Partial-wave analysis of J/ψ→ K + K − π 0
BESIII Collaboration, M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, 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, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. Chai, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, S. J. Chen, Y. B. Chen, W. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, 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, Z. L. Dou, S. X. Du, J. Z. Fan, 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, Q. Gao, X. L. Gao, Y. Gao, Y. Gao, Y. G. Gao, Z. Gao, B. Garillon, 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, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, S. Han, et al. (386 additional authors not shown)
PPartial-wave analysis of
J/ψ → K + K − π M. Ablikim , M. N. Achasov ,d , P. Adlarson , S. Ahmed , M. Albrecht , M. Alekseev A, C , A. Amoroso A, C ,F. F. An , Q. An , , Y. Bai , O. Bakina , R. Baldini Ferroli A , I. Balossino A , Y. Ban , K. Begzsuren ,J. V. Bennett , N. Berger , M. Bertani A , D. Bettoni A , F. Bianchi A, C , J Biernat , J. Bloms , I. Boyko ,R. A. Briere , H. Cai , X. Cai , , A. Calcaterra A , G. F. Cao , , N. Cao , , S. A. Cetin B , J. Chai C , J. F. Chang , ,W. L. Chang , , G. Chelkov ,b,c , D. Y. Chen , G. Chen , H. S. Chen , , J. C. Chen , M. L. Chen , , S. J. 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 , 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 , , , Z. L. Dou , S. X. Du , J. Z. Fan , 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 ,Q. Gao , X. L. Gao , , Y. Gao , Y. Gao , Y. G. Gao , Z. Gao , , B. Garillon , I. Garzia A , 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 , A. Q. Guo , L. B. Guo , R. P. Guo , Y. P. Guo , A. Guskov , S. Han , X. Q. Hao , F. A. Harris ,K. L. He , , F. H. Heinsius , T. Held , Y. K. Heng , , , M. Himmelreich ,g , Y. R. Hou , Z. L. Hou , H. M. Hu , ,J. F. Hu ,h , T. Hu , , , Y. Hu , G. S. Huang , , J. S. Huang , X. T. Huang , X. Z. Huang , N. Huesken ,T. Hussain , W. Ikegami Andersson , W. Imoehl , M. Irshad , , Q. Ji , Q. P. Ji , X. B. Ji , , X. L. Ji , ,H. L. Jiang , X. S. Jiang , , , X. Y. Jiang , J. B. Jiao , Z. Jiao , D. P. Jin , , , 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. Kurth ,M. G. Kurth , , W. K¨uhn , J. S. Lange , P. Larin , L. Lavezzi C , H. Leithoff , T. Lenz , C. Li , Cheng Li , ,D. M. Li , F. Li , , F. Y. Li , G. Li , H. B. Li , , H. J. Li ,j , J. C. Li , J. W. Li , Ke Li , L. K. Li , Lei Li , P. L. Li , ,P. R. Li , Q. Y. Li , W. D. Li , , W. G. Li , X. H. Li , , X. L. Li , X. N. Li , , Z. B. Li , Z. Y. Li , H. Liang , ,H. Liang , , Y. F. Liang , Y. T. Liang , G. R. Liao , L. Z. Liao , , J. Libby , C. X. Lin , D. X. Lin , Y. J. 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. Y. Liu , Ke Liu , L. Y. Liu , Q. Liu , S. B. Liu , ,T. Liu , , X. Liu , X. Y. Liu , , Y. B. Liu , Z. A. Liu , , , Zhiqing Liu , Y. F. Long , X. C. Lou , , , H. J. Lu ,J. D. Lu , , J. G. Lu , , Y. Lu , Y. P. Lu , , C. L. Luo , M. X. Luo , P. W. Luo , T. Luo ,j , X. L. Luo , , S. Lusso C ,X. R. Lyu , F. C. Ma , H. L. Ma , L. L. Ma , M. M. Ma , , Q. M. 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 ,Z. P. Mao , S. Marcello A, C , Z. X. Meng , J. G. Messchendorp , G. Mezzadri A , J. Min , , T. J. Min ,R. E. Mitchell , X. H. Mo , , , Y. J. Mo , C. Morales Morales , N. Yu. Muchnoi ,d , H. Muramatsu , A. Mustafa ,S. Nakhoul ,g , Y. Nefedov , F. Nerling ,g , I. B. Nikolaev ,d , Z. Ning , , S. Nisar ,k , S. L. Niu , , S. L. Olsen ,Q. Ouyang , , , S. Pacetti B , Y. Pan , , M. Papenbrock , 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. R. Qi , M. Qi , T. Y. Qi ,S. Qian , , C. F. Qiao , N. Qin , X. P. Qin , X. S. Qin , Z. H. Qin , , J. F. Qiu , S. Q. Qu , K. H. Rashid ,i ,K. Ravindran , C. F. Redmer , M. Richter , A. Rivetti C , V. Rodin , M. Rolo C , G. Rong , , Ch. Rosner ,M. Rump , A. Sarantsev ,e , M. Savri´e B , Y. Schelhaas , K. Schoenning , W. Shan , X. Y. Shan , , M. Shao , ,C. P. Shen , P. X. Shen , X. Y. Shen , , H. Y. Sheng , X. Shi , , X. D Shi , , J. J. Song , Q. Q. Song , , X. Y. Song ,S. Sosio A, C , C. Sowa , S. Spataro A, C , F. F. Sui , G. X. Sun , J. F. Sun , L. Sun , S. S. Sun , , X. H. Sun ,Y. J. Sun , , Y. K Sun , , Y. Z. Sun , Z. J. Sun , , Z. T. Sun , Y. T Tan , , C. J. Tang , G. Y. Tang , X. Tang ,V. Thoren , B. Tsednee , I. Uman D , B. Wang , B. L. Wang , C. W. Wang , D. Y. Wang , K. Wang , , L. L. Wang ,L. S. Wang , M. Wang , M. Z. Wang , Meng Wang , , P. L. Wang , R. M. Wang , W. P. Wang , , X. Wang ,X. F. Wang , X. L. Wang ,j , Y. Wang , , Y. Wang , Y. F. Wang , , , Z. Wang , , Z. G. Wang , , Z. Y. Wang ,Zongyuan Wang , , T. Weber , D. H. Wei , P. Weidenkaff , H. W. Wen , S. P. Wen , U. Wiedner , G. Wilkinson ,M. Wolke , L. H. Wu , L. J. Wu , , Z. Wu , , L. Xia , , Y. Xia , S. Y. Xiao , Y. J. Xiao , , Z. J. Xiao , Y. G. Xie , ,Y. H. Xie , T. Y. Xing , , X. A. Xiong , , Q. L. Xiu , , G. F. Xu , J. J. Xu , L. Xu , Q. J. Xu , W. Xu , , X. P. Xu ,F. Yan , L. Yan A, C , W. B. Yan , , W. C. Yan , Y. H. Yan , H. J. Yang ,h , H. X. Yang , L. Yang , R. X. Yang , ,S. L. Yang , , Y. H. Yang , Y. X. Yang , Yifan Yang , , Z. Q. Yang , M. Ye , , M. H. Ye , J. H. Yin , Z. Y. You ,B. X. Yu , , , C. X. Yu , J. S. Yu , T. Yu , C. Z. Yuan , , X. Q. Yuan , Y. Yuan , A. Yuncu B,a , A. A. Zafar ,Y. Zeng , B. X. Zhang , B. Y. Zhang , , C. C. Zhang , D. H. Zhang , H. H. Zhang , H. Y. Zhang , , J. Zhang , ,J. L. Zhang , J. Q. Zhang , J. W. Zhang , , , J. Y. Zhang , J. Z. Zhang , , K. Zhang , , L. Zhang , S. F. Zhang ,T. J. Zhang ,h , X. Y. Zhang , Y. Zhang , , Y. H. Zhang , , Y. T. Zhang , , Yang Zhang , Yao Zhang , Yi Zhang ,j ,Yu Zhang , Z. H. Zhang , Z. P. Zhang , Z. Y. Zhang , G. Zhao , J. W. Zhao , , J. Y. Zhao , , J. Z. Zhao , ,Lei Zhao , , Ling Zhao , M. G. Zhao , Q. Zhao , S. J. Zhao , T. C. Zhao , Y. B. Zhao , , Z. G. Zhao , ,A. Zhemchugov ,b , B. Zheng , J. P. Zheng , , Y. Zheng , Y. H. Zheng , B. Zhong , L. Zhou , , L. P. Zhou , ,Q. Zhou , , X. Zhou , X. K. Zhou , X. R. Zhou , , Xiaoyu Zhou , Xu Zhou , A. N. Zhu , , J. Zhu , J. Zhu ,K. Zhu , K. J. Zhu , , , S. H. Zhu , W. J. Zhu , X. L. Zhu , Y. C. Zhu , , Y. S. Zhu , , Z. A. Zhu , , J. Zhuang , ,B. S. Zou , J. H. Zou (BESIII Collaboration) Institute of High Energy Physics, Beijing 100049, People’s Republic of China Beihang University, Beijing 100191, People’s Republic of China a r X i v : . [ h e p - e x ] N ov 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 Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia 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 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 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 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 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 Key Laboratoryfor Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China i Also at Government College Women University, Sialkot - 51310. Punjab, Pakistan. j Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, FudanUniversity, Shanghai 200443, People’s Republic of China k Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA
A partial-wave analysis of the decay
J/ψ → K + K − π has been made using (223 . ± . × J/ψ events collected with the BESIII detector in 2009. The analysis, which is performed within theisobar-model approach, reveals contributions from K ∗ (1430) ± , K ∗ (1980) ± and K ∗ (2045) ± decayingto K ± π . The two latter states are observed in J/ψ decays for the first time. Two resonance signalsdecaying to K + K − are also observed. These contributions can not be reliably identified and theirpossible interpretations are discussed. The measured branching fraction B ( J/ψ → K + K − π ) of(2 . ± . ± . × − is more precise than previous results. Branching fractions for the reportedcontributions are presented as well. The results of the partial-wave analysis differ significantly fromthose previously obtained by BESII and BABAR. I. INTRODUCTION
A good knowledge of the spectrum and properties ofhadrons is one of the key issues for understanding thestrong interaction at low and intermediate energies. Theconventional quark model implies that quark-antiquarkstates are produced as nonets, which consist of mesonswith strange and non-strange quarks. Therefore, an ac-curate identification of mesons with one strange quarkcan help to establish nonet members in the isoscalar sec-tor, where the situation is more complicated. This is dueto a potential mixing between octet and singlet states aswell as possible mixing with glueball states.The identification of meson radial excitations alsohelps in the understanding of quark-antiquark interac-tion at intermediate energies. Quark potential models [1]predict that the squared masses of radial excitations de-pend on the excitation number quadratically. However,in the analysis of proton-antiproton annihilation in flight,it was found that this dependence is close to the linearone similar to the Regge trajectories [2]. If correct, thisbehavior has the potential to reveal a new symmetry ofthe quark-antiquark interaction [3, 4]. Therefore, the ex-perimental confirmation (or disproof) of this behavior isan important task in experimental hadron physics.
J/ψ decays are ideal for the study of meson spectra andthe determination of meson properties. They can provideimportant information about meson states with massesup to 3 GeV/ c and partial-wave analysis is facilitateddue to the well-known quantum numbers of the initialstate. Moreover, the J/ψ radiative decay is favored forthe production of glueball states which makes it a perfecttool to search for and study such exotics [5].In this paper we report the results of a partial-wave analysis (PWA) of the decay
J/ψ → K + K − π . This de-cay channel has been previously studied by the MARK[6], MARK-II [7], MARK-III [8], DM2 [9], BESII [10],and BABAR [11, 12] Collaborations, but only two recentpublications report PWA results. In the first of these [10],BESII analyzes 58 million J/ψ decays and observes avery broad exotic resonance X (1575) with pole position (cid:2) (1576 +49 −
55 +98 − ) − i (409 +11 −
12 +32 − ) (cid:3) MeV /c and branchingfraction B ( J/ψ → X (1575) π → K + K − π ) = (cid:0) . ± . +2 . − . (cid:1) × − . In the second analysis [12],BABAR reports a PWA solution based on a smallerdata set of 2102 events, which consists of K ∗ (892) ± , K ∗ (1410) ± and K ∗ (1430) ± states in the K ± π channels,while the enhancement at low K + K − invariant masses isattributed to the ρ (1450). The analysis presented in thispaper is based on a data set of 182,972 event candidatesselected from (223 . ± . × J/ψ decays [13] collectedby the BESIII experiment in 2009. The high statisticsand good data quality allow us to reveal signals fromstates that have not been observed before and preciselydetermine properties of intermediate states. Moreover,the obtained PWA solution can be used for the simula-tion of the irreducible background from this channel tothe
J/ψ → γK + K − decay, which is one of the key chan-nels to be studied in the search for a low-mass glueball. II. BESIII EXPERIMENTAL FACILITY
The BESIII detector is a magnetic spectrome-ter [14] located at the Beijing Electron Positron Col-lider (BEPCII) [15]. 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 superconduct-ing solenoidal magnet providing a 1.0 T magnetic field.The solenoid is supported by an octagonal flux-returnyoke with resistive plate counter muon identifier mod-ules interleaved with steel. The geometrical acceptanceof charged particles and photons is 93% over the 4 π solidangle. The charged-particle momentum resolution at1 GeV /c is 0 . dE/dx resolution is 6% forelectrons from Bhabha scattering. The EMC measuresphoton energies with a resolution of 2 .
