Branching fraction measurements of χc0 and χc2 to π0π0 and ηη

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1 Title Author(s Citation Branching fraction measurements of χc and χc to ππ and ηη Ablikim, M; Achasov, MN; An, L; An, Q; An, ZH; Bai, JZ; Ban, Y; Berger, N; Bian, JM; Boyko, I; Briere, RA; Zhang, XY; Zhang, Y; Zhang, YH; Zhang, ZP; Zhao, C; CroninHennessy, D; Zhao, HS; Zhao, J; Zhao, J; Liu, CL; Sun, YJ; Zhao, L; Zhao, L; Zhao, MG; Zhao, Q; Zhao, SJ; Zhao, TC; Zhao, XH; Dai, HL; Zhao, YB; Zhao, ZG; Sun, YZ; Liu, CX; Zhemchugov, A; Zheng, B; Zheng, JP; Zheng, YH; Zheng, ZP; Zhong, B; Zhong, J; Zhou, L; Dai, JP; Sun, ZJ; Zhou, ZL; Bytev, V; Zhu, C; Zhu, K; Zhu, KJ; Zhu, QM; Zhu, XW; Zhu, YS; Zhu, ZA; Zhuang, J; Sun, ZT; Zou, BS; Dedovich, D; Liu, CY; Zou, JH; Zuo, JX; Zweber, P; Deng, ZY; Denysenko, I; Destefanis, M; Ding, Y; Tang, CJ; Dong, LY; Dong, MY; Du, SX; Liu, FH; Duan, MY; Fang, J; Feng, CQ; Fu, CD; Fu, JL; Gao, Y; Tang, X; Geng, C; Goetzen, K; Gong, WX; Greco, M; Liu, F; Grishin, S; Gu, YT; Guo, AQ; Guo, LB; Guo, YP; Tang, XF; Han, SQ; Harris, FA; He, KL; He, M; He, ZY; Liu, F; Heng, YK; Hou, ZL; Hu, HM; Hu, JF; Tian, HL; Hu, T; Hu, XW; Huang, B; Huang, GM; Huang, JS; Huang, XT; Liu, GC; Huang, YP; Ji, CS; Ji, Q; Toth, D; Ji, XB; Ji, XL; Jia, LK; Jiang, LL; Jiang, XS; Jiao, JB; Jin, DP; Liu, H; Jin, S; Komamiya, S; Chen, JC; Kuehn, W; Lange, S; Leung, JKC; Li, C; Li, C; Li, DM; Li, F; Li, G; Liu, HB; Li, HB; Li, ZB; Li, J; Li, JC; Li, L; Li, L; Li, QJ; Li, WD; Li, WG; Li, XL; Li, XN; Liu, HM; Varner, GS; Li, XQ; Li, XR; Li, YX; Liu, HW; Liu, J; Cai, X; Liu, JP; Liu, K; Liu, KY; Liu, Q; Wan, X; Liu, SB; Liu, XH; Liu, YB; Liu, YF; Liu, YW; Liu, Y; Cao, GF; Liu, ZA; Lu, GR; Lu, JG; Wang, BQ; Lu, QW; Lu, XR; Lu, YP; Luo, CL; Luo, MX; Luo, T; Luo, XL; Cao, XX; Ma, CL; Ma, FC; Wang, JK; Ma, HL; Ma, QM; Ma, X; Ma, XY; Maggiora, M; Mao, YJ; Mao, ZP; Min, J; Chang, JF; Mo, XH; Wang, K; Muchnoi, NYu; Nefedov, Y; Ning, FP; Olsen, SL; Ouyang, Q; Pelizaeus, M; Peters, K; Ping, JL; Ping, RG; Chelkov, G; Wang, LL; Poling, R; Pun, CSJ; Qi, M; Qian, S; Qiao, CF; Qiu, JF; Rong, G; Ruan, XD; Sarantsev, A; Shao, M; Wang, LS; Chen, G; Shen, CP; Shen, XY; Sheng, HY; Sonoda, S; Spataro, S; Spruck, B; Sun, DH; Sun, GX; Sun, JF; Wang, P; Sun, SS; Chen, HS; Sun, XD; Wang, PL; Wang, Q; Liang, H; Chen, LP; Wang, SG; Wang, XD; Wang, XL; Wang, YD; Wang, YF; Wang, YQ; Wang, Z; Wang, ZG; Wang, ZY; Liang, TR; Wei, DH; Chen, ML; Wen, SP; Wiedner, U; Wu, LH; Wu, N; Wu, W; Wu, YM; Wu, Z; Xiao, ZJ; Liang, YT; Xie, YG; Xu, GF; Chen, P; Xu, GM; Xu, H; Xu, M; Xu, M; Xu, XP; Xu, Y; Xu, ZZ; Liang, YF; Xue, Z; Yan, L; Yan, WB; Chen, SJ; Yan, YH; Yang, HX; Yang, M; Yang, P; Yang, SM; Yang, YX; Liao, GR; Ye, M; Ye, MH; Yu, BX; Yu, CX; Chen, YB; Yu, L; Yuan, CZ; Yuan, Y; Zeng, Y; Zhang, BX; Liao, XT; Zhang, BY; Zhang, CC; Zhang, DH; Zhang, HH; Zhang, HY; Chu, YP; Zhang, JW; Zhang, JY; Zhang, JZ; Zhang, L; Liu, BJ; Zhang, SH Physical Review D - Particles, Fields, Gravitation And Cosmology, 1, v. 81 n. 5, article no. 55

2 PHYSICAL REVIEW D 81, 55 (1 Branching fraction measurements of c and c to and M. Ablikim, 1 M. N. Achasov, 5 L. An, 9 Q. An, 31 Z. H. An, 1 J. Z. Bai, 1 Y. Ban, 18 N. Berger, 1 J. M. Bian, 1 I. Boyko, 13 R. A. Briere, 3 V. Bytev, 13 X. Cai, 1 G. F. Cao, 1 X. X. Cao, 1 J. F. Chang, 1 G. Chelkov, 13, * G. Chen, 1 H. S. Chen, 1 J. C. Chen, 1 L. P. Chen, 1 M. L. Chen, 1 P. Chen, 1 S. J. Chen, 16 Y. B. Chen, 1 Y. P. Chu, 1 D. Cronin-Hennessy, 3 H. L. Dai, 1 J. P. Dai, 1 D. Dedovich, 13 Z. Y. Deng, 1 I. Denysenko, 13, M. Destefanis, 3 Y. Ding, 14 L. Y. Dong, 1 M. Y. Dong, 1 S. X. Du, 36 M. Y. Duan, 1 J. Fang, 1 C. Q. Feng, 31 C. D. Fu, 1 J. L. Fu, 16 Y. Gao, 7 C. Geng, 31 K. Goetzen, 7 W. X. Gong, 1 M. Greco, 3 S. Grishin, 13 Y. T. Gu, 9 A. Q. Guo, 17 L. B. Guo, 15 Y. P. Guo, 17 S. Q. Han, 15 F. A. Harris, 9 K. L. He, 1 M. He, 1 Z. Y. He, 17 Y. K. Heng, 1 Z. L. Hou, 1 