DSpace at VNU: First observations ofψ(2S)andχcJ(1P)decays to four-body final statesh + h −K0 SK0 S

Physics Letters B 630 (2005) 21–30 www.elsevier.com/locate/physletb First observations of ψ(2S) and χcJ (1P) decays to four-body final states h+ h−KS0KS0 ✩ BES Collaboration M Ablikim a , J.Z Bai a , Y Ban j , J.G Bian a , X Cai a , J.F Chang a , H.F Chen p , H.S Chen a , H.X Chen a , J.C Chen a , Jin Chen a , Jun Chen f , M.L Chen a , Y.B Chen a , S.P Chi b , Y.P Chu a , X.Z Cui a , H.L Dai a , Y.S Dai r , Z.Y Deng a , L.Y Dong a , S.X Du a , Z.Z Du a , J Fang a , S.S Fang b , C.D Fu a , H.Y Fu a , C.S Gao a , Y.N Gao n , M.Y Gong a , W.X Gong a , S.D Gu a , Y.N Guo a , Y.Q Guo a , Z.J Guo o , F.A Harris o , K.L He a , M He k , X He a , Y.K Heng a , H.M Hu a , T Hu a , G.S Huang a,2 , L Huang f , X.P Huang a , X.B Ji a , Q.Y Jia j , C.H Jiang a , X.S Jiang a , D.P Jin a , S Jin a , Y Jin a , Y.F Lai a , F Li a , G Li a , H.H Li a , J Li a , J.C Li a , Q.J Li a , R.B Li a , R.Y Li a , S.M Li a , W.G Li a , X.L Li g , X.Q Li i , X.S Li n , Y.F Liang m , H.B Liao e , C.X Liu a , F Liu e , Fang Liu p , H.M Liu a , J.B Liu a , J.P Liu q , R.G Liu a , Z.A Liu a , Z.X Liu a , F Lu a , G.R Lu d , J.G Lu a , C.L Luo h , X.L Luo a , F.C Ma g , J.M Ma a , L.L Ma k , Q.M Ma a , X.Y Ma a , Z.P Mao a , X.H Mo a , J Nie a , Z.D Nie a , S.L Olsen o , H.P Peng p , N.D Qi a , C.D Qian l , H Qin h , J.F Qiu a , Z.Y Ren a , G Rong a , L.Y Shan a , L Shang a , D.L Shen a , X.Y Shen a , H.Y Sheng a , F Shi a , X Shi j , H.S Sun a , S.S Sun p , Y.Z Sun a , Z.J Sun a , X Tang a , N Tao p , Y.R Tian n , G.L Tong a , G.S Varner o , D.Y Wang a , J.Z Wang a , K Wang p , L Wang a , L.S Wang a , M Wang a , P Wang a , P.L Wang a , S.Z Wang a , W.F Wang a , Y.F Wang a , Zhe Wang a , Z Wang a , Zheng Wang a , Z.Y Wang a , C.L Wei a , D.H Wei c , N Wu a , Y.M Wu a , X.M Xia a , X.X Xie a , B Xin g , G.F Xu a , H Xu a , Y Xu a , S.T Xue a , M.L Yan p , F Yang i , H.X Yang a , J Yang p , S.D Yang a , Y.X Yang c , M Ye a , M.H Ye b , Y.X Ye p , L.H Yi f , Z.Y Yi a , C.S Yu a , G.W Yu a , C.Z Yuan a , J.M Yuan a , Y Yuan a , Q Yue a , S.L Zang a , Yu Zeng a , Y Zeng f , B.X Zhang a , B.Y Zhang a , C.C Zhang a , D.H Zhang a , H.Y Zhang a , J Zhang a , J.Y Zhang a , J.W Zhang a , L.S Zhang a , Q.J Zhang a , S.Q Zhang a , X.M Zhang a , X.Y Zhang k , Y.J Zhang j , Y.Y Zhang a , Yiyun Zhang m , Z.P Zhang p , Z.Q Zhang d , D.X Zhao a , J.B Zhao a , J.W Zhao a , M.G Zhao i , P.P Zhao a , W.R Zhao a , X.J Zhao a , Y.B Zhao a , Z.G Zhao a,1 0370-2693/$ – see front matter  2005 Elsevier B.V All rights reserved doi:10.1016/j.physletb.2005.09.050 22 BES Collaboration / Physics Letters B 630 (2005) 21–30 H.Q Zheng j , J.P Zheng a , L.S Zheng a , Z.P Zheng a , X.C Zhong a , B.Q Zhou a , G.M Zhou a , L Zhou a , N.F Zhou a , K.J Zhu a , Q.M Zhu a , Y.C Zhu a , Y.S Zhu a , Yingchun Zhu a , Z.A Zhu a , B.A Zhuang a , B.S Zou a a Institute of High Energy Physics, Beijing 100039, People’s Republic of China b China Center for Advanced Science and Technology (CCAST), Beijing 100080, People’s Republic of China c Guangxi Normal University, Guilin 541004, People’s Republic of China d Henan Normal University, Xinxiang 453002, People’s Republic of China e Huazhong Normal University, Wuhan 430079, People’s Republic of China f Hunan University, Changsha 410082, People’s Republic of China g Liaoning University, Shenyang 110036, People’s Republic of China h Nanjing Normal