Search for new decay modes of the ψ2(3823) and the process e+e-→π0π0ψ2(3823)

M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, R. Aliberti, A. Amoroso, M. R. An, Q. An, X. H. Bai, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Bloms, A. Bortone, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, M. L. Chen, S. J. Chen, X. R. Chen, Y. B. Chen, Z. J. Chen, W. S. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, X. C. Dai, A. Dbeyssi, R. E. de Boer, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, X. Dong, S. X. Du, Y. L. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, J. H. Feng, M. Fritsch, C. D. Fu, Y. Gao, Y. Gao, Y. Gao, Y. G. Gao, I. Garzia, P. T. Ge, C. Geng, E. M. Gersabeck, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, C. Y. Guan, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, T. T. Han, W. Y. Han, X. Q. Hao, F. A. Harris, N. Hüsken, K. L. He, F. H. Heinsius, C. H. Heinz, T. Held, Y. K. Heng, C. Herold, M. Himmelreich, T. Holtmann, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, T. Hu, Y. Hu, G. S. Huang, L. Q. Huang, X. T. Huang, Y. P. Huang, Z. Huang, T. Hussain, W. Ikegami Andersson, W. Imoehl, M. Irshad, S. Jaeger, S. Janchiv, Q. Ji, Q. P. Ji, X. B. Ji, X. L. Ji, Y. Y. Ji, H. B. Jiang, X. S. Jiang, J. B. Jiao, Z. Jiao, S. Jin, Y. Jin, 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. Kopf, M. Kuemmel, M. Kuessner, A. Kupsc, M. G. Kurth, W. Kühn, J. J. Lane, J. S. Lange, P. Larin, A. Lavania, L. Lavezzi, Z. H. Lei, H. Leithoff, M. Lellmann, T. Lenz, C. Li, C. H. Li, Cheng Li, D. M. Li, F. Li, G. Li, H. Li, H. Li, H. B. Li, H. J. Li, H. J. Li, J. L. Li, J. Q. Li, J. S. Li, Ke Li, L. K. Li, Lei Li, P. R. Li, S. Y. Li, W. D. Li, W. G. Li, X. H. Li, X. L. Li, Xiaoyu Li, Z. Y. Li, H. Liang, H. Liang, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, L. Z. Liao, J. Libby, C. X. Lin, B. J. Liu, C. X. Liu, D. Liu, F. H. Liu, Fang Liu, Feng Liu, H. B. Liu, H. M. Liu, Huanhuan Liu, Huihui Liu, J. B. Liu, J. L. Liu, J. Y. Liu, K. Liu, K. Y. Liu, Ke Liu, L. Liu, M. H. Liu, P. L. Liu, Q. Liu, Q. Liu, S. B. Liu, Shuai Liu, T. Liu, W.M. Liu, X. Liu, Y. Liu, Y. B. Liu, Z. A. Liu, Z. Q. Liu, X. C. Lou, F. X. Lu, F. X. Lu, H. J. Lu, J. D. Lu, J. G. Lu, X. L. Lu, Y. Lu, Y. P. Lu, C. L. Luo, M. X. Luo, P. W. Luo, T. Luo, X. L. Luo, S. Lusso, X. R. Lyu, F. C. Ma, H. L. Ma, L. L. Ma, M. M.Ma, Q. M.Ma, R. Q. Ma, R. T. Ma, X. X. Ma, X. Y. Ma, F. E. Maas, M. Maggiora, S. Maldaner, S. Malde, Q. A. Malik, A. Mangoni, Y. J. Mao, Z. P. Mao, S. Marcello, Z. X. Meng, J. G. Messchendorp, G. Mezzadri, T. J. Min, R. E. Mitchell, X. H. Mo, Y. J. Mo, N. Yu. Muchnoi, H. Muramatsu, S. Nakhoul, Y. Nefedov, F. Nerling, I. B. Nikolaev, Z. Ning, S. Nisar, S. L. Olsen, Q. Ouyang, S. Pacetti, X. Pan, Y. Pan, A. Pathak, P. Patteri, M. Pelizaeus, H. P. Peng, K. Peters, J. Pettersson, J. L. Ping, R. G. Ping, R. Poling, V. Prasad, H. Qi, H. R. Qi, K. H. Qi, M. Qi, T. Y. Qi, T. Y. Qi, S. Qian, W. B. Qian, Z. Qian, C. F. Qiao, L. Q. Qin, X. P. Qin, X. S. Qin, Z. H. Qin, J. F. Qiu, S. Q. Qu, K. H. Rashid, K. Ravindran, C. F. Redmer, A. Rivetti, V. Rodin, M. Rolo, G. Rong, Ch. Rosner, M. Rump, H. S. Sang, A. Sarantsev, Y. Schelhaas, C. Schnier, K. Schoenning, M. Scodeggio, D. C. Shan, W. Shan, X. Y. Shan, J. F. Shangguan, 