Observation of
cJdecays to
þ
M. Ablikim,1M. N. Achasov,5D. J. Ambrose,39F. F. An,1Q. An,40Z. H. An,1J. Z. Bai,1Y. Ban,27J. Becker,2 J. V. Bennett,17M. Bertani,18aJ. M. Bian,38E. Boger,20,*O. Bondarenko,21I. Boyko,20R. A. Briere,3V. Bytev,20X. Cai,1 O. Cakir,35aA. Calcaterra,18aG. F. Cao,1S. A. Cetin,35bJ. F. Chang,1G. Chelkov,20,*G. Chen,1H. S. Chen,1J. C. Chen,1
M. L. Chen,1S. J. Chen,25Y. B. Chen,1H. P. Cheng,14Y. P. Chu,1D. Cronin-Hennessy,38H. L. Dai,1J. P. Dai,1 D. Dedovich,20Z. Y. Deng,1A. Denig,19I. Denysenko,20,†M. Destefanis,43a,43cW. M. Ding,29Y. Ding,23L. Y. Dong,1
M. Y. Dong,1S. X. Du,46J. Fang,1S. S. Fang,1L. Fava,43b,43cF. Feldbauer,2C. Q. Feng,40R. B. Ferroli,18aC. D. Fu,1 J. L. Fu,25Y. Gao,34C. Geng,40K. Goetzen,7W. X. Gong,1W. Gradl,19M. Greco,43a,43cM. H. Gu,1Y. T. Gu,9Y. H. Guan,6
A. Q. Guo,26L. B. Guo,24Y. P. Guo,26Y. L. Han,1F. A. Harris,37K. L. He,1M. He,1Z. Y. He,26T. Held,2Y. K. Heng,1 Z. L. Hou,1H. M. Hu,1J. F. Hu,6T. Hu,1G. M. Huang,15J. S. Huang,12X. T. Huang,29Y. P. Huang,1T. Hussain,42C. S. Ji,40
Q. Ji,1X. B. Ji,1X. L. Ji,1L. L. Jiang,1X. S. Jiang,1J. B. Jiao,29Z. Jiao,14D. P. Jin,1S. Jin,1F. F. Jing,34 N. Kalantar-Nayestanaki,21M. Kavatsyuk,21W. Kuehn,36W. Lai,1J. S. Lange,36C. H. Li,1Cheng Li,40Cui Li,40 D. M. Li,46F. Li,1G. Li,1H. B. Li,1J. C. Li,1K. Li,10Lei Li,1Q. J. Li,1S. L. Li,1W. D. Li,1W. G. Li,1X. L. Li,29X. N. Li,1 X. Q. Li,26X. R. Li,28Z. B. Li,33H. Liang,40Y. F. Liang,31Y. T. Liang,36G. R. Liao,34X. T. Liao,1B. J. Liu,1C. L. Liu,3
C. X. Liu,1C. Y. Liu,1F. H. Liu,30Fang Liu,1Feng Liu,15H. Liu,1H. B. Liu,6H. H. Liu,13H. M. Liu,1H. W. Liu,1 J. P. Liu,44K. Y. Liu,23Kai Liu,6P. L. Liu,29Q. Liu,6S. B. Liu,40X. Liu,22X. H. Liu,1Y. B. Liu,26Z. A. Liu,1 Zhiqiang Liu,1Zhiqing Liu,1H. Loehner,21G. R. Lu,12H. J. Lu,14J. G. Lu,1Q. W. Lu,30X. R. Lu,6Y. P. Lu,1C. L. Luo,24
M. X. Luo,45T. Luo,37X. L. Luo,1M. Lv,1C. L. Ma,6F. C. Ma,23H. L. Ma,1Q. M. Ma,1S. Ma,1T. Ma,1X. Y. Ma,1 Y. Ma,11F. E. Maas,11M. Maggiora,43a,43cQ. A. Malik,42Y. J. Mao,27Z. P. Mao,1J. G. Messchendorp,21J. Min,1
T. J. Min,1R. E. Mitchell,17X. H. Mo,1C. Morales Morales,11C. Motzko,2N. Yu. Muchnoi,5H. Muramatsu,39 Y. Nefedov,20C. Nicholson,6I. B. Nikolaev,5Z. Ning,1S. L. Olsen,28Q. Ouyang,1S. Pacetti,18bJ. W. Park,28 M. Pelizaeus,37H. P. Peng,40K. Peters,7J. L. Ping,24R. G. Ping,1R. Poling,38E. Prencipe,19M. Qi,25S. Qian,1C. F. Qiao,6
X. S. Qin,1Y. Qin,27Z. H. Qin,1J. F. Qiu,1K. H. Rashid,42G. Rong,1X. D. Ruan,9A. Sarantsev,20,‡B. D. Schaefer,17 J. Schulze,2M. Shao,40C. P. Shen,37,§X. Y. Shen,1H. Y. Sheng,1M. R. Shepherd,17X. Y. Song,1S. Spataro,43a,43c B. Spruck,36D. H. Sun,1G. X. Sun,1J. F. Sun,12S. S. Sun,1Y. J. Sun,40Y. Z. Sun,1Z. J. Sun,1Z. T. Sun,40C. J. Tang,31
X. Tang,1I. Tapan,35cE. H. Thorndike,39D. Toth,38M. Ullrich,36G. S. Varner,37B. Wang,9B. Q. Wang,27K. Wang,1 L. L. Wang,4L. S. Wang,1M. Wang,29P. Wang,1P. L. Wang,1Q. Wang,1Q. J. Wang,1S. G. Wang,27X. L. Wang,40 Y. D. Wang,40Y. F. Wang,1Y. Q. Wang,29Z. Wang,1Z. G. Wang,1Z. Y. Wang,1D. H. Wei,8P. Weidenkaff,19Q. G. Wen,40