University, Nanjing 210097, People’s Republic of China i Nankai University, Tianjin 300071, People’s Republic of China j Peking University, Beijing 100871, People’s Republic of China k Shandong University, Jinan 250100, People’s Republic of China l Shanghai Jiaotong University, Shanghai 200030, People’s Republic of China m Sichuan University, Chengdu 610064, People’s Republic of China n Tsinghua University, Beijing 100084, People’s Republic of China o University of Hawaii, Honolulu, HI 96822, USA p University of Science and Technology of China, Hefei 230026, People’s Republic of China q Wuhan University, Wuhan 430072, People’s Republic of China r Zhejiang University, Hangzhou 310028, People’s Republic of China Received 11 May 2005; accepted September 2005 Available online 30 September 2005 Editor: M Doser Abstract First observations of χc0 , χc1 , and χc2 decays to π + π − KS0 KS0 and K + K − KS0 KS0 , as well as ψ(2S) decay to π + π − KS0 KS0 , are presented The branching fractions of these decay channels are determined using 14 × 106 ψ(2S) events collected at BESII/BEPC The branching fractions of χc0 , χc2 → KS0 KS0 are measured with improved statistical precision  2005 Elsevier B.V All rights reserved PACS: 13.25.Gv; 12.38.Qk; 14.40.Gx Introduction Experimental data on charmonia and their decay properties are essential input to test QCD models and QCD based calculations The importance of the Color Octet Mechanism (COM) [1] in radiative decays of The h± denote charged pions or kaons E-mail address: wangzhe@ihep.ac.cn (Zhe Wang) Visiting professor to University of Michigan, Ann Arbor, MI 48109, USA Current address: Purdue University, West Lafayette, IN 47907, USA ✩ the Υ [2], J /ψ production in inclusive B decays [3], as well as inclusive decays of P-wave charmonia [4] has been emphasized for many years Recently, QCD predictions of two-body exclusive decays of P-wave charmonium with the inclusion of the COM have been made [5,6] and compared to previous measurements [7,8] More experimental data of two- and four-body exclusive decays of P-wave charmonia with improved precision are important for further testing this new QCD approach including the effect of the COM In this Letter, results on ψ(2S) and χcJ (J = 0, 1, 2) two- and four-body hadronic decays with inclusion of a pair of KS0 mesons are presented This analysis is BES Collaboration / Physics Letters B 630 (2005) 21–30 based on 14 × 106 ψ(2S) decays collected with BESII at the BEPC e+ e− collider A sample of 6.42 pb−1 data taken at 3.65 GeV is used for continuum background studies BES detector The BESII detector is described elsewhere [9] Charged particle momenta are determined with a resolution of σp /p = 1.78% + p (p in GeV/c) in a 40-layer main drift chamber (MDC) Particle identification is accomplished using specific ionization (dE/dx) information in the drift chamber and timeof-flight (TOF) information in a barrel-like array of 48 scintillation counters The dE/dx resolution is σdE/dx = 8%; the TOF resolution is σTOF = 200 ps for hadrons A 12-radiation-length barrel shower counter (BSC) measures energies of photons with a resolution √ of σE /E = 21%/ E (E in GeV) Monte Carlo simulation A Geant3 based Monte Carlo, SIMBES [10], which simulates the detector response, including interactions of secondary particles in the detector material, is used to determine detection efficiencies and mass resolutions, as well as to optimize selection criteria and estimate backgrounds