Measurements of the branching fractions for J/\psi and \psi^{\prime}\rightarrow\Lambda\bar{\Lambda}\pi^{0} and \Lambda\bar{\Lambda}\eta

Measurements of the branching fractions for and and

M. Ablikim, M. N. Achasov, O. Albayrak, D. J. Ambrose, F. F. An, Q. An, J. Z. Bai, Y. Ban, J. Becker, J. V. Bennett, M. Bertani, J. M. Bian, E. Boger, O. Bondarenko, I. Boyko, R. A. Briere, V. Bytev, X. Cai, O.  Cakir, A. Calcaterra, G. F. Cao, S. A. Cetin, J. F. Chang, G. Chelkov, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, S. J. Chen, X. Chen, Y. B. Chen, H. P. Cheng, Y. P. Chu, D. Cronin-Hennessy, H. L. Dai, J. P. Dai, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, W. M. Ding, Y. Ding, L. Y. Dong, M. Y. Dong, S. X. Du, J. Fang, S. S. Fang, L. Fava, C. Q. Feng, R. B. Ferroli, P. Friedel, C. D. Fu, Y. Gao, 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, T. Guo, Y. P. Guo, Y. L. Han, F. A. Harris, K. L. He, M. He, Z. Y. He, T. Held, Y. K. Heng, Z. L. Hou, C. Hu, H. M. Hu, J. F. Hu, T. Hu, G. M. Huang, G. S. Huang, J. S. Huang, L. Huang, X. T. Huang, Y. Huang, Y. P. Huang, T. Hussain, C. S. Ji, Q. Ji, Q. P. Ji, X. B. Ji, X. L. Ji, L. L. Jiang, X. S. Jiang, J. B. Jiao, Z. Jiao, D. P. Jin, S. Jin, F. F. Jing, N. Kalantar-Nayestanaki, M. Kavatsyuk, B. Kopf, M. Kornicer, W. Kuehn, W. Lai, J. S. Lange, M. Leyhe, C. H. Li, Cheng Li, Cui Li, D. M. Li, F. Li, G. Li, H. B. Li, J. C. Li, K. Li, Lei Li, Q. J. Li, S. L. Li, W. D. Li, W. G. Li, X. L. Li, X. N. Li, X. Q. Li, X. R. Li, Z. B. Li, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, X. T. Liao, D. Lin, B. J. Liu, C. L. Liu, C. X. Liu, F. H. Liu, Fang Liu, Feng Liu, H. Liu, H. B. Liu, H. H. Liu, H. M. Liu, H. W. Liu, J. P. Liu, K. Liu, K. Y. Liu, Kai Liu, P. L. Liu, Q. Liu, S. B. Liu, X. Liu, Y. B. Liu, Z. A. Liu, Zhiqiang Liu, Zhiqing Liu, H. Loehner, G. R. Lu, H. J. Lu, J. G. Lu, Q. W. Lu, X. R. Lu, Y. P. Lu, C. L. Luo, M. X. Luo, T. Luo, X. L. Luo, M. Lv, C. L. Ma, F. C. Ma, H. L. Ma, Q. M. Ma, S. Ma, T. Ma, X. Y. Ma, F. E. Maas, M. Maggiora, Q. A. Malik, Y. J. Mao, Z. P. Mao, J. G. Messchendorp, J. Min, T. J. Min, R. E. Mitchell, X. H. Mo, C. Morales Morales, N. Yu. Muchnoi, H. Muramatsu, Y. Nefedov, C. Nicholson, I. B. Nikolaev, Z. Ning, S. L. Olsen, Q. Ouyang, S. Pacetti, J. W. Park, M. Pelizaeus, H. P. Peng, K. Peters, J. L. Ping, R. G. Ping, R. Poling, E. Prencipe, M. Qi, S. Qian, C. F. Qiao, L. Q. Qin, X. S. Qin, Y. Qin, Z. H. Qin, J. F. Qiu, K. H. Rashid, G. Rong, X. D. Ruan, A. Sarantsev, B. D. Schaefer, M. Shao, C. P. Shen, X. Y. Shen, H. Y. Sheng, M. R. Shepherd, X. Y. Song, S. Spataro, B. Spruck, D. H. Sun, 