5% (5%) at 1 GeVin the barrel (end cap) region. The time resolution of theTOF barrel part is 68 ps, while that of the end-cap partis 110 ps.The geant4 -based simulation software BOOST [16]is used to simulate the detector response. An inclusive
J/ψ
Monte Carlo (MC) sample is used to estimate thebackground. In this sample the production of the
J/ψ resonance is simulated by the MC event generator KKMC[17, 18] and decays are generated by evtgen [19, 20].The branching fractions of known decay modes are setto the Particle Data Group (PDG) [21] world-averagevalues and the remaining unknown decays are generatedaccording to the Lund-Charm model [22].
III. EVENT SELECTION
The K + K − π candidate events are required to havetwo charged tracks with zero net charge and at least twogood photons.Charged tracks must be reconstructed within the geo-metrical acceptance of the detector ( | cos θ | < .
93, where θ is the angle with respect to the beam axis) and originatefrom the interaction point ( | z | <
10 cm and
R < z and R are minimal distances from a track tothe run-averaged interaction point along the beam direc-tion and in the transverse plane, respectively). An eventis rejected if the transverse momentum of at least onecharged track is too low ( p T <
120 MeV/ c ). Particleidentification (PID) is performed using TOF and MDC dE/dx information. Their measurements are combinedto form particle identification confidence levels (C.L.) for π , K , and p hypotheses, and the particle type with thehighest C.L. is assigned to the track. Both tracks arerequired to be identified as kaons.Signal clusters in the EMC within the acceptance re-gion, which are not associated with charged tracks andpossess energy E >
25 MeV in the barrel part of the de-tector and
E >
50 MeV in the end caps, are treated asphoton candidates. To exclude showers from associationwith charged particles, the angle between the shower di-rection and the charged tracks extrapolated to the EMCmust be greater than 10 degrees. The requirement on theEMC cluster time with respect to the start of the event(0 ns ≤ t ≤
700 ns) is used to reject electronic noise andenergy deposits not related to the analyzed event.Consistency between the detector response and a final state hypothesis (for the signal and specific backgrounddecays) is evaluated by a four-momentum constrained(4C) kinematic fit. Firstly, the accepted pair of chargedtracks and each pair of the selected photon candidateswith invariant mass M γγ <
300 MeV/ c are fitted underthe γγK + K − hypothesis. A combination with the lowestvalue of χ C ) γγK + K − is selected and an event is retainedif χ C ) γγK + K − <
60. Secondly, the χ C ) γγK + K − iscompared to the corresponding value obtained in the bestfits under the main background hypotheses: γγπ + π − , γK + K − , and, in the cases more than two good photoncandidates are selected, γγγK + K − . If any of the back-ground hypotheses results in a lower χ value, the eventis rejected. Finally, the π candidates are reconstructedrequiring the two-photon mass of the selected pair to bewithin a 110 MeV/ c < M γγ <
150 MeV/ c interval.For the partial-wave analysis, we use particle momentaafter the five-constrained (5C) kinematic fit, which alsoconstrains the invariant mass of the selected photon pairto the nominal π mass.A total of 182,972 candidates satisfy the selection cri-teria. The corresponding number of background eventsis estimated from the inclusive MC: N bg = 565 ±
24 (or0.3%). The largest background contributions come fromthe decay channels
J/ψ → γη c , η c → K + K − π and J/ψ → γK + K − . The continuum background, i.e. thatdue to the e + e − → γ ∗ → K + K − π process, is estimatedfrom the analysis of a data sample of approximately280 nb − collected from e + e − collisions at 3 .
08 GeV. Itgives N continuum = 855 ± K ∗ (892) ± signal. In the internal region of the plot a clear sig-nal from K ∗ (1430) ± is seen as well as structures at M ( K ± π ) ≈ / c . These structures are likelyto be the result of positive interference of resonances inthe K ± π channels. In the K + K − channel there are in-dications for a resonance signal at 1.6 – 1.7 GeV/ c anda signal at higher masses. IV. PARTIAL-WAVE ANALYSIS
We use the isobar model to describe the
J/ψ decayinto K + K − π . The amplitude is parameterized as a sumof sequential quasi two-body decay processes in this ap-proach. The subprocess described by intermediate stateproduction and the subsequent decay to a specific pairof the final state mesons is referred to as the decaykinematic channel. The angular-dependent parts of thepartial-wave amplitudes are calculated in the frameworkof the covariant tensor approach as described in detail inRef. [23]. Note that in our case the conservation of P - and C -parities restricts the number of allowed partial wavesfor production and decay of any resonance to one. Toaccount for the finite size of a hadron each decay vertex ) /c (GeV p + K2 M0 1 2 3 4 5 6 7 ) / c ( G e V p - K M (a) ) /c (GeV p + K2 M0 1 2 3 4 5 6 7 ) / c ( G e V p - K M (b) ) /c (GeV p + K2 M0 1 2 3 4 5 6 7 ) / c ( G e V p - K M (c) Figure 1. Dalitz plots for the selected data (a), the PWAsolution I (b) and the PWA solution II (c). also includes Blatt-Weisskopf form factors, which dependon the Blatt-Wesskopf radius r . The Breit-Wigner termfor the resonance a in the kinematic channel m (labeledby the number of the spectator particle) is A BWm,a = 1 M a − s m − iM a Γ( s m , J a ) . Here M a , J a and s m are the resonance mass, spin andthe invariant mass squared of its daughter particles, re-spectively. The width of the K ∗ (892) ± state is definedby its decay to Kπ and is parameterized as:Γ( s m , J a ) = ρ J ( s m ) ρ J ( M a ) Γ a ,ρ J ( s m ) = 2 q √ s m q J F ( q , r, J ) . Here, Γ a is the resonance width, q is the relative mo-mentum of the daughter particles calculated in the reso-nance rest frame and F ( q , r, J ) is the above-mentionedBlatt-Weisskopf form factor. The same parameterizationis used for the width of the K ∗ (1430) ± resonance, whosedecay branching fraction to Kπ is about 0.5. For otherstates we use a constant width Γ( s m , J a ) = Γ a due tothe absence of reliable information about their branch-ing fractions.The masses, widths, decay radii (for the J/ψ , K ∗ (892) ± and K ∗ (1430) ± ) of resonances as well as theproduct of their production and decay couplings (com-plex numbers in general case) are initially free parame-ters of our fit. We find fit results weakly sensitive to the J/ψ decay radius. Hence, we set this parameter to be0 . − (cid:88) i ln ω i (cid:15) i (cid:82) (cid:15)ωd Φ = − (cid:88) i ln ω i (cid:82) (cid:15)ωd Φ + const and is minimized. Here index i runs over the selecteddata events, ω i is the decay-amplitude squared, summedover transverse J/ψ polarizations and evaluated from thefour-momenta of final particles in the event i . The detec-tor and event selection efficiency for the measured four-momenta is denoted by (cid:15) i , the denominator is a normal-ization integral over the phase space (Φ), and the const term is independent of the fit parameters. The nor-malization integral is calculated using phase-space dis-tributed MC events that pass the detector simulation andthe event reconstruction. To take the background intoaccount we estimate its contribution to the NLL func-tion and subtract it. This is done by the evaluation ofthe NLL function over properly normalized data sam-ples that have a kinematic distribution similar to that ofthe background. We consider two types of backgroundchannels: those producing a peak at the π mass in thetwo-photon invariant-mass distribution (“peaking” back-ground) and those exhibiting a smooth shape below thepeak (“non-peaking” background). The former is esti-mated from J/ψ → γη c , η c → γK + K − π events selectedunder criteria similar to ones of the main event selection,and the latter is estimated from the π mass cut side-band: 190 MeV/ c < M γγ <
