1.5 0.3Total 4.3 6.5 6.2 VII. SEARCH FOR RESONANTCONTRIBUTIONS
The final Born cross sections for the e + e − → p ¯ pη and e + e − → p ¯ pω processes are displayed in Fig. 3. In order tosearch for possible e + e − → V → p ¯ pη ( e + e − → V → p ¯ pω )resonant contributions, we perform two different fits. Inthe first fit, only a non-resonant contribution of the type σ nr ( s ) = (cid:18) C √ s (cid:19) λ (4)defined in Ref. [12] is used. The second fit includes asingle Breit-Wigner amplitude of the form A res ( s ) = A V (cid:18) m Γ s − m + im Γ (cid:19) (5)0that is coherently added to the non-resonant term. (GeV)s ) ( pb ) h p p fi - e + ( e B s data continuum l (C/s) + BW (coherent) l (C/s) (a) (GeV)s ) ( pb ) w p p fi - e + ( e B s data continuum l (C/s) + BW (coherent) l (C/s) (b)Figure 3. (Color online) Born cross sections of the e + e − → p ¯ pη (a) and e + e − → p ¯ pω (b) processes as a function of thecenter-of-mass energy. Black points represent our result in-cluding both statistical and systematic uncertainties. Thefull (red) and long-dashed (blue) lines represent the fits us-ing a continuum contribution and a Breit-Wigner coherentlyadded to the continuum contribution, respectively. The fitsdisplayed ( m = 4 . /c and Γ = 44 MeV) are thosefor the current world average parameters of the ψ (4230) [25]. Unbinned maximum likelihood fits are performedwhere the likelihood L ( x ; Θ) given the data x and thefit parameters Θ is defined as the product L ( x ; Θ) = (cid:81) i,j L ij (Θ), where L ij is a set of likelihood functions,one each for each dataset i and decay mode j . Theselikelihood functions are transformed such that they onlydepend on the expected number of signal events N ≡ N ij (Θ) which can be calculated for each dataset accord-ing to Eq. 3. The likelihood L ij ( N ) is then obtainedfrom data via a likelihood scan of the number of signalevents in the invariant mass distributions of the mesondecay systems. These likelihood scans are parameterizedby asymmetric Gaussian distributions. Incorporating thesystematic uncertainties of dataset i and channel j , the likelihood is L ij ( N ) = 1 (cid:114) π (cid:16)(cid:0) σ L + σ R (cid:1) + σ (cid:17) · e − ( N − µ )22( σ k + σ with σ k = (cid:26) σ L , N ≤ µσ R , N > µ . (6)In the fit, all systematic uncertainties apart from the oneon the branching ratio of the meson decays are consid-ered uncorrelated between the different c.m. energies.While a correlation of a systematic uncertainty betweentwo c.m. energies can not in general be ruled out, ourassumption of a vanishing correlation leads to the mostconservative upper limit estimation. We find no evidencefor a resonant contribution from the fits and set upperlimits at the 90% confidence level. As the resonant con-tribution is added coherently, the fit finds two ambiguoussolutions for constructive and destructive interference byconstruction. The upper limits are obtained by integrat-ing L ( x ; Θ) = (cid:81) i,j L ij (Θ) according to σ UL V (cid:82) −∞ L ( x, Θ) π (Θ) dσ V ∞ (cid:82) −∞ L ( x, Θ) π (Θ) dσ V = 0 . , (7)where the prior π (Θ) is given by π (Θ) = (cid:26) , σ V ≥ , σ V < . (8)The procedure outlined above is repeated with a step sizeof 1 MeV for different masses m in the range 4 GeV /c 300 MeV for a potential resonant contribution. Theresults are shown in Fig. 4.The most stringent upper limits are found for resonantcontributions with mass m = 4 . 389 GeV /c and widthΓ = 40 MeV (Γ = 296 MeV) in the p ¯ pη ( p ¯ pω ) channelwith values of 4 . 03 pb and 7 . 88 pb at the 90% CL, re-spectively. The upper limits for a resonant contributionof the ψ (4230), using current world average values formass ( m = 4 . /c ) and width (Γ = 44 MeV)[25] are 7 . . VIII. SUMMARY The processes e + e − → p ¯ pη and e + e − → p ¯ pω havebeen studied using 14 . − of electron-positron anni-hilation data at 17 different center-of-mass energies be-tween 3.7730 GeV and 4.5995 GeV. Both processes areclearly identified at all center-of-mass energies and Borncross sections are determined. We find no evidence for aresonant contribution from a fit to the e + e − → p ¯ pη and e + e − → p ¯ pω Born cross sections, and set upper limits atthe 90% confidence level for a wide range of resonance1 ) mass m (GeV/c ( G e V ) G w i d t h ( pb ) U L s ) mass m (GeV/c ( G e V ) G w i d t h ( pb ) U L s Figure 4. (Color online) Upper limits on a possible resonantcontribution with mass m and width Γ for the two processes e + e − → p ¯ pη (top) and e + e − → p ¯ pω (bottom). parameters m and Γ. Using the approach outlined in Ref. [17], these upper limits will serve as valuable inputfor model calculations of the processes p ¯ p → V η and p ¯ p → V ω for the upcoming PANDA experiment. 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 NationalKey Basic Research Program of China under Con-tract No. 2015CB856700; National Natural ScienceFoundation of China (NSFC) under Contracts Nos.11625523, 11635010, 11735014, 11822506, 11835012,11935015, 11935016, 11935018, 11961141012; the Chi-nese Academy of Sciences (CAS) Large-Scale Scien-tific Facility Program; Joint Large-Scale Scientific Fa-cility Funds of the NSFC and CAS under ContractsNos. U1732263, U1832207; CAS Key Research Pro-gram of Frontier Sciences under Contracts Nos. 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