H. M. Hu, 1 J. F. Hu, 6 T. Hu, 1 X. W. Hu, 16 B. Huang, 1 G. M. Huang, 11 J. S. Huang, 1 X. T. Huang, Y. P. Huang, 1 C. S. Ji, 31 Q. Ji, 1 X. B. Ji, 1 X. L. Ji, 1 L. K. Jia, 1 L. L. Jiang, 1 X. S. Jiang, 1 J. B. Jiao, D. P. Jin, 1 S. Jin, 1 S. Komamiya, 6 W. Kuehn, 8 S. Lange, 8 J. K. C. Leung, 5 Cheng Li, 31 Cui Li, 31 D. M. Li, 36 F. Li, 1 G. Li, 1 H. B. Li, 1 J. Li, 1 J. C. Li, 1 Lei Li, 1 Lu Li, 1 Q. J. Li, 1 W. D. Li, 1 W. G. Li, 1 X. L. Li, X. N. Li, 1 X. Q. Li, 17 X. R. Li, 1 Y. X. Li, 36 Z. B. Li, 3 H. Liang, 31 T. R. Liang, 17 Y. T. Liang, 8 Y. F. Liang, G. R Liao, 8 X. T. Liao, 1 B. J. Liu, 4,5 C. L. Liu, 3 C. X. Liu, 1 C. Y. Liu, 1 F. H. Liu, 1 Fang Liu, 1 Feng Liu, 11 G. C. Liu, 1 H. Liu, 1 H. B. Liu, 6 H. M. Liu, 1 H. W. Liu, 1 J. Liu, 1 J. P. Liu, 34 K. Liu, 18 K. Y Liu, 14 Q. Liu, 9 S. B. Liu, 31 X. H. Liu, 1 Y. B. Liu, 17 Y. F. Liu, 17 Y. W. Liu, 31 Yong Liu, 1 Z. A. Liu, 1 G. R. Lu, 1 J. G. Lu, 1 Q. W. Lu, 1 X. R. Lu, 6 Y. P. Lu, 1 C. L. Luo, 15 M. X. Luo, 35 T. Luo, 1 X. L. Luo, 1 C. L. Ma, 6 F. C. Ma, 14 H. L. Ma, 1 Q. M. Ma, 1 X. Ma, 1 X. Y. Ma, 1 M. Maggiora, 3 Y. J. Mao, 18 Z. P. Mao, 1 J. Min, 1 X. H. Mo, 1 N. Yu. Muchnoi, 5 Y. Nefedov, 13 F. P. Ning, 1 S. L. Olsen, 19 Q. Ouyang, 1 M. Pelizaeus, K. Peters, 7 J. L. Ping, 15 R. G. Ping, 1 R. Poling, 3 C. S. J. Pun, 5 M. Qi, 16 S. Qian, 1 C. F. Qiao, 6 J. F. Qiu, 1 G. Rong, 1 X. D. Ruan, 9 A. Sarantsev, 13, M. Shao, 31 C. P. Shen, 9 X. Y. Shen, 1 H. Y. Sheng, 1 S. Sonoda, 6 S. Spataro, 3 B. Spruck, 8 D. H. Sun, 1 G. X. Sun, 1 J. F. Sun, 1 S. S. Sun, 1 X. D. Sun, 1 Y. J. Sun, 31 Y. Z. Sun, 1 Z. J. Sun, 1 Z. T. Sun, 31 C. J. Tang, X. Tang, 1 X. F. Tang, 8 H. L. Tian, 1 D. Toth, 3 G. S. Varner, 9 X. Wan, 1 B. Q. Wang, 18 J. K. Wang, 1 K. Wang, 1 L. L. Wang, 4 L. S. Wang, 1 P. Wang, 1 P. L. Wang, 1 Q. Wang, 1 S. G. Wang, 18 X. D. Wang, 1 X. L. Wang, 31 Y. D. Wang, 31 Y. F. Wang, 1 Y. Q. Wang, Z. Wang, 1 Z. G. Wang, 1 Z. Y. Wang, 1 D. H. Wei, 8 S. P. Wen, 1 U. Wiedner, L. H. Wu, 1 N. Wu, 1 W. Wu, 14 Y. M. Wu, 1 Z. Wu, 1 Z. J. Xiao, 15 Y. G. Xie, 1 G. F. Xu, 1 G. M. Xu, 18 H. Xu, 1 Min Xu, 31 Ming Xu, 9 X. P. Xu, 11,x Y. Xu, 17 Z. Z. Xu, 31 Z. Xue, 31 L. Yan, 31 W. B. Yan, 31 Y. H. Yan, 1 H. X. Yang, 1 M. Yang, 1 P. Yang, 17 S. M. Yang, 1 Y. X. Yang, 8 M. Ye, 1 M. H. Ye, 4 B. X. Yu, 1 C. X. Yu, 17 L. Yu, 11 C. Z. Yuan, 1 Y. Yuan, 1 Y. Zeng, 1 B. X. Zhang, 1 B. Y. Zhang, 1 C. C. Zhang, 1 D. H. Zhang, 1 H. H. Zhang, 3 H. Y. Zhang, 1 J. W. Zhang, 1 J. Y. Zhang, 1 J. Z. Zhang, 1 L. Zhang, 16 S. H. Zhang, 1 X. Y. Zhang, Y. Zhang, 1 Y. H. Zhang, 1 Z. P. Zhang, 31 C. Zhao, 31 H. S. Zhao, 1 Jiawei Zhao, 31 Jingwei Zhao, 1 Lei Zhao, 31 Ling Zhao, 1 M. G. Zhao, 17 Q. Zhao, 1 S. J. Zhao, 36 T. C. Zhao, 33 X. H. Zhao, 16 Y. B. Zhao, 1 Z. G. Zhao, 31 A. Zhemchugov, 13, * B. Zheng, 1 J. P. Zheng, 1 Y. H. Zheng, 6 Z. P. Zheng, 1 B. Zhong, 15 J. Zhong, L. Zhou, 1 Z. L. Zhou, 1 C. Zhu, 1 K. Zhu, 1 K. J. Zhu, 1 Q. M. Zhu, 1 X. W. Zhu, 1 Y. S. Zhu, 1 Z. A. Zhu, 1 J. Zhuang, 1 B. S. Zou, 1 J. H. Zou, 1 J. X. Zuo, 1 and P. Zweber 3 (BESIII Collaboration 1 Institute of High Energy Physics, Beijing 149, People s Republic of China Bochum Ruhr-University, 4478 Bochum, Germany 3 Carnegie Mellon University, Pittsburgh, Pennsylvania 1513, USA 4 China Center of Advanced Science and Technology, Beijing 119, People s Republic of China 5 G.I. Budker Institute of Nuclear Physics SB RAS (BINP, Novosibirsk 639, Russia 6 Graduate University of Chinese Academy of Sciences, Beijing 149, People s Republic of China 7 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-6491 Darmstadt, Germany 8 Guangxi Normal University, Guilin 5414, People s Republic of China 9 Guangxi University, Naning 534, People s Republic of China 1 Henan Normal University, Xinxiang 4537, People s Republic of China 11 Huazhong Normal University, Wuhan 4379, People s Republic of China 1 Hunan University, Changsha 418, People s Republic of China 13 Joint Institute for Nuclear Research, Dubna, Russia 14 Liaoning University, Shenyang 1136, People s Republic of China 15 Nanjing Normal University, Nanjing 146, People s Republic of China 16 Nanjing University, Nanjing 193, People s Republic of China 17 Nankai University, Tianjin 371, People s Republic of China 18 Peking University, Beijing 1871, People s Republic of China 19 Seoul National University, Seoul, Korea =1=81(5=55( Ó 1 The American Physical Society

