Observation of e
þe
! J=
c
at center-of-mass energy ffiffiffis
p
¼ 4:009 GeV
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,17W. M. Song,1X. Y. Song,1 S. Spataro,43a,43cB. 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,40
C. J. Tang,31X. Tang,1I. Tapan,35cE. H. Thorndike,39D. Toth,38M. Ullrich,36G. S. Varner,37B. Wang,9B. Q. Wang,27 K. Wang,1L. L. Wang,4L. S. Wang,1M. Wang,29P. Wang,1P. L. Wang,1Q. Wang,1Q. J. Wang,1S. G. Wang,27 X. L. Wang,40Y. D. Wang,40Y. F. Wang,1Y. Q. Wang,29Z. Wang,1Z. G. Wang,1Z. Y. Wang,1D. H. Wei,8P. Weidenkaff,19
Q. G. Wen,40S. P. Wen,1M. Werner,36U. Wiedner,2L. H. Wu,1N. Wu,1S. X. Wu,40W. Wu,26Z. Wu,1L. G. Xia,34 Z. J. Xiao,24Y. 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,1 L. Yan,40W. 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,26 J. S. Yu,22S. 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,40Y. M. Zhu,26
Y. 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
11Helmholtz Institute Mainz, J. J. Becherweg 45,D 55099 Mainz, Germany
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, 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 9 August 2012; published 1 October 2012)
Using a 478 pb1 data sample collected with the BESIII detector operating at the Beijing Electron Positron Collider storage ring at a center-of-mass energy ofpffiffiffis¼ 4:009 GeV, the production of eþe! J=c is observed for the first time with a statistical significance of greater than 10. The Born cross section is measured to be ð32:1 2:8 1:3Þ pb, where the first error is statistical and the second systematic. Assuming the J=c signal is from a hadronic transition of the c ð4040Þ, the fractional transition rate is determined to beBðc ð4040Þ ! J=c Þ ¼ ð5:2 0:5 0:2 0:5Þ 103, where the first, second, and third errors are statistical, systematic, and the uncertainty from thec ð4040Þ resonant parameters, respectively. The production ofeþe! 0J=c is searched for, but no significant signal is observed, andBðc ð4040Þ ! 0J=c Þ < 2:8 104 is obtained at the 90% confidence level.
DOI:10.1103/PhysRevD.86.071101 PACS numbers: 13.25.Gv, 13.40.Hq, 14.40.Pq
The properties of excitedJPC¼ 1charmonium states above the D D production threshold are of great interest but not well understood, even decades after their first observation [1]. The current experimentally well estab-lished structures in the hadronic cross section are the
cð3770Þ,cð4040Þ, cð4160Þ, andcð4415Þ resonances [2]. *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.
§Present address: Nagoya University, Nagoya, Japan.
Unlike the low-lying vectorcc states J=c andcð3686Þ, all of these states couple to open-charm final states with large partial widths and disfavor hidden-charm decays.
Recently, new vector charmoniumlike states, the Yð4260Þ, the Yð4360Þ and the Yð4660Þ, have been discov-ered via their decays into exclusive þJ=c and þcð3686Þ final states [3]. The common properties of these states are relatively narrow widths and strong couplings to hidden-charm final states. These Y states cannot be assigned to any of the conventional cc 1 c family states [4] in any natural way and suggest the existence of a nonconventional meson spectroscopy [5].
Hadronic transitions play an important role in under-standing the nature of conventional heavy quarkonium. An excess of over þhidden-bottom transition rates of the ð4SÞ [6] has been explained as an admixture of a four-quark state in the ð4SÞ wave function [7]. A similar picture might be expected in the charm sector but, as of yet, there are no experimental data available for transi-tions in the high-mass charmonium and charmoniumlike states, except for evidence ofcð3770Þ ! J=cð3:5Þ [8] andcð4160Þ ! J=cð4:0Þ [9]. Moreover, there are pre-dictions of many new states in various models trying to explain the conventional and unconventional states observed in this mass region [5].