230 MeV/ c .This approach neglects the detector resolution, whichis a good approximation for all resonances except for the K ∗ (892) ± . The MC simulation shows that estimated biasto the measured width of K ∗ (892) ± is much larger thanthe corresponding systematic uncertainty estimated fromother sources. At the same time, this bias is much smallerthan the K ∗ (892) ± width, which allows us to use the ap-proximation proposed in Ref. [25] to take into accountthe detector resolution. Due to the significant computa-tion time, this method is used only to correct the finalPWA results.The quality and consistency of the obtained solutionis evaluated by the comparison of the mass and angulardistributions of the experimental data and reconstructedphase-space generated MC events weighted according tothe PWA solution.The conservation of P - and C -parities strongly re-stricts the allowed quantum numbers of intermediatestates. In the K ± π channels only resonances with quan-tum numbers I = 1 / J P = 1 − , + , − , + . . . can beproduced. The reaction is dominated by K ∗ (892) ± pro-duction. There are two other established vector stateswhich are in the accessible mass region: K ∗ (1410) and K ∗ (1680) [26]. In the 2 + , 3 − and 4 + partial wavesthree states are well established: K ∗ (1430), K ∗ (1780)and K ∗ (2045). Possible contributions must also be con-sidered from two observations reported by the LASS Col-laboration: a 2 + state at 1980 MeV/ c [27] (also claimedto be seen by SPEC [28]) and a 5 − state at 2380 MeV/ c [29], which needs confirmation. As for the K + K − chan-nel, the produced resonances are restricted to quantumnumbers J P C = J −− , where J = 1 , , . . . . For thestrong decays of the J/ψ isospin and G -parity conserva-tion requires I G = 1 + . There are two well known isovec-tor resonances in the J P C = 1 −− sector: the ρ (1450) and ρ (1700), and a set of observations that needs confirma-tion: the ρ (1570), ρ (1900) and ρ (2150) (see Ref. [26]). Inthe isovector J P C = 3 −− sector one can expect the pro-duction of the well known and relatively narrow ρ (1690)state. At higher energies there have been observationsof two J P C = 3 −− states: the ρ (1990) and ρ (2250).The first isovector J P C = 5 −− state is expected to havea mass of around 2350 MeV/ c . Such a resonance isobserved in the analysis of the GAMS2 data for the re-action π − p → ωπ n [30] and in the analyses of proton-antiproton annihilation in flight into different meson finalstates (e.g. see Ref. [31]). The decay of the J/ψ througha virtual photon does not forbid but even favors the pro-duction of I G = 0 − resonances. The J/ψ → φπ decayis strongly suppressed [32], hence the production of ex-cited φ mesons is expected to be negligible assuming the absence of strong mixing of excited φ and ω states. How-ever, the production of excited ω resonances is possible.The isovector and isoscalar states can be distinguishedin a combined analysis of the decay under considerationand the J/ψ decay to K ± K π ∓ . A. Fit to the data
The masses and widths of all states included in thesolution (with the sole exception of the ρ (770)) are ini-tially free fit parameters. For the well-established Kπ resonances we use results of the LASS fits to the elastic Kπ scattering amplitudes [33] as reference values. Themasses and widths of these states are allowed to varywithin ± σ of the LASS measurements (here σ stands forthe LASS uncertainty). If no NLL minimum is foundfor the mass or width within this range or the mini-mum is unstable (with respect to variations of the PWAsolution used for estimation of systematic errors), theparameter is set to the central value of the LASS re-sults. Motivated by the claim of an observation of the K ∗ (1980) ± by LASS [27] and by Regge trajectories pre-dicting a state at approximately 1.8 GeV/ c we introducea second J P = 2 + contribution with a mass allowed tovary within the 1.75 GeV/ c – 2.1 GeV/ c interval. Twoclear resonance-like K + K − signals are found to signifi-cantly contribute to the data description in all fits. Thefirst contribution has a mass of around 1.65 GeV/ c andis likely a manifestation of the ρ (1700) or ω (1650), orinterference between the two. Note that the parametersof both these states remain highly uncertain. For the ρ (1700), the PDG quotes the results with the mass vary-ing roughly from 1540 MeV/ c to 1860 MeV/ c , whichmay indicate the presence of two states. Quark poten-tial models [1] suggest two resonances close to this massrange: 1 D and 3 S . This possibility is implied in theinterpretation of the fit results. The second contributionhas a mass of around 2.0 GeV/ c – 2.1 GeV/ c , close tothe mass of the ρ (2150). No limitations on their param-eters are imposed in the fits. For the ρ (1450) the massrange from 1.3 GeV/ c up to 1.5 GeV/ c is studied, butno NLL minima are found, and so its mass and width arefixed to the PDG estimates [26].In the analysis we find that the PWA solution can notbe saturated with well-known states included as Breit-Wigner resonances and constant contributions in the low-est partial waves. At the same time, the “missing part”of the PWA solution can not be reliably attributed toa single resonance and mainly manifests itself as a slowchanging background in the J P = 3 − partial wave of the K ± π pairs at high K ± π masses. Below we providetwo solutions constructed with and without the smoothcontribution in this partial wave to demonstrate that theconclusions of this analysis are not strongly affected byassumptions on the “missing part” of the PWA solution. B. Solution I
The results for the best fit based on the well-established resonances and constant contributions in thelowest partial waves are given in Table I. Only contri-butions improving the NLL by more than 17 are in-cluded to the fit (corresponding to a statistical signif-icance of 5 σ for 4 degrees of freedom). The data de-scription as a Dalitz plot are shown in Fig. 1(b). Fig. 2and Fig. 3 show the corresponding invariant mass spectraand angular distributions. The kinematic distributions inFig. 3 are restricted to the inner part of the Dalitz plot( M ( K ± π ) > .
