Observation of a resonant structure in e + e − →ωη and another in e + e − →ω π 0 at center-of-mass energies between 2.00 and 3.08 GeV
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, A. Amoroso, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, J. V. Bennett, 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, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, J. P. 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, 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. Fu, X. L. 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, S. Han, T. T. Han, T. Z. Han, X. Q. Hao, F. A. Harris, et al. (394 additional authors not shown)
aa r X i v : . [ h e p - e x ] O c t Observation of a resonant structure in e + e − → ωη and another in e + e − → ωπ at center-of-mass energies between 2.00 and 3.08 GeV M. Ablikim , M. N. Achasov ,d , 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 ,l , 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,c , D. Y. Chen , G. Chen , H. S. Chen , , M. L. Chen , ,S. J. Chen , X. R. Chen , Y. B. Chen , , W. Cheng C , G. Cibinetto A , F. Cossio C , X. F. Cui ,H. L. Dai , , J. P. Dai ,h , 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, B , 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 ,l ,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 , Y. P. Guo ,i , A. Guskov , S. Han , T. T. Han , T. Z. Han ,i ,X. Q. Hao , F. A. Harris , K. L. He , , F. H. Heinsius , T. Held , Y. K. Heng , , , M. Himmelreich ,g ,T. Holtmann , Y. R. Hou , Z. L. Hou , H. M. Hu , , J. F. Hu ,h , T. Hu , , , Y. Hu , G. S. Huang , ,L. Q. Huang , X. T. Huang , Z. Huang ,l , N. Huesken , T. Hussain , W. Ikegami Andersson , W. Imoehl ,M. Irshad , , S. Jaeger , S. Janchiv ,k , 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,f , 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 ,i , 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 ,h , B. J. Liu , C. X. Liu , D. Liu , ,D. Y. Liu ,h , 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 ,l , 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 ,i , 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 ,l , 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 ,d , H. Muramatsu , S. Nakhoul ,g , Y. Nefedov , F. Nerling ,g ,I. B. Nikolaev ,d , Z. Ning , , S. Nisar ,j , S. L. Olsen , Q. Ouyang , , , S. Pacetti B , X. Pan , Y. Pan ,A. Pathak , P. Patteri A , M. Pelizaeus , H. P. Peng , , K. Peters ,g , 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 ,e , M. Savri´e B , 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 ,l ,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 , 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 ,l , H. P. Wang , , K. Wang , , L. L. Wang , M. Wang , M. Z. Wang ,l , Meng Wang , ,W. H. Wang , W. P. Wang , , X. Wang ,l , X. F. Wang , X. L. Wang ,i , Y. Wang , , Y. Wang ,1. D. Wang , Y. F. Wang , , , Y. Q. Wang , Z. Wang , , Z. Y. Wang , Ziyi Wang , Zongyuan Wang , ,T. Weber , 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 ,i , Z. Wu , , L. Xia , , H. Xiao ,i ,S. Y. Xiao , Y. J. Xiao , , Z. J. Xiao , X. H. Xie ,l , Y. G. Xie , , Y. H. Xie , T. Y. Xing , , X. A. Xiong , ,G. F. Xu , J. J. Xu , Q. J. Xu , W. Xu , , X. P. Xu , L. Yan ,i , L. Yan A, C , W. B. Yan , , W. C. Yan ,Xu Yan , H. J. Yang ,h , 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 ,m , T. Yu , C. Z. Yuan , , W. Yuan A, C , X. Q. Yuan ,l , Y. Yuan , Z. Y. Yuan ,C. X. Yue , A. Yuncu B,a , A. A. Zafar , Y. Zeng ,m , 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 ,h , X. Y. Zhang , Y. Zhang ,Y. H. Zhang , , Y. T. Zhang , , Yan Zhang , , Yao Zhang , Yi Zhang ,i , 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 Zhao , Z. G. Zhao , , A. Zhemchugov ,b , B. Zheng ,J. P. Zheng , , Y. Zheng ,l , 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 and University of Perugia, I-06100,Perugia, Italy (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy 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 Netherlands2 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 ofChina 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 Bilgi University, 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 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 Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia d Also at the Novosibirsk State University, Novosibirsk, 630090, Russia e Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russia f Also at Istanbul Arel University, 34295 Istanbul, Turkey g Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany h Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai KeyLaboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240,People’s Republic of China i Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics,3udan University, Shanghai 200443, People’s Republic of China j Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA k Currently at: Institute of Physics and Technology, Peace Ave.54B, Ulaanbaatar 13330, Mongolia l Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People’sRepublic of China m School of Physics and Electronics, Hunan University, Changsha 410082, China
Abstract
Born cross sections for the processes e + e − → ωη and e + e − → ωπ have been determined for center-of-mass energiesbetween 2.00 and 3.08 GeV with the BESIII detector at the BEPCII collider. The results obtained in this work areconsistent with previous measurements but with improved precision. Two resonant structures are observed. In the e + e − → ωη cross sections, a resonance with a mass of (2179 ± ± MeV /c and a width of (89 ± ± MeVis observed with a significance of 6.1 σ . Its properties are consistent with the φ (2170) . In the e + e − → ωπ crosssections, a resonance denoted Y (2040) is observed with a significance of more than 10 σ . Its mass and width aredetermined to be (2034 ± ± MeV /c and (234 ± ± MeV, respectively, where the first uncertainties arestatistical and the second ones are systematic.
