Observation of OZI-suppressed decays χ cJ → ωφ

M. Ablikim, M. N. Achasov, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, J. Z. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, Y. Ban, K. Begzsuren, D.W. Bennett, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, E. Boger, I. Boyko, R. A. Briere, H. Cai, X. Cai, O. Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. Chai, J. F. Chang, G. Chelkov, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, P. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, W. Cheng, X. K. Chu, G. Cibinetto, F. Cossio, H. L. Dai, J. P. 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, P. F. Duan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, S. Fegan, F. Feldbauer, G. Felici, C. Q. Feng, E. Fioravanti, M. Fritsch, C. D. Fu, Q. Gao, X. L. Gao, Y. Gao, Y. G. Gao, Z. Gao, B. Garillon, I. Garzia, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, Y. T. Gu, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, Z. Haddadi, S. Han, X. Q. Hao, F. A. Harris, K. L. He, X. Q. He, F. H. Heinsius, T. Held, Y. K. Heng, Z. L. Hou, H. M. Hu, J. F. Hu, T. Hu, Y. Hu, G. S. Huang, J. S. Huang, X. T. Huang, X. Z. Huang, Z. L. Huang, T. Hussain, W. Ikegami Andersson, M. Irshad, Q. Ji, Q. P. Ji, X. B. Ji, X. L. Ji, X. S. Jiang, X. Y. Jiang, J. B. Jiao, Z. Jiao, D. P. Jin, S. Jin, Y. Jin, T. Johansson, A. Julin, N. Kalantar-Nayestanaki, X. S. Kang, M. Kavatsyuk, B. C. Ke, I. K. Keshk, T. Khan, A. Khoukaz, P. Kiese, R. Kiuchi, R. Kliemt, L. Koch, O. B. Kolcu, B. Kopf, M. Kornicer, M. Kuemmel, M. Kuessner, A. Kupsc, M. Kurth, W. Kühn, J. S. Lange, P. Larin, L. Lavezzi, S. Leiber, H. Leithoff, C. Li, Cheng Li, D. M. Li, F. Li, F. Y. Li, G. Li, H. B. Li, H. J. Li, J. C. Li, J. W. Li, K. J. Li, Kang Li, Ke Li, Lei Li, P. L. Li, P. R. Li, Q. Y. Li, T. Li, W. D. Li, W. G. Li, X. L. Li, X. N. Li, X. Q. Li, Z. B. Li, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, L. Z. Liao, J. Libby, C. X. Lin, D. X. Lin, B. Liu, B. J. Liu, C. X. Liu, D. Liu, D. Y. Liu, F. H. Liu, Fang Liu, Feng Liu, H. B. Liu, H. L. Liu, H. M. Liu, Huanhuan Liu, Huihui Liu, J. B. Liu, J. Y. Liu, K. Liu, K. Y. Liu, Ke Liu, L. D. Liu, Q. Liu, S. B. Liu, X. Liu, Y. B. Liu, Z. A. Liu, Zhiqing Liu, Y. F. Long, X. C. Lou, H. J. Lu, J. G. Lu, Y. Lu, Y. P. Lu, C. L. Luo, M. X. Luo, T. Luo, X. L. Luo, S. Lusso, X. R. Lyu, F. C. Ma, H. L. Ma, L. L. Ma, M.M. Ma, Q. M. Ma, T. Ma, X. N. Ma, X. Y. Ma, Y. M. Ma, F. E. Maas, M. Maggiora, S. Maldaner, Q. A. Malik, A. Mangoni, Y. J. Mao, Z. P. Mao, S. Marcello, Z. X. Meng, J. G. Messchendorp, G. Mezzadri, J. Min, T. J. Min, R. E. Mitchell, X. H. Mo, Y. J. Mo, C. Morales Morales, N. Yu. Muchnoi, H. Muramatsu, A. Mustafa, S. Nakhoul, Y. Nefedov, F. Nerling, I. B. Nikolaev, Z. Ning, S. Nisar, S. L. Niu, X. Y. Niu, S. L. Olsen, Q. Ouyang, S. Pacetti, Y. Pan, M. Papenbrock, P. Patteri, M. Pelizaeus, J. Pellegrino, H. P. Peng, Z. Y. Peng, K. Peters, 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. S. Qin, Z. H. Qin, J. F. Qiu, S. Q. Qu, K. H. Rashid, C. F. Redmer, M. Richter, M. Ripka, A. Rivetti, M. Rolo, G. Rong, Ch. Rosner, A. Sarantsev, M. Savrié, K. Schoenning, W. Shan, X. Y. Shan, M. Shao, C. P. Shen, P. X. Shen, X. Y. Shen, H. Y. Sheng, X. Shi, J. J. Song, W.M. Song, X. Y. Song, S. Sosio, C. Sowa, S. Spataro, 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, I. Tapan, M. Tiemens, B. Tsednee, I. Uman, B. Wang, B. L. Wang, C.W. Wang, D. Wang, D. Y. Wang, Dan Wang, K. Wang, L. L. Wang, L. S. Wang, M. Wang, Meng Wang, P. Wang, P. L. Wang, W. P. Wang, X. F. Wang, Y. Wang, Y. F. Wang, Z. Wang, Z. G. Wang, Z. Y. Wang, ZongyuanWang, T. Weber, D. H. Wei, P. Weidenkaff, S. P. Wen, U. Wiedner, M. Wolke, L. H. Wu, L. J. Wu, Z. Wu, L. Xia, X. Xia, Y. Xia, D. Xiao, Y. J. Xiao, Z. J. Xiao, Y. G. Xie, Y. H. Xie, X. A. Xiong, Q. L. Xiu, G. F. Xu, J. J. Xu, L. Xu, Q. J. Xu, Q. N. Xu, X. P. Xu, F. Yan, L. Yan, W. B. Yan, W. C. Yan, Y. H. Yan, H. J. Yang, H. X. Yang, L. Yang, R. X. 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, J. S. Yu, C. Z. Yuan, Y. Yuan, A. Yuncu, 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, X. Y. Zhang, Y. Zhang, Y. H. Zhang, Y. T. Zhang, Yang Zhang, Yao Zhang, 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. Zheng, J. P. Zheng, W. J. Zheng, Y. H. Zheng, B. Zhong, L. Zhou, Q. Zhou, X. Zhou, X. K. Zhou, X. R. Zhou, X. Y. Zhou, Xiaoyu Zhou, Xu Zhou, A. N. Zhu, J. Zhu, J. Zhu, PHYSICAL REVIEW D 99, 012015 (2019)