05 GeV/ c ) to exclude the huge peaksfrom the K ∗ (892) ± .The dominant contribution stems from the K ∗ (892) ± and K ∗ (1430) ± resonances in the K ± π kinematic chan-nels. The first decay is well-known and contributes about90% to the total decay rate. The interference term be-tween the K ∗ (892) + K − and K ∗ (892) − K + intermediatestates contributes about 10%. The mass and the width ofthe K ∗ (892) ± are determined with high statistical pre-cision. The Blatt-Weisskopf radius of the resonance isfound to be r = 0 . ± .
02 fm. The second largestcontribution, with a decay fraction of about 10%, is the K ∗ (1430) ± , which also can be clearly seen in Fig. 1. Themass and width of this state are also determined withhigh precision. Its Blatt-Weisskopf radius can not be re-liably determined from the fit and is set to 0 . K ∗ (1430) ± K ∓ channel to the reac-tion is approximately 10 times smaller than the contri-bution from the K ∗ (892) ± K ∓ channel. Taking into ac-count this result and using a branching fraction of 49.9%for the K ∗ (1430) ± decay to Kπ [26], we find that the J/ψ decay to K ∗ (1430) ± K ∓ is suppressed by an approx-imate factor of 5 compared to the decay to K ∗ (892) ± K ∓ .For J P = 1 − , the inclusion of the K ∗ (1680) ± providesa significant improvement in the data description, butno NLL minima consistent with its mass and width arefound. The J P = 2 + partial wave requires another 2 + state with a relative contribution of approximately 0.4%.Its mass and width are found to be 1817 ±
11 MeV/ c and312 ±
28 MeV/ c , respectively. This mass is much lowerthan the mass of the K ∗ (1980) ± observed by LASS. The K ∗ (1780) ± state provides a significant improvement inthe log-likelihood, but no NLL minima consistent with itsmeasured parameters are found. Finally, there is a small ,but very distinct and stable contribution of (0 . ± . K ∗ (2045) ± . Its fitted mass is lower than thatobtained in other measurements [26], which can be at-tributed to the uncertainties of the PWA solution (seesolution II).In the K + K − kinematic channel, the first stable con-tribution has J P C = 1 −− , a mass of 1643 ± c ,a width of 167 ±
12 MeV/ c and a decay fraction of 1%.It can also be clearly seen in the Dalitz plot. As men-tioned above, this contribution can be attributed to the ρ (1700). The structure is also reasonably consistent with the ω (1650) (the mass is consistent with the PDG es-timate, and the width is well within the spread of theresults quoted by PDG) or an interference between thesestates. The second contribution that can be reliably de-termined from the data is a J P C = 1 −− resonance with amass of 2078 ± c and width of 149 ±
21 MeV/ c .The largest relative contribution of (1 . ± . ρ (770). Since the mass of this state issignificantly below the K + K − production threshold, noreliable claim can be made about its observation. The ρ (1690) and ρ (1450) provide NLL improvement by 144and 27, but no NLL minimum consistent with the param-eters of each state is found. The smooth contribution inthe J P C = 1 −− K + K − partial wave is also found to besignificant.Additionally, we try to set the mass and the widthof the J P C = 1 −− K + K − contribution at 1.65 GeV/ c to the PDG mean values for the ρ (1700) averaged from ηρ (770) and π + π − modes. In this case, the NLL worsensby 42, and so one may consider including the ω (1420)and ω (1650) in the fit. In these fits we set their massesand width to the mean values of the PDG estimates. Ifthe ω (1420) ( ω (1650)) is included, the NLL is still worseby 14 (7) compared to the result of solution I. If the ρ (1450) is substituted by the X (1575), instead of addinga resonance, the NLL improves by 28, but remains worseby 14 than the result for solution I.Adding further well-established resonances with thenominal PDG parameters does not improve log-likelihoodby more than 17 units. Despite this, the solution is notsaturated: if additional contributions (parametrized asBreit-Wigner resonances with parameters not required tocorrespond to a physical state) are added, they can im-prove NLL by up to 95 in a single partial wave, which ismuch larger than the contribution of other resonances in-cluded to the solution. The only notable additional con-tribution indicating resonance behavior is in the J P = 1 − Kπ partial wave with a mass of around 2.4 GeV/ c , butthere is lack of qualitative evidence to report a new state.The largest improvement in the NLL function comes fromcontributions that tend to be broad and cannot be inter-preted as resonances. These conclusions are not surpris-ing if one considers the measured two-particle Kπ scat-tering amplitudes obtained by the LASS Collaboration[33]. Here the F -wave intensity, apart from the K ∗ (1780)peak, has a strong contribution from nontrivial struc-tures, which are not resolved in the LASS analysis. Theinability to provide a consistent data description for thissolution prevents us from making a reliable estimation ofsystematic uncertainties. C. Solution II
We find that the largest improvement to the NLL of thesolution I comes from the inclusion of a smooth contribu-tion in the J P = 3 − partial wave, which we parametrizewith a broad Breit-Wigner shape. Its mass is found to Table I. List of contributions for solution I, showing for each contribution the mass, width, decay fraction and increase innegative log-likelihood for the removal of the state. In the Kπ channel b stands for decay fraction through both chargedconjugated modes and b +( − ) gives the contribution of one charged mode, which allows their interference to be determined. Theuncertainties are statistical. Parameters marked with (cid:63) are fixed. K ± π channels J PC PDG M (MeV/ c ) Γ(MeV/ c ) b (%) b +( − ) (%) ∆NLL1 − K ∗ (892) ± . ± . . ± . . ± . . ± . − − K ∗ (1680) ± (cid:63) (cid:63) . ± .
04 0 . ± .
02 3982 + K ∗ (1430) ± . ± . . ± . . ± . . ± . − + K ∗ (1980) ± ±
11 312 ±
28 0 . ± .
05 0 . ± .
02 2383 − K ∗ (1780) ± (cid:63) (cid:63) . ± .
01 0 . ± .
01 834 + K ∗ (2045) ± ± ±
17 0 . ± .
02 0 . ± .
01 192 K + K − channel J PC PDG M (MeV/c ) Γ(MeV/c ) b(%) ∆ ln L −− ρ (770) 771 (cid:63) (cid:63) . ± . −− ρ (1450) 1465 (cid:63) (cid:63) . ± . −− ± ±
12 1 . ± . −− ± ±
21 0 . ± .
03 731 −− non-resonant −− −− . ± . −− ρ (1690) 1696 (cid:63) (cid:63) . ± .