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, D. Toth, M. Ullrich, G. S. Varner, B. Q. Wang, D. Wang, D. Y. Wang, K. Wang, L. L. Wang, L. S. Wang, M. Wang, P. Wang, P. L. Wang, Q. J. Wang, S. G. Wang, X. F.  Wang, X. L. Wang, Y. F. Wang, Z. Wang, Z. G. Wang, Z. Y. Wang, D. H. Wei, J. B. Wei, P. Weidenkaff, Q. G. Wen, S. P. Wen, M. Werner, U. Wiedner, L. H. Wu, N. Wu, S. X. Wu, W. Wu, Z. Wu, L. G. Xia, Y. X Xia, Z. J. Xiao, Y. G. Xie, Q. L. Xiu, G. F. Xu, G. M. Xu, Q. J. Xu, Q. N. Xu, X. P. Xu, Z. R. Xu, F. Xue, Z. Xue, L. Yan, W. B. Yan, Y. H. Yan, H. X. Yang, Y. Yang, Y. X. Yang, H. Ye, M. Ye, M. H. Ye, B. X. Yu, C. X. Yu, H. W. Yu, J. S. Yu, S. P. Yu, C. Z. Yuan, Y. Yuan, 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. Q. Zhang, J. W. Zhang, J. Y. Zhang, J. Z. Zhang, LiLi Zhang, R. Zhang, S. H. Zhang, X. J. Zhang, X. Y. Zhang, Y. Zhang, Y. H. Zhang, Z. P. Zhang, Z. Y. Zhang, Zhenghao Zhang, G. Zhao, H. S. Zhao, J. W. Zhao, K. X. Zhao, Lei Zhao, Ling Zhao, M. G. Zhao, Q. Zhao, Q. Z. Zhao, S. J. Zhao, T. C. Zhao, Y. B. Zhao, Z. G. Zhao, A. Zhemchugov, B. Zheng, J. P. Zheng, Y. H. Zheng, B. Zhong, Z. Zhong, L. Zhou, X. K. Zhou, X. R. Zhou, C. Zhu, K. Zhu, K. J. Zhu, S. H. Zhu, X. L. Zhu, Y. C. Zhu, Y. M. 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
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
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
Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
KVI, 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
Seoul National University, Seoul, 151-747 Korea
Shandong University, Jinan 250100, 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)Ankara University, Dogol Caddesi, 06100 Tandogan, Ankara, Turkey; (B)Dogus University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey
Universitaet Giessen, D-35392 Giessen, Germany
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
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 the Moscow Institute of Physics and Technology, Moscow 141700, Russia
On leave from the Bogolyubov Institute for Theoretical Physics, Kiev 03680, Ukraine
Also at the PNPI, Gatchina 188300, Russia
Present address: Nagoya University, Nagoya 464-8601, Japan
Abstract