S. P. Wen,1M. Werner,36U. Wiedner,2L. H. Wu,1N. Wu,1S. X. Wu,40W. Wu,26Z. Wu,1L. G. Xia,34Z. J. Xiao,24 Y. G. Xie,1Q. L. Xiu,1G. F. Xu,1G. M. Xu,27H. Xu,1Q. J. Xu,10X. P. Xu,32Z. R. Xu,40F. Xue,15Z. Xue,1L. Yan,40 W. B. Yan,40Y. H. Yan,16H. X. Yang,1Y. Yang,15Y. X. Yang,8H. Ye,1M. Ye,1M. H. Ye,4B. X. Yu,1C. X. Yu,26J. S. Yu,22
S. P. Yu,29C. Z. Yuan,1Y. Yuan,1A. A. Zafar,42A. Zallo,18aY. Zeng,16B. X. Zhang,1B. Y. Zhang,1C. C. Zhang,1 D. H. Zhang,1H. H. Zhang,33H. Y. Zhang,1J. Q. Zhang,1J. W. Zhang,1J. Y. Zhang,1J. Z. Zhang,1S. H. Zhang,1 X. J. Zhang,1X. Y. Zhang,29Y. Zhang,1Y. H. Zhang,1Y. S. Zhang,9Z. P. Zhang,40Z. Y. Zhang,44G. Zhao,1H. S. Zhao,1
J. W. Zhao,1K. X. Zhao,24Lei Zhao,40Ling Zhao,1M. G. Zhao,26Q. Zhao,1S. J. Zhao,46T. C. Zhao,1X. H. Zhao,25 Y. B. Zhao,1Z. G. Zhao,40A. Zhemchugov,20,*B. Zheng,41J. P. Zheng,1Y. H. Zheng,6B. Zhong,1J. Zhong,2L. Zhou,1
X. K. Zhou,6X. R. Zhou,40C. Zhu,1K. Zhu,1K. J. Zhu,1S. H. Zhu,1X. L. Zhu,34X. W. Zhu,1Y. C. Zhu,40 Y. M. Zhu,26Y. S. Zhu,1Z. A. Zhu,1J. Zhuang,1B. S. Zou,1and J. H. Zou1
(BESIII Collaboration)
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2Bochum Ruhr-University, 44780 Bochum, Germany
3Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
4China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China 5G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia 6
Graduate University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 7GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
8Guangxi Normal University, Guilin 541004, People’s Republic of China 9GuangXi University, Nanning 530004, People’s Republic of China 10Hangzhou Normal University, Hangzhou 310036, People’s Republic of China
12Henan Normal University, Xinxiang 453007, People’s Republic of China
13Henan University of Science and Technology, Luoyang 471003, People’s Republic of China 14Huangshan College, Huangshan 245000, People’s Republic of China
15Huazhong Normal University, Wuhan 430079, People’s Republic of China 16Hunan University, Changsha 410082, People’s Republic of China
17Indiana University, Bloomington, Indiana 47405, USA 18aINFN Laboratori Nazionali di Frascati, Frascati, Italy 18bINFN and University of Perugia, I-06100, Perugia, Italy 19
Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, 55099 Mainz, Germany 20Joint Institute for Nuclear Research, 141980 Dubna, Russia
21KVI/University of Groningen, 9747 AA Groningen, The Netherlands 22Lanzhou University, Lanzhou 730000, People’s Republic of China 23Liaoning University, Shenyang 110036, People’s Republic of China 24Nanjing Normal University, Nanjing 210046, People’s Republic of China
25Nanjing University, Nanjing 210093, People’s Republic of China 26Nankai University, Tianjin 300071, People’s Republic of China 27Peking University, Beijing 100871, People’s Republic of China
