Search for the isospin violating decay Y(4260)\rightarrow J/\psi\eta\pi^{0}

Search for the isospin violating decay

M. Ablikim, M. N. Achasov, X. C. Ai, O. Albayrak, M. Albrecht, D. J. Ambrose, A. Amoroso, F. F. An, Q. An, J. Z. Bai, R. Baldini Ferroli, Y. Ban, D. W. Bennett, J. V. Bennett, M. Bertani, D. Bettoni, J. M. Bian, F. Bianchi, E. Boger, I. Boyko, R. A. Briere, H. Cai, X. Cai, O.  Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. F. Chang, G. Chelkov, G. Chen, H. S. Chen, H. Y. Chen, J. C. Chen, M. L. Chen, S. J. Chen, X. Chen, X. R. Chen, Y. B. Chen, H. P. Cheng, X. K. Chu, G. Cibinetto, 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, S. X. Du, P. F. Duan, E. E. Eren, J. Z. Fan, J. Fang, S. S. Fang, X. Fang, Y. Fang, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, E. Fioravanti, M.  Fritsch, C. D. Fu, Q. Gao, X. Y. Gao, Y. Gao, Z. Gao, I. Garzia, C. Geng, K. Goetzen, W. X. Gong, W. Gradl, M. Greco, M. H. Gu, Y. T. Gu, Y. H. Guan, A. Q. Guo, L. B. Guo, Y. Guo, Y. P. Guo, Z. Haddadi, A. Hafner, S. Han, Y. L. Han, X. Q. Hao, F. A. Harris, K. L. He, Z. Y. He, T. Held, Y. K. Heng, Z. L. Hou, C. Hu, H. M. Hu, J. F. Hu, T. Hu, Y. Hu, G. M. Huang, G. S. Huang, H. P. Huang, J. S. Huang, X. T. Huang, Y. Huang, T. Hussain, Q. Ji, Q. P. Ji, X. B. Ji, X. L. Ji, L. L. Jiang, L. W. Jiang, X. S. Jiang, X. Y. Jiang, J. B. Jiao, Z. Jiao, D. P. Jin, S. Jin, T. Johansson, A. Julin, N. Kalantar-Nayestanaki, X. L. Kang, X. S. Kang, M. Kavatsyuk, B. C. Ke, P.  Kiese, R. Kliemt, B. Kloss, O. B. Kolcu, B. Kopf, M. Kornicer, W. Kühn, A. Kupsc, J. S. Lange, M. Lara, P.  Larin, C. Leng, C. Li, C. H. Li, Cheng Li, D. M. Li, F. Li, G. Li, H. B. Li, J. C. Li, Jin Li, K. Li, K. Li, Lei Li, P. R. Li, T.  Li, W. D. Li, W. G. Li, X. L. Li, X. M. Li, X. N. Li, X. Q. Li, Z. B. Li, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, D. X. Lin, B. J. Liu, C. X. Liu, F. H. Liu, Fang Liu, Feng Liu, H. B. Liu, H. H. Liu, H. H. Liu, H. M. Liu, J. Liu, J. B. Liu, J. P. Liu, J. Y. Liu, K. Liu, K. Y. Liu, L. D. Liu, P. L. Liu, Q. Liu, S. B. Liu, X. Liu, X. X. Liu, Y. B. Liu, Z. A. Liu, Zhiqiang Liu, Zhiqing Liu, H. Loehner, X. C. Lou, H. J. Lu, J. G. Lu, R. Q. Lu, Y. Lu, Y. P. Lu, C. L. Luo, M. X. Luo, T. Luo, X. L. Luo, M. Lv, X. R. Lyu, F. C. Ma, H. L. Ma, L. L.  Ma, Q. M. Ma, T. Ma, X. N. Ma, X. Y. Ma, F. E. Maas, M. Maggiora, Y. J. Mao, Z. P. Mao, S. Marcello, J. G. Messchendorp, J. Min, T. J. Min, R. E. Mitchell, X. H. Mo, Y. J. Mo, C. Morales Morales, K. Moriya, N. Yu. Muchnoi, H. Muramatsu, Y. Nefedov, F. Nerling, I. B. Nikolaev, Z. Ning, S. Nisar, S. L. Niu, X. Y. Niu, S. L. Olsen, Q. Ouyang, S. Pacetti, P. Patteri, M. Pelizaeus, H. P. Peng, K. Peters, J. Pettersson, J. L. Ping, R. G. Ping, R. Poling, V. Prasad, Y. N. Pu, M. Qi, S. Qian, C. F. Qiao, L. Q. Qin, N. Qin, X. S. Qin, Y. Qin, Z. H. Qin, J. F. Qiu, K. H. Rashid, C. F. Redmer, H. L. Ren, M. Ripka, G. Rong, Ch. Rosner, X. D. Ruan, V. Santoro, A. Sarantsev, M. Savrié, K. Schoenning, S. Schumann, W. Shan, M. Shao, C. P. Shen, P. X. Shen, X. Y. Shen, H. Y. Sheng, W. M. Song, X. Y. Song, S. Sosio, S. Spataro, G. X. Sun, J. F. Sun, S. S. Sun, Y. J. Sun, Y. Z. Sun, Z. J. Sun, Z. T. Sun, C. J. Tang, X. Tang, I. Tapan, E. H. Thorndike, M. Tiemens, M. Ullrich, I. Uman, G. S. Varner, B. Wang, B. L. Wang, D. Wang, D. Y. Wang, K. Wang, L. L. Wang, L. S. Wang, M. Wang, P. Wang, P. L. Wang, S. G. Wang, W. Wang, X. F.  