We report on a study of the isospin-violating and conserving decays of the and charmonium state to and , respectively. The data are based on 225 million and 106 million events that were collected with the BESIII detector. The most accurate measurement of the branching fraction of the isospin-violating process is obtained, and the isospin-conserving processes and are observed for the first time. The branching fractions are measured to be and . No significant signal events are observed for decay resulting in an upper limit of the branching fraction of at the 90% confidence level. The two-body decay of is searched for, and the upper limit is at the 90% confidence level.

pacs:
13.25.Gv, 12.38.Qk, 14.20.Gk

I Introduction

The charmonium vector meson, , is usually interpreted as an SU(3) singlet bound states with an isospin =0. Systematic measurements of its decay rates into final states that are isospin violating are of particular interest, since these results will provide a sensitive probe to study symmetry-breaking effects in a controlled environment. In this paper, we present a systematic study of isospin-conserving and violating decays of charmonium vector mesons into baryonic decays accompanied by a light pseudoscalar meson, namely and , respectively.

This work is for a large part motivated by a controversial observation that was made in the past while studying the baryonic decay of the . Surprisingly, the average branching fraction of the isospin violating decay of measured by DM2 dm2 and by BESI bes1 was determined to be , while the isospin conserving decay mode was not reported by either experiment. In 2007, the decays of and to the final states with a pair plus a neutral pseudoscalar meson were studied using 58 million and 14 million events collected with the BESII detector xuxp . The new measurement suggested that the two previous studies of may have overlooked the sizable background contribution from . The BESII experiment removed this type of background contribution and only a few statistically insignificant signal events remained, resulting in an upper limit of . Moreover, the isospin conserving decay mode, , was observed for the first time with a significance of 4.8. However, signal events of the channels and were not observed by BESII, and resulted in upper limits of and .

In 2009, BESIII collected 225 million  jpsinumber and 106 million  psipnumber events. These samples provide a unique opportunity to revisit these isospin conserving and violating decays with improved sensitivity to confirm the previous observations in decays with BESII. The ambition is to investigate as well the same final states in decays with the new record in statistics, and look for possible anomalies. A measurement of these branching fractions would be a test of the “” rule rule . The data allow in addition a search for the two-body decays .

Ii Experimental details

BEPCII is a double-ring collider that has reached a peak luminosity of about at the center of mass energy of 3.77 GeV. The cylindrical core of the BESIII detector consists of a helium-based main drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance for charged particles and photons is 93% over 4 stereo angle, and the charged-particle momentum and photon energy resolutions at 1 GeV are 0.5% and 2.5%, respectively. The detector is described in more detail in BESIII .

The optimization of the event selection criteria and the estimates of physics background sources are performed through Monte Carlo (MC) simulations. The BESIII detector is modeled with the geant4 toolkit geant4 ; geant42 . Signal events are generated according to a uniform phase-space distribution. Inclusive and decays are simulated with the kkmc kkmc generator. Known decays are modeled by the evtgen evt1 generator according to the branching fractions provided by the Particle Data Group (PDG) PDG , and the remaining unknown decay modes are generated with the lundcharm model evt2 .

Iii Event selection

The decay channels investigated in this paper are and . The final states include , and one neutral pseudoscalar meson ( or ), where  () decays to (), while the and decay to . Candidate events are required to satisfy the following common selection criteria:

  1. Only events with at least two positively charged and two negatively charged tracks are kept. No requirements are made on the impact parameters of the charged tracks as the tracks are supposed to originate from secondary vertices.

  2. The transverse momenta of the proton and anti-proton are required to be larger than 0.2 GeV/. Tracks with smaller transverse momenta are removed since the MC simulation fails to describe such extremely soft tracks.

  3. Photon candidates are identified from the reconstructed showers in the EMC. Photon energies are required to be larger than 25 MeV in the EMC barrel region () and larger than 50 MeV in the EMC end-cap (). The overlapping showers between the barrel and end-cap () are poorly reconstructed, therefore, excluded from the analysis. In addition, timing requirements are imposed on photon candidates to suppress electronic noise and energy deposits from uncorrelated events.

  4. The and candidates are identified by a reconstruction of decay vertices from pairs of oppositely charged tracks and  xum . At least one and one candidate are required to pass the  () vertex fit successfully by looping over all the combinations of positive and negative charged tracks. In the case of multiple pair candidates, the one with the minimum value of is chosen, where () is the nominal mass of (), obtained from the PDG PDG .

  5. To further reduce the background and to improve the resolution of the reconstructed particle momenta, candidate signal events are subjected to a four constraint energy-momentum conservation (4C) kinematic fit under the hypothesis of . In the case of several combinations due to additional photons, the one with the best value is chosen. In addition, a selection is made on the . Its value is determined by optimizing the signal significance , where is the number of signal (background) events in the signal region. This requirement is effective against background with one or several additional photons like or decays (for instance , ,  etc.). For , backgrounds are suppressed by requiring (see Fig. 1(a)). For , the requirement is set to (see Fig. 1(b)). For , due to the peaking background the is required to be less than 15 (see Fig. 1(c)). For , we select events with (see Fig. 1(d)).