In this Letter, we report cross section measurements for eþe! J=c and0J=c at the center-of-mass energy
ffiffiffi s p
¼ ð4:009 0:001Þ GeV. The analysis is performed with a 478 pb1 data sample collected with the BESIII detector located at the Beijing Electron Positron Collider storage ring [10]. The integrated luminosity of this data sample was measured using Bhabha events, with an esti-mated uncertainty of 1.1%. In order to control systematic errors, an accompanying data sample of about 7 106 cð3686Þ events was accumulated under the same experi-mental conditions. In the analysis, theJ=cis reconstructed through its decays into lepton pairs (eþe and þ) while=0 is reconstructed in the final state.
TheGEANT4-based Monte Carlo (MC) simulation soft-ware, which includes the geometric description and the detector response, is used to optimize the event selection criteria, determine the detection efficiency, and estimate the backgrounds. Signal eþe! J=c and0J=c MC samples containing 20 000 events for each channel are generated. Initial state radiation (ISR) is simulated with
KKMC[11], assumingJ=c and0J=c are produced via cð4040Þ decays, and thecð4040Þ is described by a Breit-Wigner function with a constant width. The maximum energies of the ISR photons are 347 and 700 MeV, corre-sponding to J=c and 0J=c production thresholds, respectively. For backgrounds studies, MC samples equivalent to 1 fb1 integrated luminosity are generated: inclusive cð4040Þ decays, ISR production of low-mass vector charmonium states, and QED events. The known decay modes of the charmonium states are generated with
EVTGEN [12] with branching fractions set to their world
average values [2] and the remaining events are generated withLUNDCHARM[13] orPYTHIA[14].
Charged tracks are reconstructed in the main drift cham-ber, and the number of good charged tracks is required to be two with zero net charge. For each track, the polar angle must satisfy j cosj < 0:93, and the point of closest approach to the eþe interaction point must be within 10 cm in the beam direction and within 1 cm in the plane perpendicular to the beam direction. A charged track with deposited energy in the electromagnetic calorimeter less than 0.4 GeV is identified as a candidate while that with a deposited energy over momentum (E=p) ratio larger than 0.8 is identified as an electron candidate. Both of the charged tracks are required to be either identified as muons or as electrons.
Showers identified as photon candidates must satisfy fiducial and shower-quality requirements. The minimum energy is 25 MeV for electromagnetic calorimeter barrel showers (j cosj < 0:8) and 50 MeV for end-cap showers (0:86 < j cosj < 0:92). To eliminate showers produced by charged particles, a photon must be separated by at least 20 from any charged track. Final-state radiation and bremsstrahlung energy loss of leptons are corrected by adding the momentum of photons detected within a 5 cone around the lepton momentum direction. The number of good photon candidates is required to be two (the effi-ciency is over 95%), and the recoil mass of the two photons MrecoilðÞ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðPCM P1 P2Þ2 p
2 ½2:9; 3:4 GeV=c2 is required to select goodJ=c candidates. HerePCMis the four-momentum of the initial states, andP1 and P2 are the four-momenta of the two photons.
The lepton pair and the two photons are subject to a four-constraint (4C) kinematic fit to improve the momen-tum resolution and reduce the background. The chi-square (2) of the kinematic fit is required to be less than 40. In order to reject radiative Bhabha and radiative dimuon (eþe=þ) backgrounds associated with an ener-getic radiative photon (H) and a low energy fake photon, the invariant massMðH‘þ‘Þ is determined from a three-constraint (3C) kinematic fit in which the energy of the low energy photon is allowed to float. Since the fake photon does not contribute in the 3C fit, the MðH‘þ‘Þ mass distribution is not distorted by the photon energy threshold cutoff, and backgrounds are clearly separated from signal. The requirement MðH‘þ‘Þ < 3:93 GeV=c2 removes over 50% of radiative Bhabha and radiative dimuon back-ground events with an efficiency greater than 99% for J=c and 89% for0J=c.