Keywords:
BESIII, φ (2170) , excited ω states, excited ρ states
1. Introduction
In low-energy e + e − collision experiments, the vec-tor mesons ρ , ω , and φ and their low lying excited statescan be produced abundantly. The Particle Data Group(PDG) [1] has tabulated experimental results for thesestates. However, some of the higher lying excitationsare not fully identified yet. It is especially in the re-gion around 2 GeV where further experimental insightis needed to resolve the situation involving resonancessuch as the ρ (2000) , ρ (2150) and φ (2170) states.Considerable efforts have been made theoreticallyto understand the nature of the φ (2170) resonance, andseveral interpretations have been proposed, such as an s ¯ sg hybrid [2, 3], an s ¯ s meson [4–7], an s ¯ ss ¯ s tetraquarkstate [8–13], a Λ ¯Λ bound state [14–16], as well as φK ¯ K [17] and φf (980) [18] resonances. These mod-els differ in their predictions of the branching frac-tions of the φ (2170) to decay channels such as φη or K ( ∗ ) ¯ K ( ∗ ) as certain decay modes can either be sup-pressed or favored depending on its nature [2, 4, 19–21]. It is therefore of great importance to measure thebranching fractions for a variety of different decay chan-nels in order to help in discriminating between differentmodels.The φ (2170) state was first observed by the BaBarexperiment in the initial state radiation (ISR) pro- cess e + e − → γ ISR φf (980) [22] and later confirmedby the BESII and BESIII experiments in J/ψ → ηφf (980) [23, 24] as well as by both the BaBarand Belle experiments in the aforementioned ISR pro-cess [25, 26]. The observed masses and widths of the φ (2170) range from (2079 ± +79 − ) MeV /c [26] to (2200 ± ± MeV /c [24] and (58 ± ± MeV [22]to (192 ± +25 − ) MeV [25], respectively.Several studies of the properties of the φ (2170) res-onance have recently been made by the BESIII ex-periment. A partial-wave analysis was performed forthe e + e − → K + K − π π process [27], in whichindications for sizable partial widths of the φ (2170) resonance to the K + (1460) K − , K +1 (1270) K − and K +1 (1400) K − channels (here, charge-conjugation isimplied) were found. Attempts were also made to studychannels with simpler topologies, including e + e − → K + K − , where a resonance with mass (2239 . ± . ± . MeV /c and width (139 . ± . ± . MeVwas found [28, 29], and e + e − → φη ′ [30], where a res-onance with mass (2177 . ± . ± . MeV /c and width (149 . ± . ± . MeV was found, In e + e − → φK + K − , a sharp enhancement is observed inthe Born cross section at √ s = 2 . GeV, which isclose to the mass of the φ (2170) resonance [31], how-ever its width seems to be incompatible with that of the Preprint submitted to Physics Letters B November 2, 2020 (2170) .A comparison of decay channels without hidden oropen strangeness such as e + e − → ωη to those observedthus far can provide additional information about theproperties of the φ (2170) resonance. In addition, thisprocess can also be used to study excited ω resonancesappearing as ω ∗ → ωη [32], which is expected to be oneof the dominant decay channels for excited ω mesonsand a benchmark process to study their properties.In contrast to the e + e − → ωη process, the reac-tion e + e − → ωπ allows the study of the isovectorvector mesons and their excited states. Generally, theexcited ρ states around GeV /c are not well under-stood. Although there are two results on the so-called ρ (2000) [33, 34], its existence is not well-established.Furthermore, several experiments have claimed the ob-servation of the ρ (2150) state with mass and width ly-ing in the range of . to . GeV /c and to MeV, respectively [35–39].In an approach based on the quark-pair-creationmodel, the ρ (2150) state is identified as a candidatefor the S state [40, 41]. The Born cross section of e + e − → ωπ in the energy region below 2 GeV hasbeen measured by several experiments [42–49], whilethe data above 2 GeV is rather scarce. Thus, more mea-surements of e + e − → ωπ above 2 GeV are of highinterest to study the properties of excited ρ states.In this letter, we present Born cross section measure-ments of the processes e + e − → ωη and e + e − → ωπ with subsequent ω → π + π − π , π → γγ and η → γγ decays.
2. Detector and data sample
The BESIII detector is a magnetic spectrome-ter [50] located at the Beijing Electron Position Collider(BEPCII) [51]. 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 calorimeter(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 par-ticles and photons is 93% over π solid angle. Thecharged-particle momentum resolution at /c is . , and the dE/dx resolution is for the electronsfrom Bhabha scattering. The EMC measures photon en-ergies with a resolution of . ( ) at GeV in thebarrel (end cap) region. The time resolution of the TOF barrel part is 68 ps, while that of the end cap part is110 ps.The data samples used in this letter have been col-lected with the BESIII detector at 22 center-of-mass(c.m.) energies from 2.000 to 3.080 GeV, correspond-ing to a total integrated luminosity of 651 pb − .The GEANT
BOOST [53] is used to produce Monte Carlo (MC)simulation samples. Events are generated using theC ON E XC generator [54] with ISR and vacuum polar-ization (VP) taken into account. Inclusive hadron pro-duction of the type e + e − → hadrons is simulated to es-timate possible background processes and to optimizeevent selection criteria. Exclusive MC samples are gen-erated to determine the detection efficiencies of the sig-nal processes. Since the beam energy spread of BEPCIIis less than 1 MeV at √ s < , it is much smallerthan the experimental resolution of the BESIII detectorand can thus be ignored in the simulation.