Under the assumption of a pure E1 transition, the distribution of polar angle θ of the photon in ψ(2S) → γ χcJ decays is given by + k cos2 θ for J = 0, 1, and 2, re[11] with k = 1, − 13 , and 13 spectively The angular distributions for KS0 mesons from χc0,2 → KS0 KS0 decays are produced according to the model of χcJ → M M¯ [12], where M stands for a 0− meson Angular distributions for daughters from other decays are generated isotropically in the centerof-mass system of the ψ(2S) or χcJ Data analysis To be regarded as a good photon, a shower cluster in the BSC must have an energy deposit of more than 50 MeV and at least one hit in the first six layers of the BSC To remove soft photons emitted by charged particles, the differences of azimuthal angles, dφ, and 23 z coordinates at the first layer of the BSC, dz, between good photons and each charged track must satisfy either a loose requirement (selection-A: dφ > 10◦ or dz > 0.3 m) or a tight requirement (selection-B: dφ > 20◦ or dz > 1.0 m) Here the z coordinate is defined to point in the positron direction Each charged track is required to have a good helix fit For final states containing charged kaons, particle identification is required; usable particle identification information in one or both of the MDC (dE/dx) and TOF subsystems is necessary A particle identification χ is calculated for each track for the pion, kaon or proton hypotheses using this information, and the associated probability prob is determined A track is identified as a kaon, if the probability of the track being a kaon prob(K) > 0.01; otherwise it is regarded as a pion For final states containing only pions, no particle identification is done and all tracks are assumed to be pions Each event is required to contain two KS0 mesons The reconstruction of the decay KS0 → π + π − and related checks are described in detail elsewhere [13] A KS0 candidate must satisfy |Mπ + π − − MK | < S 20 MeV and have a decay length transverse to the beam axis Rxy > 0.3 cm The KS0 sideband sample, used for background estimation, is selected with one π + π − pair within the KS0 mass window and the other pair in the KS0 mass sideband region defined by 40 MeV < |Mπ + π − − MK | < 60 MeV S Four constraint (4C) kinematic fits are performed on the selected events for the following decay modes: (1) ψ(2S) → γ KS0 KS0 , (2) ψ(2S) → γ π + π − KS0 KS0 , and (3) ψ(2S) → γ K + K − KS0 KS0 The fits are made to each combination of a good photon and two KS0 candidates in an event, the combination with the min2 is selected, and the χ is required to be imum χ4C 4C less than 35 The associated probability prob4C is calculated Background from ψ(2S) → π + π − J /ψ decay is removed by calculating the mass recoiling, Mrecoil , against all pairs of oppositely charged tracks, assuming them to be pions, and requiring |Mrecoil − MJ /ψ | > 25 MeV Background contamination from continuum production is found to be negligible for all decay channels An unbinned maximum likelihood method is used in fitting the signal for all decay channels except ψ(2S) → h+ h− KS0 KS0 The branching fractions of 24 BES Collaboration / Physics Letters B 630 (2005) 21–30 Fig Distribution of KS0 KS0 invariant mass of ψ(2S) → γ KS0 KS0 candidates (a) Points with error bars are data, and the histogram is sideband background (b) Points with error bars are data, and the solid line is the fit described in the text ψ(2S) → γ χcJ (J = 0, 1, 2) needed in the measurement are taken