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, W.M. Song, Y. X. Song, S. Sosio, S. Spataro, K. X. Su, P. P. Su, F. F. Sui, G. X. Sun, H. K. Sun, J. F. Sun, L. Sun, S. S. Sun, T. Sun, W. Y. Sun, W. Y. Sun, X. Sun, Y. J. Sun, Y. K. Sun, Y. Z. Sun, Z. T. Sun, Y. H. Tan, Y. X. Tan, C. J. Tang, G. Y. Tang, J. Tang, J. X. Teng, V. Thoren, Y. T. Tian, I. Uman, B. Wang, C.W. Wang, D. Y. Wang, H. J. Wang, H. P. Wang, K. Wang, L. L. Wang, M. Wang, M. Z. Wang, Meng Wang, W. Wang, W. H. Wang, W. P. Wang, X. Wang, X. F. Wang, X. L. Wang, Y. Wang, Y. Wang, Y. D. Wang, Y. F. Wang, Y. Q. Wang, Y. Y. Wang, Z. Wang, Z. Y. Wang, Ziyi Wang, Zongyuan Wang, D. H. Wei, P. Weidenkaff, F. Weidner, S. P. Wen, D. J. White, U. Wiedner, G. Wilkinson, M. Wolke, L. Wollenberg, J. F. Wu, L. H. Wu, L. J. Wu, X. Wu, Z. Wu, L. Xia, H. Xiao, S. Y. Xiao, Z. J. Xiao, X. H. Xie, Y. G. Xie, Y. H. Xie, T. Y. Xing, G. F. Xu, Q. J. Xu, W. Xu, X. P. Xu, Y. C. Xu, F. Yan, L. Yan, W. B. Yan, W. C. Yan, Xu Yan, H. J. Yang, H. X. Yang, L. Yang, S. L. Yang, Y. X. Yang, Yifan Yang, Zhi Yang, M. Ye, M. H. Ye, J. H. Yin, Z. Y. You, B. X. Yu, C. X. Yu, G. Yu, J. S. Yu, T. Yu, C. Z. Yuan, L. Yuan, X. Q. Yuan, Y. Yuan, Z. Y. Yuan, PHYSICAL REVIEW D 103, L091102 (2021)

The lightest charmonium resonance above the DD threshold is the ψð3770Þ, which is identified as the ψð1 3 D 1 Þ state, the J ¼ 1 member of the D-wave spin triplet [10]. Recently, two more states have been observed, which are considered to be good candidates for members of this spin triplet. The ψ 2 ð3823Þ, for which first evidence was found by the Belle Collaboration and which was later observed by the BESIII Collaboration in ψ 2 ð3823Þ → γχ c1 , is considered to be the ψð1 3 D 2 Þ state [11,12]. The LHCb Collaboration also observed the ψ 2 ð3823Þ in its decay to π þ π − J=ψ [13]. The other newly observed resonance is the ψ 3 ð3842Þ seen by the LHCb Collaboration in ψ 3 ð3842Þ → DD [14]. It is suggested to be the ψð1 3 D 3 Þ state.
The motivation of this paper is to provide additional experimental evidence for the correct assignment of the ψ 2 ð3823Þ to be the J ¼ 2 spin-triplet partner, by comparing its decay channels to the theory predictions of Refs. [15][16][17][18][19][20][21][22][23][24]. Experimental information on the ψ 2 ð3823Þ is still sparse. The partial widths for decays of the ψð1 3 D 2 Þ state to several channels have been predicted by various different models. These models agree that the dominant decay of the ψð1 3 D 2 Þ is to γχ c1 , with the next most probable decays being to γχ c2 and to π þ π − J=ψ.