Wang, Y. D. Wang, Y. F. Wang, Y. Q. Wang, Z. Wang, Z. G. Wang, Z. H. Wang, Z. Y. Wang, T. Weber, D. H. Wei, J. B. Wei, P. Weidenkaff, S. P. Wen, U. Wiedner, M. Wolke, L. H. Wu, Z. Wu, L. G. Xia, Y. Xia, D. Xiao, Z. J. Xiao, Y. G. Xie, Q. L. Xiu, G. F. Xu, L. Xu, Q. J. Xu, Q. N. Xu, X. P. Xu, L. Yan, W. B. Yan, W. C. Yan, Y. H. Yan, H. J. Yang, H. X. Yang, L. Yang, Y. Yang, Y. X. Yang, H. Ye, M. Ye, M. H. Ye, J. H. Yin, B. X. Yu, C. X. Yu, H. W. Yu, J. S. Yu, C. Z. Yuan, W. L. Yuan, Y. Yuan, A. Yuncu, A. A. Zafar, A. Zallo, Y. Zeng, B. X. Zhang, B. Y. Zhang, C. Zhang, C. C. Zhang, D. H. Zhang, H. H. Zhang, H. Y. Zhang, J. J. Zhang, J. L. Zhang, J. Q. Zhang, J. W. Zhang, J. Y. Zhang, J. Z. Zhang, K. Zhang, L. Zhang, S. H. Zhang, X. Y. Zhang, Y. Zhang, Y.  N. Zhang, Y. H. Zhang, Y. T. 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, Q. W. 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, Li Zhou, X. Zhou, X. K. Zhou, X. R. Zhou, X. Y. Zhou, K. Zhu, K. J. Zhu, S. Zhu, X. L. Zhu, Y. C. Zhu, Y. S. Zhu, Z. A. Zhu, J. Zhuang, L. Zotti, B. S. Zou, J. H. Zou
(BESIII Collaboration)
Institute of High Energy Physics, Beijing 100049, People’s Republic of China
Beihang University, Beijing 100191, People’s Republic of China
Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China
Bochum Ruhr-University, D-44780 Bochum, Germany
Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
Central China Normal University, Wuhan 430079, People’s Republic of China
China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China
COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
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 University, Changsha 410082, People’s Republic of China
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
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 University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany
KVI-CART, University of Groningen, NL-9747 AA Groningen, 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
Seoul National University, Seoul, 151-747 Korea
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
Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
Tsinghua University, Beijing 100084, People’s Republic of China
(A)Istanbul Aydin University, 34295 Sefakoy, Istanbul, Turkey; (B)Dogus University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
University of Hawaii, Honolulu, Hawaii 96822, USA
University of Minnesota, Minneapolis, Minnesota 55455, USA
University of Rochester, Rochester, New York 14627, USA
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
Zhejiang University, Hangzhou 310027, People’s Republic of China
Zhengzhou University, Zhengzhou 450001, People’s Republic of China
Also at State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, People’s Republic of China
Also at Ankara University,06100 Tandogan, Ankara, Turkey
Also at Bogazici University, 34342 Istanbul, Turkey
Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia
Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia
Also at the Novosibirsk State University, Novosibirsk, 630090, Russia
Also at the NRC ”Kurchatov Institute, PNPI, 188300, Gatchina, Russia
Also at University of Texas at Dallas, Richardson, Texas 75083, USA
Present address: Istanbul Arel University, 34295 Istanbul, Turkey
July 15, 2019
Abstract