01 144 be close the maximal allowed invariant mass of the K ± π system. The width can vary in the approximate intervalof 0.5 GeV/ c – 1.2 GeV/ c , depending on small varia-tions of the PWA solution, and its value only slightly af-fects other components in the fit. Such a mass and widthdoes not allow an interpretation of this contribution asa single resonance. The solution where this broad com-ponent is added and the significance of the resonancesis reevaluated is shown in Table II. For this solution, weuse the more conservative resonance significance criteria:the minimum NLL improvement is required to be 40.We ensure that no other allowed resonance contributionsimprove the NLL value above this number, consideringpossibilities with spins up to J = 5, which is the max-imum spin of previously reported states allowed in thisdecay. Those contributions which give the most signifi-cant NLL improvement are used to estimate systematicuncertainties. The NLL value for this solution is betterby 116 than that of solution I. The systematic uncertain-ties listed in Table II will be discussed later. The Dalitzplot for the solution II is shown in Fig. 1(c). Mass andangular distributions are given in Fig. 2 and Fig. 3 forthe data and for the two models. The two descriptionsare very similar, but solution II is superior in specifickinematic regions.Solution II has the same set of well-defined contribu-tions as solution I. The fitted mass and width for the K ∗ (892) ± and K ∗ (1430) ± are almost the same. Themass, width and Blatt-Weisskopf radius of the K ∗ (892) are found to be M = 893 . ± . +0 . − . MeV/ c , Γ =46 . ± . +0 . − . MeV/ c and r = 0 . ± . +0 . − . fm, respec-tively, where here and subsequently the first uncertaintyis statistical, and the second systematic. The mass liesbetween the PDG averages for measurements performedwhere the K ∗ (892) ± is produced in hadronic collisionsand those were it is produced in τ decays [26]. Thefitted width is consistent with the τ -decay results [34].For the K ∗ (1430) ± we fix the Blatt-Weisskopf radius to0.4 fm. The 2 + partial amplitude in the K ± π kine-matic channels also requires a second contribution with amass higher than that of the previous solution with largesystematic uncertainties for both the mass and width: M = 1868 ± +40 − MeV/ c and Γ = 272 ± +50 − MeV/ c .The mass is approximately 100 MeV/ c below the LASSmeasurement for the K ∗ (1980) [27], but both the massand the width are compatible with the PDG averageswithin 2 . J P = 4 + partial wave with M = 2090 ± +11 − MeV/ c and Γ = 201 ± +57 − MeV/ c ,which is consistent with the parameters of the K ∗ (2045) ± [26]. For the K ∗ (1410), which is required in this solution,the K ∗ (1680) ± and the K ∗ (1780) ± , no NLL minima con-sistent with parameters of these resonances are found.In the K + K − kinematic channel we see again two sta-ble contributions at 1.65 GeV/ c and 2.05 GeV/ c . Thecontributions from the ρ (1450), ρ (1690) and ρ (770) aremarginal. ) (GeV/c - K + K M ) E ve n t s / ( M e V / c · (a) ) (GeV/c p K M ) E ve n t s / ( M e V / c · (b) p q cos -1 -0.5 0 0.5 1 E ve n t s / . · (c) K q cos -1 -0.5 0 0.5 1 E ve n t s / . · (d) - K + K q cos -1 -0.5 0 0.5 1 E ve n t s / . · (e) K p q cos -1 -0.5 0 0.5 1 E ve n t s / . · (f) Figure 2. Kinematical distributions for the data (dots), thePWA solution I (shaded histograms) and the PWA solution II(solid line). The notation K without any specified chargeindicates the sum of the K + and K − distributions. (a-b)Invariant mass of the K + K − and K ± π systems. (c-d) Dis-tributions of the final state particles polar angle ( θ π , θ K )with respect to the beam axis in the J/ψ rest frame. (e-f)Polar angle distributions ( θ KK , θ πK ) for K + in the K + K − helicity frame (e) and for π in the Kπ helicity frame (f).The uncertainties are statistical and are within the size of thedots. A striking feature of solution II is the presence of anon-resonance component in the J P = 3 − K ± π par-tial waves, which can not be clearly interpreted as aninterference between Breit-Wigner states. A possible in-terpretation is that this component is the manifestationof non-resolved contributions present in the F -wave Kπ scattering amplitude [33]. This may include the pres-ence of several resonances, non-resonant production andfinal-state particle rescattering effects.The stability of the found NLL minimum with respectto the parameters of the reported resonances is demon-strated in Fig. 4.The systematic errors due to the uncertainty of thePWA solution are assigned to be the largest deviations ) (GeV/c - K + K M ) E ve n t s / ( M e V / c · (a) ) (GeV/c p K M ) E ve n t s / ( M e V / c · (b) p q cos -1 -0.5 0 0.5 1 E ve n t s / . · (c) K q cos -1 -0.5 0 0.5 1 E ve n t s / . · (d) - K + K q cos -1 -0.5 0 0.5 1 E ve n t s / . · (e) K p q cos -1 -0.5 0 0.5 1 E ve n t s / . · (f) Figure 3. Kinematical distributions for the data (dots), PWAsolution I (shaded histograms) and PWA solution II (solidline) in the inner region of the Dalitz plot ( M ( K ± π ) > . c ). The notation K without any specified charge in-dicates the sum of the K + and K − distributions. (a-b) In-variant mass of the K + K − and K ± π systems. (c-d) Distri-butions of the final-state state particles polar angle ( θ π , θ K )with respect to the beam axis in the J/ψ rest frame. (e-f)Polar angle distributions ( θ KK , θ πK ) for K + in the K + K − helicity frame (e) and for the π in the Kπ helicity frame(f). The error bars represent the statistical uncertainties. for the following variations of the solution: • variation of the masses and widths for the K ± π resonances with the parameters fixed in the fit, andvaried by one standard deviation of the LASS re-sults [33]; • variation of the Blatt-Weisskopf radius of the K ∗ (1430) ± by ± . • inclusion of contributions that strongly improve