from Particle Data Group (PDG) tables [8] 4.1 ψ(2S) → γ KS0 KS0 The decay ψ(2S) → γ KS0 KS0 has one photon plus a pair of KS0 candidates The event should have four charged tracks with total charge zero The loose photon selection, selection-A, is applied because of the low background in the channel The KS0 KS0 invariant mass distribution of the selected events is shown in Fig A few KS0 sideband events survive the selection, which is consistent with the low background observed in Fig 1(a) No background is expected from ψ(2S) → γ χcJ with χcJ → 2(π + π − ) for J = 0, 1, and ψ(2S) → γ χc1 with χc1 → KS0 K ± π ∓ according to the analysis of simulated MC events The KS0 KS0 invariant mass distribution is fitted with two Breit–Wigner resonances for χc0 and χc2 , each convoluted with Gaussian resolution functions, plus a second-order polynomial background The χc0,2 widths in the fitting are fixed to their PDG values [8] The resulting fit is shown in Fig 1(b) Including the χc1 resonance in the fit yields zero events for the CP violating decay χc1 → KS0 KS0 4.2 ψ(2S) → γ π + π − KS0 KS0 The ψ(2S) → γ π + π − KS0 KS0 decay channel contains one photon and six charged tracks with total charge zero The requirements here are similar to the previous case, but there are two additional pions Background from π/K misidentification is suppressed by the requirement prob4C (γ π + π − KS0 KS0 ) > prob4C (γ K + K − KS0 KS0 ) The π + π − KS0 KS0 invariant BES Collaboration / Physics Letters B 630 (2005) 21–30 25 Fig Distribution of π + π − KS0 KS0 invariant mass for ψ(2S) → γ π + π − KS0 KS0 candidates Points with error bars are data The light shaded area in (a) is background simulation, where some unknown branching ratios are normalized to agree with the overall χcJ background level, and the dark shaded area is KS0 sideband The solid line in (b) is the fit mass distribution for selected events is shown in Fig In Fig there are two kinds of background in the mass region between 3.0 and 3.64 GeV/c2 : (1) background corresponding to KS0 sidebands, and (2) ψ(2S) decays and χcJ decays different from the signal channel, where the decays also include a pair of KS0 mesons Studies with KS0 sideband events for both data and MC show that KS0 sideband background from wrong combinations of π + π − is slightly enhanced in the χcJ signal region MC studies show that the smooth background spread over the whole mass region from (2) results mainly from the following decay channels: (a) ψ(2S) → γ χcJ with χcJ → 3(π + π − ) and χcJ → K + K − KS0 KS0 , (b) ψ(2S) → π π + π − KS0 KS0 , and (c) ψ(2S) → ωKS0 KS0 with ω → π + π − π Background events in the high mass region above 3.64 GeV/c2 in Fig are from ψ(2S) → π + π − KS0 KS0 decays combined with an unassociated low energy photon The π + π − KS0 KS0 invariant mass distribution between 3.0 to 3.64 GeV/c2 is fitted with three Breit– Wigner resonances χcJ (J = 0, 1, 2), convoluted with Gaussian resolution functions, plus a second-order polynomial background The widths of the χc0,1,2 resonances in the fit are fixed to their PDG values The fit is shown in Fig The numbers of events in the three peaks determined from the fit include signal and KS0 sideband background, which is somewhat enhanced in the regions of the peaks The KS0 sideband sample for data is fitted with a fake signal shape, found by fitting the MC KS0 sideband sample, plus a second order polynomial background The numbers of sideband background events, 