3 M. ABLIKIM et al. PHYSICAL REVIEW D 81, 55 (1 Shandong University, Jinan 51, People s Republic of China 1 Shanxi University, Taiyuan 36, People s Republic of China Sichuan University, Chengdu 6164, People s Republic of China 3 Sun Yat-Sen University, Guangzhou 5175, People s Republic of China 4 The Chinese University of Hong Kong, Shatin, Hong Kong 5 The University of Hong Kong, Pokfulam, Hong Kong 6 The University of Tokyo, Tokyo Japan 7 Tsinghua University, Beijing 184, People s Republic of China 8 Universitaet Giessen, 3539 Giessen, Germany 9 University of Hawaii, Honolulu, Hawaii 968, USA 3 University of Minnesota, Minneapolis, Minnesota 55455, USA 31 University of Science and Technology of China, Hefei 36, People s Republic of China 3 University of Turin and INFN, Turin, Italy 33 University of Washington, Seattle, Washington 98195, USA 34 Wuhan University, Wuhan 437, People s Republic of China 35 Zhejiang University, Hangzhou 317, People s Republic of China 36 Zhengzhou University, Zhengzhou 451, People s Republic of China (Received 31 January 1; published 11 March 1 Using a sample of 1:6 1 8 c decays collected by the BESIII detector, c and c decays into and are studied. The branching fraction results are Brð c! Þ¼ð3:3 :3 :3 :14Þ1 3, Brð c! Þ¼ð8:8::6:4Þ1 4, Brð c! Þ ¼ð3:44 :1 :4 :Þ1 3, and Brð c! Þ ¼ð6:5:4:5:3Þ1 4, where the uncertainties are statistical, systematic due to this measurement, and systematic due to the branching fractions of c! cj. The results provide information on the decay mechanism of c states into pseudoscalars. DOI: 1.113/PhysRevD PACS numbers: 13.5.Gv, 14.4.Pq I. INTRODUCTION In the quark model, the cj (J ¼, 1, mesons are L ¼ 1 cc states. Since they cannot be produced directly in e þ e collisions, they are not as well studied as the c states. On the other hand, c! cj decays yield many cj mesons, providing a clean environment for cj investigations. In this paper, we study two-body decays of the c and c into and final states. 1 Knowledge gained from these decays provides information on both the cj parents and their pseudoscalar daughters, as well as a greater understanding of the decay mechanisms of cj mesons [1]. Recently, c and c decays into two-meson final states were studied by the CLEOc collaboration []. In this analysis, we use a sample of 1:6 1 8 c decays collected by the BESIII detector to perform a study of these decays. *Also at the Moscow Institute of Physics and Technology, Moscow, Russia. On leave from the Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine. Also at the PNPI, Gatchina, Russia. x Currently at Suzhou University, Suzhou 156, People s Republic of China. 1 We do not consider c1 decays into these final states, as they are forbidden by spin-parity conservation. II. BESIII AND BEPCII The analysis reported here is based on about 1:6 1 8 c events collected by the Beijing Spectrometer III (BESIII at the Beijing Electron Positron Collider II (BEPCII. BEPCII/BESIII [3] is a major upgrade of the BESII experiment at the BEPC accelerator [4] for studies of hadron spectroscopy and -charm physics [5]. The design peak luminosity of the double-ring e þ e collider, BEPCII, is 1 33 cm s 1 at a beam current of.93 A. The BESIII detector with a geometrical acceptance of 93% of 4 consists of the following main components: (1 A small-celled, helium-based main draft chamber with 43 layers. The average single wire resolution is 135 m, and the momentum resolution for 1 GeV=c charged