After imposing all of these selection criteria, the invari-ant mass distribution of lepton pairs is shown in Fig.1. A clear J=c signal is observed in the þ mode while indications of a peak around 3:1 GeV=c2 also exist in the eþe mode. The remaining dominant backgrounds are surviving radiative dimuon events inþ and radiative OBSERVATION OFeþe! J=c AT . . . PHYSICAL REVIEW D 86, 071101(R) (2012)
Bhabha events ineþe; these contribute flat components in the Mð‘þ‘Þ distributions with no associated peaks in the MðÞ invariant mass distribution. The high background level in the eþe mode is due to the huge background from the Bhabha process. Other possible back-ground sources include eþe!00J=c, þ0= þ, and
cJð1PÞ=cJð2PÞ. The 00J=c back-ground is estimated by MC simulation to be at the 4.5 pb level and, thus, negligibly small [9]. Potential cJð1PÞ and cJð2PÞ radiative transition backgrounds are esti-mated using the selected data sample; no significant signal is found for eithercJð1PÞ or cJð2PÞ in MðJ=cÞ mass distribution. Theþ0 andþ backgrounds are estimated usingJ=c sideband events. The ISR-produced vector charmonium backgrounds, including ISRJ=c, ISRcð3686Þ and ISRcð3770Þ, are estimated by means of an inclusive MC sample and only 3.3 events in the þ mode and 3.1 events in theeþe mode are found (normalized to data luminosity). As they would peak at neither the nor the 0signal region, they are neglected in the analysis.
The resolution of the invariant mass of the lepton pairs is determined to be 14 MeV=c2 by MC simulation and is in good agreement with events in the cð3686Þ data sample. The mass window of the J=c signal is defined as 3:075 GeV=c2< Mð‘þ‘Þ < 3:125 GeV=c2, and the sidebands are defined as 2:95 GeV=c2< Mð‘þ‘Þ < 3:05 GeV=c2 or 3:15GeV=c2<Mð‘þ‘Þ<3:25GeV=c2, which is 4 times as wide as the signal region. Figure 2
shows the MðÞ invariant mass distributions for events in theJ=c ! þ andJ=c ! eþe signal regions. A significant signal is observed in both modes. In the MðÞ distribution for J=c mass-sideband events, there are backgrounds that peak in the 0 signal region in J=c ! þ that originate from eþe! þ0. In order to suppresseþe! þ0backgrounds, at least one charged track is required to have a muon counter hit a depth larger than 30 cm for the 0J=c signal search. The efficiency for this requirement is 87.9% for signal while about 74% eþe ! þ0 background events are rejected. Figure 3 shows the MðÞ invariant mass distribution below 0:3 GeV=c2 for J=c ! þ.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2 Events / 0.01 GeV/c 0 10 20 30 40 50 60 ) 2 ) (GeV/c M(γγ Data Best fit Background ) 2 ) (GeV/c γ γ M( 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 2 Events / 0.01 GeV/c 0 5 10 15 20 25 30 35 40 45 Data Best fit Background
FIG. 2 (color online). Distributions ofMðÞ between 0.2 and 0:9 GeV=c2forJ=c ! þ (left panel) and forJ=c ! eþe
(right panel). Dots with error bars are data in theJ=c mass signal region, and the green shaded histograms are from normalized J=c mass sidebands. The curves show the total fit and the background term.
2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 2 Events / 0.008 GeV/c 0 10 20 30 40 50 60 70 80 90 data background ) 2 M(ee) (GeV/c 2.9 2.95 3 3.05 3.1 3.15 3.2 3.25 3.3 2 Events / 0.008 GeV/c 0 20 40 60 80 100 120 140 160 180 ) 2) 2
FIG. 1 (color online). (Left panel)MðþÞ and (right panel) MðeþeÞ invariant mass distributions. Dots with error bars are data and the open histogram in the left panel shows inclusive-MC-estimated background events.
No significant 0 signal is observed. We do not analyze 0J=c production inJ=c ! eþedue to the huge back-ground from Bhabha events. The final selection efficien-cies are 38.0% inþ and 26.9% ineþe for J=c, and 31.1% in þ for 0J=c, according to MC simulation.