4.7
GeV with the BESIII detector [25]. Additionally, a search is performed for the process e þ e − → π 0 π 0 ψ 2 ð3823Þ with ψ 2 ð3823Þ → γχ c1 . The BESIII detector is a magnetic spectrometer located at the Beijing Electron Positron Collider (BEPCII). For more details on the detector or the accelerator, we refer to Refs. [25][26][27]. Simulated samples produced with the GEANT4-based [28] Monte Carlo (MC) package, which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate background contributions. The simulation includes the beam energy spread and initial-state radiation (ISR) in e þ e − annihilations modeled with the generator KKMC [29]. Signal MC samples for e þ e − → ππψ 2 ð3823Þ are generated using isotropic phasespace populations, assuming that the cross section follows a coherent sum of ψð4360Þ and the ψð4660Þ Breit-Wigner (BW) distributions, whose magnitude and phase parameters we obtain from a fit to the observed cross section, with the ψ 2 ð3823Þ mass fixed to the Particle Data Group (PDG) value [10] and width fixed to zero. The subsequent ψ 2 ð3823Þ decays are generated uniformly in the phase space, and the effects from the angular distributions of ψ 2 ð3823Þ decays are studied and found to be small. Inclusive MC samples consist of the production of opencharm processes, the ISR production of vector charmonium (like) states, and the continuum processes incorporated in KKMC [29]. Known decay modes are modeled with EvtGen [30] using branching fractions summarized and averaged by the PDG [10]. The remaining unknown decays from the charmonium states are generated with LUNDCHARM [31]. Final-state radiation from charged final-state particles is incorporated with the PHOTOS package [32].
The χ c1;2 are reconstructed via χ c1;2 → γJ=ψ decays, the J=ψ is reconstructed in its decay to an e þ e − or μ þ μ − pair, the π 0 and η are reconstructed via π 0 =η → γγ decays, and the χ c0 is reconstructed in its decay to a π þ π − or K þ K − pair. For each charged track, the distance of closest approach to the interaction point is required to be within AE10 cm in the beam direction and within 1 cm in the plane perpendicular to the beam direction. The polar angle (θ) of the tracks must be within the fiducial volume of the multilayer drift chamber ðj cos θj < 0.93Þ. Photons are reconstructed from isolated showers in the electromagnetic calorimeter (EMC), which are at least 10°away from the nearest charged track. The photon energy is required to be at least 25 MeV in the barrel region ðj cos θj < 0.8Þ or 50 MeV in the end-cap region ð0.86 < j cos θj < 0.92Þ. To suppress electronic noise and energy depositions unrelated to the event, the time at which the photon is recorded in the EMC is required to be within 700 ns of the event start time. Candidate events must have the exact same number of charged tracks with zero net charge and at least the same number of photons as required for the respective final state. Tracks with momenta larger than 1 GeV=c are assigned to be leptons from the decay of a J=ψ or to be π=K from the decay of a χ c0 . Otherwise, tracks are considered pions. Leptons from the J=ψ decay with an energy deposit in the EMC larger than 1.0 GeV are identified as electrons, and those with less than 0.4 GeV as muons. To reduce background contributions and to improve the mass resolution, a four-constraint kinematic fit is performed to constrain the total four-momentum of the final-state particles to the fourmomentum of the colliding beams. Additionally, for the ψ 2 ð3823Þ → π 0 π 0 J=ψ and e þ e − → π 0 π 0 ψ 2 ð3823Þ channels the invariant masses of the two pairs of photons are constrained to the nominal mass of the π 0 meson [10]. The two track candidates from the decay of χ c0 mesons are considered to be either a π þ π − or a K þ K − pair depending on the χ 2 of the four-constraint kinematic fit. If χ 2 ðπ þ π − Þ < χ 2 ðK þ K − Þ, the two tracks are identified as a π þ π − pair, otherwise, as a K þ K − pair. For all these channels, if there is more than one combination of photons in an event, the one with the smallest χ 2 of the kinematic fit is selected. The χ 2 of the candidate process is required to be less than 60 in all cases.