5.3, 0.6 and 5.5 for χc0 , χc1 and χc2 , respectively, are then subtracted from the total numbers of events in three peaks 26 BES Collaboration / Physics Letters B 630 (2005) 21–30 Fig Distribution of K + K − KS0 KS0 invariant mass of ψ(2S) → γ K + K − KS0 KS0 candidates Points with error bars are data, and the histogram is sideband background The solid line is the fit 4.3 ψ(2S) → γ K + K − KS0 KS0 The ψ(2S) → γ K + K − KS0 KS0 decay has the same topology as ψ(2S) → γ π + π − KS0 KS0 , and thus it is subject to similar event selection criteria except for the kaon identification requirement for two of the charged tracks First, the KS0 KS0 pair is searched for under the assumption that all charged tracks are pions Kaon identification is only done for the two charged tracks remaining after reconstruction of the KS0 KS0 pair We also require prob4C (γ K + K − KS0 KS0 ) > prob4C (γ π + π − KS0 KS0 ) for the 4C kinematic fit probabilities to suppress contamination from ψ(2S) → γ π + π − KS0 KS0 decays The K + K − KS0 KS0 invariant mass distribution for selected events is shown in Fig As seen from Fig 3, only one event survives from the KS0 sideband sample for data MC events for the following possible background channels are generated: (1) ψ(2S) → γ χcJ with χcJ → 3(π + π − ) and π + π − KS0 KS0 , (2) ψ(2S) → π + π − KS0 KS0 , and (3) ψ(2S) → ωKS0 KS0 with ω → π + π − π However, no event from these background channels survives the selection criteria Another study with a large sample of simulated ψ(2S) → anything [14] shows that negligible background comes from decays of ψ(2S) → φK ∗ K → π K + K − KS0 KS0 The K + K − KS0 KS0 invariant mass distribution is fitted with three Breit–Wigner resonances, χcJ (J = 0, 1, 2), convoluted with Gaussian resolution functions, plus a flat background Because of low statistics in the signal region, not only the widths and mass resolutions for the χcJ (J = 0, 1, 2), but also the masses of the χc1 and χc2 in the fitting are fixed to their PDG values The fitting results are shown in the Fig 4.4 ψ(2S) → h+ h− KS0 KS0 The selection of ψ(2S) → h+ h− KS0 KS0 decays requires six charged tracks with total charge zero and no good photon in the event, as defined above Good photons are rejected with the tight selection, selection-B, in order to gain higher detection efficiency for signal events The KS0 reconstruction uses all combinations of oppositely charged tracks assuming all tracks are pions To further suppress background of ψ(2S) radiative decays, a requirement on the missing momentum of six charged tracks is employed: Pmiss < 80 MeV The two charged tracks h+ and h− recoiling against the KS0 pair are assumed to have the same mass m Using energy–momentum conservation, the mass squared m2 is calculated from m2 = E + (Ph2+ − Ph2− )2 − 2E (Ph2+ + Ph2− ) 4E , (1) BES Collaboration / Physics Letters B 630 (2005) 21–30 27 Fig Distribution of invariant mass squared of the two remaining charged particles after KS0 KS0 selection for ψ(2S) → h+ h− KS0 KS0 (a) Points with error bars are data The histogram is the KS0 sideband background (b) Points with error bars are the data with the KS0 sideband background subtracted The solid line is the fit where E = Mψ(2S) − EKS0 KS0 , and Ph± is the momentum of h+ or h− The distribution of m2 for selected events is shown in Fig The peak at low mass is consistent with π + π − ; there is no evidence for K + K − Two events from the continuum data sample survive the above