Using data samples collected at center-of-mass energies of = 4.009, 4.226, 4.257, 4.358, 4.416, and 4.599 GeV with the BESIII detector operating at the BEPCII storage ring, we search for the isospin violating decay . No signal is observed, and upper limits on the cross section at the 90% confidence level are determined to be 3.6, 1.7, 2.4, 1.4, 0.9, and 1.9 pb, respectively.

pacs:
14.40.Rt, 13.66.Bc, 14.40.Pq, 13.20.Gd

I Introduction

The charmoniumlike state was first observed in its decay to  bib1 () and has a small coupling to open charm decay modes bib2 (). is a vector () state that is only barely observable as an s-channel resonance in collisions and that appears at an energy where no conventional charmonium state is expected. Since its discovery, many theoretical studies have been carried out considering the as a tetraquark state bib3 (), or hadronic molecule bib4 (), hybrid charmonium bib5 (), baryonium state bib6 (), etc.

Recently, in the study of , a charged charmoniumlike structure, the , was observed in the invariant mass spectrum by the BESIII bib7 () and Belle experiments bib8 () and confirmed shortly thereafter with CLEO-c data bib9 (). In the molecule model bib10 (), the is proposed to have a large component, while has a component.

BESIII recently reported the observation of  bib11 (). The cross section measurements strongly support the existence of the radiative transition . One significant feature of the that differs from conventional charmonium is that the decay branching fraction of to is comparable to  bib12 (); bib13 (), so the isospin violating process occurs on a large scale.

Isospin violating decays can be used to probe the nature of heavy quarkonium. The hadro-charmonium model bib14 () and tetraquark models bib15 (); bib16 () predict that the reaction bottomonium should be observable. The tetraquark model bib17 () also predicts that can be produced in with decaying into and possibly in the presence of sizable isospin violation. The molecular model bib18 () predicts a peak in the cross section of at the threshold and a narrow peak in the invariant mass spectrum at the threshold.

In this paper, we present results on a search for the isospin violating decay , with , , and (the other decay modes of are not used due to much lower detection efficiency and branching fraction), based on annihilation data collected with the BESIII detector operating at the BEPCII storage ring bib19 () at center-of-mass energies of = 4.009, 4.226, 4.257, 4.358, 4.416, and 4.599 GeV.

Ii BESIII detector and Monte Carlo Simulation

The BESIII detector, described in detail in Ref. bib19 (), has a geometrical acceptance of 93% of 4. A small-cell helium-based main drift chamber (MDC) provides a charged particle momentum resolution of 0.5% at 1 GeV/ in a 1 T magnetic field and supplies energy-loss () measurements with a resolution of 6% for minimum-ionizing pions. The electromagnetic calorimeter (EMC) measures photon energies with a resolution of 2.5% (5%) at 1.0 GeV in the barrel (end caps). Particle identification is provided by a time-of-flight system with a time resolution of 80 ps (110 ps) for the barrel (end caps). The muon system (MUC), located in the iron flux return yoke of the magnet, provides 2 cm position resolution and detects muon tracks with momentum greater than 0.5 GeV/.

