Observation of
c1Decays into Vector Meson Pairs , !!, and !
M. Ablikim,1M. N. Achasov,5L. An,9Q. An,39Z. H. An,1J. Z. Bai,1R. Baldini,20Y. Ban,26J. Becker,2N. Berger,1 M. Bertani,20J. M. Bian,1O. Bondarenko,19I. Boyko,15R. A. Briere,3V. Bytev,15X. Cai,1G. F. Cao,1X. X. Cao,1
J. F. Chang,1G. Chelkov,16G. Chen,1H. S. Chen,1J. C. Chen,1M. L. Chen,1S. J. Chen,24Y. Chen,1Y. B. Chen,1 H. P. Cheng,11Y. P. Chu,1D. Cronin-Hennessy,38H. L. Dai,1J. P. Dai,1D. Dedovich,15Z. Y. Deng,1I. Denysenko,17
M. Destefanis,41Y. Ding,22L. Y. Dong,1M. Y. Dong,1S. X. Du,45M. Y. Duan,29R. R. Fan,1J. Fang,1S. S. Fang,1 C. Q. Feng,39C. D. Fu,1J. L. Fu,24Y. Gao,35C. Geng,39K. Goetzen,7W. X. Gong,1M. Greco,41S. Grishin,15M. H. Gu,1
Y. T. Gu,9Y. H. Guan,6A. Q. Guo,25L. B. Guo,23Y. P. Guo,25X. Q. Hao,1F. A. Harris,37K. L. He,1M. He,1Z. Y. He,25 Y. K. Heng,1Z. L. Hou,1H. M. Hu,1J. F. Hu,6T. Hu,1B. Huang,1G. M. Huang,12J. S. Huang,10X. T. Huang,28 Y. P. Huang,1T. Hussain,40C. S. Ji,39Q. Ji,1X. B. Ji,1X. L. Ji,1L. K. Jia,1L. L. Jiang,1X. S. Jiang,1J. B. Jiao,28Z. Jiao,11 D. P. Jin,1S. Jin,1F. F. Jing,35M. Kavatsyuk,19S. Komamiya,34W. Kuehn,36J. S. Lange,36J. K. C. Leung,33Cheng Li,39 Cui Li,39D. M. Li,45F. Li,1G. Li,1H. B. Li,1J. C. Li,1Lei Li,1N. B. Li,23Q. J. Li,1W. D. Li,1W. G. Li,1X. L. Li,28 X. N. Li,1X. Q. Li,25X. R. Li,1Z. B. Li,31H. Liang,39Y. F. Liang,30Y. T. Liang,36G. R. Liao,8X. T. Liao,1B. J. Liu,33 B. J. Liu,32C. L. Liu,3C. X. Liu,1C. Y. Liu,1F. H. Liu,29Fang Liu,1Feng Liu,12G. C. Liu,1H. Liu,1H. B. Liu,6H. M. Liu,1 H. W. Liu,1J. P. Liu,43K. Liu,26K. Y. Liu,22Q. Liu,37S. B. Liu,39X. Liu,21X. H. Liu,1Y. B. Liu,25Y. W. Liu,39Yong Liu,1
Z. A. Liu,1Z. Q. Liu,1H. Loehner,19G. R. Lu,10H. J. Lu,11J. G. Lu,1Q. W. Lu,29X. R. Lu,6Y. P. Lu,1C. L. Luo,23 M. X. Luo,44T. Luo,1X. L. Luo,1C. L. Ma,6F. C. Ma,22H. L. Ma,1Q. M. Ma,1T. Ma,1X. Ma,1X. Y. Ma,1M. Maggiora,41
Q. A. Malik,40H. Mao,1Y. J. Mao,26Z. P. Mao,1J. G. Messchendorp,19J. Min,1R. E. Mitchell,14X. H. Mo,1 N. Yu. Muchnoi,5Y. Nefedov,15Z. Ning,1S. L. Olsen,27Q. Ouyang,1S. Pacetti,20M. Pelizaeus,37K. Peters,7J. L. Ping,23
R. G. Ping,1R. Poling,38C. S. J. Pun,33M. Qi,24S. Qian,1C. F. Qiao,6X. S. Qin,1J. F. Qiu,1K. H. Rashid,40G. Rong,1 X. D. Ruan,9A. Sarantsev,18J. Schulze,2M. Shao,39C. P. Shen,37X. Y. Shen,1H. Y. Sheng,1M. R. Shepherd,14 X. Y. Song,1S. Sonoda,34S. Spataro,41B. Spruck,36D. H. Sun,1G. X. Sun,1J. F. Sun,10S. S. Sun,1X. D. Sun,1Y. J. Sun,39
Y. Z. Sun,1Z. J. Sun,1Z. T. Sun,39C. J. Tang,30X. Tang,1X. F. Tang,8H. L. Tian,1D. Toth,38G. S. Varner,37X. Wan,1 B. Q. Wang,26K. Wang,1L. L. Wang,4L. S. Wang,1M. Wang,28P. Wang,1P. L. Wang,1Q. Wang,1S. G. Wang,26 X. L. Wang,39Y. D. Wang,39Y. F. Wang,1Y. Q. Wang,28Z. Wang,1Z. G. Wang,1Z. Y. Wang,1D. H. Wei,8Q. G. Wen,39 S. P. Wen,1U. Wiedner,2L. H. Wu,1N. Wu,1W. Wu,22Z. Wu,1Z. J. Xiao,23Y. G. Xie,1G. F. Xu,1G. M. Xu,26H. Xu,1 Y. Xu,25Z. R. Xu,39Z. Z. Xu,39Z. Xue,1L. Yan,39W. B. Yan,39Y. H. Yan,13H. X. Yang,1M. Yang,1T. Yang,9Y. Yang,12