Followed by the common selection criteria, a further background reduction is obtained by applying various mass constraints depending on the channel of interest. To select a clean sample of and signal events, the invariant masses of and are required to be within the mass window of  5 MeV/. Here, the invariant mass is reconstructed with improved momenta from the 4C kinematic fit. The mass resolutions of and are about 1.0 MeV/. For , a mass selection of  10 MeV/ is used to exclude background from which can form a peak near the mass. The background from is removed by selecting events with GeV/ as shown in Fig. 2(a). For , a selection of events with GeV/ rejects all background contributions from decays as shown in Fig. 2(b). For and , events must satisfy the condition  8 MeV/ to remove the background from and . The background from and is rejected by the requirement 3.08 GeV/. The invariant-mass distributions for data and MC events from , and are shown in Fig. 3. The scatter plot of versus after applying all selection criteria is shown in Fig. 4. No visible signal of is observed.

(a)
(b)
(c)
(d)
Figure 1: The distributions of 4C fits. Dots with error bars denote data, and the histograms correspond to the result of MC simulations. (a) . The dashed line is the dominant background distribution from with MC simulated events, the arrow denotes the selection of 40. (b) , the arrow denotes the selection of 70. (c) . The dashed line is the dominant background distribution from with MC simulated events, the arrow denotes the selection of 15. (d) , and the arrow denotes the selection of 40.
(a)
(b)
Figure 2: The invariant-mass, , distributions for candidates. Dots with errors denote data. The dashed-line shows the result of MC simulated events of which is normalized according to the branching fraction from the PDG. (a) Histogram shows the MC simulated events of , where the arrow denotes the selection of 2.8 GeV/. (b) Histogram shows the MC simulated events of , and the arrow shows the selection of 2.6 GeV/.
(a)(b)(c)(d)
Figure 3: The invariant-mass, , distributions for candidates. (a) MC simulated events of , (b) MC simulated events of , (c) MC simulated events of , and (d) data. The arrow denotes the selection of 3.08 GeV/. The peak around the mass is from the decay of .

.

(a)
(b)
(c)
(d)
Figure 4: A scatter plot of versus for and data. (a) , (b) , (c) , and (d) .

Iv Background study

Backgrounds that have the same final states as the signal channels such as are either suppressed to a negligible level or completely removed. Background channels that contain one or more photons than the signal channels like have very few events passing event selection. The line shape of the peaking background sources, , is used in the fitting procedure to estimate their contributions. The contribution of remaining backgrounds from non- decays including is estimated using sideband studies as illustrated in Fig. 4. The square with a width of  MeV/ around the nominal mass of the and is taken as the signal region. The eight squares surrounding the signal region are taken as sideband regions. The area of all the squares is equal. The sum of events in the sideband squares, , times a normalization factor is taken as the background contribution in the signal region. The normalization factor is defined as

The normalization factor is obtained from phase-space MC simulations of or with as the number of MC events in the signal region and as the sum of MC events in the sideband regions.

With 44 pb of data collected at a center-of-mass energy of  GeV, the contribution from the continuum background is determined. From this data sample, no events survive in the or mass region in the two-photon invariant-mass, , distribution after applying all selection criteria. Therefore, we neglect this background.

V Signal yields and Dalitz analyses

The invariant-mass spectra of , and of the remaining events after the previously described signal selection procedure are shown in Fig. 5. A clear and signal can be observed in the data. The data set shows a significant signal, but lacks a pronounced peak near the mass.

The number of signal events are extracted by fitting the distributions with the parameterized signal shape from MC simulations. For , the dominant peaking backgrounds from are estimated by MC simulation. The fit also accounts for background estimates from a normalized sideband analysis. Other background sources are described by a Chebychev polynomial for all channels except where there are too few events surviving. The fit yields events, events in data and events in data. For , the upper limit on is 9 at the 90% confidence level (C.L.) and is determined with a Bayesian method bayes . For , the change in log likelihood value in the fit with and without the signal function is used to determine the signal significance, which is estimated to be 10.5.