selection and their effect will be included in the systematic error No background is found in MC studies of the following decay channels: (1) ψ(2S) → γ χcJ with χcJ → 3(π + π − ), π + π − KS0 KS0 , and K + K − KS0 KS0 and (2) ψ(2S) → ωKS0 KS0 with ω → π + π − π Background estimated using the KS0 sideband data is subtracted from the observed number of signal events A MC study shows that the shape of the charged pion signal in the m2 spectrum is well described by a Gaussian function, and its mean and resolution are consistent with data The spectrum is fitted with a Gaussian signal function and a flat background using a binned maximum likelihood fit where the resolution is fixed to the MC determined value The fitting result is shown in the Fig 4.5 Systematic errors Systematic errors for the efficiency are caused by differences between data and MC simulation Our studies have determined these errors to be 2% per track for the tracking efficiency, 2% for photon identification, 5% for the 4C kinematic fit, and 2.1% for the KS0 reconstruction efficiency A correction factor due to the overestimate of the KS0 reconstruction efficiency of the MC relative to data is determined to be 95.8% The change of fitting range and background shape function contributes a difference of final results less than 3% Other systematic errors arise from the uncertainties in the total number of ψ(2S) events, (14.00 ± 0.56) × 106 [15], and in the branch- 28 BES Collaboration / Physics Letters B 630 (2005) 21–30 Table Summary of the fitting results Errors for the signal yield ns , background nb , mass M, and mass squared m2 are statistical The detection efficiency and resolution σ for each decay channel from MC are shown ns Channel χc0 → KS0 KS0 nb 322 ± 20 χc1 → KS0 KS0 χc2 → KS0 KS0 6.4 ± 2.6 65.1 ± 8.7 χc0 → π + π − KS0 KS0 152 ± 14 χc1 → π + π − KS0 KS0 χc2 → π + π − KS0 KS0 χc0 → K + K − KS0 KS0 13.3 12.8 3555.7 ± 1.8 8.48 11.8 3412.9 ± 2.0 2.03 16.8 2.20 16.4 2.04 17.2 16.8 ± 4.8 3415.4 ± 6.1 0.91 16.1 3.2 ± 2.4 1.8 ± 0.8 fixed 1.12 15.3 2.3 ± 2.2 1.8 ± 0.8 fixed 1.05 15.9 nb m2 (10−3 ) (GeV2 /c4 ) (%) σ (10−3 ) (GeV2 /c4 ) 18.0 ± 3.1 2.82 26.5 83.2 ± 9.4 4.6 Result and discussion Possible resonance structures have been searched for the χc0 → π + π − KS0 KS0 final state which is the channel with the highest number of observed events Some excess for inclusive decays of K ∗ (892)+ → KS0 π + , f0 (1710) → KS0 KS0 , ρ(770) → π + π − and f0 (980) → π + π − can be seen from the selected events Insufficient statistics and complicated structures in these decay modes make it difficult to identify clear signals for two-body decays with intermediate resonances Efficiencies for final states with resonances, such as K0∗ (1430)+ K0∗ (1430)− , K0∗ (1430)+ K2∗ (1430)− , f0 (980)f0 (980), f0 (980)f0 (2200) and 7.96 8.50 3501.1 ± 6.2 ing fractions for KS0 → π + π − and ψ(2S) → γ χcJ (J = 0, 1, 2) In ψ(2S) → π + π − KS0 KS0 decay, with two events found in continuum data, an additional error of 7.7% is added f0 (1370)f0 (1710), 3413.1 ± 1.2 fixed 3548.2 ± 3.1 ns K ∗ (892)+ K ∗ (892)− , σ (MeV/c2 ) 57 ± 11 χc2 → K + K − KS0 KS0 ψ(2S) → π + π − KS0 KS0 (%) 19.8 ± 7.7 χc1 → K + K − KS0 KS0 Channel MχcJ (MeV/c2 ) K1 (1270)0 K [16] are studied using phase-space MC events The averaged difference in efficiency between final states with and without intermediate resonance is estimated to be 7.7%, which is regarded as systematic error in the measurements of the branching