particles in a 1 T magnetic field is.5%. ( An electromagnetic calorimeter (EMC made of 64 CsI (Tl crystals arranged in a cylindrical shape (barrel plus two end caps. For 1. GeV photons, the energy resolution is.5% in the barrel and 5% in the end caps, and the position resolution is 6 mm in the barrel and 9 mm in the end caps. (3 A time-offlight system for particle identification composed of a barrel part made of two layers with 88 pieces of 5 cm thick,.4 m long plastic scintillators in each layer, and two end caps with 96 fan-shaped, 5 cm thick, plastic scintillators in each end cap. The time resolution is 8 ps in the barrel, and 11 ps in the end caps, corresponding to better than a sigma K=pi separation for momenta below about 1 GeV=c. (4 A muon chamber system made of 1 m 55-

4 BRANCHING FRACTION MEASUREMENTS OF c... PHYSICAL REVIEW D 81, 55 (1 TABLE I. Efficiencies (in % obtained from analysis of Monte Carlo generated events. of resistive plate chambers arranged in 9 layers in the barrel and 8 layers in the end caps and incorporated in the return iron of the superconducting magnet. The position resolution is about cm. The optimization of the event selection and the estimation of physics backgrounds are performed through Monte Carlo simulations. The GEANT4-based simulation software BOOST [6] includes the geometric and material description of the BESIII detectors, the detector response and digitization models, as well as the tracking of the detector running conditions and performance. The production of the c resonance is simulated by the Monte Carlo event generator KKMC [7], while the decays are generated by EVTGEN [8] for known decay modes with branching ratios being set to the PDG [9] world average values, and by LUNDCHARM [1] for the remaining unknown decays. The analysis is performed in the framework of the BESIII Offline Software System (BOSS, [11] which takes care of the detector calibration, event reconstruction, and data storage. III. EVENT SELECTION A photon candidate is defined as a shower in the EMC with an energy deposit exceeding 5 MeV. The and candidates are reconstructed from pairs of photon candidates, using the average event vertex of each run as the assumed origin of the photons. For!, the invariant mass is required to satisfy :75 GeV=c < MðÞ < :175 GeV=c.For!, the invariant mass is required to satisfy :458 GeV=c <MðÞ < :68 GeV=c. The decay angle of a photon is the polar angle measured in the or rest frame with respect to the or direction in the c rest frame. Real and mesons decay isotropically, and their angular distributions are flat. However, the and candidates that originate from a wrong photon combination do not have a flat distribution in this variable. To remove wrong photon combinations, the decay angle is required to satisfy j cos decay j < :95. Candidate events for the final states of interest ( and are selected using the following basic selection criteria. An event must have 5 or 6 photons and no charged tracks. All possible two photon pairings (the radiative photon from the c decay which has E<:4 GeV is excluded in the event are used to form and candidates. The candidate event uses the photon pairings giving the minimum qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi = ¼ P 1 ð =ÞþP ð =Þ; with P 1 and P being the pulls, defined as Pð =Þ ¼½M m =Š= ; where M is the reconstructed invariant mass, m = is the known or mass [9], and is the mass Mode c c 55:6 : 59:8 : 4:3 : 43:9 : resolution, with typical values of 7 MeV=c for the and 1 MeV=c for the. If there is more than one radiative photon candidate (E<:4 GeV, the one that gives the least jm 5 m c j is used. Backgrounds with missing final state particles are suppressed by requiring small transverse momentum squared p t, p t ¼ 4p miss sin ð =Þ; where p miss is the missing momentum opposite to the or system and is the angle between the radiative photon and the direction of