The J=ψ signal region is defined by the mass range ½3.075; 3.125 GeV=c 2 in Mðe þ e − =μ þ μ − Þ, apart from in the decay channel ψ 2 ð3823Þ → π þ π − J=ψ, where the J=ψ signal region is narrowed to the range ½3.09; 3.11 GeV=c 2 due to the better resolution for the four charged-track final states. The χ c1 and χ c2 signal regions are chosen as the ranges [3.49, 3.53] and ½3.54; 3.57 GeV=c 2 in Mðγ H J=ψÞ, respectively, and sideband regions, defined as the ranges [3.43, 3.48] and ½3.58; 3.63 GeV=c 2 , are used to study the nonresonant background. The η, π 0 and χ c0 signal regions are chosen to be [0.52, 0.57] and ½0.12; 0.15 GeV=c 2 in MðγγÞ and ½3.39; 3.44 GeV=c 2 in Mðπ þ π − =K þ K − Þ, respectively. Figure 1 shows the π þ π − recoil-mass distribution RMðπ þ π − Þ for the γχ c1 channel. A clear ψ 2 ð3823Þ signal is observed for 9 fb −1 of data at 4.3 < ffiffi ffi s p < 4.7 GeV, while no significant ψ 2 ð3823Þ signal is seen for the 10 fb −1 sample at 4.1 < ffiffi ffi s p < 4.3 GeV. The green shaded histograms correspond to the normalized events from the χ c1 sideband region. Thus, only data at 4.3 < ffiffi ffi s p < 4.7 GeV are used to search for new ψ 2 ð3823Þ decay channels. Figure 2 shows the distributions of RMðπ þ π − Þ for the decays ψ 2 ð3823Þ → γχ c1 , γχ c2 , π þ π − J=ψ, π 0 π 0 J=ψ, ηJ=ψ, π 0 J=ψ, γχ c0 and a scatter plot of Mðγ H J=ψÞ versus RMðπ þ π − Þ for the decays ψ 2 ð3823Þ → γχ c1;2 for data at 4.3 < ffiffi ffi s p < 4.7 GeV. Here, all valid RMðπ þ π − Þ combinations of the π þ π − J=ψ decay are retained. In addition to the ψ 2 ð3823Þ signal observed in the ψ 2 ð3823Þ → γχ c1 channel, there are also events clustered in the signal region for the mode ψ 2 ð3823Þ → γχ c2 . No significant ψ 2 ð3823Þ signals are observed for the other channels. The distribution of Mðπ þ π − J=ψÞ after a four-constraint kinematic fit for the FIG. 1. π þ π − recoil-mass distribution RMðπ þ π − Þ for γχ c1 channel for the data at 4.3 < ffiffi ffi s p < 4.7 GeV (a) and data at 4.1 < ffiffi ffi s p < 4.3 GeV (b). The green shaded histograms correspond to the normalized events from the χ c1 sideband region. π þ π − J=ψ decay is also checked, but no significant ψ 2 ð3823Þ signals are seen. Furthermore, in any of these channels, no significant e þ e − → π þ π − ψ 3 ð3842Þ signals are found. A detailed study of the inclusive MC samples indicates that there are no peaking background contributions in the ψ 2 ð3823Þ signal region [33]. In order to extract the ψ 2 ð3823Þ signal yield, a simultaneous unbinned maximum-likelihood fit is performed to the seven decay channels. The expected shape of RMðπ þ π − Þ from the signal process is modeled by the shape from the MC simulation convolved with a Gaussian function. The parameters of mean and width are free parameters in the fit but are constrained to be the same in all channels. The background is described by a constant. The solid curves in Fig. 2 show the fit results. The significances with systematic uncertainty included for the decays ψ 2 ð3823Þ → γχ c1 and ψ 2 ð3823Þ → γχ c2 are 11.8σ and 3.2σ, respectively. For the other decays, where there are no significant signals, upper limits of the relative branching ratio compared to the decay ψ 2 ð3823Þ → γχ c1 at the 90% confidence level (C.L.) are determined. These upper limits are calculated from the likelihood curve of the fits as a function of signal yield after being convolved with a Gaussian distribution, where the width of Gaussian distribution is the quadratic sum of the systematic uncertainty and statistical uncertainty of the ψ 2 ð3823Þ → γχ c1 signal yield. Those limits together with the corresponding limits on the number of signal events are summarized in Table I.