28Seoul National University, Seoul, 151-747 Korea 29Shandong University, Jinan 250100, People’s Republic of China
30Shanxi University, Taiyuan 030006, People’s Republic of China 31Sichuan University, Chengdu 610064, People’s Republic of China
32Soochow University, Suzhou 215006, People’s Republic of China 33Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
34Tsinghua University, Beijing 100084, People’s Republic of China 35a
Ankara University, Ankara, Turkey 35bDogus University, Istanbul, Turkey 35cUludag University, Bursa, Turkey 36Universitaet Giessen, 35392 Giessen, Germany 37University of Hawaii, Honolulu, Hawaii 96822, USA 38University of Minnesota, Minneapolis, Minnesota 55455, USA
39University of Rochester, Rochester, New York 14627, USA
40University of Science and Technology of China, Hefei 230026, People’s Republic of China 41University of South China, Hengyang 421001, People’s Republic of China
42University of the Punjab, Lahore-54590, Pakistan 43aUniversity of Turin, Turin, Italy
43bUniversity of Eastern Piedmont, Alessandria, Italy 43cINFN, Turin, Italy
44Wuhan University, Wuhan 430072, People’s Republic of China 45Zhejiang University, Hangzhou 310027, People’s Republic of China 46Zhengzhou University, Zhengzhou 450001, People’s Republic of China
(Received 25 July 2012; published 13 September 2012)
Decays of thecJstates (J ¼ 0, 1, 2) to þ, including processes with intermediateð1385Þ, are studied through the E1 transition c0! cJ using 106 106 c0 events collected with the BESIII detector at BEPCII. This is the first observation ofcJdecays to the final state þ. The branching ratio of the intermediate processcJ! ð1385Þð1385Þis also measured for the first time, and the results agree with the theoretical predictions based on the color-octet effect.
DOI:10.1103/PhysRevD.86.052004 PACS numbers: 13.25.Gv, 13.30.Eg, 14.20.Pt
I. INTRODUCTION
Decays of P-wave charmonium states, e.g., the cJ, cannot be well explained by the color-singlet contribution alone, although this works well in explaining the decays of S-wave charmonium, e.g., the J=c andc0. In calculations of the color-octet contribution, Ref. [1] predicted branch-ing ratios of cJ! baryon þ anti-baryon in which the cJ! p p result is consistent with experimental observa-tion, while thecJ ! [2] result is not. The calculated *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 §Now at Nagoya University, Nagoya, Japan
branching ratios are Bðc1! Þ ¼ ð3:91 0:24Þ 105 and Bð
c2! Þ ¼ ð3:49 0:20Þ 105, while the experimental results are ð11:8 1:9Þ 105 and ð18:6 2:7Þ 105, respectively. In addition to , Ref. [1] also calculated the branching ratios of c1! ð1385Þ ð1385Þ and c2! ð1385Þ ð1385Þ to be ð2:15 0:12Þ 105 and ð3:61 0:20Þ 105, respec-tively, but there are no previous experimental results on these decay channels. Therefore, it is meaningful to test these predictions experimentally. In addition, due to the helicity selection rule, the decay of c0 into baryon-antibaryon is expected to be suppressed [3].