(a)
(b)
(c)
(d)
Figure 5: The two-photon invariant-mass, , distributions in the and mass regions for the channels (a) , (b) , (c) , and (d) . Dots with error bars are data. The solid lines are the fit to data, and the dot-dashed lines are the signal shape determined from MC simulations. The hatched histograms are the background contributions obtained from a normalized sideband analysis. The dashed lines in correspond to the peaking background from . The long dashed lines denote other background contributions which are described by Chebychev polynomials.

To study the existence of intermediate resonance states in the decay of , and and to validate the phase-space assumption that was used in the MC simulations, we have performed a Dalitz plot analysis of the invariant masses involved in the three-body decay. These results are shown in Fig. 6. For these plots, and candidates are selected within mass windows of 0.12 GeV/0.14 GeV/ and 0.532 GeV/ GeV/, respectively. In all the Dalitz plots, no clear structures are observed. A test is performed to confirm the consistency between data and the phase-space distributed MC events. The is determined as follows:

where is the scaling factor between data and MC , refers to the number of data/MC events in a particular bin in the Dalitz plot, and the sum runs over all bins. We divide the Dalitz plots into 8 bins. Boxes with very few events are combined into an adjacent bin. The are equal to 1.1 and 2.1 for and , respectively, which validates the usage of a phase-space assumption in the MC simulations.

(a)
(b)
(c)
(d)
(e)
(f)
Figure 6: Dalitz plots of the invariant masses versus for the channels (a) (data), (b) (MC), (c) (data), (d) (MC), (e) (data), and (f) (MC). See text for more details.

We have studied the branching fraction of the decay by combining and analyzing the invariant-mass spectra of and pairs as depicted in Fig. 7. For this analysis, events are selected by applying a two-photon invariant-mass selection of 0.12 GeV/0.14 GeV/. For the fit, the signal function is taken from a MC simulation of , and the background function is taken from a MC simulation of . A Bayesian analysis gives an upper limit on the number of events of 37 at the 90% C.L..

Figure 7: A search for events by fitting the combined and invariant-mass distributions. Dots with error bars are data. The solid line is the fit to data. The hatched histogram is the signal function obtained from a MC simulation, and the dashed line is the background function obtained from a MC simulation of .

Vi Systematic errors

To estimate the systematic errors in the measured branching fractions of the channels of interest, we include uncertainties in the efficiency determination of charged and photon tracks, in the vertex and 4C kinematic fits, in the selection criteria for the signal and sideband region, and in the fit range. The uncertainties in the total number of and events and in the branching fractions of intermediate state are considered as well. Below we discuss briefly the analysis that is used to determine the various sources of systematic uncertainties.

  • Tracking efficiency. We estimate this type of systematic uncertainty by taking the difference between the tracking efficiency obtained via a control channel from data with the efficiency obtained from MC simulations. The control sample is employed to study the systematic error of the tracking efficiency from the decay. For example, to determine the tracking efficiency of the tracks, we select events with at least three charged tracks, the proton, kaon and anti-proton. The total number of tracks, , can be determined by fitting the recoiling mass distribution of the system, . In addition, one obtains the number of detected tracks, , by fitting , after requiring all four charged tracks be reconstructed. The tracking efficiency is simply . Similarly, we obtained the tracking efficiencies for , and . With inclusive MC events, we obtained the corresponding tracking efficiency for the MC simulation. The tracking efficiency difference between data and MC simulation is about 1.0% for each pion track. This difference is also about 1.0% for a proton (anti-proton) if its transverse momentum, , is larger than 0.3 GeV/. The difference increases to about 10% for the range  GeV/ GeV/. Conservatively, we take a systematic error due to tracking of 1% for each pion. For the proton (anti-proton), we use weighted systematic errors, namely 2% in , 3.5% in , 1.5% in , and 2% in .

  • Vertex fit. The uncertainties due to the and vertex fits are determined to be 1.0% for each by using the same control samples and a similar procedure as described for the tracking efficiency.