the missing momentum p miss. The events are required to satisfy p t < :4 ðgev=cþ, while the events are required to satisfy p t < :1 ðgev=cþ and < 4. To study the efficiency of the c! cj, cj!, and cj! selection, Monte Carlo samples for each cj state into each final state are generated using a (1 þ cos distribution, where is the radiative photon angle relative to the positron beam direction, and ¼ 1 for c and ¼ 1=13 for c, in accordance with expectations for E1 transitions. The decay products of the c are generated using a flat angular distribution, while those of the c are generated according to a double correlation function of the polar angles of the mesons measured in the c rest frame relative to the transition photon direction [8,1]. The efficiencies obtained from the Monte Carlo simulation are shown in Table I. Figures 1 and show comparisons in the c region between data and Monte Carlo simulation for the selection criteria used. The good agreement across the distributions shows that the efficiency estimated from Monte Carlo simulation is reliable. IV. BACKGROUND ANALYSIS The backgrounds in the selected event sample from a number of potential background channels listed in the PDG [9] are studied with Monte Carlo simulations. The main background to cj! originates from c! cj, cj! J=c, J=c!. Using the world average branching fractions [9] for this mode, we estimate that 48 events from this channel are in the signal region. However, the simulation also shows that the background does not peak at the c or the c mass region. The main backgrounds to cj! originate from c! J=c and c! J=c, J=c!. There are about 33 surviving background events in the signal region. 55-3

5 M. ABLIKIM et al. PHYSICAL REVIEW D 81, 55 (1 Entries / (a Entries / (5 MeV/c 6 4 (b N γ M γγ A 1 8 inclusive c Monte Carlo event sample is also used to investigate other possible surviving background events. Figures 3(a and 3(b show the radiative photon energy distribution of the selected cj! and cj! events, respectively, and the normalized backgrounds estimated with the inclusive c Monte Carlo sample. In the cj signal region, there is no peaking background from the inclusive c Monte Carlo sample. Entries / (a Entries / (5 MeV/c (GeV/c /c Entries / ( MeV 6 4 (c Entries /. 1 (d p tγ (GeV /c χ π π FIG. 1 (color online. Comparisons between data and Monte Carlo simulation of c! cj, cj! for selection criteria used. (a Photon multiplicity distribution. (b The invariant mass distribution for candidates. (c The distribution of p t. (d The distribution. Dots with error bars are data in the c region. The histogram is the Monte Carlo simulation for c! c, c! plus the normalized background estimated from inclusive c Monte Carlo samples. 4 (b N γ M γγ (GeV/c 15 /c Entries / ( MeV (c Entries /. 1 5 (d p tγ (GeV /c χ ηη FIG. (color online. Comparisons between data and Monte Carlo simulation for c! cj, cj! for the selection criteria used. (a Photon multiplicity distribution. (b The invariant mass distribution for candidates. (c The distribution of p t. (d The distribution. Dots with error bars are data in the c region. The histogram is the Monte Carlo simulation for c! c, c! plus the normalized background estimated from inclusive c Monte Carlo samples. 55-4

6 BRANCHING FRACTION MEASUREMENTS OF c... PHYSICAL REVIEW D 81, 55 (1 5 3 Entries / (5 MeV (a Entries / (5 MeV (b (GeV E γ (GeV E γ FIG. 3 (color online. Radiative photon energy distributions of (a selected c! events, and (b selected c! events. Dots with error bars are data. The open histogram is the normalized background estimated from the inclusive c Monte Carlo sample and from the continuum. The shaded histogram is the normalized contribution from the continuum. The background in our signal region originating from nonresonant processes is studied using a continuum data sample collected at a center of mass energy of 3.65 GeV. Normalized according to the