In this paper, we report measurements of cJ ! þ (J ¼ 0, 1, 2) (including the intermediate ð1385Þ resonance), cJ! ð1385Þþ c:c:, and cJ! ð1385Þð1385Þ through the E1 transition c0!
cJ, where ð1385Þ! and ! p. This work is based on a106 106 c0 event sample col-lected with the BESIII detector at the Beijing Electron-Positron Collider II (BEPCII) [4]. Continuum data taken at the center of mass energy pffiffiffis¼ 3:65 GeV, with an inte-grated luminosity of 42:9 pb1, is used to study non-c0 decay background.
II. THE BESIII DETECTOR
BEPCII [5] is a double-ring, multibuncheþecollider with collision energies ranging from 2.0 GeV to 4.6 GeV. The BESIII detector [5] is a general-purpose spectrometer with 93% coverage of full solid angle. From the interaction point outwards, BESIII is composed of the following: a main drift chamber consisting of 43 layers of drift cells with a space resolution of about135 m and momentum resolution of about 0.5% at 1 GeV=c; a time-of-flight counter, which is comprised of two layers of scintillator with time resolution of 80 ps in the barrel part and one layer with time resolution of 110 ps in the end-cap part; an electromagnetic calorimeter (EMC), which is comprised of 6240 CsI(Tl) crystals, with energy resolution of 2.5% in the barrel and 5.0% in the end-cap for a 1 GeV photon, and position resolution of 6 mm in the barrel and 9 mm in the end-cap; a superconducting solenoid magnet, which can provide a 1 T magnetic field parallel to the beam direction; and a muon counter, which is made of1000 m2 resistive-plate-chambers sandwiched in iron absorbers.
III. MONTE-CARLO SIMULATION
For evaluation of the detection efficiency and under-standing backgrounds, a Monte-Carlo (MC) simulation framework for BESIII was developed. A GEANT4-based MC simulation program, BOOST, is designed to simulate the interaction of particles in the spectrometer and the responses of the detector. For the generation of charmo-nium states, e.g., c0, an event generator, KKMC [6,7], is employed, which handles the initial state radiative
correction and the beam energy spread. For simulation of the resonant decay, BesEvtGen, based on EvtGen [8,9], is used to realize well-measured processes, while LundCharm [8] is used for the unknown possible processes.
In the MC simulations for the processes presented here, c0! cJ is assumed to be a pureE1 transition, and the polar angle, , follows a distribution of the form 1 þ cos2 with ¼ 1, 1=3, and 1=13 for J ¼ 0, 1 and 2, respectively [10]. Momenta in the decay of cJ! ð1385Þð1385Þ, cJ! ð1385Þðc:c:Þ and cJ! þ are uniformly distributed in phase space. For the decay modecJ! ð1385Þð1385Þ, an extreme angular distribution is used to test the phase space assumption and no significant differences in efficiencies are observed. This is because, with the current level of statistics, the detection efficiencies of the final states are determined mainly by the detection of theE1 photons, and the angular distributions of the hadrons in the subsequent decays are not dependent on their MC decay models.
IV. EVENT SELECTION
The candidate events for the decay modes c0! cJ! þ, with ! p, were chosen with the following selection criteria:
(1) Charged tracks, i.e., candidates for , p and p, must satisfy j cosj 0:93, where is the polar angle with respect to the beam direction. Particle identification is not used.
(2) The charged tracks not assigned to anyð Þ decay candidates must have their point of closest approach to the interaction point within 10 cm along the beam direction and 1 cm in the perpendicular plane. (3) A common vertex constraint is applied to each pair
of charged tracks assumed to decay from= i.e., p and pþ, and the production points of= candidates are constrained to the interaction point. (4) A photon candidate is a shower cluster in the EMC
that is not associated with any charged track and has a minimum energy deposit of 25 MeV in the barrel or 50 MeV in the end-cap.
(5) The total momentum of all final particle candidates is constrained to the initial four-momentum of the eþe system in a kinematic fit. The events with 2
4C< 80 are retained; for an event with more than one photon candidate, only the one with the smallest 2
4Cis kept.
(6) Backgrounds from the decay c0 ! þJ=c followed byJ=c ! are rejected by requiring the þ recoil mass be greater than 3:108 GeV=c2 or less than 3:088 GeV=c2. The background from c0! ð1385Þ ð1385Þ, followed by ð1385Þ ! 0 and 0 ! , is rejected by discarding events with ( ) mass in the range ½1:183; 1:202 GeV=c2.