fractions for the four-body final states The results of four-body final states h+ h− KS0 KS0 in our measurements include those of both non-resonance and intermediate resonance Final results of signal yield and branching fractions for the χcJ (1P) and ψ(2S) two- and fourbody hadronic decays involving KS0 pair production are summarized in Table The masses of the χcJ (J = 0, 1, 2) extracted from the fits are also listed The 90% confidence level (CL) upper limits on the branching fractions in the table are obtained using the Feldman–Cousins method [17] The branching fractions of χcJ (J = 0, 1, 2) decays to π + π − KS0 KS0 and K + K − KS0 KS0 , as well ψ(2S) decay to π + π − KS0 KS0 are observed for the first time The branching fractions of χc0 and χc2 decays to KS0 KS0 are measured with improved precision Decay rates, determined using updated χcJ total widths [8] and branching fractions for χcJ → π π , π + π − (J = 0, 2) and χcJ → p p¯ (J = 1, 2) decays [8], provide support for the COM (see Table 3) According to isospin symmetry, the χcJ → K K¯ and K + K − decays should have the same partial width Assuming equal decay widths for χcJ → KS0 KS0 and KL0 KL0 , we find that the partial width of the χc0 → K K¯ decay estimated using the result obtained in this Letter is not consistent (2.7σ ) with the COM prediction for χc0 → K + K − , while the BES Collaboration / Physics Letters B 630 (2005) 21–30 29 Table The branching fractions from this measurement, as well as previous results, are listed The first and second errors for the branching fractions BR are statistical and systematic, respectively BR(ψ(2S) → γ χc )BR(χc → X) (10−5 ) Channel BR(χc → X) (10−4 ) χc0 → KS0 KS0 30.2 ± 1.9 ± 3.3 35.1 ± 2.2 ± 4.7 χc1 → KS0 KS0 < 0.6 (CL = 90%) < 0.8 (CL = 90%) χc2 χc0 → KS0 KS0 → π + π − KS0 KS0 → π + π − KS0 KS0 → π + π − KS0 KS0 → K + K − KS0 KS0 → K + K − KS0 KS0 5.72±0.76±0.63 55.8 ± 5.1 ± 8.9 BRPDG (χc → X) [8] (10−4 ) 21 ± – 8.9 ± 1.2 ± 1.3 65 ± ± 12 7.2±2.7 – 6.7 ± 2.6 ± 1.1 8.0 ± 3.1 ± 1.5 – 20.7 ± 3.9 ± 3.3 32.4 ± 6.1 ± 6.2 – 13.8 ± 3.9 ± 2.5 16.0 ± 4.6 ± 3.2 – 2.1 ± 1.6 ± 0.4 < 4.2 (CL = 90%) 1.6 ± 1.6 ± 0.3 < 3.5 (CL = 90%) 2.5 ± 1.9 ± 0.5 < 5.1 (CL = 90%) 2.6 ± 2.4 ± 0.5 < 5.5 (CL = 90%) – Channel – BR(ψ(2S) → X) (10−4 ) BRPDG (ψ(2S) → X) [8] (10−4 ) ψ(2S) → π + π − KS0 KS0 – χc1 χc2 χc0 χc1 χc2 → K + K − KS0 KS0 2.20 ± 0.25 ± 0.37 Table Comparison of partial widths for χcJ → π π, K K¯ and pp¯ decays between PDG [8] and the COM predictions Also shown is the result based on this analysis Decay χc0 → π + π − χc2 → π + π − χc0 → π π χc2 → π π χc1 → p p¯ χc2 → p p¯ χc0 → K + K − χc2 → K + K − χc0 → K K¯ χc2 → K K¯ Γi (PDG) in KeV/c2 49.5 ± 6.7 3.73 ± 0.64 25.3 ± 3.3 2.3 ± 1.5 0.066 ± 0.015 0.143 ± 0.018 61 ± 10 1.98 ± 0.47 71 ± 12 (this Letter) 3.76±0.80 (this Letter) Γi (COM) in KeV/c2 45.4 [5] 3.64 [5] 23.5 [5] 1.93 [5] 0.05627 [6] 0.15419 [6] 38.6 [5] 2.89 [5] agreement between them for the corresponding χc2 decay is within 1.1σ A comparison for the χcJ → K + K − (J = 0, 2) decays shows that the discrepancy between PDG values and the COM predictions is 2.2σ and 1.9σ for χc0 and χc2 decays, respectively Furthermore, the sum of all known χc0 two-body branching fractions is less than 2% It therefore is important to measure more χcJ decay modes, including two-body modes with intermediate resonance and many-body modes, because of their large contribution – – to the hadronic decay width Theoretical predictions with inclusion