3. Event selection and determination of the Borncross section e + e − → ωη For e + e − → ωη (with subsequent ω → π + π − π , π → γγ and η → γγ decays), candidate eventsare required to have at least two reconstructed chargedtracks and at least four reconstructed photons. Eachcharged track is required to be located within the MDCacceptance, | cos θ | < . , where θ is the polar an-gle of the charged track, and to originate from a cylin-der around the interaction point of 1 cm radius and ex-tending ± cm along the detector axis. Informationfrom TOF and dE/dx measurements is combined toform particle identification (PID) likelihoods for the π , K , and p hypotheses. Each track is assigned a parti-cle type corresponding to the hypothesis with the high-est PID likelihood. Exactly two oppositely charged pi-ons are required in each event. Photon candidates arereconstructed using clusters of energy deposited in theEMC crystals. The energy is required to be larger than MeV in the barrel region ( | cos θ | < . ) and largerthan MeV in the end cap region ( . < | cos θ | < . ). The energy deposited in nearby TOF countersis included to improve the reconstruction efficiency andenergy resolution. The difference of the EMC time fromthe event start time is required to be within [0,700] ns tosuppress electronic noise and showers unrelated to theevent.To improve the momentum and energy resolutionand to suppress background events, a four-constraint54C) kinematic fit imposing four-momentum conser-vation is performed under the hypothesis e + e − → π + π − γ . For the goodness of the kinematic fit, χ < is required. For events with more than four photoncandidates, the combination with the smallest χ is re-tained. In addition, a kinematic fit for the alternative hy-pothesis e + e − → π + π − γ is performed and only thoseevents that satisfy χ ( π + π − γ ) < χ ( π + π − γ ) are retained in order to suppress backgrounds from e + e − → ωπ π events. Two photon pairs correspond-ing to the best π η , π π and ηη candidates are se-lected separately by choosing the combination with thesmallest value of χ αβ = ( M ( γ γ ) − m α ) /σ + ( M ( γ γ ) − m β ) /σ , where α and β represent either π or η , and the mass resolution σ in the invariantmass region of the π or η meson is obtained from MCsimulations. Only combinations with χ π η < χ π π and χ π η < χ ηη are retained. The π and η candi-dates are selected by requiring | M ( γ γ ) − m π | < . GeV /c and | M ( γ γ ) − m η | < . GeV /c , cor-responding to about σ intervals around the respectivenominal masses of π and η , m π and m η [1]. Eventswith | E γ − E γ | /p η > . , where p η is the momentumof the η meson in the laboratory system, are rejected tosuppress background events from the e + e − → ωγ ISR and e + e − → ωπ π processes. ) ) (GeV/c γγ M(0.4 0.5 0.6 0.7 ) ) ( G e V / c π - π + π M ( (a) ) ) (GeV/c γγ M(0.4 0.5 0.6 0.7 ) E v en t s / ( . G e V / c DataSignalBackground MC π πω Total fit (b) ) ) (GeV/c π - π + π M(0.65 0.7 0.75 0.8 0.85 0.9 ) E v en t s / ( . G e V / c DataSignalBackgroundTotal fit (c) ) ) (GeV/c π - π + π M(0.65 0.7 0.75 0.8 0.85 0.9 ) E v en t s / ( . G e V / c DataSignalBackgroundTotal fit (d)
Fig. 1: (Color online) Invariant mass distributions for data taken at √ s = 2 . GeV. (a) Distribution of the π + π − π invariant mass versus thetwo-photon invariant mass. The area marked in red corresponds to the signal region. (b) Fit to the M ( γγ ) distribution, where the (black) dots witherror bars are data, the (blue) solid curve is the total fit result, the (green) dashed curve indicates background described by a second order Chebychevpolynomial, the (red) dotted curve is the η → γγ signal shape described by a Voigt function and the (green) histogram is the e + e − → ωπ π MC sample scaled to the integral of the background function in the fit. The vertical lines indicate the signal (red) and sideband regions (blue).(c) and (d) represent the M ( π + π − π ) invariant mass distributions in the η signal and sideband region, respectively. The dots with error barsare data, the solid curves are the total fit results, the dashed curves indicate the background described by a second order Chebychev polynomialand the dotted curves are the ω signal shapes determined from MC simulations convolved with a Gaussian accounting for a potential difference inresolution between data and MC simulation. π + π − π invariant mass ver-sus the two-photon invariant mass of the selected eventsat √ s = 2 . GeV is shown as an example in Fig. 1(a),where an ω signal around the nominal ω meson mass isvisible. Potential background reactions to the e + e − → ωη process are studied using both inclusive e + e − → hadrons and exclusive MC samples. Simulated eventsare subject to the same selection procedure as that ap-plied to the experimental data. According to MC simu-lations, the dominant background stems from e + e − → π + π − π η , which contains the same final state parti-cles as the signal reaction. The e + e − → ωπ π and e + e − → ωγ ISR processes form a peaking backgroundcontribution in the π + π − π invariant mass distribution.The total peaking background from e + e − → ωγ ISR isestimated by MC simulations normalized to the exper-imental luminosity and is found to be negligible. Thepeaking background from e + e − → ωπ π is inferredfrom the η sidebands, which are defined as .