Y. X. Yang,8M. Ye,1M. H. Ye,4B. X. Yu,1C. X. Yu,25L. Yu,12C. Z. Yuan,1W. L. Yuan,23Y. Yuan,1A. A. Zafar,40 A. Zallo,20Y. Zeng,13B. X. Zhang,1B. Y. Zhang,1C. C. Zhang,1D. H. Zhang,1H. H. Zhang,31H. Y. Zhang,1J. Zhang,23 J. W. Zhang,1J. Y. Zhang,1J. Z. Zhang,1L. Zhang,24S. H. Zhang,1T. R. Zhang,23X. J. Zhang,1X. Y. Zhang,28Y. Zhang,1 Y. H. Zhang,1Z. P. Zhang,39Z. Y. Zhang,43G. Zhao,1H. S. Zhao,1Jiawei Zhao,39Jingwei Zhao,1Lei Zhao,39Ling Zhao,1 M. G. Zhao,25Q. Zhao,1S. J. Zhao,45T. C. Zhao,42X. H. Zhao,24Y. B. Zhao,1Z. G. Zhao,39Z. L. Zhao,9A. Zhemchugov,16
B. Zheng,1J. P. Zheng,1Y. H. Zheng,6Z. P. Zheng,1B. Zhong,1J. Zhong,2L. Zhong,35L. Zhou,1X. K. Zhou,6 X. R. Zhou,39C. Zhu,1K. Zhu,1K. J. Zhu,1S. H. Zhu,1X. L. Zhu,35X. W. Zhu,1Y. S. Zhu,1Z. A. Zhu,1J. Zhuang,1
B. S. Zou,1J. H. Zou,1J. X. Zuo,1and P. Zweber38 (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 6Graduate 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
9
Guangxi University, Naning 530004, People’s Republic of China
10Henan Normal University, Xinxiang 453007, People’s Republic of China 11Huangshan College, Huangshan 245000, People’s Republic of China 12Huazhong Normal University, Wuhan 430079, People’s Republic of China
13Hunan University, Changsha 410082, People’s Republic of China 14Indiana University, Bloomington, Indiana 47405, USA
15Joint Institute for Nuclear Research, 141980 Dubna, Russia 16also at the Moscow Institute of Physics and Technology, Moscow, Russia 17on leave from the Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
18also at the PNPI, Gatchina, Russia
19KVI/University of Groningen, 9747 AA Groningen, The Netherlands 20Laboratori Nazionali di Frascati - INFN, 00044 Frascati, Italy 21Lanzhou University, Lanzhou 730000, People’s Republic of China 22Liaoning University, Shenyang 110036, People’s Republic of China 23
Nanjing Normal University, Nanjing 210046, People’s Republic of China
24Nanjing University, Nanjing 210093, People’s Republic of China 25Nankai University, Tianjin 300071, People’s Republic of China 26Peking University, Beijing 100871, People’s Republic of China
27Seoul National University, Seoul, 151-747 Korea 28Shandong University, Jinan 250100, People’s Republic of China
29Shanxi University, Taiyuan 030006, People’s Republic of China 30Sichuan University, Chengdu 610064, People’s Republic of China 31Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China
32The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. 33The University of Hong Kong, Pokfulam, Hong Kong
34The University of Tokyo, Tokyo 113-0033 Japan
35Tsinghua University, Beijing 100084, People’s Republic of China 36Universitaet Giessen, 35392 Giessen, Germany
37University of Hawaii, Honolulu, Hawaii 96822, USA 38University of Minnesota, Minneapolis, Minnesota 55455, USA 39
University of Science and Technology of China, Hefei 230026, People’s Republic of China
40University of the Punjab, Lahore-54590, Pakistan 41University of Turin and INFN, Turin, Italy 42University of Washington, Seattle, Washington 98195, USA 43Wuhan University, Wuhan 430072, People’s Republic of China 44Zhejiang University, Hangzhou 310027, People’s Republic of China 45Zhengzhou University, Zhengzhou 450001, People’s Republic of China
(Received 27 April 2011; published 22 August 2011)
Using ð106 4Þ 106 c ð3686Þ events accumulated with the BESIII detector at the BEPCII eþe collider, we present the first measurement of decays of c1 to vector meson pairs , !!, and !.