  • Photon efficiency. The photon detection efficiency was studied by comparing the photon efficiency between MC simulation and the control sample . The relative efficiency difference is about 1% for each photon bianjm , which value was used as a systematic uncertainty.

  • Efficiency of the kinematic fit. The control sample of is used to study the efficiency of the 4C kinematic fit since its final state is the same as our signal. The event selection criteria for charged tracks and photons and the reconstruction of are the same as in our analysis. If there are more than two photon candidates in an event, we loop over all possible combinations and keep the one with the smallest value for . Furthermore, the remaining backgrounds are suppressed by limiting the momentum windows of and , i.e.,  MeV/ and MeV/. Figure 8 shows the scatter plot of versus for the inclusive MC events and data after applying all event selection criteria. The square in the center with a width of 10 MeV/ is taken as the signal region. Almost no background is found according to the topology analysis from inclusive MC events. The candidate signal events for both data and MC events are subjected to the same 4C kinematic fit as that in our analysis. The efficiency of the 4C kinematic fit is defined as the ratio of the number of signal events with and without a 4C kinematic fit. A correction factor, , can be obtained by comparing the efficiency of the 4C kinematic fit between data and MC simulation. i.e., . The efficiency corrections corresponding to are %, % and %, respectively. The errors in the efficiency corrections are taken as a systematic uncertainty.

    Figure 8: The scatter plot of versus for for (left) data and (right) inclusive MC events.
  • Fit range. The , , and yields are obtained by fitting the data around the corresponding mass value. By changing the mass ranges for the fits, the number of signal events changes slightly. These differences are taken as the errors due to the uncertainty of the fit range.

  • Signal and sideband regions. By changing the signal and sideband region from 5 MeV/ MeV/ to 6 MeV/ MeV/, the number of fitted and events changes slightly for data and MC. The differences in yield between the two region sizes are taken as systematic errors.

  • Background shape. A part of the background depicted in Fig. 5 is estimated by a fit with a third-order Chebychev polynomial. The differences in signal yield with a background function that is changed to a second-order polynomial, are taken as a systematic error due to the uncertainty in the description of the background shape.

  • Total number of and events. The total numbers of and events are obtained from inclusive hadronic and decays with uncertainties of 1.24% jpsinumber and 0.81% psipnumber , respectively.

All the sources of systematic errors are summarized in Table 1. The total systematic error is calculated as the quadratic sum of all individual terms.

Source +c.c.
Photon efficiency 2.0 2.0 2.0 2.0 2.0
Tracking efficiency 6.0 9.0 4.0 5.0 6.0
Vertex fit 2.0 2.0 2.0 2.0 2.0
Correction factor of 4C fit 0.6 0.3 0.6 0.8 0.6
Background function 0.6 0.2 1.5 negligible 2.5
Signal and sidebands 3.6 1.7 negligible 9.1 2.0
Fit range 0.6 0.4 negligible negligible 1.5
0.8 0.8 0.8 0.8 0.8
negligible 0.6 negligible negligible 0.6
- - 1.7 - -
1.24 1.24 1.24 - -
- - - 0.81 0.81
Total 7.8 9.7 5.6 10.9 7.6
Table 1: Systematic errors in the measurements of the branching fractions (%).

Vii Results

The branching fraction of is determined by the relation

and if the signal is not significant, the corresponding upper limit of the branching fraction is obtained by

where, is the number of observed signal events or its upper limit , is the final state, is the intermediate state, is the detection efficiency, and is the systematic error. The branching fraction of is taken from the PDG PDG . Table 2 lists the various numbers that were used in the calculation of the branching fractions.

Channel +c.c.
Number of events / 323 454 60.4
Efficiency  (%) 9.65 8.10 6.22 8.95 14.64
97.5 98.7 97.5 90.3 97.5
225.3 225.3 225.3 - -
- - - 106.41 106.41
63.9 63.9 63.9 63.9 63.9
 (%) - - 87.5 - -
98.8 39.4 98.8 98.8 39.4
Table 2: Numbers used in the calculations of the branching fractions.

With these, we obtain