The GEANT4-based bib20 () Monte Carlo (MC) simulation software BOOST bib21 () includes the geometric description of the BESIII detector and a simulation of the detector response. It is used to optimize event selection criteria, estimate backgrounds, and evaluate the detection efficiency. For each energy point, we generate large signal MC samples of , , , and uniformly in phase space. Effects of initial state radiation (ISR) are simulated with KKMC bib22 (), where the Born cross section of is assumed to follow a BreitWigner line shape with resonance parameters taken from the Particle Data Group (PDG) bib23 (). Final state radiation effects associated with charged particles are handled with PHOTOS bib24 ().

To study possible backgrounds, a MC sample of inclusive decays, equivalent to an integrated luminosity of 825.6 pb, is also generated at = 4.260 GeV. In these simulations, the is allowed to decay generically, with the main known decay channels being generated using EVTGEN bib25 () with branching fractions set to world average values bib23 (). The remaining events associated with charmonium decays are generated with LUNDCHARM bib26 (), while continuum hadronic events are generated with PYTHIA bib27 (). QED events (, , and ) are generated with KKMC bib22 (). Backgrounds at other energy points are expected to be similar.

Iii Event selection

Events with two charged tracks with a net charge of zero are selected. For each good charged track, the polar angle in the MDC must satisfy , and the point of closest approach to the interaction point must be within 10 cm in the beam direction and within 1 cm in the plane perpendicular to the beam direction. The momenta of leptons from the decays in the laboratory frame are required to be larger than 1.0 GeV/. is used to separate electrons from muons, where is the energy deposited in the EMC and is the momentum measured by the MDC. For electron candidates, should be larger than 0.7, while for muons, it should be less than 0.3. To suppress background from events with pion tracks in the final state, at least one of the two muons is required to have at least five layers with valid hits in the MUC.

Showers identified as photon candidates must satisfy fiducial and shower quality as well as timing requirements. The minimum EMC energy is 25 MeV for barrel showers ( 0.80) and 50 MeV for end cap showers (0.86 0.92). To eliminate showers produced by charged particles, a photon must be separated by at least 5 deg from any charged track. The time information from the EMC is also used to suppress electronic noise and energy deposits unrelated to the event. At least four good photon candidates in each event are required.

To improve the momentum resolution and reduce the background, the event is subjected to a four-constraint (4C) kinematic fit under the hypothesis ( = ), and the is required to be less than 40. For events with more than four photons, the four photons with the smallest from the 4C fit are assigned as the photons from and .

After selecting the candidate, scatter plots of with all six combinations of photon pairs for events in the signal region (3.067 3.127 GeV/) for data at = 4.226 and 4.257 GeV are shown in the left two panels of Fig. 1. Distributions of for events in the signal region (both photon pairs satisfy 10 MeV/) for data at = 4.226 and 4.257 GeV are shown in the right two panels of Fig. 1. Clear peaks are observed, corresponding to events. To remove this background, events with any combination of photon pairs in the region of the scatter plot are rejected.

Figure 1: Scatter plot of with all six combinations for events in the signal region (left) and distribution of for events in the signal region (right) for data at = 4.226 GeV (top) and 4.257 GeV (bottom).

After rejecting the background, we choose the combination of photon pairs closest to the signal region by minimizing , where and are the and resolutions obtained from the signal MC, respectively. The scatter plots of with the combination closest to the signal region for events in the signal region for data at = 4.226 and 4.257 GeV are shown in the top two panels of Fig. 2. No cluster of events is observed in the signal region, with a vertical band for clearly visible, but no prominent band for is observed. The projections of the scatter plots on with in the signal region ( MeV/) and projections on with in the signal region ( MeV/) for data are shown in the middle and bottom panels of Fig. 2, respectively.

Figure 2: Scatter plot of for the combination closest to the signal region for events in the signal region (top), projection of the scatter plot on with in signal region (middle), and projection of the scatter plot on with in signal region (bottom) for data at = 4.226 GeV (left) and 4.257 GeV (right).