The branching fractions are measured to be ð4:4 0:3 0:5Þ 104, ð6:0 0:3 0:7Þ 104, and ð2:2 0:6 0:2Þ 105, for
c1! , !!, and !, respectively, which indicates that the hadron
helicity selection rule is significantly violated in cJdecays. In addition, the measurement of cJ! !
provides the first indication of the rate of doubly OZI-suppressed cJdecay. Finally, we present improved
measurements for the branching fractions of c0and c2to vector meson pairs.
DOI:10.1103/PhysRevLett.107.092001 PACS numbers: 13.25.Gv, 12.38.Qk, 14.40.Pq
Decays of the cJðJ ¼ 0; 1; 2Þ P-wave charmonium
states are considered to be an ideal laboratory to test QCD theory. The initial theoretical calculations of cJ
exclusive decays into light hadrons predicted branching fractions that were smaller than the experimental measure-ments [1]. With the inclusion of the color-octet mechanism [2], calculations of cJ decays into pairs of pseudoscalar
mesons and pairs of baryons came into reasonable agree-ment with the experiagree-mental measureagree-ments, indicating the importance of the color-octet mechanism.
In the case of cJ decays into pairs of vector (JPC¼
1) mesons VV, where V is an ! or , the branching
fractions for c0=2 decays to and !! have been
measured to be at the 103 level [3,4], which is much larger than predictions based on perturbative QCD calcu-lations [5]. Decays of the c1into , !! and ! violate
the helicity selection rule (HSR) and are expected to be highly suppressed [6]. In addition, the decays cJ ! !
are doubly OZI suppressed and have yet to be observed. Recently, long-distance effects in c1 decays [7,8] have
been proposed to account for the HSR violation. Precise measurements of c1! VV decays will help
clar-ify the influence of long-distance effects in this energy region.
In this Letter, we report measurements of cJ decays
into , !!, and ! modes, where is reconstructed from KþKor þ0, ! from þ0, and 0 from . The data samples used in this analysis consist of ð106 4Þ 106 cð3686Þ decays and 42:6 pb1 of
continuum data at pffiffiffis¼ 3:65 GeV acquired with the BESIII detector [9]. The cylindrical core of the BESIII detector consists of a helium-gas-based Main Drift
Chamber (MDC), a plastic scintillator Time-of-Flight system (TOF), a CsI(Tl) Electromagnetic Calorimeter (EMC), and a muon counter. The charged particle and photon acceptance is 93% of 4, and the charged particle momentum and photon energy resolutions at 1 GeV are 0.5% and 2.5%, respectively. The BESIII detector is mod-eled with a Monte Carlo (MC) simulation based onGEANT4
[10,11]. The optimization of the event selection and the estimation of physics backgrounds are performed with Monte Carlo simulations ofcð3686Þ inclusive or exclusive decays [12].
The final states of interest are 2ðKþKÞ, 52ðþÞ, and 3KþKþ. Event candidates are required to have four well reconstructed charged tracks with net charge zero, and at least one, five, or three good photons, for , !!, and !, respectively.