I. INTRODUCTION
The lowest triplet P-wave states of charmonium (the cc bound state), χ cJ ð1PÞ, with quantum numbers I G J PC ¼ 0 þ J þþ and J ¼ 0, 1, and 2, can be found abundantly in the electromagnetic decays ψð3686Þ → γχ cJ with an approximate branching fraction of 30% [1].The ψð3686Þ meson can be directly produced at the e þ e − colliders, such as the BEPCII [2], where the χ cJ mesons are easily accessible by the electromagnetic decays ψð3686Þ → γχ cJ .
The hadronic χ cJ decays are important probes of the strong force dynamics.First of all, the mass of the c quark (∼1.5 GeV=c 2 ) is well known between the perturbative and nonperturbative QCD domains in theoretical calculations.Due to the complexity and entanglement of the long-and short-distance contributions, large theoretical uncertainties of branching ratios for the χ cJ → VV decays are known [3][4][5][6][7][8][9].(In this paper, the symbol of V denotes the ω and ϕ mesons).The hadronic χ cJ decays provide a prospective laboratory to limit theoretical parameters and test various phenomenological models.Second, the χ cJ mesons have the same quantum numbers J PC as some glueballs and hybrids, although none of the glueball and hybrid states has been seen until now [10].The hadronic χ cJ → VV decays are ideal objects to exploit the glueballq q mixing and the quark-gluon coupling of the strong interactions at the relatively low energies.Third, the χ cJ mesons are below the open-charm threshold.Most of the hadronic χ cJ decay modes are suppressed by the Okubo-Zweig-Iizuka (OZI) rule [11].It is shown in the previous theoretical researches that the contributions from the intermediate glueballs or hadronic loops can scuttle the OZI rule in the χ cJ → VV decays [12][13][14][15], and avoid the so-called helicity selection (HS) rule (also called the "naturalness" which is defined as σ ¼ ð−1Þ S P [16], where S and P are respectively the spin and parity of the particle.) in the χ c1 → VV decays [8,9].
The χ cJ , ϕ and ω mesons differ from each other in their quark components according to the quark model assignments.This fact causes the χ cJ → ωϕ decay modes to be doubly OZI (DOZI) suppressed and results in the branching fractions for the χ cJ → ωϕ decays much less than those for the singly OZI-suppressed χ cJ → ωω, ϕϕ decays [1,17].In reality, ω and ϕ are not ideal mixtures of the flavor SU(3) octet and singlet [18], which would provide a source that violates the DOZI-suppressed rule for χ c1 → ωϕ.The DOZI-suppressed χ cJ → ωϕ decays have been observed based on the 106 × 10 6 ψð3686Þ events accumulated with the BESIII detector in 2009, with significances of 10σ, 4.1σ and 1.5σ for the χ c0 , χ c1 and χ c2 decays, respectively [17].