V. SIGNAL ESTIMATION
The invariant mass distributions ofMpandMpþare shown in Figs.1(a)and1(b), where the signals of and are clean. Figure 1(c) shows a scatter plot (Mp versus Mpþ). Events whereMp andMpþ fall within the box in Fig. 1(c) are used for further analysis. The invariant mass distribution of þ, M þ is shown in Fig.1(d), and the threecJ peaks are clearly observed.
The invariant masses of þ and ( and þ) are displayed in Figs. 2(a), 2(c), 2(b), and 2(d), respectively.ð1385Þ peaks are clearly seen. peak is also seen in Figs.2(c) and2(d), around its nominal mass 1:322 GeV=c2 [2]. The is a relatively long-lived parti-cle, and the selection criteria in this analysis are not optimized for a study of the . Hence, this work does not include study of processes involving. Events around thepeaks are rejected by requiringMð þÞbe less than1:331 GeV=c2 or greater than1:312 GeV=c2.
We divide the remainingcJdecays into five processes: (1) þ (nonresonant); (2) ð1385Þþþ c:c:; (3) ð1385Þþþ c:c:; (4) ð1385Þþð1385Þ; and (5) ð1385Þð1385Þþ. To study the five processes, re-quirements on Mð þÞ are implemented as shown in Fig.2. The areas between1:32 GeV=c2 and1:46 GeV=c2 (two solid arrows) are defined asð1385Þ signal regions, while the areas smaller than1:30 GeV=c2 or larger than
1:50 GeV=c2 (two dashed arrows) are defined as non-ð1385Þ regions.
Because of the broad width and the long tails of the ð1385Þ, the ð1385Þ and non-ð1385Þ events feed into the non-ð1385Þ and ð1385Þ regions. As a result, the cJ events that decay into the above five processes cannot be completely separated using invariant mass regions alone. In this study, we separate the data into five independent categories, with data set labels set-j (j ¼ 1; ; 5) defined as follows:
(i) Data set-1: the category to detect the nonresonant process 1. That is, events withMþ, M,M andMþ all in non-ð1385Þ regions. The invariant mass spectrum of þis displayed in Fig.3(a); (ii) Data set-2: the category to detect the single resonant ð1385Þþð ð1385ÞÞ process 2. That is, events with Mþ=Min theð1385Þ signal region and with M(Mþ), M, Mþ in non-ð1385Þ re-gions are required. The two types of events in this category are combined and displayed in Fig.3(b); (iii) Data set-3: the category to detect the single
reso-nant ð1385Þð ð1385ÞþÞ process 3. Similarly, events with M=Mþ in ð1385Þ signal region and with MþðMÞ, Mþ, M in non-ð1385Þ regions are required. The two types of events in this category are combined and dis-played in Fig.3(c); ) 2 (GeV/c -π p M ) 2 Events/(0.30 MeV/c 0 100 200 300 400 500 600 ) 2 (GeV/c + π p M ) 2 Events/(0.30 MeV/c 0 100 200 300 400 500 600 ) 2 (GeV/c -π p M ) 2 (GeV/c+π p M 1.105 1.11 1.115 1.12 1.125 1.13 ) 2 (GeV/c -π + π ΛΛ M 1.105 1.11 1.115 1.12 1.125 1.13 1.105 1.11 1.115 1.12 1.125 1.13 1.10 5 1.11 1.115 1.1 2 1.12 5 1.13 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 ) 2 Events/(5.00 MeV/c 0 20 40 60 80 100 120
FIG. 1. (a) The invariant mass distributionMpforp. (b) The invariant mass distributionM pþfor pþ. (c) The scatter plot ofMpversusM pþ; the box indicates the signal region used in this analysis. (d) The invariant mass distribution M þfor
(iv) Data set-4: the category to detect process 4. Events with Mþ, M in ð1385Þ signal region and M, Mþ in non-ð1385Þ region are selected and displayed in Fig.3(d);
(v) Data set-5: the category to detect process 5. Events withM,Mþ inð1385Þ signal region and withMþ, M in non-ð1385Þ region are selected and displayed in Fig.3(e).
The yield in each data set is estimated by a fit to thecJ peaks, and the yields of each process in the full phase space will be disentangled with Eq. (1), as described in Sec.V B. The cJ signal events are clearly observed in each category, as shown in Figs. 3(a)–3(e). In the fits of the cJ in each data set category, a Breit-Wigner function convolved with a Gaussian resolution function is used to describe cJ peaks, while a first-order polynomial line is used to model the background distribution. ThecJ invari-ant mass parameters are allowed to float, while the cJ widths are fixed to the PDG values [2]. The Gaussian parameters are obtained from MC simulation of detector responses. A simultaneous unbinned maximum likelihood method is applied, and the fit results are listed in TableI.