The values of the branching-fraction ratio Bðψ 2 ð3823Þ→γχ c2 Þ Bðψ 2 ð3823Þ→γχ c1 Þ and the upper limits of the branching-fraction ratios for ψ 2 ð3823Þ → π þ π − J=ψ, π 0 π 0 J=ψ, ηJ=ψ, π 0 J=ψ and γχ c0 relative to the decay ψ 2 ð3823Þ → γχ c1 shown in Table I are calculated using the definition in Table II, where N is the yield of signal events, L is the integrated luminosity [34], σ is the cross section, 1 þ δ is the radiative correction factor [29,35], ϵ is the efficiency, B is the branching fraction [10], and i denotes each energy point. Figure 3 shows the π 0 π 0 recoil-mass distribution RMðπ 0 π 0 Þ for the decay ψ 2 ð3823Þ → γχ c1 for data at 4.3 < ffiffi ffi s p < 4.7 GeV. A signal peak corresponding to the process e þ e − → π 0 π 0 ψ 2 ð3823Þ can be seen. In order to determine the signal yield, an unbinned maximumlikelihood fit is performed. The ψ 2 ð3823Þ signal is modeled by the MC-determined shape convolved with a Gaussian function, whose mean value and width are fixed to be the values obtained from the same final-state process e þ e − → π 0 π 0 ψð3686Þ. The background is described with a constant. The solid curve in Fig. 3 shows the fit results. The number of signal events is determined to be 15.9 þ5.1 −4.4 , and the significance for the process e þ e − → π 0 π 0 ψ 2 ð3823Þ with systematic uncertainties included is found to be 4.3σ. Results of the simultaneous fits to the seven distributions of RMðπ þ π − Þ for the decays ψ 2 ð3823Þ → γχ c1 (a), γχ c2 (b), π þ π − J=ψ (c), π 0 π 0 J=ψ (d), ηJ=ψ (e), π 0 J=ψ (f), and γχ c0 (g) and a scatter plot of Mðγ H J=ψÞ versus RMðπ þ π − Þ for the decays ψ 2 ð3823Þ → γχ c1;2 (h) for data at 4.3 < ffiffi ffi s p < 4.7 GeV. The red solid lines are the total fit results and the blue dashed lines are the background components. The average cross-section ratio σðe þ e − →π 0 π 0 ψ 2 ð3823ÞÞ σðe þ e − →π þ π − ψ 2 ð3823ÞÞ for the γχ c1 channel for data at 4.3 < ffiffi ffi s p < 4.7 GeV is determined to be 0.64 þ0.22 −0.20 AE 0.05, which is calculated using the definition in Table II, and is consistent with the expectation of isospin symmetry.
The considered sources of systematic uncertainties related to the branching-fraction ratios and average cross-section ratio are summarized in Table III, where those that are common to the numerator and denominator cancel. The uncertainty in the tracking efficiency and photon efficiency is 1% per track or per photon [36]. The uncertainty from the branching fractions is taken from the PDG [10]. The uncertainty due to the kinematic fit is estimated by correcting the helix parameters of charged tracks, and the difference between the results with and without this correction is taken as the uncertainty [37]. To estimate the uncertainty related to the input line shape of the process e þ e − → ππψ 2 ð3823Þ, we change the input line shape to a coherent sum of BW functions of ψð4415Þ and ψð4660Þ with the parameters fixed to PDG values, where magnitude and phase parameters are obtained from a fit to the cross section of e þ e − → π þ π − ψ 2 ð3823Þ. The process e þ e − → ππψ 2 ð3823Þ is generated by the three-body phasespace model, and the uncertainty of the MC decay model is obtained by changing the phase-space model to the model e þ e − → f 0 ð500Þψ 2 ð3823Þ with a D wave in the MC simulation. The angular distribution of the angle between the two low-momentum pions in the lab frame is sensitive to the MC model for the ψ 2 ð3823Þ → γχ c0 decay, which leads to the dominant systematic uncertainty contribution for this mode. The uncertainty from the fit range is obtained by varying the limits of the fit range by AE5 MeV=c 2 , and the uncertainty associated with the background shape is estimated by changing the constant background to a linear background. The influence from the possible presence of a ψ 3 ð3842Þ state is accounted for by including this component in the fit. In each case, the difference to the nominal result is taken as the systematic uncertainty. The uncertainties from the J=ψ, π 0 =η, χ c1;2 and χ c0 mass-window requirements are 1.6%, 1.0%, 1.0%, and 1.7%, respectively [38,39]. The overall systematic uncertainties are obtained by adding all the sources of systematic uncertainties in quadrature, assuming they are uncorrelated. The effect of the systematic uncertainties on the upper limit or significance is accounted for by changing the fit range and the background shape and then choosing the largest value of the upper limit or the lowest value of the significance. Bðψ 2 ð3823Þ→γχ c1 Þ and σðe þ e − →π 0 π 0 ψ 2 ð3823ÞÞ σðe þ e − →π þ π − ψ 2 ð3823ÞÞ , where Bðψ 2 ð3823Þ → Á Á ÁÞ represents the branching fraction of ψ 2 ð3823Þ decays into a certain channel and Bð…Þ represents the branching fraction of subsequent decays.
The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Research and