4C Angle Bkg Sig Range m( η ) m( π ) Peak δ Total2.0000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.12.0500 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.6 8.22.1000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 2.7 8.62.1250 1.0 2.0 4.0 2.0 0.9 0.5 0.5 1.1 1.9 2.5 2.2 0.4 3.0 9.6 1.1 122.1500 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 1.5 8.32.1750 1.0 2.0 4.0 2.0 0.9 0.5 0.7 1.1 0.5 2.5 0.5 0.4 3.0 3.7 1.2 7.72.2000 1.0 2.0 4.0 2.0 0.9 0.5 0.5 1.1 0.3 1.6 0.2 0.4 3.0 2.6 1.8 7.02.2324 1.0 2.0 4.0 2.0 0.9 0.5 0.7 1.1 0.2 0.8 0.7 0.4 3.0 1.6 1.5 6.52.3094 1.0 2.0 4.0 2.0 0.9 0.5 0.7 1.1 0.0 2.0 0.1 0.4 3.0 2.1 0.7 6.82.3864 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 1.0 1.6 1.2 0.4 3.0 2.3 0.5 6.92.3960 1.0 2.0 4.0 2.0 0.9 0.5 0.5 1.1 0.0 2.2 0.2 0.4 3.0 2.6 0.5 7.02.5000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.12.6444 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.2 1.4 0.6 0.4 3.0 1.6 0.5 6.52.6464 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 0.8 0.8 0.4 3.0 1.7 0.5 6.42.7000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.12.8000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.12.9000 1.0 2.0 4.0 2.0 0.9 0.5 0.5 1.1 0.2 0.4 0.8 0.4 3.0 1.7 0.5 6.42.9500 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.12.9810 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.13.0000 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.13.0200 1.0 2.0 4.0 2.0 0.9 0.5 0.6 1.1 0.1 2.5 0.2 0.4 3.0 4.8 0.5 8.13.0800 1.0 2.0 4.0 2.0 0.9 0.5 0.7 1.1 0.4 1.6 0.9 0.4 3.0 2.7 0.5 6.9 (GeV)s ) ( nb ) η ω → - e + ( e σ This work SNDCMD3 BaBar (a) (GeV)s ) ( nb ) π ω → - e + ( e σ This work SND(2000)SND(2016) BABARCMD2(1999) CMD2(2003)DM2 ND (b)
Fig. 2: (Color online) Dressed cross sections for the processes (a) e + e − → ωη and (b) e + e − → ωπ . In comparison to the data presented inthis work (red dots), in (a) the data from the CMD3 [56] (brown open circles), SND [55] (green open crosses) and BaBar [57] (blue open triangles)experiments are shown. In (b), our data is compared to the results of the CMD2 [46, 47] (green open upward triangles and green open circles),SND [42, 44] (green filled crosses and brown filled triangles), BaBar [49] (blue filled X crosses), DM2 [48] (magenta open stars) and ND [45](cyan filled downward triangles) experiments. Due to the limited statistics in the data samples, a con-trol sample of the
J/ψ → ωη decay is used to estimatethe uncertainties arising from the selection conditions χ ( π + π − γ ) < χ ( π + π − γ ) , χ π η < χ π π , χ π η < χ ηη , | M ( γ γ ) − m π | < . GeV /c , | M ( γ γ ) − m η | < . GeV /c and | E γ − E γ | /p η < . . For this, the single-requirement efficiency is stud-ied, removing one of the selection conditions at a timeand studying the change in the number of observedevents. In case a significant difference is found be- tween the data control sample and a MC simulation ofthe J/ψ → ωη decay, this difference is taken as thesystematic uncertainty.Due to large statistical fluctuations in the data, toyMC samples are used to estimate the systematic uncer-tainties stemming from the description of the signal andbackground shape as well as from the fit range when de-termining N obs . A total of 500 sets of toy MC samplesare generated according to the final fit result shown inFig. 1(c) with the same statistics as in data. For each9oy MC sample, the following procedure is performed:the ω signal shape is changed to a Breit-Wigner func-tion convolved with a Gaussian, the background shapeis varied from a second to a third order Chebychev poly-nomial and the fit range is varied by ± MeV /c . Themean value of the differences of the signal yield be-tween the nominal and the alternative fits is taken asthe systematic uncertainty. The uncertainty of peakingbackground is related to the uncertainty of N bkg and f scale . We estimate uncertainty of N bkg with the samemethod for N obs , and that of f scale by considering the fituncertainty of the non- η background at 2.125 GeV.The total systematic uncertainty for the Born crosssection measurement is determined to be 12% for the e + e − → ωη process at √ s = 2 . GeV. The uncer-tainties at the other c.m. energies are determined ac-cordingly and are summarized in Table 2. e + e − → ωπ The event selection criteria for the e + e − → ωπ process are mostly the same as described in Sec. 3.1.The π π candidate pairs are selected by minimiz-ing χ π π = ( M ( γ γ ) − m π ) /σ + ( M ( γ γ ) − m π ) /σ . These π candidates are required to bein a mass window of ( m π − . GeV /c , m π +0 . GeV /c ) . Since there are two π candidates, the π + π − π combination whose invariant mass is closestto m ω is retained as the ω candidate, where the π isdenoted as π ω to distinguish it from the bachelor pion π .Using the above selection criteria, the distributionof the invariant mass of π + π − π ω versus the two-photon invariant mass for π candidates is depictedin Fig. 3(a). The ω signal is clearly evident. ) ) (GeV/c γγ M(0.05 0.1 0.15 0.2 ) ) ( G e V / c ω π - π + π M ( (a) ) ) (GeV/c γγ M(0.05 0.1 0.15 0.2 ) E v en t s / ( . G e V / c
10 DataSignal match bach0 π (b) ) ) (GeV/c ω π - π + π M(0.7 0.75 0.8 0.85 0.9 ) E v en t s / ( . G e V / c DataSignalBackgroundTotal fit (c) ) ) (GeV/c ω π - π + π M(0.7 0.75 0.8 0.85 0.9 ) E v en t s / ( . G e V / c DataSignalBackgroundTotal fit (d)
Fig. 3: (Color online) Invariant mass distributions at √ s = 2 . GeV. (a) Distribution of the π + π − π ω invariant mass versus the two-photoninvariant mass corresponding to the π → γγ decay. The red box indicates the signal region. (b) Distribution of the two-photon invariantmass M ( γγ ) corresponding to the π → γγ decay, where the (black) dots with error bars are data, the (red) solid histogram and the (red)dashed histogram is the signal MC before and after π matching with the MC truth information. The red and blue vertical lines indicatethe signal and sideband regions, respectively. (c) and (d) represent the M ( π + π − π ω ) distribution corresponding to π signal and sidebandregions, respectively. The (black) dots with error bars are data, the (blue) solid curves are the total fit results, the (green) dashed curves indicate thebackground contributions described by a second order Chebychev polynomial and the (red) dotted curves show the ω signal shapes described bythe MC lineshape convolved with a Gaussian function.