The background for is studied using the inclusive MC sample at = 4.260 GeV. After imposing all event selection requirements, there are two background events from and nine background events arising from , and . No other background survives. The background can be evaluated with sideband events. Distributions of for events in the signal region for data at = 4.226 and 4.257 GeV are shown in Fig. 3. Distributions of for events corresponding to the normalized two-dimensional sidebands are shown as shaded histograms. The sideband regions are defined as 0.3978 0.4578 GeV/ and 0.6378 0.6978 GeV/. The sideband regions are defined as 0.0849 0.1049 GeV/ and 0.1649 0.1849 GeV/. The counted number of observed events in the signal region and number of background events estimated from sidebands are listed in Table 1.

Figure 3: Distributions of for events in signal region and sideband regions for data at = 4.226 GeV (left) and 4.257 GeV (right). The error bars are the distributions for events in the signal region, and the shaded histograms are those in the sideband regions.

Iv Cross section upper limits

Since no signal above the background is observed, upper limits on the Born cross section of at the 90% C.L. are determined using the formula

(1)

where is the upper limit on the number of signal events; is the integrated luminosity; is the radiative correction factor, which is taken from a QED calculation assuming the cross section is described by a BreitWigner line shape with parameters taken from the PDG bib23 (); is the vacuum polarization factor including leptonic and hadronic parts and taken from a QED calculation with an accuracy of 0.5% bib28 (); and are the efficiencies for and modes, respectively; and are the branching fractions of and  bib23 (), respectively; and and are the branching fractions of and  bib23 (), respectively.

The efficiency corrected upper limit on the number of signal events is estimated with and using the profile likelihood method, which is implemented by TRolke in the ROOT framework bib29 (). The calculation for obtaining includes the background fluctuation and the systematic uncertainty of the cross section measurement. The background fluctuation is assumed to follow a Poisson distribution. The systematic uncertainty of the cross section is taken as a Gaussian uncertainty.

The systematic uncertainty of the cross section measurement in Eq. (1) includes the luminosity measurement, detection efficiency, and intermediate decay branching fractions. The systematic uncertainties of the luminosity, track reconstruction, and photon detection are 1.0% bib11 (), 1.0% per track bib30 (), and 1.0% per photon bib31 (), respectively. The systematic uncertainties from the branching fraction of and decays are taken from the PDG bib23 (). These sources of systematic uncertainty, which are summarized in the top part of Table 2, are common for and modes. The following sources of systematic uncertainty, which are uncorrelated for the and modes, are summarized in the bottom part of Table 2. The systematic uncertainty from the branching fraction of decay is taken from the PDG bib23 (). The systematic uncertainty from the requirement on the number of MUC hits is 3.6% and estimated by comparing the efficiency of the MUC requirement between data and MC in the control sample at = 4.257 GeV. The systematic uncertainty from the requirement of the signal region is estimated by smearing the invariant mass of of the signal MC with a Gaussian function to compensate for the resolution difference between the data and MC when calculating the efficiency. The parameters for smearing are determined by fitting the distribution of data with the MC shape convoluted with a Gaussian function for the control sample . The difference in the detection efficiency between signal MC samples with and without the smearing is taken as the systematic uncertainty. The systematic uncertainty from the MC model is estimated by generating a MC sample with the angular distribution of leptons determined from the data. The systematic uncertainty due to kinematic fitting is estimated by correcting the helix parameters of charged tracks according the method described in Ref. bib32 (), where the correction factors are obtained from the control sample and the difference in the detection efficiency between with and without making the correction to the MC is taken as the systematic uncertainty. The uncorrelated systematic uncertainties for the electron and muon channels are combined by taking the weighted average with weights and , respectively. The total systematic uncertainty is obtained by summing all the sources of the systematic uncertainty in quadrature.