A. Background study
A106 106 inclusive c0-decay MC sample is used to investigate possible c0 decay backgrounds. No peaking backgrounds are observed, as shown in Fig.1(d). Since a
large proportion of the cJ decays are poorly known and their simulations based on the BESIII LundCharm model have large uncertainty, we investigate possible underesti-mated peaking backgrounds beneath the cJ peaks. One major source could be from cJ ! Kþp ! p pþK0
s ! p p2þ2ðc:c:Þ; however, the þ and invariant mass distributions of candidate events were examined, and no evidence of a Ks peak was found. Therefore, negligible peaking background is assumed in this study. A study of the continuum data did not reveal any non-c0 decay backgrounds.
B. Calculation of branching ratios
To calculate the branching ratios of each mode incJ! þ decay, one has to compute the efficiency-corrected number of cJ decays. The numbers of cJ events in data set-j, which is selected to detect process i, also consists of events from the other processes. We de-scribe the number of events of processi in data set-j as
"11 "12 "13 "14 "15 "21 "22 "23 "24 "25 "31 "32 "33 "34 "35 "41 "42 "43 "44 "45 "51 "52 "53 "54 "55 0 B B B B B B B B @ 1 C C C C C C C C A N1 N2 N3 N4 N5 0 B B B B B B B B @ 1 C C C C C C C C A ¼ n1 n2 n3 n4 n5 0 B B B B B B B B @ 1 C C C C C C C C A ; (1) ) 2 (GeV/c + π Λ M ) 2 Events/(20.00 MeV/c 0 20 40 60 80 100 120 ) 2 (GeV/c -Λπ M ) 2 Events/(20.00 MeV/c 0 20 40 60 80 100 ) 2 (GeV/c -π Λ M ) 2 Events/(20.00 MeV/c 0 20 40 60 80 100 ) 2 (GeV/c + Λπ M 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 ) 2 Events/(20.00 MeV/c 0 20 40 60 80 100 120
FIG. 2. The invariant mass distributions of (a)þ, (b) , (c)and (d) þ. The areas between the two solid arrows are taken as theð1385Þ signal regions, while the areas outside the two dashed arrows are non-ð1385Þ regions. The peaks of in (c) and (d) will be rejected with the requirementMð þÞ> 1:331 GeV=c2 orMð þÞ< 1:312 GeV=c2.
where Ni is the efficiency-corrected number of events of processi, njare the numbers ofcJevents in the data set-j (as listed in Table I), and "ji denotes the efficiency of process i being selected in data set-j, obtained with MC
simulation. In practice, thecJsignals are fitted in the five data sets simultaneously, and with the constraint of the three efficiency matrices, N1–N5 are obtained by the fit. Equations (2)–(4) are used to calculate branching ratios (B) of the signal processes, and the results are listed in TableII. The significance of each decay mode, which is estimated using Eq. (5), is listed in TableII. HereLmis the likelihood of the simultaneous fit, while LmðNj¼0Þ is the likelihood of the fit with the assumption that Nj is equal to zero. BðcJ! þðnon-resonantÞÞ ¼ N1 Nc0Bðc0! cJÞBð ! pÞ2 (2) ) 2 (GeV/c (1385)) Σ (w/o -π + Λπ Λ M ) 2 Events / ( 0.005 GeV/c 0 2 4 6 8 10 12 14 16 18 20 ) 2 (GeV/c +c.c. -Λπ + (1385) Σ M ) 2 Events / ( 0.005 GeV/c 0 5 10 15 20 25 ) 2 (GeV/c +c.c. + Λπ -(1385) Σ M ) 2 Events / ( 0.005 GeV/c 0 2 4 6 8 10 12 14 16 18 20 22 ) 2 (GeV/c -(1385) Σ + (1385) Σ M ) 2 Events / ( 0.005 GeV/c 0 2 4 6 8 10 12 ) 2 (GeV/c + (1385) Σ -(1385) Σ M ) 2 Events / ( 0.005 GeV/c 0 2 4 6 8 10 12 ) 2 (GeV/c (total) -π + Λπ Λ M 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 ) 2 Events / ( 0.005 GeV/c 0 20 40 60 80 100 120 140
FIG. 3. The invariant mass distributions of þ in the following data samples: (a) data set-1, (b) data set-2, (c) data set-3, (d) data set-4, (e) data set-5 and (f) total data set. The selections of data set-j (j ¼ 1; 5) are defined in Sec.V. Points with error bars are data. The solid curves show the sum of the fitted curves, while the dashed lines are the backgrounds.