10 method similar to that described in Sec. 3.1is used to study possible background contributions.According to the study, the dominant background stemsfrom the four body process e + e − → π + π − π π , whichhas the same final state particles as the signal chan-nel. In a similar way as in the e + e − → ωη case,possible peaking background contributions are inferredfrom the π sideband regions defined as . < | M ( γ γ ) − m π | < . GeV /c (as illustrated inFig. 3(b)). Note that due to mis-combination of pho-tons, a large fraction of the π sideband is composed ofsignal reactions. Still, while a peaking sideband con-tribution is found, its fraction is negligible (and wouldstill have to be scaled down in a similar procedure asdescribed for the ωη process) compared to the signal re-gion as shown in Figs. 3 (c) and (d).The signal yield is determined using the M ( π + π − π ω ) mass spectra (as shown in Fig. 3(c)) witha similar method as described in Sec. 3.1, with the dif-ference being that peaking backgrounds are neglected,so that the fit reduces to a one-dimensional unbinnedlikelihood fit. The fit yields N sig = 22627 ± events.The Born cross section of the e + e − → ωπ pro-cess is calculated using Eq. (1), with the product ofthe branching fractions determined by B = B ( ω → π + π − π ) · B ( π → γγ ) = 87 . . The valuesused in the calculation of the Born cross section of the e + e − → ωπ process are listed in Table 3, togetherwith the results at all c.m. energies. The results areconsistent with most of the previous measurements [42–48] but with improved precision, however, there existsa small difference with the BaBar measurement [49] atcenter-of-mass energies around . GeV. A comparisonis shown in Fig. 2(b).Concerning the systematic uncertainties, the contri-bution stemming from the luminosity determination iscommon for the e + e − → ωη and e + e − → ωπ reac- tions. Furthermore, for the uncertainties relating to thedetection efficiencies, the radiative corrections, the fit-ting procedure and the branching fractions taken fromthe literature, the same method is applied as previouslystated in Sec. 3.1. In addition, the uncertainty aris-ing from the π selection is obtained by varying themass window requirements for both π ω and π andexamining the changes in the resulting cross sections.The total systematic uncertainty of the determinationof the Born cross section is determined to be 6.7% for e + e − → ωπ at √ s = 2 . GeV. The uncertainties atthe other c.m. energies are determined accordingly andare summarized in Table 4.
Table 3: The Born cross sections of the e + e − → ωπ process. Thesymbols are the same as those in Eq. (1). In the column of the Borncross section σ , the first uncertainty is statistical and the second oneis systematic. √ s (GeV) N sig L ( pb − ) ε · (1 + δ ) σ (pb)2.0000 1677 ±
50 10.1 0.202 946 ± ± ±
31 3.34 0.205 1086 ± ± ±
62 12.2 0.209 1181 ± ± ±
180 108 0.211 1136 ± ± ±
28 2.84 0.213 1021 ± ± ±
51 10.6 0.217 914 ± ± ±
54 13.7 0.218 791 ± ± ±
46 11.9 0.222 659 ± ± ±
51 21.1 0.223 452 ± ± ±
48 22.5 0.222 366 ± ± ±
80 66.9 0.222 352 ± ± ± ± ± ±
42 33.7 0.234 195 ± ± ±
41 34.1 0.233 184 ± ± ± ± ± ± ± ± ±
54 105 0.243 93.8 ± ± ±
20 15.9 0.244 89.0 ± ± ±
19 16.0 0.246 74.0 ± ± ±
18 15.9 0.244 76.1 ± ± ±
18 17.3 0.242 73.3 ± ± ±
40 126 0.223 61.8 ± ± able 4: Summary of relative systematic uncertainties (in %) associated with the luminosity ( L ), the tracking efficiency (Track), the photondetection efficiency (Photon), PID, branching fraction (Br), 4C kinematic fit (4C), background shape (Bkg), signal shape (Sig), fit range (Range), π mass windows (m( π ) and m( π ω )), the initial state radiation and the vacuum polarization correction factor ( δ ) in the measurement of theBorn cross section of the e + e − → ωπ process. Ecm L Track Photon PID Br 4C Bkg Sig Range m ( π ) m ( π ω ) (1 + δ ) Total2.0000 1.0 2.0 4.0 2.0 0.7 0.2 0.4 1.4 5.1 0.1 0.3 0.7 7.42.0500 1.0 2.0 4.0 2.0 0.7 0.3 0.4 0.3 4.4 0.4 0.4 0.6 6.82.1000 1.0 2.0 4.0 2.0 0.7 0.3 0.4 1.6 4.2 0.1 0.1 0.5 6.82.1250 1.0 2.0 4.0 2.0 0.7 0.3 0.2 1.1 4.2 0.1 0.1 0.5 6.72.1500 1.0 2.0 4.0 2.0 0.7 0.4 0.9 1.5 0.7 0.4 0.2 0.5 5.42.1750 1.0 2.0 4.0 2.0 0.7 0.4 0.0 0.4 4.1 0.0 0.2 0.5 6.62.2000 1.0 2.0 4.0 2.0 0.7 0.4 0.1 0.8 4.4 0.1 0.2 0.5 6.82.2324 1.0 2.0 4.0 2.0 0.7 0.4 0.1 0.8 3.9 0.2 0.3 0.5 6.52.3094 1.0 2.0 4.0 2.0 0.7 0.3 0.5 0.4 4.1 0.2 0.4 0.5 6.62.3864 1.0 2.0 4.0 2.0 0.7 0.3 1.4 0.9 4.7 0.3 0.4 0.5 7.12.3960 1.0 2.0 4.0 2.0 0.7 0.3 0.4 1.4 1.5 0.1 0.4 0.5 5.52.5000 1.0 2.0 4.0 2.0 0.7 0.4 0.4 2.4 4.2 1.3 1.0 0.5 7.22.6444 1.0 2.0 4.0 2.0 0.7 0.3 0.6 0.6 2.6 0.3 0.2 0.5 5.82.6464 1.0 2.0 4.0 2.0 0.7 0.1 0.9 1.4 3.4 0.5 0.3 0.5 6.42.7000 1.0 2.0 4.0 2.0 0.7 0.6 2.7 1.5 2.9 1.2 1.4 0.5 6.92.8000 1.0 2.0 4.0 2.0 0.7 0.1 0.2 1.6 2.1 0.7 0.9 0.5 5.82.9000 1.0 2.0 4.0 2.0 0.7 0.6 1.1 1.7 1.2 0.2 0.6 0.5 5.72.9500 1.0 2.0 4.0 2.0 0.7 0.2 0.5 1.2 2.3 0.7 0.2 0.5 5.82.9810 1.0 2.0 4.0 2.0 0.7 0.3 0.4 1.9 0.5 0.1 0.8 0.5 5.53.0000 1.0 2.0 4.0 2.0 0.7 0.4 0.3 0.5 1.4 0.7 0.6 0.5 5.43.0200 1.0 2.0 4.0 2.0 0.7 0.2 0.6 1.2 2.1 1.2 0.8 0.5 5.83.0800 1.0 2.0 4.0 2.0 0.7 0.5 0.8 1.7 3.5 1.1 0.8 0.5 6.6
