First Observation of ð1405Þ Decays into f
0ð980Þ
0M. Ablikim,1M. N. Achasov,5D. Alberto,41D. J. Ambrose,38F. F. An,1Q. An,39Z. H. An,1J. Z. Bai,1
R. B. F. Baldini Ferroli,17Y. Ban,25J. Becker,2N. Berger,1M. B. Bertani,17J. M. Bian,1E. Boger,18,*O. Bondarenko,19 I. Boyko,18R. A. Briere,3V. Bytev,18X. Cai,1A. C. Calcaterra,17G. F. Cao,1J. F. Chang,1G. Chelkov,18,*G. Chen,1
H. S. Chen,1J. C. Chen,1M. L. Chen,1S. J. Chen,23Y. Chen,1Y. B. Chen,1H. P. Cheng,13Y. P. Chu,1 D. Cronin-Hennessy,37H. L. Dai,1J. P. Dai,1D. Dedovich,18Z. Y. Deng,1I. Denysenko,18,†M. Destefanis,41 W. L. Ding Ding,27Y. Ding,21L. Y. Dong,1M. Y. Dong,1S. X. Du,44J. Fang,1S. S. Fang,1C. Q. Feng,39C. D. Fu,1 J. L. Fu,23Y. Gao,34C. Geng,39K. Goetzen,7W. X. Gong,1M. Greco,41M. H. Gu,1Y. T. Gu,9Y. H. Guan,6A. Q. Guo,24
L. B. Guo,22Y. P. Guo,24Y. L. Han,1X. Q. Hao,1F. A. Harris,36K. L. He,1M. He,1Z. Y. He,24Y. K. Heng,1Z. L. Hou,1 H. M. Hu,1J. F. Hu,6T. Hu,1B. Huang,1G. M. Huang,14J. S. Huang,11X. T. Huang,27Y. P. Huang,1T. Hussain,40C. S. Ji,39
Q. Ji,1X. B. Ji,1X. L. Ji,1L. K. Jia,1L. L. Jiang,1X. S. Jiang,1J. B. Jiao,27Z. Jiao,13D. P. Jin,1S. Jin,1F. F. Jing,34 N. Kalantar-Nayestanaki,19M. Kavatsyuk,19W. Kuehn,35W. Lai,1J. S. Lange,35J. K. C. Leung,33C. H. Li,1Cheng Li,39 Cui Li,39D. M. Li,44F. Li,1G. Li,1H. B. Li,1J. C. Li,1K. Li,10Lei Li,1N. B. Li,22Q. J. Li,1S. L. Li,1W. D. Li,1W. G. Li,1 X. L. Li,27X. N. Li,1X. Q. Li,24X. R. Li,26Z. B. Li,31H. Liang,39Y. F. Liang,29Y. T. Liang,35G. R. Liao,34X. T. Liao,1
B. J. Liu,32C. L. Liu,3C. X. Liu,1C. Y. Liu,1F. H. Liu,28Fang Liu,1Feng Liu,14H. Liu,1H. B. Liu,6H. H. Liu,12 H. M. Liu,1H. W. Liu,1J. P. Liu,42K. Liu,25K. Liu,6K. Y. Liu,21Q. Liu,36S. B. Liu,39X. Liu,20X. H. Liu,1Y. B. Liu,24 Yong Liu,1Z. A. Liu,1Zhiqiang Liu,1Zhiqing Liu,1H. Loehner,19G. R. Lu,11H. J. Lu,13J. G. Lu,1Q. W. Lu,28X. R. Lu,6 Y. P. Lu,1C. L. Luo,22M. X. Luo,43T. Luo,36X. L. Luo,1M. Lv,1C. L. Ma,6F. C. Ma,21H. L. Ma,1Q. M. Ma,1S. Ma,1
T. Ma,1X. Y. Ma,1M. Maggiora,41Q. A. Malik,40H. Mao,1Y. J. Mao,25Z. P. Mao,1J. G. Messchendorp,19J. Min,1 T. J. Min,1R. E. Mitchell,16X. H. Mo,1N. Yu. Muchnoi,5Y. Nefedov,18I. B. Nikolaev,5Z. Ning,1S. L. Olsen,26 Q. Ouyang,1S. P. Pacetti,17,‡J. W. Park,26M. Pelizaeus,36K. Peters,7J. L. Ping,22R. G. Ping,1R. Poling,37C. S. J. Pun,33 M. Qi,23S. Qian,1C. F. Qiao,6X. S. Qin,1J. F. Qiu,1K. H. Rashid,40G. Rong,1X. D. Ruan,9A. Sarantsev,18,§J. Schulze,2 M. Shao,39C. P. Shen,36,kX. Y. Shen,1H. Y. Sheng,1M. R. Shepherd,16X. Y. Song,1S. Spataro,41B. Spruck,35D. H. Sun,1
G. X. Sun,1J. F. Sun,11S. S. Sun,1X. D. Sun,1Y. J. Sun,39Y. Z. Sun,1Z. J. Sun,1Z. T. Sun,39C. J. Tang,29X. Tang,1 E. H. Thorndike,38H. L. Tian,1D. Toth,37G. S. Varner,36X. Wan,1B. Wang,9B. Q. Wang,25K. Wang,1L. L. Wang,4