TABLE I. The number of fittedcJ events in each data set-j (j ¼ 1; ; 5) and the total data set. nj is the number of fitted cJ events in data set-j. ntotis that in the total data sample.
Number of events c0 c1 c2 n1 10:8 3:8 12:7 3:9 36:4 6:4 n2 36:4 6:7 14:7 4:1 47:6 7:2 n3 30:9 6:6 12:5 4:1 54:4 7:9 n4 27:4 5:9 7:6 3:2 14:6 4:0 n5 32:8 6:3 3:6 2:2 8:7 3:3 ntot 426 23 105 11 371 20
BðcJ! ð1385ÞþðÞðþÞþc:c:Þ ¼ N2ð3Þ Nc0Bðc0! cJÞBðð1385Þ ! Þ 1:0 Bð ! pÞ2 (3) BðcJ! ð1385ÞþðÞð1385ÞðþÞÞ ¼ N4ð5Þ Nc0Bðc0! cJÞBðð1385Þ ! Þ2 1:0 Bð ! pÞ2 (4) Sj¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðlnLm lnLmðNj¼0ÞÞ q (5) As shown in Fig.4, the sum of measured components in the decays of cJ into the final states þ in MC simulation agrees well with the data. This supports the credibility of the decomposition into the different compo-nents described above.
C.cJ! þ(total)
Based on the selection criteria in Sec. IV, the process cJ! þ (total), including the intermediate-resonant processes, is studied. The þ invariant mass distributions and the fit are displayed in Fig. 3(f ), while the fit results are listed in TableI. According to the measured branching ratios of the intermediate resonances in this analysis, signal MC samples are generated. This
makes the momentum distributions of the final particles in the MC sample similar to those in experimental data and allows the determination of the overall detection efficiency, "tot, of the sum of all the processes with the same final states c0! cJ! þ. The branching ratio of cJ! þ(total) is calculated with the formula
BðcJ! þðtotalÞÞ
¼ ntot
"tot Nc0Bðc0! cJÞBð ! pÞ2: (6) VI. SYSTEMATIC UNCERTAINTY
The systematic uncertainties in this analysis are summa-rized in Table III. Sources of systematic uncertainty in-clude= reconstruction, tracking, photon detection, four-momentum constraint kinematic fitting, background rejection, cJ signal fitting, and the number of c0 events and branching ratios cited from the PDG [2]. Charged tracking and photon detection systematic errors are studied following the methods in Refs. [4,5].
For the systematic uncertainty due to= reconstruc-tion, J=c ! þ and c0! þJ=c ! þ are used to select a = control sample. = reconstruction efficiency is calculated by taking the ratio of the fitted= yields in the missing mass spectrum before and after = is found. = reconstruction effi-ciencies consist of tracking efficiency of the daughter TABLE II. Results of the branching ratios ( 105) for different decay modes. ‘‘UL’’ stands for the upper limit of the branching ratio at the 90% C.L. ‘‘S’’ stands for the statistical significance. The first errors are statistical and the second systematic.