Electromagnetic showers in BESIII detector are recon-structed from clusters of energy deposits in the EMC. The energy deposited in nearby TOF counters is included to improve the reconstruction efficiency. A good photon is a shower in the barrel region (j cosj < 0:8) with at least 25 MeV energy deposition, or in the end caps (0:86 < j cosj < 0:92) with at least 50 MeV energy deposition, where is the polar angle of the shower. Showers in the region between the barrel and the end caps are poorly measured and excluded. Timing requirements are used in the EMC to suppress electronic noise and energy deposits unrelated to the event.
Charged tracks are reconstructed from MDC hits. Each charged track is required to be in the polar angle region j cosj < 0:93 and to pass within 10 cm of the interac-tion point in the beam direcinterac-tion and within1 cm in the plane perpendicular to the beam.
A kinematic fit constrained by the initial eþe four-momentum in the laboratory frame is applied to the decay hypotheses cð3686Þ ! 2ðKþKÞ, 52ðþÞ, and 3KþKþ. The final state photons are identified
with the photon-charged-track combination that has a minimum 24C value (for definition of 24C, see [13])
when sampling all candidate photons. The vertex of all charged tracks must be consistent with the measured beam interaction point. The 24Cselection efficiency is optimized using the ratio of signal to backgrounds in the data: 24C<
60 for 2ðKþKÞ, 3KþKþ, and 2
4C< 200 for
52ðþÞ is required. To separate the K from in
the 3KþKþ final state, two kaons are identified with the requirements that PðKÞ > PðÞ and PðKÞ > PðpÞ, where PðXÞ is the probability of hypothesis X as evaluated from the TOF and dE=dx information.
The mass windows for resonance candidates are set according to the optimized ratio of signals to back-grounds in the data. The 0 candidates are selected by requiring 0:1 < M< 0:15 GeV=c2. The and !
candidates are selected by requiring jMKþK 1:019j < 0:015 GeV=c2,jM
þ0 1:019j < 0:030 GeV=c2, and
jMþ00:783j<0:050 GeV=c2, for ! KþK,
! þ0, and ! ! þ0, respectively.
For cJ! ! 2ðKþKÞ, the two candidates with
the minimum value of ðMð1ÞKþK 1:019Þ2þ ðMð2ÞKþK 1:019Þ2 are taken as the signal. No artificial -pair peaks
are produced when this selection criteria is applied to MC simulation of the process cJ ! 2ðKþKÞ. A scatterplot of
masses for one KþKpair versus the other KþK pair is shown in Fig. 1(a), where a clear signal can be seen. The MKþK distribution, after requiring that the other two
kaons are consistent with being a , is shown in Fig.1(b). A peak is clearly seen with very low background. The invariant mass distribution for the selected events is shown in Fig.2(a), where cJsignals are clearly observed.
The MC simulation shows that the peaking backgrounds, i.e., backgrounds that produce cJsignal peaks, are mostly
from cJ ! KþK and 2ðKþKÞ final states; the
) 2 (GeV / c -K + K (a) M 1.0 1.1 1.2 ) 2 (GeV / c -K + K M 1.00 1.05 1.10 1.15 1.20 1.25 A A B ) 2 (GeV / c -K + K (b) M 0.9 1.0 1.1 1.2 2 Events/ 5 MeV/ c 0 100 200 300 400 500 600 700 ) 2 (GeV / c 0 π -π + π (c) M 0.6 0.8 1.0 ) 2 (GeV / c 0π -π +π M 0.5 0.6 0.7 0.8 0.9 1.0 1.1 A A A A B B B B ) 2 (GeV / c 0 π -π + π (d) M 0.7 0.8 0.9 1.0 2 Events/ 5 MeV/ c 0 100 200 300 400 500 ) 2 (GeV / c 0 π -π + π (e) M 0.8 1.0 1.2 1.4 ) 2 ( GeV / c -K + K M 1.00 1.05 1.10 1.15 1.20 1.25 A A A B B 0.900 1.015 1.13 0.98 1.03 1.08 A A A B B ) 2 (GeV / c 0 π -π + π (f) M 0.7 0.8 0.9 1.0 1.1 2 Events/ 5 MeV/ c 0 20 40 60 80 100 120 140
FIG. 1. The left column shows scatterplots for events within the cJ mass region. The boxes indicate the signal region
(without label) and sideband regions labeled as A and B. The plots in the right column are the one-dimensional projections of the system recoiling against a selected or ! resonance. Plots (a) and (b) are for the 2ðKþKÞ mode; (c) and (d) for the 52ðþÞ mode; and (e) and (f) for the 3KþKþ
backgrounds from misidentified charged particles are negligible. The levels of the peaking backgrounds are evaluated from NAB¼ rANAdt rBNBdt, where NAdtðNBdtÞ is
the number of data events falling into box A (B), as indicated in Fig. 1(a), and the normalizing factors ri¼ NsigMC=NMCi with i ¼ A or B are determined from
MC simulation for modes cJ ! KþK and 2ðKþKÞ,
respectively. Here NMCsigðNMCi Þ is the number of MC events
falling into the signal box (A or B). These backgrounds will be indistinguishable from signal events; therefore, we fix their normalization, independently for each cJpeak, in the
final fit.