luminosities, the contribution to cj! is 384 events, as shown in Fig. 3(a, and the contribution to cj! is 48 events, as shown in Fig. 3(b. These backgrounds are small, do not peak in the signal region, and are included as part of the polynomial background below. V. NUMBER OF c EVENTS The number of c events, N c, used in this analysis is determined from the number of inclusive hadronic c decays. Charged tracks are selected requiring their point of closest approach to the beam axis be within 1 cm of the beam line, and their angle with respect to the beam axis,, must satisfy j cosj < :93. Photon candidates must have at least 5 (5 MeVof energy in the barrel (end cap EMC, and have j cosj < :93. Event selection requires at least one charged track. To remove beam associated background and background from Bhabha events, there are special requirements on low charged multiplicity events. For events with one charged track, there must be at least three photons, the acolinearity angle between the two highest energy photons must be greater than 7, and the total energy in the EMC, E EMC, must be greater than. of the center of mass energy, E cm, and less than :85E cm. Events with two or three tracks must have E EMC > :E cm in order to suppress beam associated backgrounds. Backgrounds from Bhabha events are reduced by requiring the presence of at least two photons and E EMC < :85E cm or the largest energy deposit in the calorimeter less than.85 times the beam energy, E beam.in addition, the second highest momentum track must have momentum less than :9E beam, and the acolinearity angle in the x-y plane of the two highest momentum tracks must be greater than 7. The number of hadronic events is determined from the distribution of z, which is the average of the distances, z, from the interaction point along the beam of the point of closest approach of tracks to the beam line. Two methods are used: fitting the distribution with a Gaussian plus a second order polynomial background and counting events in a signal region and subtracting sideband events. Backgrounds from Bhabha, dimuon, and ditau events surviving the selection criteria are very small. The continuum contribution and the surviving backgrounds are removed Entries / 1. 1 (a Entries / (b N trk Total E EMC /E cm FIG. 4 (color online. (a The distribution of the number of charged tracks for events satisfying selection criteria. (b The distribution of the total energy in the EMC divided by the center of mass energy, E EMC =E cm, for events satisfying selection criteria. All requirements are applied to events with one to three charged tracks except the EMC requirements. Dots are data, the light shaded histogram is the sum of normalized continuum and c! hadrons simulated events, and the dark shaded histogram is from continuum data. 55-5

7 M. ABLIKIM et al. PHYSICAL REVIEW D 81, 55 (1 by subtracting the number of events selected with the above criteria from a continuum sample taken at a center of mass energy of 3.65 GeV and normalized by relative luminosity and the 1=s dependence. The efficiency for c! hadrons is determined by simulation [7] and is.8. The agreement between data and Monte Carlo simulation is shown for the distribution of the number of charged tracks in Fig. 4(a and for E EMC in Fig. 4(b. The result is N c ¼ð1:6 :4Þ1 8, where the error is systematic and is determined mostly by the track efficiency difference between data and Monte Carlo (1.