II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector operating at the BEPCII collider is described in detail in Ref. [2].The detector is cylindrically symmetric and covers 93% of 4π solid angle.It consists of the following four subdetectors: a 43-layer main drift chamber (MDC), which is used to determine momentum of the charged tracks with a resolution of 0.5% at 1 GeV=c in the axial magnetic field of 1 T; a plastic scintillator timeof-flight system (TOF), with a time resolution of 80 ps (110 ps) in the barrel (end caps); an electromagnetic calorimeter (EMC) consisting of 6240 CsI(Tl) crystals, with photon energy resolution at 1 GeVof 2.5% (5%) in the barrel (end caps); and a muon counter consisting of 9 (8) layers of resistive plate chambers in the barrel (end caps), with position resolution of 2 cm.
The GEANT4-based [20,21] Monte Carlo (MC) simulation software BOOST  [22] includes the geometry and material description of the BESIII detectors, the detector response and digitization models, as well as a database that keeps track of the running conditions and the detector performance.MC samples are used to optimize the selection criteria, evaluate the signal efficiency, and estimate physics backgrounds.An inclusive MC sample of ψð3686Þ events is used for the background studies.The ψð3686Þ resonance is produced by the event generator KKMC [23], where the initial state radiation is included, and the decays are simulated by EVTGEN [24] with known branching fractions taken from Ref. [1], while the unmeasured decays are generated according to LUNDCHARM [25].The signal is simulated with the decay ψð3686Þ → γχ cJ generated assuming an electric-pole (E1) transition.The decay χ cJ → ωϕ is generated using HELAMP [24], the helicity amplitude model where the angular correlation between ω decay and ϕ decay has been considered.Ref. [17] shows that the model describes the experimental angular distribution well.We assume χ cJ → ωϕ and χ cJ → ϕϕ have the same helicity amplitudes with the same HELAMP parameters.In addition, χ cJ states are simulated using a relativistic Breit-Wigner incorporated within the helicity amplitudes in the EVTGEN package [24].The background decays π 0 are generated using the phase space model.

III. EVENT SELECTION
In this analysis, the ϕ mesons are reconstructed by K þ K − , while ω by π þ π − π 0 .Event candidates are required to have four well-reconstructed tracks from charged particles with zero net charge, and at least three good photon candidates.
A charged track reconstructed from MDC hits should have the polar angle, θ,j cos θj < 0.93 and pass within AE10 cm of the interaction point along the beam direction and within 1 cm in the plane perpendicular to the beam.To separate K AE from π AE , we require that at least one track is identified as a kaon using dE=dx and TOF information.If the identified kaon has a positive (negative) charge, the second kaon is found by searching for a combination that minimizes jM K þ K − − M ϕ j, among all identified kaons and the negative (positive) charged tracks, where M K þ K − is the invariant mass of the identified kaon and an unidentified track with kaon mass hypothesis, and M ϕ is the nominal ϕ mass [1].The remaining two charged tracks are assumed to be pions.
The photon energy deposit is required to be at least 25 MeV in the barrel region of the EMC ðj cos θj < 0.80Þ or 50 MeV in the EMC end caps (0.86 < j cos θj < 0.92).To suppress electronic noise and energy deposits unrelated to the event, the EMC time t of the photon candidates must be in coincidence with collision events within the range 0 ≤ t ≤ 700 ns.At least three photons are required in an event.
In order to improve the mass resolution, a four-constraint (4C) kinematic fit is performed by assuming energymomentum conservation for the ψð3686Þ→3γK þ K − π þ π − process.If the number of photons is larger than three, then looping all 3γK þ K − π þ π − combinations and the one with the smallest χ 2 4C is chosen.The event is kept for further analysis if , where S and B are the numbers of MC simulated signal and background events, respectively.In addition, is applied to suppress the background with an extra photon in the final state.
The π 0 candidates are selected from the three γγ combinations as the pair with the minimum jM γγ − M π 0 j, where M π 0 is the nominal π 0 mass [1]. Figure 1(a) shows the plot of the K þ K − vs π þ π − π 0 invariant mass for the selected events in the χ cJ signal region ð½3.3;3.6 GeV=c 2 Þ, and a clear accumulation at the ω and ϕ masses is observed.The bottom-central square jM π þ π − π 0 − M ω j < 0.05 GeV=c 2 and jM K þ K − − M ϕ j < 0.015 GeV=c 2 obtained by optimizing FOM, is taken as the ωϕ signal region (labeled as D), and the five squares around the signal region are taken as the sideband regions (labeled as A, B and C), where   and C) and the signal (D) regions.The dots with error bars are data, the solid lines are the fit results, and the dotted lines represent the signal components.The long-dashed line is background normalized using the simultaneous fit to the ωϕ sidebands, and the short-dashed line is the remaining background.
within the ϕ signal region, as shown in Fig. 1(c), indicates clear ω and ϕ peaks.The latter is from the decay for events in the ωϕ sideband regions (subfigures labeled A, B, and C) and the signal region (subfigure labeled D) with clear χ cJ peaks in all plots.Analysis of the ψð3686Þ inclusive MC sample indicates that the peaking background in the χ cJ signal region can be described by the sideband events.The data collected at ffiffi ffi s p ¼