To study cJ! !! decays into the 2ðþ0Þ final
state, two 0 candidates are selected by minimizing the value of ðMð1Þ 0:135Þ2þ ðMð2Þ 0:135Þ2 when
sam-pling all four-photon combinations from the selected five photons. The þ0combination closest to the nominal ! mass is taken as one ! candidate, and the remaining
three pions are assumed to be from the other !. No artificial !-pair peaks are produced from the application of this !-selection criteria to a MC simulation for cJ!
2ðþ0Þ. A scatterplot of the mass for one þ0
pair versus the other þ0 pair is shown in Fig. 1(c), and the Mþ0 distribution for the three pions recoiling
against an ! candidate is plotted in Fig.1(d). The !! mass spectrum is shown in Fig. 2(c), where cJ signals are
prominent. The MC simulation shows that the backgrounds in the !! signal region include peaking backgrounds from cJ! !þ0and 2ðþ0Þ, and nonpeaking
back-grounds from thecð3686Þ decays into the same final states without intermediate cJ states. The backgrounds from
misidentified charged particles are negligible. Potential backgrounds from cJ! ! 2ðþ0Þ and c0=2!
! 2ðþ0Þ do not survive our selection criteria. As in the cJ! mode, the sizes of the peaking
backgrounds from cJ! !þ0 and 2ðþ0Þ
are evaluated by selecting data events located in sideband boxes A and B, respectively, as indicated in Fig.1(c). The peaking backgrounds are normalized according to the ratio of MC events falling into the signal region and those falling into the sidebands. The normalization of these peaking backgrounds is fixed in the final fit.
To study cJ ! ! and decays into the
KþKþ0 final state, the photon pair with invariant mass closest to the 0 nominal mass is taken as the 0 candidate. A scatterplot of masses for KþK pairs versus that for þ0 pairs is shown in Fig. 1(e), and the Mþ0 distribution for events satisfying ! KþK is
shown in Fig. 1(f ), where the ! ! þ0 and ! þ0 signals are clearly seen. The and ! mass spectra are shown in Figs. 2(b) and 2(d), respectively. Similar to the case for cJ! ! 2ðKþKÞ, the
peak-ing backgrounds from the cJ! þ0 or KþK,
and KþKþ0are evaluated by selecting data events falling into sideband boxes A and B, respectively, as in-dicated in the inserted plot in Fig. 1(e). The peaking backgrounds are normalized according to the ratio of MC events falling into the signal region and those falling into the sidebands. The normalization of these peaking back-grounds is fixed in the final fit.
The numbers of observed events are obtained by fitting the MVV distributions. The observed line shapes are
de-scribed with modified cJ MC shapes plus backgrounds.
Possible interference effects between the signal mode and the peaking background modes are not considered for all modes. The original cJ MC shapes are generated by a
relativistic Breit-Wigner incorporated with full helicity amplitudes in the EvtGen package [14], and their masses and widths are set to the nominal values [15]. In the fits they are modified by convolving them with Gaussian func-tions GðMVV MJ; JÞ, where MJ and J correct the
cJ mass and width or resolution, respectively, in the
simulation. The values of MJ and J, determined from
2 Events / 5 MeV / c 500 100 150 200 250 2 Events / 5 MeV / c 0 20 40 60 80 100 2 Events / 5 MeV / c 0 50 100 150 200 250 3.30 3.35 3.40 3.45 3.50 3.55 3.60 ) 2 ( GeV/c VV M 2 Events / 10 MeV / c 05 10 15 20 25 30 35 (a) (b) (c) (d)
FIG. 2 (color online). Invariant mass of VV for (a) mode in the 2ðKþKÞ final state, (b) mode in the þ0KþK final state, (c) !! mode in the 2ðþ0Þ final state, and (d) ! mode in the þ0KþKfinal state. The points with error bars are the data; the solid lines are the fit results; and dotted lines represent the signal components. The shaded and open histograms in (a),(b) and (c), respectively, are peaking back-grounds. In (c), the shaded histogram denotes the non-cJ
back-grounds. In (d) the long dash line is background normalized by a simultaneous fit to ! sidebands, and the dash-dot line is non-cJbackground.