thelog-likelihood below the acceptance criteria ( J P =1 − ( Kπ ) at approximately 2.5 GeV/ c and J P C =1 −− ( K + K − ) at M ( K + K − ) ≈ . c );0 ) M (GeV/c1.425 1.43 1.435 1.44 1.445 N LL D – *(1430) K ) M (GeV/c1.8 2 N LL D – *(1980) K ) M (GeV/c2 2.05 2.1 2.15 2.2 N LL D – *(2045) K ) M (GeV/c1.5 1.6 1.7 1.8 N LL D at 1650 MeV/c) - K + (K - - ) M (GeV/c1.9 2 2.1 2.2 N LL D at 2050 MeV/c) - K + (K - - ) (GeV/c G N LL D – *(1430) K ) (GeV/c G N LL D – *(1980) K ) (GeV/c G N LL D – *(2045) K ) (GeV/c G N LL D at 1650 MeV/c) - K + (K - - ) (GeV/c G N LL D at 2050 MeV/c) - K + (K - - Figure 4. Mass and width scans for the K ∗ (1430), K ∗ (1980), K ∗ (2045) and 1 −− structures at 1650 MeV/ c and 2050 MeV/ c for solution II. • reparametrization of the broad background part ofpartial waves.To evaluate the latter variation, broad contributions inthe 1 − , 2 + ( Kπ ) amplitudes and 1 −− ( K + K − ) partialwave parametrized with ρ (770) and ρ (1450) are stud-ied. In all these fits the states K ∗ (892) ± , K ∗ (1430) ± , K ∗ (2045) ± and the structures at 1.65 GeV/ c and2.05 GeV/ c in the K + K − channels remain stable. Thehigh-mass broad K ± π − contribution always remainssignificant, but its relative fraction varies to much smallervalues in some fits. The 1 − additional contributionmostly manifests resonant behavior. No stable contribu-tion can be associated with the ρ (1450), but its relativedecay fraction at the level of 1% does not contradict thedata.The total systematic uncertainties for the masses,widths and decay fraction given in Table II are calcu-lated as a quadratic sum of: • the variation in results due to the uncertainty ofthe PWA solution; • the bias introduced by imperfections of the detectorsimulation and the event reconstruction; • the uncertainties due to the differences in kaontracking and PID efficiencies between data and theMC simulation.The differences in kaon tracking and PID efficiencies be-tween data and the MC simulation are studied with ahigh-purity control sample of J/ψ → K S K ± π ∓ decaysas a function of kaon transverse momentum p T and arefound to be within 1% per track both for the trackingand the PID. The effect on the PWA result is estimatedby varying the selection efficiency difference for data andMC in p T bins within these errors. Uncertainties on thefit parameters due to the efficiency variation in each binare summed quadratically.The background uncertainty, estimated by varying thesubtracted NLL contribution by 50%, is found to be neg-ligible. D. Summary on PWA
Our analysis shows that there is a set of states inthe PWA solutions that remains stable for both consid-ered cases: when contributions corresponding to well-known resonances are considered or when broad contri-butions are introduced to parameterize the missing partof the partial amplitudes. In the K ± π channels this setof resonances includes the K ∗ (892) ± , K ∗ (1430) ± , and K ∗ (2045) ± . The second J P = 2 + state, labeled here as K ∗ (1980) ± , has a mass much lower than that observed bythe LASS Collaboration [27]. However, given the largesystematic uncertainties on this quantity, our result iscompatible within 2.2 standard deviations. The first sta-ble structure in the K + K − channel has a mass of about1.65 GeV/ c and a decay fraction of 1.0% – 1.5%. Theabsence of a distinct contribution from the first radialexcitation of the ρ (770) favors its interpretation as a D ρ -resonance. At the same time such a small decay frac-tion is consistent with ω (1650) production in J/ψ decaythrough a virtual photon. Its mass is consistent with thePDG estimate for the ω (1650) and its width is well withinthe spread of experimental results quoted by the PDG.It could also be the result of interference between theseisovector and isoscalar states. The second stable contri-bution has a mass of about 2.05 GeV/ c – 2.10 GeV/ c and decay fraction of 0.1% – 0.2%. Given the large sys-tematic uncertainties it could be interpreted as either the ρ (2150) or as another isovector-vector state observed inproton-antiproton annihilation in flight [35]. Clarifica-tion of the nature of these excited vector mesons requiresfurther investigation. V. BRANCHING FRACTIONS
The
J/ψ → K + K − π branching fraction is deter-mined as B ( J/ψ → K + K − π ) = N sel − N bg − N continuum (cid:15)N J/ψ B ( π → γγ ) .Here N sel , N bg and N continuum are the number of selectedevents, the estimated background from the J/ψ decays,and the continuum production, respectively. The numberof
J/ψ events N J/ψ = (223 . ± . syst. )) × is taken1 Table II. List of components for solution II. For the reported states in the Kπ channel ( K ∗ (892) ± , K ∗ (1430) ± , K ∗ (1980) ± and K ∗ (2045) ± ) and the reported signals in the K + K − channel ( J PC = 1 −− signals with masses around 1650 MeV/ c and2050 MeV/ c ) the first uncertainty is statistical and the second is systematic. In the Kπ channel the decay fraction is givenfor both charged conjugated modes ( b ) and for the contribution of one charged mode ( b +( − ) ), so that their interference canbe determined. As the K ∗ (1410) ± , K ∗ (1680) ± and K ∗ (1780) ± contributions are not reliably identified (see main text), theirmasses and widths are fixed (marked with (cid:63) ) and only statistical uncertainties are given for their decay fractions. K ± π channels J PC PDG M (MeV/ c ) Γ(MeV/ c ) b (%) b +( − ) (%) ∆NLL1 − K ∗ (892) ± . ± . +0 . − . . ± . +0 . − . . ± . +1 . − . . ± . +0 . − . − − K ∗ (1410) ± (cid:63) (cid:63) . ± .
04 0 . ± .
02 801 − K ∗ (1680) ± (cid:63) (cid:63) . ± .
03 0 . ± .
01 562 + K ∗ (1430) ± . ± . +2 . − . . ± . +3 . − . . ± . +0 . − . . ± . +0 . − . − + K ∗ (1980) ± ± +40 − ± +50 − . ± . +0 . − . . ± . +0 . − . − K ∗ (1780) ± (cid:63) (cid:63) . ± .
02 0 . ± .
01 1054 + K ∗ (2045) ± ± +11 − ± +57 − . ± . +0 . − . . ± . +0 . − . − non-resonant −− −− ∼ . ∼ .