(GeV) (pb) (1+) (1+) ( + ) (%) (pb)
4.009 482.0 0.838 1.044 5 1 598.1 3.6
4.226 1047.3 0.844 1.056 12 11 592.9 1.7
4.257 825.6 0.847 1.054 12 8 654.1 2.4
4.358 539.8 0.942 1.051 5 4 283.2 1.4
4.416 1028.9 0.951 1.053 5 6 342.7 0.9
4.599 566.9 0.965 1.055 6 3 418.4 1.9
Table 1: Results on . Listed in the table are the integrated luminosity , radiative correction factor (1+) taken from QED calculation assuming the cross section follows a BreitWigner line shape, vacuum polarization factor (1+), average efficiency ( + ), number of observed events , number of estimated background events , the efficiency corrected upper limits on the number of signal events , and upper limits on the Born cross section (at the 90 % C.L.) at each energy point.
Sources/ (GeV) 4.009 4.226 4.257 4.358 4.416 4.599
Luminosity 1.0 1.0 1.0 1.0 1.0 1.0
MDC tracking 2.0 2.0 2.0 2.0 2.0 2.0
Photon reconstruction 4.0 4.0 4.0 4.0 4.0 4.0
), B() 0.5 0.5 0.5 0.5 0.5 0.5
) (0.5, 0.5) (0.5, 0.5) (0.5, 0.5) (0.5, 0.5) (0.5, 0.5) (0.5, 0.5)
MUC hits (0, 3.6) (0, 3.6) (0, 3.6) (0, 3.6) (0, 3.6) (0, 3.6)
mass resolution (0.2, 1.3) (0.8, 1.2) (0.5, 1.3) (0.2, 0.7) (0.7, 1.6) (0.1, 0.6)
Decay model (1.5, 1.9) (0.9, 1.1) (0.4, 0.6) (0.2, 0.7) (0.7, 0.2) (0.2, 0.2)
Kinematic fitting (1.2, 0.9) (1.1, 1.2) (0.9, 0.9) (0.7, 1.2) (1.1, 1.0) (1.0, 1.4)
Total 5.3 5.3 5.2 5.2 5.3 5.2
Table 2: Systematic uncertainties in the cross section measurement at each energy point (in %). The items in parentheses in the bottom part of the table are the uncorrelated systematic uncertainties for the (first) and (second) modes.

The systematic uncertainty on the size of the background is estimated by evaluating with different signal and sideband regions for and . The most conservative is taken as the final result, as listed in Table 1. The upper limits on the Born cross section of () assuming it follows a BreitWigner line shape are listed in Table 1.

For comparison, the radiative correction factor and detection efficiency have been recalculated assuming the cross section follows alternative line shapes. If the cross section follows the line shape of the , the upper limit on the Born cross section is 4.1 pb at = 4.009 GeV. For a line shape, it is 1.6 pb at = 4.358 GeV. For a line shape, it is 1.5 pb at = 4.358 GeV and 1.0 pb at = 4.416 GeV. For a line shape, it is 2.0 pb at = 4.599 GeV.

It is also possible to set upper limits on . The number of observed events and number of estimated background events in the signal region () are 7 and 4 , respectively, at = 4.226 GeV, and 8 and , respectively, at = 4.257 GeV. The upper limit on ) is determined to be 1.3 pb at = 4.226 GeV and 2.0 pb at = 4.257 GeV, where only the statistical uncertainty is given. Compared to the measured cross section of  bib33 (), the upper limit on the ratio of the branching fraction at the 90% confidence level is 0.15 at = 4.226 GeV and 0.65 at = 4.257 GeV.

V Summary

In summary, using data collected with the BESIII detector, a search for the isospin violating decay is performed. No statistically significant signal is observed. The Born cross sections of at the 90% confidence level limits at = 4.009, 4.226, 4.257, 4.358, 4.416, and 4.599 GeV are determined to be 3.6, 1.7, 2.4, 1.4, 0.9, and 1.9 pb, respectively. The upper limits are well above the prediction for the molecule model bib18 ().

Acknowledgement

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 Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts No. 11125525, No. 11235011, No. 11322544, No. 11335008, and No. 11425524; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts No. 11179007, No. U1232201, and No. U1332201; CAS under Contracts No. KJCX2-YW-N29 and No. KJCX2-YW-N45; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; Russian Foundation for Basic Research under Contract No. 14-07-91152; US Department of Energy under Contracts No. DE-FG02-04ER41291, No. DE-FG02-05ER41374, No. DE-FG02-94ER40823, and No. DESC0010118; US National Science Foundation; University of Groningen and the Helmholtzzentrum fuer Schwerionenforschung GmbH, Darmstadt; and the WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.

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