the fits, are less than 1 MeV for all modes and from 1 to 5 MeV, respectively. Backgrounds from QED processes, which are estimated from the application of a similar analysis to the continuum data, are negligible. For cJ !
, the peaking backgrounds are fixed to the sideband estimates as mentioned above, and other combinatorial backgrounds are parameterized by a second-order polyno-mial with parameters that are allowed to float in the fit. For all modes, a maximum-likelihood technique [16] is em-ployed to estimate parameters. After projecting the best fit into the binned histograms shown in Fig.2, we determine 2=NDF ¼ 0:46 for cJ! ! 2ðKþKÞ and 0.50 for
the cJ! ! KþKþ0, where NDF is the
number of degrees of freedom. The fitted results are plotted in Fig.2(a)and2(b), respectively. The numbers of signal events are listed in TableI.
For the cJ! !! channel, backgrounds include the
peaking backgrounds estimated from ! sidebands indi-cated in Fig. 1(c), non-cJ backgrounds [cð3686Þ !
!!] fixed at the normalized MC shape of phase space using the data information, and smooth combinatorial backgrounds that are parametrized by a second-order polynomial. The 2=NDF for the fit is 0.97. The fit results are shown in Fig.2(c).
To extract the signal yield, as well as to estimate the statistical significance for the cJ! ! mode, a
simultaneous fit is performed to M! distributions both
in ! signal and sideband regions of boxes A and B [see Fig. 1(e)]. The peaking backgrounds are normalized
according to the ratio of MC events falling into the signal region to those falling into the sideband regions for the
cð3686Þ ! þ0, !KþK and cð3686Þ !
KþKþ0 events that are within the cJ mass
region. Because of the low signal yield in this mode, the parameters MJ and J of the modified MC shapes are
fixed at the values determined in the fit of cJ! !
KþKþ0. The 2=NDF is 0.62. The fit results are shown in Fig. 2(d), and the numbers of signal events are listed in TableI.
The uncertainties due to the modified cJMC shapes are
estimated by replacing them with Breit-Wigner functions convolved with the instrumental resolution functions in the fits. The quality of the resulting fit is not as good as using the modified MC shapes. The difference of signal yields varies from 1% to 4%, and this is included as a systematic error.
The detection efficiencies are determined from MC simulations for the sequential decays cð3686Þ ! cJ!
VV, V decays into the selected final state. The decays
cð3686Þ ! cJ are generated by assuming a pure E1
transition. The cJ! VV decays and subsequent decays
of the V are modeled with helicity amplitudes that provide angular distributions consistent with the data.
The systematic uncertainties on the cJdecay branching
fractions arise from the and K tracking, K identi-fication, EMC shower reconstruction, number of cð3686Þ decays, kinematic fitting, modified MC shapes, back-ground estimation, cJ signal extraction and uncertainties
from branching fractions of cð3686Þ ! cJ, ! KþK, ! ! þ0 and 0 ! . The uncertainties caused by MDC tracking are estimated to be 2% for each charged track [17]. The uncertainty due to K identifica-tion is evaluated to be 2% per kaon [17]. The uncertainty due to the photon reconstruction is determined to be 1% for each photon [17]. The uncertainty in the number of
cð3686Þ decays is 4% [12]. The uncertainties due to the kinematic fit are determined by comparing the efficiency at the given 24Cvalues for the MC sample to control samples
selected from data, i.e., cð3686Þ ! ! 2ðKþKÞ,
cð3686Þ ! 00J=c, J=c ! 2ðþÞ, 02ðþÞ
and cð3686Þ ! þJ=c, J=c ! KþK0. The kinematic-fit uncertainty varies from 0.5% (2ðþ0Þ mode) to 3.7% (KþKþ0 mode). The uncertain-ties of the peaking backgrounds for cJ! !