4. Line shape analysis e + e − → ωη process To study possible resonant structures in e + e − → ωη , a maximum likelihood fit of the type used inRef. [61] is performed to the dressed cross sections,which are the products of Born cross sections andVP factors. Previous results from the SND [55] andCMD3 [56] collaborations are also included to be ableto describe the low-energy behavior of the cross sec-tion, while BaBar’s result is not used due to their largeuncertainties or non-observation without uncertainty. Inthe fit, a possible resonant amplitude is parameterizedusing a Breit-Wigner function with a mass-independentwidth. The flat contribution in the c.m. energy re-gion between and GeV dominantly stems from tailsof the ω (1420) and ω (1650) (or φ (1680) ) resonances.Following Ref. [55], the dressed cross section is mod-eled as σ ( s ) = 12 πs (cid:12)(cid:12) f − f + e iϕ f (cid:12)(cid:12) P f ( s ) , (2)where f R = q Γ eeR · B ωηR P f ( m R ) m / R √ Γ R s − m R + i √ s Γ R (here R = 1 , , is an index for the resonance) describes the resonantcontributions from the ω (1420) , ω (1650) (or φ (1680) )and Y (2180) (referring to the structure around √ s =2 . GeV) and Γ eeR · B ωηR is the product of the electronicwidth of the resonance R and the branching fraction ofthe R → ωη decay. Furthermore, m R and Γ R are the mass and width of the resonance R , and ϕ is the rel-ative phase angle of the f contribution relative to the f − f contribution. The phase space factor P f ( s ) is given by P f ( s ) = q , where q is the ω momentumin the e + e − c.m. frame calculated for the mass value m ( ω ) = 0 . GeV /c given in Ref. [1]. The free fitparameters are taken as Γ ee · B ωη , m , Γ , Γ ee · B ωη , m , Γ , Γ ee · B ωη and ϕ . The m and Γ values are fixedto the values determined by the SND Collaboration [55],since the significance of the ω (1420) resonance is notlarge enough at the given c.m. energies. In the fit, uncer-tainties from previous experiments are considered un-correlated, while the uncertainties derived in this workare split into the uncorrelated and the correlated contri-butions. The former contributions include those stem-ming from the choice of signal and background shapeas well as fit range and the treatment of peaking back-grounds whereas the latter include the remaining sys-tematic uncertainties. Figure 4 and Table 5 show theresults from our fit. Two solutions are found with thesame fit quality of χ / ndf = 78 / , where ndf is thenumber of degrees of freedom. Solution I correspondsto constructive interference between the f amplitudeand the remaining f − f contribution, while solution IIcorresponds to the case of destructive interference. Thetwo solutions share all parameters other than those givenin Table 5. Among the other free parameters, the massand width of f are determined to be ± MeV /c and ± MeV, respectively, with Γ ee · B ωηf equal to ± eV.12 able 5: Resonance parameters of the Y (2180) as obtained in the fitto the e + e − → ωη dressed cross section.parameters solution I solution II m Y (2180) ( MeV /c ) 2179 ± Y (2180) ( MeV ) 89 ± ee · B ωη ( eV ) 0 . ± .
16 1 . ± . ϕ . ± . . ± . significance 6.1 σ (GeV)s )( nb ) η ω → - e + ( e σ − − )( nb ) η ω → - e + ( e σ − − This work SNDCMD3 Total fitY(2200) (1420) ω (1680) φ (1650)/ ω Interference (a)(b)
Fig. 4: (Color online) Fit to the dressed cross sections of e + e − → ωη . (a) Solution I. (b) Solution II. (Red) filled circles represent thedata from this work, whereas (brown) open circles show the data fromCMD3 and the (green) open crosses the data from SND. The (black)solid curves are the total fit results, the (red) long-dashed curves in-dicate the Y (2180) resonance contribution, the (blue) short-dashedcurves represent the ω (1650) or φ (1680) contribution, the (green)dotted curves display the ω (1420) contribution and (magenta) dotted-dashed curves show the interference contribution. In the upper rightpanel of both (a) and (b), a zoom into the region of the Y (2180) res-onance is shown. e + e − → ωπ process A fit is performed to the dressed cross sections of e + e − → ωπ using a similar method as described inSec. 4.1. Previous results from the SND collabora-tion [43, 44] are included in order to provide the low-energy contributions that will only appear as tails in theenergy region under study. BaBar’s result is not usedsince there is an obvious bias compared to the result inthis work in the overlap region, and others are not used due to their large uncertainties. Here, the fit model isparameterized as a coherent sum of four Breit-Wignerfunctions, σ ( s ) = 12 πs (cid:12)(cid:12) f + e iϕ f + e iϕ f + e iϕ f (cid:12)(cid:12) P f ( s ) , (3)where f R (with R =
1, 2, 3, 4) are the Breit-Wigner functions for the ρ (770) , ρ (1450) , ρ (1700) and Y (2040) (referring to the structure around √ s = 2 . GeV) resonances, which take the the same form as de-scribed in Eq. (2) except for the ρ (770) . Since the massof the ρ (770) resonance is below the ωπ threshold, weinstead use f ρ (770) = As − m ρ (770) + i √ s Γ ρ (770) ( s ) . The for-mula for the energy-dependent width Γ ρ (770) ( s ) is givenin Ref. [42]. The free fit parameters are taken as A , Γ ρ (1450) , Γ ρ (1700) , m Y (2040) , Γ Y (2040) , Γ eeR · B ωηR and ϕ R .The masses of the ρ (1450) and ρ (1700) resonancesare fixed to the average values as given by the PDG [1].In the fit, a possible effect of omitting other data avail-able in the literature on the results obtained in this workis studied and will be discussed in Sec. 4.3. Correlatedand uncorrelated uncertainties of the present work areincorporated in the same way as described in Sec. 4.1,while the uncertainties of the previous experiments areconsidered uncorrelated.The fit shown in Fig. 5 finds a resonance with amass of (2034 ± MeV /c , width of (234 ± MeVand Γ ee · B ωπ of (34 ± eV with a fit quality of χ / ndf = 128 / . The significance of the Y (2040) contribution is found to be larger than 10 σ .13 (GeV)s − ) ( nb ) π ω → - e + ( e σ This work SND(2000)SND(2016) Total fitY(2040) ρ (1450) ρ (1700) ρ Interference