cJ decay mode c0 c1 c2 B UL S B UL S B UL S þðw=oð1385ÞÞ 28:6 12:6 2:7 <54 2.2 26:2 5:5 3:3 4.8 71:8 14:5 8:2 6.4 ð1385Þþþ c:c: 34:8 13:2 3:4 <55 2.2 <14 0.3 23:6 11:8 2:7 <42 1.7 ð1385Þþþ c:c: 24:6 12:7 2:4 <50 1.6 <14 0.0 37:8 11:8 4:4 <61 2.6 ð1385Þþð1385Þ 16:4 5:7 1:6 3.1 4:4 2:5 0:6 <10 1.9 7:9 4:0 0:9 <17 2.0 ð1385Þð1385Þþ 23:5 6:2 2:3 4.3 <5:7 0.9 <8:5 0.0 þ (total) 119:0 6:4 11:4 >10 31:1 3:4 3:9 >10 137:0 7:6 15:7 >10 ) 2 (GeV/c -Λπ / + Λπ M ) 2 Events/( 20.00 MeV/c 200 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 ) 2 (GeV/c + Λπ / -Λπ M ) 2 Events/( 20.00 MeV/c ) 2 (GeV/c -π + Λπ Λ M 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 ) 2 Events/( 5.00) (MeV/c 0 20 40 60 80 100 120
FIG. 4. The invariant mass distributions of (a)þ= , (b)= þ, and (c) þ. Points with error bars are the data with subtraction of the backgrounds, while solid lines are the MC simulation of the signals. The backgrounds subtracted are estimated from inclusive MC. The signal components are scaled based on their branching ratios measured in this work. The data within 1:312 GeV=c2< M
ð þÞ< 1:331 GeV=c2are removed to reject thecandidates.
particles and the vertex-constraint of= . The differences in the efficiencies between experimental data and the MC sample are included in the systematic uncertainties.
To study the efficiency of the kinematic fitting in the four-momentum constraint, event candidates for the three processes c0! þ, c0! cJ! 3ðþÞ andc0! J=cþ! 3ðþÞ0 ! 3ðþÞ2 are used as control samples. The ratio of the event rates before and after the kinematic fitting is taken as the efficiency of the kinematic fitting. These efficiencies are calculated both in experimental data and in the MC sample, and their difference determines the uncertainty of the kinematic fitting.
For the rejection of the resonancesJ=c,0= 0and, differentJ=c,0, 0 and mass region requirements are applied ranging from3, 3:5 to 4, where is the detector resolution. The largest deviation on the branching ratios is taken as the systematic uncertainty. The systematic uncertainty of the fitting method is obtained by changing the fitting range, the shape of the backgrounds, and chang-ing the detector resolution from the value obtained with MC simulation to that obtained by fitting with a free parameter. The relative uncertainty of the estimated num-ber of c0 is 4.0% [4]. The uncertainty of the branching ratios of intermediate decays are taken from the PDG [2].
The total systematic uncertainty is obtained by summing all the individual uncertainties in quadrature.
VII. RESULTS AND DISCUSSION
The branching ratios of cJ decays to ð1385Þ ð1385Þ, ð1385Þþ c:c: and þ (with or without the ð1385Þ resonance) are measured with 106 106c0decay events collected at BESIII. The results are listed in Table II. The process cJ ! þ is observed for the first time. Evidence of c0! ð1385Þð1385Þ, which strongly violates the helicity selection rule, is presented. The branching ratios of c1;2! ð1385Þð1385Þ are consistent with the theo-retical predictions [1].
ACKNOWLEDGMENTS
The BESIII collaboration thanks the staff of BEPCII and the computing center for their hard work. This work is supported in part by the Ministry of Science and Technology of China under Contract No. 2009CB825200; National Natural Science Foundation of China (NSFC) under Contracts Nos. 10625524, 10821063, 10825524, 10835001, 10935007, 10905091, 11079030, and 11125525; Joint Funds of the National Natural Science Foundation of China under Contracts Nos. 11079008 and 11179007; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts Nos. KJCX2-YW-N29 and KJCX2-YW-N45; 100 Talents Program of CAS; Research Fund for the Doctoral Program of Higher Education of China under Contract No. 20093402120022; Istituto Nazionale di Fisica Nucleare, Italy; the U.S. Department of Energy under Contracts Nos. 04ER41291, DE-FG02-91ER40682, and DE-FG02-94ER40823; the U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; and the WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
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TABLE III. Sources of systematic uncertainties.
Sources Relative systematic uncertainty (%)
c0 c1 c2
reconstruction 3.5 3.5 3.5
tracking (not from ) 2.0 2.0 2.0
Photon detection 1.0 1.0 1.0 Kinematic fitting 1.0 1.0 1.0 Vetoing background 4.9 2.6 4.4 Fitting method 4.9 10.1 7.9 Number ofc0 4.0 4.0 4.0 Bðc0! cJÞ 3.2 4.3 4.0 Bðð1385Þ! Þ 1.7 1.7 1.7 Bð ð1385Þ! Þ 1.7 1.7 1.7 total 9.6 12.7 11.4