2ðKþKÞ are evaluated by comparing the sideband
estimates to the exclusive MC simulation on the modes cJ! KþKand 2ðKþKÞ, while for other modes the
uncertainties are estimated by varying the size of sideband boxes. The uncertainties of the peaking background estimates are less than 3%. The uncertainty from the MC normalization factor is found to be negligibly small. The total systematic uncertainties are 10% for cJ! !
2ðKþKÞ mode, and 11% for
cJ! !! ! 2ðþ0Þ,
cJ! , ! ! KþKþ0 modes.
TABLE I. Summary of the branching fractions (B) for cJ!
, !!, and !. Here Nnet is the number of signal events,
is the detection efficiency. The upper limit is estimated at the 90% C.L. Mode Nnet (%) Bð104Þ c0! 433 23 22.4 7:8 0:4 0:8 c1! 254 17 26.4 4:1 0:3 0:4 c2! 630 26 26.1 10:7 0:4 1:1 ! 2ðKþKÞ c0! 179 16 12.8 9:2 0:7 1:0 c1! 112 12 15.3 5:0 0:5 0:6 c2! 219 16 14.9 10:7 0:7 1:2 ! KþKþ0 Combined: c0! 8:0 0:3 0:8 c1! 4:4 0:3 0:5 c2! 10:7 0:3 1:2 c0! !! 991 38 13.1 9:5 0:3 1:1 c1! !! 597 29 13.2 6:0 0:3 0:7 c2! !! 762 31 11.9 8:9 0:3 1:1 ! 2ðþ0Þ c0! ! 76 11 14.7 1:2 0:1 0:2 c1! ! 15 4 16.2 0:22 0:06 0:02 c2! ! <13 15.7 <0:2 ! KþKþ0
The branching fractions for cJ decays are determined
from B ¼ Nnet=ðNc0 QiBiÞ, where Nnet and are the number of net signal events and the detection efficiency, respectively. The detection efficiencies are listed in TableI. Here Nc0 ¼ ð106 4Þ 106 [12] is the number of
cð3686Þ events, andQiBiis the product of world average
branching fractions values [15] for cð3686Þ ! cJ and
the other meson decays that are involved. For the cJ !
! KþKþ0 branching fraction we double the efficiency listed in TableIsince our analysis sums over the two combinations for each to decay to either KþK or þ0. The resulting branching fractions are listed in TableI. The statistical significance of cJ ! ! is derived
from the change of 2 lnL obtained from fits with and without each of the three cJ! ! signal components.
We obtain a significance of 4:1 for c1! ! and 1:5
for c2! !. The significance of the c0! ! signal is
10. Using the Bayesian method, the upper limit for the number of signal events of the c2! ! mode is 13 at the
90% confidence level (C.L.). The branching fractions for cJ! measured in 2ðKþKÞ and ðKþKÞðþ0Þ
final states are combined into a weighted average, where common systematic uncertainties are counted only once.
In summary, the HSR suppressed decays of c1! ,
!!, and the doubly OZI-suppressed decay c0! ! are
observed for the first time. The branching fractions are measured to be ð4:4 0:3 0:5Þ 104, ð6:0 0:3 0:7Þ 104, and ð1:2 0:1 0:2Þ 104, for
c1!
, !!, and c0! !, respectively, We also find
evi-dence for c1! ! decay with a signal significance of
4:1. The branching fractions for c0=2! , !!
de-cays are remeasured with a precision that is better than those of the current world average values [15]. These precise measurements will be helpful for understanding cJdecay mechanisms. In particular, the measured
branch-ing fractions for c1! VV indicate that HSR is
signifi-cantly violated and that long-distance effects play an important role in this energy region. The long-distance effects from the intermediate charmed meson loops in c1! and !! decays [7,8] can contribute to the
branching fractions at the level of 104but are more than an order of magnitude too small to explain the doubly OZI-suppressed decay rate for c1! ! that we measure [8].
We thank the accelerator group and computer staff of IHEP for their effort in producing beams and processing
data. We are grateful for support from our institutes and universities and from these agencies: Ministry of Science and Technology of China, National Natural Science Foundation of China, Chinese Academy of Sciences, Istituto Nazionale di Fisica Nucleare, Russian Foundation for Basic Research, Russian Academy of Science (Siberian branch), U.S. Department of Energy, and National Research Foundation of Korea.
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