TheMðÞ invariant mass distributions are fitted using an unbinned maximum likelihood method for MðÞ < 0:9 GeV=c2 in both modes. The probability density func-tion (pdf ) for the=0 signal inJ=c ! þ is taken from MC simulation, while in J=c ! eþe, only the pdf from MC simulation is used. To account for resolution differences between data and the MC simulation, three Gaussian functions are convolved with the and the 0 signal pdfs. For the signal, the standard deviation of these Gaussians are free while for the 0 signal it is fixed toð2:4 0:9Þ MeV=c2, which is determined from a cð3686Þ ! 0J=c control sample. Background shapes are described by a third-order polynomial. Figure2shows the fit results for the signal and the background contri-butions for J=c ! þ and J=c ! eþe. The fits yieldNfit
þðÞ ¼ 111:4 11:0, and NfiteþeðÞ ¼ 61:4
10:5. The standard deviation of the smearing Gaussian convolved with the signal is ð3:7 1:0Þ MeV=c2 in þandð3:7 1:9Þ MeV=c2ineþe. Good agreement is observed between the two modes, and these values are consistent with values from the cð3686Þ ! J=c control sample (3:4 0:6 MeV=c2 in þ and 4:6 0:6 MeV=c2 in eþe). The goodness of fit is estimated by using a 2 test method with the data distributions regrouped to ensure that each bin contains more than 10 events. The test gives 2=ndf ¼ 14:1=14 ¼ 1:1 for þ and2=ndf ¼ 42:9=43 ¼ 1:0 for eþe. Figure 3 shows the fit result for the0 signal and the background contribution forJ=c ! þ. Since the0signal is not
significant, we determine an upper limit for the0 signal yield ofNupð0Þ < 11:7 at the 90% confidence level. The eþe! þ0 backgrounds are estimated by fitting the MðÞ distribution of the J=c mass-sideband events. The signal pdf for the0is a Gaussian function and that for the background is a third-order polynomial. The fit yields Nbkg
þð0Þ ¼ 2:8 1:1 after normalization. The
statisti-cal significances of the and 0 signals are examined by means of the difference in log-likelihood value with or without signal in the fit and the change of the number of degrees of freedom (ndf). For the signal, the statistical significance is larger than 10 while that for the 0 signal is only 1:1.
The Born-order cross section is determined from the relation
B¼ Nfit Nbkg Lintð1 þ Þ B
; (1)
where Nfit andNbkg are the number of signal events from the fit and the number of background events, respectively; Lintis integrated luminosity; is selection efficiency; B is the branching fraction of intermediate states decay; and (1þ ) is the radiative correction factor, which is 0.757 according to QED calculation [15].
For the eþe! J=c cross section, we obtainB¼ 34:8 3:5 pb for the þ mode, and B ¼ 27:1 4:7 pb for the eþemode. Since the results from the two modes agree with each other, we quote a combined cross section result:
Bðeþe! J=cÞ ¼ 32:1 2:8 pb: (2) Here the errors are statistical only.
Systematic errors mainly come from the luminosity measurement, detection efficiency, background estimation and branching fractions of intermediate states decays. All the contributions are summarized in TableI.
The uncertainty from luminosity measurement is esti-mated to be 1.1% using Bhabha events. The muon tracking
) 2 ) (GeV/c γ γ M( 0.05 0.1 0.15 0.2 0.25 0.3 2 Events / 0.01 GeV/c 0 1 2 3 4 5 6 7 8 9 10 Data Best fit Background
FIG. 3 (color online). Distribution of MðÞ below 0:3 GeV=c2 forJ=c ! þ. Dots with error bars are data
in theJ=c mass signal region, and the green shaded histogram is from normalizedJ=c mass sideband. The curves show the total fit and the background term.
TABLE I. Summary of the systematic errors (%) in the cross section measurement. Source þ eþe 0þ Luminosity 1.1 1.1 1.1 Tracking 2 2 Photon detection 2 2 2 Lepton resolution 1.6 2.4 1.6 Kinematic fit 1.9 1.9 1.9 Background shape 1.5 3.0 9.4 Fit function 3.9 c ð4040Þ parameters 2.0 3.3 4.0 Branching fractions 1.2 1.2 1.0 Others 1.0 1.0 1.0 Total 5.0 6.1 11.8
efficiency is estimated to be 1% for each track. Since the luminosity is measured using Bhabha events, the tracking efficiency of electron pairs cancels. The photon detection efficiency is also estimated to be 1% for each photon. The uncertainties associated with the lepton-pair invariant mass resolutions and the kinematic fits are estimated using the cð3686Þ ! J=c control sample. It is obtained from the cð3686Þ data sample by imposing the selection criteria described above, and requiring MðHJ=cÞ < 3:49 GeV=c2 to reject
c1 and c2 events. This gives a low-backgroundcð3686Þ ! J=c events with a purity of 98.5%. The efficiency difference between data and MC simulation for theJ=c invariant mass window is 1.6% in the þ mode and 2.4% in the eþe mode. They are taken as systematic errors due to lepton-pair invariant mass resolution. For the kinematic fit, the efficiency difference between data and MC simulation is 1.9% in both modes.