6% 629 K + K − channel J PC PDG M (MeV/c ) Γ(MeV/c ) b(%) ∆ ln L −− ± +16 − ± +15 − . ± . +0 . − . −− ± +36 − ± +25 − . ± . +0 . − . from Ref. [13], and B ( π → γγ ) = (98 . ± . × − is taken from the PDG [26]. The selection efficiency (cid:15) is obtained using the PWA solution II and the detectorperformance simulation. The dominant contribution tothe statistical uncertainty comes from N sel . The system-atic uncertainty on the branching fraction is estimatedfrom the sources listed in Table III. The background un-certainty is estimated by varying N bg by ± N continuum . The charged track reconstruction effi-ciency and the PID efficiency uncertainties are 1% eachper track as is discussed above. The photon detection ef-ficiency is studied with the decays ψ (3686) → π + π − J/ψ , J/ψ → ρ π and photon conversion control samples[36, 37]. In this analysis, an uncertainty of 1% per pho-ton is assigned. The uncertainty introduced by the cut on χ K + K − γγ is estimated using a control sample. This is se-lected using similar selection criteria, with the kinematic-fit cut replaced by the requirement that at least one par-ticle out of three ( K + , K − , π ) has a mass hypothesisconsistent with the recoil mass calculated using the othertwo particles. Such a procedure accepts a signal eventeven if one of the particles is badly reconstructed. Thisgives B ( J/ψ → K + K − π ) = (2 . ± . ± . × − .Knowing the J/ψ → K + K − π branching fraction andthe decay fractions for the individual components fromthe PWA, we determine branching fractions for the de-cay via individual resonances. Results for solution II Table III. Summary of systematic uncertainties for B ( J/ψ → K + K − π ).Source Uncertainty (%) N bg N continuum N J/ψ [13] 0.6Total 4.3 are summarized in Table IV. The branching fraction B ( J/ψ → K + K − π ) and the branching fractions for thedecay via the K ∗ (892) ± that are obtained in solution IIare compared to the results from previous experimentsin Table V. Our result for B ( J/ψ → K + K − π ) is upto now the most precise measurement. It differs fromthe PDG value [26], obtained indirectly from Ref. [11],by about 2.8 standard deviation. The systematic uncer-tainty of our results for decays through the K ∗ (892) ± issomewhat larger than that of Ref. [11], which can be at-tributed to the uncertainties present in the PWA model.2 VI. CONCLUSION
A partial-wave analysis of the decay
J/ψ → K + K − π using a data sample of (223 . ± . × J/ψ events col-lected by the BESIII reveals a set of resonances that havenot been observed by previous experiments. In the K ± π channels our analysis reveals signals from K ∗ (1980) ± and K ∗ (2045) ± resonances. This is the first observation ofthese states in J/ψ decays. The mass of the former stateis determined with a central value around 100 MeV/ c lower than that reported by the LASS Collaboration [29].This lower value is in better agreement with the expec-tation from the linear Regge trajectory of radial excita-tions with the standard slope [38]. As for the knowndecays through Kπ resonances, we determine the pa-rameters, decay ratios, and branching fractions for the K ∗ (892) ± and K ∗ (1430) ± with improved precision com-pared to previous measurements. In the K + K − channelwe observe a clear J P C = 1 −− resonance structure witha mass of 1.65 GeV/ c and another J P C = 1 −− contribu-tion at 2.05 GeV/ c – 2.10 GeV/ c . The first structuremay be interpreted as the ground D isovector state. Atthe same time its mass, width and small relative contri-bution to the decay are reasonably consistent with theproduction of the ω (1650) in J/ψ decays through a vir-tual photon. The second state can be interpreted as the ρ (2150) or as another isovector-vector state that has beenobserved in proton-antiproton annihilation in flight [35].The precise identification of these two states requires fur-ther analysis of more channels, such as J/ψ → K S K ± π ∓ and J/ψ → K + K − η . Our PWA solutions have notabledifferences from those presented in Ref. [10] and more re-cently in Ref. [12]. We also report the most precise mea-surement of the branching fraction B ( J/ψ → K + K − π ). VII. ACKNOWLEDGEMENTS
The BESIII collaboration thanks the staff of BEPCIIand the IHEP computing center for their strong sup-port. This work is supported in part by NationalKey Basic Research Program of China under ContractNo. 2015CB856700; National Natural Science Founda-tion of China (NSFC) under Contracts Nos. 11625523,11635010, 11735014; National Natural Science Founda-tion of China (NSFC) under Contract No. 11835012; theChinese Academy of Sciences (CAS) Large-Scale Scien-tific Facility Program; Joint Large-Scale Scientific Facil-ity Funds of the NSFC and CAS under Contracts Nos.U1532257, U1532258, U1732263, U1832207; CAS KeyResearch Program of Frontier Sciences under ContractsNos. QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040; 100Talents Program of CAS; INPAC and Shanghai Key Lab-oratory for Particle Physics and Cosmology; German Re-search Foundation DFG under Contract No. Collab-orative Research Center CRC 1044; DFG and NSFC(CRC 110); Istituto Nazionale di Fisica Nucleare, Italy;Koninklijke Nederlandse Akademie van Wetenschappen(KNAW) under Contract No. 530-4CDP03; Ministry ofDevelopment of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; The Knutand Alice Wallenberg Foundation (Sweden) under Con-tract No. 2016.0157; The Royal Society, UK underContract No. DH160214; The Swedish Research Coun-cil; U. S. Department of Energy under Contracts Nos.DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0012069;University of Groningen (RuG) and the Helmholtzzen-trum fuer Schwerionenforschung GmbH (GSI), Darm-stadt. This paper is also supported by the NSFC underContract Nos. 10805053. [1] S. Godfrey and N. Isgur, Phys. Rev. D , 189 (1985).[2] A. Anisovich, V. 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D , 112005 (2011).[38] V. V. Anisovich, AIP Conf. Proc. , 197 (2002). Table IV. Branching fractions for decays via reliably identified intermediate states (solution II). R Kπ and R KK denotes K ± π and K + K − resonances, respectively, and R ± Kπ K ∓ denotes for one possible charged combination. The first uncertainty isstatistical and the second one is systematic. Intermediate resonance in the Kπ system R Kπ B ( J/ψ → R ± Kπ K ∓ → K + K − π ) B ( J/ψ → R + Kπ K − + c.c. → K + K − π ) K ∗ (892) (1 . ± . +0 . − . ) × − (2 . ± . +0 . − . ) × − K ∗ (1430) (1 . ± . +0 . − . ) × − (2 . ± . +0 . − . ) × − K ∗ (1980) (4 . ± . +2 . − . ) × − (1 . ± . +0 . − . ) × − K ∗ (2045) (2 . ± . +1 . − . ) × − (6 . ± . +2 . − . ) × − Intermediate resonance in the K + K − system R KK B ( J/ψ → R KK π → K + K − π )1 −− (1650 MeV/ c ) (5 . ± . +0 . − . ) × − −− (2050 MeV/ c ) (6 . ± . +2 . − . ) × − Table V. Comparison between this work and previous measurements. For B ( J/ψ → K ∗ + K − + c.c. → K + K − π ) and B ( J/ψ → K ∗ + K − + c.c. ) we give two numbers for solution II: the first one is a sum of branching fractions through K ∗ + and K ∗− andthe second number (in parenthesis) accounts for their interference. Results marked with “ † ” are obtained by averaging the K S K ± π ∓ and K + K − π final states. Results recalculated by us using numbers from this work are marked with “ †† ”. Channel B ( × − )This work BABAR[11] DM2[9] MARK-III[8] MARK-II[7] B ( J/ψ → K + K − π ) 2 . ± . ± .
12 — — — 2 . ± . B ( J/ψ → K ∗ + K − + c.c. → K + K − π ) 2 . ± . +0 . − . (2 . ± . +0 . − . ) 1 . ± . ± .
13 1 . ± . ± . †† . ± . ± . †† . ± . B ( J/ψ → K ∗ + K − + c.c. ) 7 . ± . +0 . − . (8 . ± . +0 . − . ) 5 . ± . ± . † . ± . ± . † . ± . ± . † . ± .4