of the COM for χcJ decays to manybody final states are required for comparison with data Acknowledgements The BES Collaboration thanks the staff of BEPC for their hard efforts and the members of IHEP computing center for their helpful assistance, and also K.T Chao and J.X Wang for helpful discussions on the COM This work is supported in part by the National Natural Science Foundation of China under contracts Nos 19991480, 10225524, 10225525, the Chinese Academy of Sciences under contract No KJ 95T03, the 100 Talents Program of CAS under Contract Nos U-11, U-24, U-25, and the Knowledge Innovation Project of CAS under Contract Nos U-602, U-34 (IHEP); by the National Natural Science Foundation of China under Contract No 10175060 (USTC), and No 10225522 (Tsinghua University); and by the Department of Energy under Contract No DE-FG0204ER41291 (University of Hawaii) References [1] G.T Bodwin, E Braaten, G.P Lepage, Phys Rev D 46 (1992) 1914; 30 [2] [3] [4] [5] [6] [7] BES Collaboration / Physics Letters B 630 (2005) 21–30 G.T Bodwin, E Braaten, G.P Lepage, Phys Rev D 51 (1995) 1125 F Maltoni, A Petrelli, Phys Rev D 59 (1999) 074006 M Beneke, F Maltoni, I.Z Rothstein, Phys Rev D 59 (1999) 054003 H.W Huang, K.T Chao, Phys Rev D 54 (1996) 6850; A Petrelli, Phys Lett B 380 (1996) 159 J Bolz, P Kroll, G.A Schuler, Eur Phys J C (1998) 705; J Bolz, P Kroll, G.A Schuler, Phys Lett B 392 (1997) 198 S.M.H Wong, Nucl Phys A 674 (2000) 185; S.M.H Wong, Eur Phys J C 14 (2000) 643 BES Collaboration, J.Z Bai, et al., Phys Rev D 67 (2003) 032004; BES Collaboration, J.Z Bai, et al., Phys Rev D 67 (2003) 112001; BES Collaboration, J.Z Bai, et al., Phys Rev D 60 (1999) 072001; BES Collaboration, J.Z Bai, et al., Phys Rev Lett 81 (1998) 3091; CLEO Collaboration, B.I Eisenstein, et al., Phys Rev Lett 87 (2001) 061801; E835 Collaboration, M Andreotti, et al., Phys Rev Lett 91 (2003) 091801; [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] S Bagnasco, et al., Phys Lett B 533 (2002) 237; M Ambrogiani, et al., Phys Rev Lett 83 (1999) 2902 S Eidelman, et al., Particle Data Group, Phys Lett B 592 (2004) 1, http://pdg.lbl.gov BES Collaboration, J.Z Bai, et al., Nucl Instrum Methods A 458 (2001) 627; J.Z Bai, et al., Nucl Instrum Methods A 344 (1994) 319 H.M Liu, et al., The BESII detector simulation, Nucl Instrum Methods, in press G Karl, et al., Phys Rev D 13 (1976) 1203; L.S Brown, R.N Cahn, Phys Rev D 13 (1976) 1195 P.K Kabir, A.J.G Itey, Phys Rev D 13 (1976) 3161 Z Wang, et al., High Energy Phys Nucl Phys 27 (2003) J.C Chen, Phys Rev D 62 (2000) 034003 X.H Mo, et al., High Energy Phys Nucl Phys 28 (2004) 455, hep-ex/0407055 BES Collaboration, M Ablikim, et al., Phys Rev D 70 (2004) 092003; M Ablikim, et al., contributed paper to LP2005, paper-122 G Feldman, R Cousins, Phys Rev D 57 (1998) 3873; J Conrad, et al., Phys Rev D 67 (2003) 012002  ... 4.6 Result and discussion Possible resonance structures have been searched for the χc0 → π + π − KS0 KS0 final state which is the channel with the highest number of observed events Some excess for... background The solid line is the fit 4.3 ψ( 2S) → γ K + K − KS0 KS0 The ψ( 2S) → γ K + K − KS0 KS0 decay has the same topology as ψ( 2S) → γ π + π − KS0 KS0 , and thus it is subject to similar event selection... with and without intermediate resonance is estimated to be 7.7%, which is regarded as systematic error in the measurements of the branching fractions for the four-body final states The results