Uncertainties due to the choice of background shape are estimated by varying the background function from a third-order polynomial to a second-third-order and a fourth-third-order polynomial in the fit, and these changes yield a 1.5% difference in þ and a 3.0% difference in eþe in the number of signal events. The eþe ! þ0 backgrounds subtraction gives a 9.4% difference in þin the number of0 signal events. The uncertainty due to the fit function is estimated by changing the smear-ing Gaussian parameter by 1 standard deviation in the0 signal pdf, which gives 3.9% difference in the number of 0 signal events. Uncertainties in thecð4040Þ resonance parameters and possible distortions of the cð4040Þ line shape due to interference effects with the nearby cð4160Þ resonance introduce uncertainties in the radiative correc-tion factor and the efficiency. Changing the Breit-Wigner parameters (mass and width) by 1 standard deviation according to PDG values [2] or using a coherent shape with the cð4160Þ resonance [16] results in variations in ð1 þ Þ of 2.0% in þ and 3.3% ineþe for the J=c measurement and 4.0% inþfor0J=c mea-surement. The PDG uncertainty inBðJ=c ! ‘þ‘Þ is 1% andBð ! Þ is 0.5% [2]. Other sources of systematic error, including fake photon simulation and the final-state radiation simulation, are estimated to be 1.0% in total.
Assuming all the sources are independent, the total systematic error on theJ=c cross section measurement is determined to be 5.0% forþ and 6.1% foreþe. Considering the common and uncommon errors for these two modes, the combined systematic error on the J=c cross section measurement is 4.0%. The total systematic error is 11.8% in þ for the 0J=c cross section measurement by summing up all the errors in quadrature. Since the significance of the 0J=c signal is low, an upper limit on the0J=c production cross section is set at Bðeþe ! 0J=cÞ < 1:6 pb at the 90% confidence level,
where eþe! þ0 backgrounds have been sub-tracted and the efficiency is lowered by a factor of (1 sys). If we assume the observedJ=c and0J=c are com-pletely fromcð4040Þ decays and use the total cross section of cð4040Þ at pffiffiffis¼ 4:009 GeV [ð6:2 0:6Þ nb] calcu-lated with the PDG resonance parameters [2] as input, we determine the fractional transition rate Bðcð4040Þ ! J=cÞ ¼ ð5:2 0:5 0:2 0:5Þ 103, where the first, second, and third errors are statistical, systematic, and uncertainty from cð4040Þ resonant parameters, respectively. In addition, we obtain an upper limit on Bðcð4040Þ ! 0J=cÞ < 2:8 104 at the 90% confi-dence level.
In summary, we observe for the first time eþe! J=c production at pffiffiffis¼ 4:009 GeV with a statistical significance greater than 10. The Born cross section is measured to beð32:1 2:8 1:3Þ pb, where the first error is statistical and the second systematic. We do not observe a significant eþe ! 0J=c signal, and the Born cross section is found to be less than 1.6 pb at the 90% con-fidence level. These measurements do not contradict the upper limits set by the CLEO experiment [9]. TheJ=c cross section measurement is within the range of the theo-retical calculation and the 0J=c upper limit does not exclude the prediction [17]. A transition rate of 5 103 level is measured for cð4040Þ ! J=c, corresponding to a partial decay width at the 400 keV level, which is much larger than that forcð3770Þ ! J=c [8] and is more than 2 times that forcð4040Þ ! þJ=c [9].
The BESIII Collaboration thanks the staff of Beijing Electron Positron Collider 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. 2009CB825200; National Natural Science Foundation of China (NSFC) under Contracts No. 10625524, No. 10821063, No. 10825524, No. 10835001, No. 10935007, No. 11125525, No. 11235011, and No. 11205163; Joint Funds of the National Natural Science Foundation of China under Contracts No. 11079008, No. 11079027, and No. 11179007; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts No. KJCX2-YW-N29 and No. KJCX2-YW-N45; 100 Talents Program of CAS; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Contract No. DPT2006K-120470; U.S. Department of Energy under Contracts No. DE-FG02-04ER41291, No. DE-FG02-91ER40682, and No. DE-FG02-94ER40823; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; and WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
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