3.65
GeV with an integrated luminosity of approximately 1=15 of the ψð3686Þ data are used to investigate nonresonant continuum background.After the same event selection criteria are applied, only a few events survive, and they do not have any obvious enhancements in the χ cJ mass region.

IV. SIGNAL EXTRACTION
The number of the χ cJ → ωϕ events is determined by fitting the M K þ K − π þ π − π 0 distributions within the ωϕ signal region [labeled as D in Fig. 1(a)].The signal is described by the MC simulated shape convolved with a Gaussian function, which is used to account for the difference in the χ cJ mass and resolution between data and MC simulation.The parameters of the Gaussian function are obtained using the sample The peaking backgrounds from the π 0 background are estimated using the sideband regions labeled A, B, and C in Fig. 1(a).The total peaking background contribution, N bkg , is the sum calculated as where , and N n−r bkg are numbers of the aforementioned peaking background contributions.The contributions are determined using the following equations: where N A , N B , and N C are the numbers of the fitted χ cJ events in the A, B, and C regions, respectively; f C→A , f C→B , f C→D , f A→D , and f B→D are the relative scaling factors for the different regions.The factors are estimated using the corresponding MC simulation of and ϕπ þ π − π 0 .For example, f A→D is the ratio of the χ cJ → ωK þ K − yields between the D and A regions.We perform a simultaneous unbinned maximum likelihood fit to the M K þ K − π þ π − π 0 distributions in the signal and sideband regions.The result of the fit is shown in Fig. 2. The parameters of the Gaussian functions accounting for the difference between data and MC simulation are assumed to be the same for the signal and sidebands.The shape of the distributions outside the χ cJ peaks is described by a polynomial function.The statistical significance of the χ c1 ðχ c2 Þ signal is determined by comparing the −2 ln L value with the one from the fit without the χ c1 ðχ c2 Þ signal component, and considering the change in the number of degrees of freedom.The results are 12.3σ and 4.8σ for χ c1 and χ c2 , respectively.The extracted numbers of the χ cJ → ωϕ events are given in Table I.
The product branching fractions, Bðψð3686Þ → γχ cJ Þ× Bðχ cJ → ωϕÞ ¼ B 1 × B 2 , are calculated as where N ψð3686Þ is the number of ψð3686Þ events, BðωÞ, BðϕÞ, and Bðπ 0 Þ are the branching fractions of ω → π þ π − π 0 , ϕ → K þ K − , and π 0 → γγ, respectively [1].The corresponding detection efficiencies, ϵ, are obtained from the MC simulations.The results for the product branching fractions are listed in Table I.By using the world average values of Bðψð3686Þ → γχ cJ Þ, the absolute branching fractions of χ cJ → ωϕ are determined and also listed in Table I.

V. SYSTEMATIC UNCERTAINTIES
The contribution of systematic effects on the product branching fractions from various sources is described in the following: (1) The tracking efficiency for π and K is investigated using control samples of J=ψ → ρπ [17] and ψð3686Þ → π þ π − K þ K − , respectively.The difference in the efficiency for the track reconstruction between data and MC simulation is 1.0% per pion Zhengzhou University, Zhengzhou 450001, People's Republic of China (Received 23 October 2018; published 31 January 2019)

2 (FIG. 1 .
FIG. 1.(a) Scatter plot of MK þ K − vs M π þ π − π 0 forevents within the χ cJ mass region.The boxes indicate the sideband regions (labeled as A, B, and C) and signal region (labeled as D).(b) and (c) are the one-dimensional projection of the system recoiling against selected ω and ϕ candidates, respectively.The shortdashed arrows show the signal regions while long-dashed arrows show the sideband regions.