Fig. 5: (Color online) Fit to the dressed cross sections of the e + e − → ωπ process. (Red) filled circles correspond to the data obtained inthis work, while (brown) filled triangles and (green) filled crossesare the data from SND. The (black) solid curve is the total fit re-sult, the (red) dashed curve is the Y (2040) contribution, the (blue)long-dashed curve is the contribution from the ρ (1700) , the (lightblue) dotted-dotted-dashed curve stems from the ρ (1450) , the (green)dotted-dashed curve corresponds to the ρ (770) and the (magenta) dot-ted curve is the interference contribution. The systematic uncertainties of the resonant param-eters in the fit to the Born cross sections of e + e − → ωη include contributions from the determination of the c.m.energy and the energy spread, fixed parameters in the fit,and the data from other experiments that is included inthe fit. The uncertainty of the c.m. energy from BEPCIIis small and found to be negligible comparing to thestatistic uncertainty in the determination of the reso-nance parameters. The effect resulting from fixing theparameters of the ω (1420) resonance is studied by vary-ing the mass and width within the uncertainties quotedin the PDG [1] and yields an uncertainty of ∆ m = 3 MeV /c , ∆Γ = ∆(Γ ee · B ωη ) equal to . eV for solution I and . eV for solution II.We distinguish between two different types of sys-tematic uncertainties, those that are uncorrelated be-tween the different center-of-mass energies and thosethat are correlated. While the uncorrelated uncertain-ties are included in the fit to the cross section, the cor-related uncertainties that are common for all center-of-mass energies ( ∼ ) only affect the Γ ee · B ωη mea-surement and we find a resulting systematic uncertaintyof . eV for solution I and . eV for solution II.Assuming all sources of systematic uncertainties are un-correlated and thus adding them in quadrature, the totalsystematic uncertainty is MeV /c for the mass, MeVfor the width, . eV (solution I) or . eV (solutionII) for Γ ee · B ωη of the Y (2180) . For the systematic uncertainties of the resonant pa-rameters of the Y (2040) in e + e − → ωπ , the contribu-tion introduced by taking the data points of other exper-iments into account in the fit is significant. It is investi-gated by including all available measurements [42–49]and comparing with the nominal fit result above. Otheruncertainties are considered in the same way as statedbefore for the Y (2180) → ωη case. All sources of sys-tematic uncertainties are added in quadrature, obtain-ing the total systematic uncertainty of MeV /c for themass, MeV for the width and eV for Γ ee · B ωπ of the observed Y (2040) .
5. Summary and discussion
The Born cross sections of the e + e − → ωη and e + e − → ωπ processes have been measured at √ s from 2.000 to 3.080 GeV. They are consistent withmost of previous measurements in the overlap region,but deviate with BaBar’s results, especially in the ωπ process. Two resonant structures are observed in themeasured line shapes. One resonant structure is ob-served with a significance of 6.1 σ in the cross sec-tion of the e + e − → ωη process, with mass m =(2179 ± ± MeV /c , width Γ = (89 ± ± MeV, and Γ ee · B ωη = (0 . ± . ± .
04) eV or (1 . ± . ± .
18) eV , depending on the choice be-tween two ambiguous fit solutions. The observed struc-ture agrees well with the properties of the φ (2170) reso-nance, which indicates the first observation of the decay φ (2170) → ωη .Another structure is observed in the ωπ cross sec-tion with a significance of more than 10 σ and witha mass of m = (2034 ± ± MeV /c , widthof Γ = (234 ± ± MeV and Γ ee · B ωπ of (34 ± ± eV. This structure could either be the ρ (2000) or the ρ (2150) state. However, the mass andwidth of the observed resonance is closer to the ρ (2000) resonance, which is suggested to be the D state [41]. Acknowledgements
The BESIII collaboration thanks the staff ofBEPCII, the IHEP computing center and the su-percomputing center of USTC for their strong sup-port. This work is supported in part by NationalKey Basic Research Program of China under ContractNo. 2015CB856700; National Natural ScienceFoundation of China (NSFC) under Contracts Nos.11335008, 11375170, 11475164, 11475169, 11625523,11605196, 11605198, 11635010, 11705192, 11735014,141822506, 11835012, 11935015, 11935016, 11935018,11950410506, 11961141012, 12035013; the ChineseAcademy of Sciences (CAS) Large-Scale ScientificFacility Program; Joint Large-Scale Scientific FacilityFunds of the NSFC and CAS under ContractsNos. U1532102, U1732263, U1832103, U1832207,U2032111; CAS Key Research Program of FrontierSciences under Contracts Nos. QYZDJ-SSW-SLH003,QYZDJ-SSW-SLH040; 100 Talents Program of CAS;INPAC and Shanghai Key Laboratory for ParticlePhysics and Cosmology; ERC under Contract No.758462; German Research Foundation DFG underContracts Nos. Collaborative Research Center CRC1044, FOR 2359; Istituto Nazionale di Fisica Nucleare,Italy; Ministry of Development of Turkey underContract No. DPT2006K-120470; National Scienceand Technology fund; STFC (United Kingdom); TheKnut and Alice Wallenberg Foundation (Sweden) un-der Contract No. 2016.0157; The Royal Society, UKunder Contracts Nos. DH140054, DH160214; TheSwedish Research Council; U. S. Department of Energyunder Contracts Nos. DE-FG02-05ER41374, DE-SC-0012069.