%, the variation with the minimum charged track multiplicity requirement (.86%, the difference when a minimum transverse momentum requirement is used (.95%, the uncertainty of the generator model (.61%, and error due to the continuum subtraction (.91%. The statistical error is negligible. A second analysis using a much different selection criteria with a higher efficiency determines an almost identical result. VI. FITTING RESULTS The c! branching fraction is calculated using Br ð c! Þ¼ N obs N c " Brðc! cj ÞBrð! ÞBrð! Þ ; where N obs is the number of events observed, N c is the number of c events, and " is the selection efficiency obtained from Monte Carlo simulation. The radiative photon energy spectrum of cj! candidates, shown in Fig. 5, is fitted using an unbinned maximum likelihood fit in the range from.6 GeV to.36 GeV. The shapes of the c and c are obtained from Monte Carlo simulation and the masses and widths of cj are fixed to their PDG values [9]. A second order Chebyshev polynomial is used to describe the backgrounds, including those found in the inclusive Monte Carlo study and the continuum. The fit gives a c signal yield of events and a c signal yield of events. The selection efficiency from Monte Carlo simulation of c! c ð c! ;! isð55:6 :Þ% and the efficiency of c! c ð c! ;! is ð59:8 :Þ%. The branching fractions are then determined to be Brð c! Þ¼ð3:3 :3Þ1 3 ; Brð c! Þ¼ð8:8:Þ1 4 ; where the errors are statistical only. The fit to the radiative photon energy spectrum of cj! candidates, shown in Fig. 6, gives a c signal yield of 13 6 events and a c signal yield of events. The selection efficiency is 4:3 :% and 43:9 :% for c! and c!, respectively. The branching fractions are Brð c! Þ ¼ð3:44 :1Þ1 3 ; Brð c! Þ ¼ð6:5:4Þ1 4 ; where the errors are statistical only. VII. SYSTEMATIC UNCERTAINTIES The systematic uncertainties on the branching fractions come from many different sources and are summarized in 3 Entries / (5 MeV 1 Entries / (5 MeV E(γ (GeV.1..3 E(γ (GeV FIG. 5 (color online. The radiative photon energy spectrum of selected c! events. Dots with error bars are data. The solid curve is the result of a fit described in the text. The dotted curves are the cj signals. The dashed curve is the background polynomial. FIG. 6 (color online. The radiative photon energy spectrum of selected c! events. Dots with error bars are data. The solid curve is the result of a fit described in the text. The dotted curves are the cj signals. The dashed curve is the background polynomial. 55-6

8 BRANCHING FRACTION MEASUREMENTS OF c... PHYSICAL REVIEW D 81, 55 (1 TABLE II. Systematic uncertainties expressed in percent. Mode c! c! c! c! Photon detection ðþ reconstruction p t Signal shape Background shape Fitting range Trigger N c Total Table II. The uncertainty due to photon detection and photon conversion is 1% per photon. This is determined from studies of photon detection efficiencies in well understood decays such as J=c! and study of photon conversion via e þ e!. The uncertainty due to selection is determined from a high purity control sample of J=c! þ decays. The selection efficiency is obtained from the change in the yield in the þ recoiling mass spectrum with or without the selection requirement. The difference of reconstruction efficiency between data and Monte Carlo simulation gives an uncertainty of 1% per. The uncertainty from the selection is 1% per, which is determined in a similar way from a high purity control sample of J=c! p p. The systematic error from the p t requirement is determined by not using the requirement. The change in the yield gives systematic errors of.9% for c!, 1.% for c!,.1% for c!, and.3% for c!. The uncertainties from the requirement are.6% for c! and.6% for c!, and are determined in a similar way. Since the shapes of the signals in the fit are obtained from Monte Carlo simulation, their uncertainties are estimated by changing the masses and widths of cj by 1 standard deviation from the PDG values [9] and taking into account the uncertainties of the photon energy scale and resolution in the Monte Carlo simulation. They are 1.6% for c!, 1.% for c!, 1.4% for c!, and 1.5% c!. The background uncertainties are evaluated by changing the background fitting function from a second order polynomial to third order, resulting in changes of branching ratios by.5% for c!,.5% for c!,.