L. S. Wang,1M. Wang,27P. Wang,1P. L. Wang,1Q. Wang,1Q. J. Wang,1S. G. Wang,25X. F. Wang,11X. L. Wang,39 Y. D. Wang,39Y. F. Wang,1Y. Q. Wang,27Z. Wang,1Z. G. Wang,1Z. Y. Wang,1D. H. Wei,8Q. G. Wen,39S. P. Wen,1 U. Wiedner,2L. H. Wu,1N. Wu,1W. Wu,24Z. Wu,1Z. J. Xiao,22Y. G. Xie,1Q. L. Xiu,1G. F. Xu,1G. M. Xu,25H. Xu,1 Q. J. Xu,10X. P. Xu,30Y. Xu,24Z. R. Xu,39Z. Xue,1L. Yan,39W. B. Yan,39Y. H. Yan,15H. X. Yang,1T. Yang,9Y. Yang,14 Y. X. Yang,8H. Ye,1M. Ye,1M. H. Ye,4B. X. Yu,1C. X. Yu,24S. P. Yu,27C. Z. Yuan,1W. L. Yuan,22Y. Yuan,1A. A. Zafar,40 A. Z. Zallo,17Y. Zeng,15B. X. Zhang,1B. Y. Zhang,1C. C. Zhang,1D. H. Zhang,1H. H. Zhang,31H. Y. Zhang,1J. Zhang,22 J. Q. Zhang,1J. W. Zhang,1J. Y. Zhang,1J. Z. Zhang,1L. Zhang,23S. H. Zhang,1T. R. Zhang,22X. J. Zhang,1X. Y. Zhang,27 Y. Zhang,1Y. H. Zhang,1Y. S. Zhang,9Z. P. Zhang,39Z. Y. Zhang,42G. Zhao,1H. S. Zhao,1Jingwei Zhao,1Lei Zhao,39
Ling Zhao,1M. G. Zhao,24Q. Zhao,1S. J. Zhao,44T. C. Zhao,1X. H. Zhao,23Y. B. Zhao,1Z. G. Zhao,39 A. Zhemchugov,18,*B. Zheng,1J. P. Zheng,1Y. H. Zheng,6Z. P. Zheng,1B. Zhong,1J. Zhong,2L. Zhou,1X. K. Zhou,6
X. R. Zhou,39C. Zhu,1K. Zhu,1K. J. Zhu,1S. H. Zhu,1X. L. Zhu,34X. W. Zhu,1Y. S. Zhu,1Z. A. Zhu,1J. Zhuang,1 B. S. Zou,1J. H. Zou,1and J. X. Zuo1
(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
7
GSI 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, XueLin Jie 16, Xiasha Higher Education Zone, Hangzhou, 310036 11Henan Normal University, Xinxiang 453007, People’s Republic of China
12Henan University of Science and Technology, Luoyang 471003, People’s Republic of China 13Huangshan College, Huangshan 245000, People’s Republic of China
14Huazhong Normal University, Wuhan 430079, People’s Republic of China 15Hunan University, Changsha 410082, People’s Republic of China
16Indiana University, Bloomington, Indiana 47405, USA 17INFN Laboratori Nazionali di Frascati, Frascati, Italy 18Joint Institute for Nuclear Research, Dubna, Russia 19KVI/University of Groningen, AA Groningen, The Netherlands 20
Lanzhou University, Lanzhou 730000, People’s Republic of China 21Liaoning University, Shenyang 110036, People’s Republic of China 22Nanjing Normal University, Nanjing 210046, People’s Republic of China
23Nanjing University, Nanjing 210093, People’s Republic of China 24Nankai University, Tianjin 300071, People’s Republic of China 25Peking University, Beijing 100871, People’s Republic of China
26Seoul National University, Seoul, 151-747 Korea 27Shandong University, Jinan 250100, People’s Republic of China
28Shanxi University, Taiyuan 030006, People’s Republic of China 29Sichuan University, Chengdu 610064, People’s Republic of China
30Soochow University, Suzhou 215006, 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 34Tsinghua University, Beijing 100084, People’s Republic of China
35Universitaet Giessen, 35392 Giessen, Germany 36
University of Hawaii, Honolulu, Hawaii 96822, USA 37University of Minnesota, Minneapolis, Minnesota 55455, USA
38University of Rochester, Rochester, New York 14627, USA
39University 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
42Wuhan University, Wuhan 430072, People’s Republic of China 43Zhejiang University, Hangzhou 310027, People’s Republic of China 44Zhengzhou University, Zhengzhou 450001, People’s Republic of China
(Received 14 January 2012; published 3 May 2012)
The decays J=c ! þ0and J=c ! 000are analyzed using a sample of 225 106J=c events collected with the BESIII detector. The decay of ð1405Þ ! f0ð980Þ0 with a large isospin violation is observed for the first time. The width of the f0ð980Þ observed in the dipion mass spectra is anomalously narrower than the world average. Decay rates for three-pion decays of the 0 are also measured precisely.