ReferencesReferences [1] P.A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys.2020, 083C01 (2020).[2] G. J. Ding and M. L. Yan, Phys. Lett. B , 390 (2007).[3] J. Ho, R. Berg, and T. G. Steele, Phys. Rev. D , 034012(2019).[4] G. J. Ding and M. L. Yan, Phys. Lett. B , 49 (2007).[5] C. Q. Pang, Phys. Rev. D , 074015 (2019).[6] C. G. Zhao et al. , Phys. Rev. D , 114014 (2020).[7] Q. Li et al. , arXiv: 2004.05786.[8] Z. G. Wang, Nucl. Phys. A , 106 (2007).[9] C. R. Deng, J. L. Ping, and T. Goldman, Phys. Rev. D ,074001 (2010).[10] S. S. Agaev, K. Azizi, and H. Sundu, Phys. Rev. D , 074012(2020).[11] H. W. Ke and X. Q. Li, Phys. Rev. D , 036014 (2019).[12] R. R. Dong et al. , Eur. Phys. J. C , 749 (2020).[13] F. X. Liu et al. , arXiv: 2008.01372.[14] L. Zhao et al. , Phys. Rev. D , 054034 (2013).[15] E. Klempt and A. Zaitsev, Phys. Rep. , 1 (2007).[16] Y. L. Yang, D. Y. Chen, and Z. Lu, Phys. Rev. D , 073007(2019).[17] A. M. Torres et al. , Phys. Rev. D , 074031 (2008).[18] L. Alvarez-Ruso, J. A. Oller, and J. M. Alarc ´ o n, Phys. Rev. D , 054011 (2009).[19] T. Barnes N. Black, and P. R. Page, Phys. Rev. D , 054014(2003).[20] Y. Dong et al. , Phys. Rev. D , 074027 (2017).[21] S. S. Agaev, K. Azizi, and H. Sundu, Phys. Rev. D , 074012(2020). [22] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D ,091103(R) (2006).[23] M. Ablikim et al. (BES Collaboration), Phys. Rev. Lett. ,102003 (2008).[24] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D ,052017 (2015).[25] C. P. Shen et al. (Belle Collaboration), Phys. Rev. D ,031101(R) (2009).[26] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D ,012008 (2012).[27] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. ,112001 (2020).[28] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D ,032001 (2019).[29] D. Y. Chen, J. Liu, and J. He, Phys. Rev. D , 074045 (2020).[30] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D ,012008 (2020).[31] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D ,032009 (2019).[32] C. Q. Pang et al. , Phys. Rev. D , 074022 (2020).[33] A. Hasan and D. V. Bugg, Phys. Lett. B , 215 (1994).[34] D. V. Bugg, Phys. Rept. , 257 (2004).[35] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D ,012011 (2012).[36] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D ,032013 (2012).[37] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D ,092005 (2007).[38] M. E. Biagini, S. Dubnicka and E. Etim, Il Nuovo Cimento, Vol. A, N. 3 (1991).[39] A. B. Clegg and A. Donnachie, Z. Phys. C - Particles and Fields , 677 (1990).[40] L. M. Wang, J. Z. Wang and X. Liu, Phys. Rev. D , 034037(2020).[41] L. P. He, X. Wang and X. Liu, Phys. Rev. D , 034008 (2013).[42] M.N. Achasov et al. (SND Collaboration), Phys. Lett. B , 29(2000).[43] M.N. Achasov et al. (SND Collaboration), J. Exp. Theor. Phys. , 789 (2003).[44] M.N. Achasov et al. (SND Collaboration), Phys. Rev. D ,112001 (2016).[45] S.I. Dolinsky et al. (ND Collaboration), Phys. Lett. B , 453(1986).[46] R.R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B , 392 (1999).[47] R.R. Akhmetshin et al. (CMD-2 Collaboration), Phys. Lett. B , 173 (2003).[48] D. Bisello, et al. (DM2 Collaboration), Orsay preprint LAL 90-35 (1990): contributed paper to the International Conference onHigh Energy Physics, Singapore, 1990.[49] J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D ,092009 (2017).[50] M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Meth.A , 345 (2010).[51] C. H. Yu et al. , Proceedings of IPAC2016, Busan, Korea, 2016,doi:10.18429/JACoW-IPAC2016-TUYA01.[52] S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum.Meth. A , 250 (2003).[53] Z. Y. Deng et al. Chin. Phys. C , 371 (2006).[54] R. G. Ping, Chin. Phys. C , 083001 (2014).[55] M.N. Achasov et al. (SND Collaboration), Phys. Rev. D ,092002 (2016).[56] R.R. Akhmetshin et al. (CMD-3 Collaboration), Phys. Lett. B , 150 (2017).[57] B. Aubert et al. (BABAR Collaboration), Phys. Rev. D , et al. (BESIII Collaboration), Chin. Phys. C ,063001 (2017).[59] W. L. Yuan et al. , Chin. Phys. C , 026201 (2016). [60] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D ,012002 (2013).[61] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. ,092002 (2017).,092002 (2017).