% for c!, and.3% for c!. The systematic uncertainties due to the fitting of the radiative photon energy spectrum were evaluated by changing the fitting range from (.5,.37 GeV to (.7,.35 GeV. The change in yield for this variation gives systematic uncertainties of.3% for c!,.3% for c!,.8% for c!, and 1.3% for c!. The systematic uncertainties due to the trigger efficiency in these neutral channels are estimated to be <:1%, based on cross-checks using different trigger conditions. The uncertainty on the number of c events is 4%. The total systematic uncertainties, shown in Table. II, are obtained by adding all the above systematic errors in quadrature. The uncertainty due to the c! c branching fractions is kept separate and quoted as a second systematic uncertainty. TABLE III. Branching fraction results (in units of 1 3 for each decay mode. The uncertainties are statistical, systematic due to this measurement, and systematic due to the branching fractions of c! cj. CLEOc results are determined using their own branching fractions for c! cj, while ours are determined using branching fractions from the PDG. If we use the CLEOc branching fractions, we find Brð c! Þ¼3:9 1 3, Brð c! Þ ¼3:51 1 3, Brð c! Þ¼:78 1 3, and Brð c! Þ ¼: Mode c c This work 3:3 :3 :3 :14 :88 : :6 :4 CLEOc [] :94 :7 :3 :15 :68 :3 :7 :4 PDG [9] :43 : :71 :8 This work 3:44 :1 :4 :13 :65 :4 :5 :3 CLEOc [] 3:18 :13 :31 :16 :51 :5 :5 :3 PDG [9] :4 :4 <:5 55-7

9 M. ABLIKIM et al. PHYSICAL REVIEW D 81, 55 (1 VIII. SUMMARY In summary, with a sample of 1:6 1 8 c events in the BESIII detector, improved measurements of the branching fractions of c;! and c;! are performed: Brð c! Þ¼ð3:3 :3 :3 :14Þ1 3, Brð c! Þ¼ð8:8::6 :4Þ1 4, Brð c! Þ ¼ð3:44 :1 :4 :Þ1 3, and Brð c! Þ ¼ð6:5:4:5 :3Þ1 4, where the uncertainties are statistical, systematic due to this measurement, and systematic due to the branching fractions of c! cj. Results are listed in Table III and compared with previous measurements. ACKNOWLEDGMENTS The BESIII collaboration thanks the staff of BEPC and the computing center for their hard efforts. This work is supported in part by the Ministry of Science and Technology of China under Contract No. 9CB85; National Natural Science Foundation of China (NSFC under Contracts No , No , No , No , No ; the Chinese Academy of Sciences (CAS Large-Scale Scientific Facility Program; CAS under Contracts No. KJCX-YW-N9, No. KJCX-YW-N45; 1 Talents Program of CAS; Istituto Nazionale di Fisica Nucleare, Italy; Russian Foundation for Basic Research under Contracts No , No NSFC-a; Siberian Branch of Russian Academy of Science, joint project No. 3 with CAS; the Chinese University of Hong Kong Focused Investment Grant under Contract No ; U.S. Department of Energy under Contracts No. DE-FG-4ER4191, No. DE-FG- 91ER468, No. DE-FG-94ER483; WCU Program of National Research Foundation of Korea under Contract No. R D. Cronin- Hennessy thanks the A.P. Sloan Foundation. This paper is also supported by the NSFC under Contracts No , No [1] Q. Zhao, Phys. Rev. D 7, 741 (5. [] D. M. Asner et al. (CLEO Collaboration, Phys. Rev. D 79, 77 (9. [3] M. Ablikim et al., arxiv: [Nucl. Instrum. Meth. A (to be published]. [4] J. Z. Bai et al. (BES Collaboration, Nucl. Instrum. Methods Phys. Res., Sect. A 344, 319 (1994; 458, 67 (1. [5] Physics at BESIII, edited by K. T. Chao and Y. F. Wang, Int. J. Mod. Phys. A 4, suppl. 1 (9. [6] Z. Y. Deng et al., Chinese Physics C 3, 371 (6. [7] S. Jadach, B. F. L. Ward, and Z. Was, Comput. Phys. Commun. 13, 6 (; Phys. Rev. D 63, 1139 (1. [8] R. G. Ping et al., Chinese Physics C 3, 599 (8. [9] C. Amsler et al. (Particle Data Group, Phys. Lett. B 667,1 (8. [1] J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang, and Y. S. Zhu, Phys. Rev. D 6, 343 (. [11] W. D Li et al., The Offline Software for the BESIII Experiment, Proceeding of CHEP 6. [1] P. K. Kumar and A. J. G. Hey, Phys. Rev. D 13, 3161 (

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