DOI:10.1103/PhysRevLett.108.182001 PACS numbers: 13.25.Gv, 12.38.Qk, 14.40.Be
A state near 1440 MeV=c2 was discovered in p p
anni-hilation at rest decaying to þand was subsequently observed decaying to K K [1]. Considerable theoretical and experimental efforts have since been devoted to under-stand its nature. It was proposed to be a candidate for a pseudoscalar glueball [2,3]; the measured mass, however, is much lower than that obtained from lattice QCD calcu-lations, which is above 2 GeV=c2 [4]. Later, experiments
produced evidence that this state was really two different pseudoscalar states, the ð1405Þ and the ð1475Þ. The former has large couplings to a0ð980Þ and K K, while
the latter mainly couples to KK. A detailed review of the experimental situation can be found in Ref. [5].
The nature of the well-established light scalars f0ð980Þ
and a0ð980Þ is also a matter of controversy. It is not clear
whether they belong to the light scalar meson nonet or are
examples of mesons beyond the naive quark model (e.g., tetra-quark states, hybrids, or K K molecules) [6–11]. The possibility of mixing between the f0ð980Þ and a00ð980Þ was
suggested long ago, and its measurement sheds light on the nature of these two resonances [12–17].
The three-pion decays of the 0have garnered attention because their branching ratios (Br) can probe isospin breaking [18,19]. The ratios of the branching ratios [r
Brð0! þ0Þ=ðBr0 ! þÞ and r 0
Brð0! 30Þ=Brð0! 00Þ] are related to the strange
quark mass and SU(3) breaking [18].
In this Letter, we present the results of a study of J=c ! þ0 and J=c ! 000. A single structure
around 1:4 GeV=c2in the þ0(000) mass
spec-trum is observed, associated with a narrow structure around 980 MeV=c2 in the þ (00) mass spectrum. This
analysis is based on a sample ofð225:2 2:8Þ 106 J=c
events [20] accumulated in the Beijing Spectrometer (BESIII) [21] operating at the Beijing Electron-Positron Collider (BEPCII) [22].
BEPCII is a double-ring eþe collider designed to provide eþe collisions with a peak luminosity of 1033 cm2s1at a beam current of 0.93 A. The cylindrical
core of the BESIII detector consists of a helium-based main drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a supercon-ducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance of charged particles and photons is 93% over 4 stereo angle, and the charged-particle momentum and photon energy resolutions at 1 GeV are 0.5% and 2.5%, respectively. The BESIII detec-tor is modeled with a Monte Carlo (MC) simulation based onGEANT4[23,24].
The charged-particle tracks in the polar angle range j cosj < 0:93 are reconstructed from hits in the MDC. Tracks that extrapolate to be within 20 cm of the interac-tion point in the beam direcinterac-tion and 2 cm in the plane perpendicular to the beam are selected. The TOF and dE=dx information are combined to form particle identi-fication confidence levels for the , K, and p hypotheses; each track is assigned to the particle type that corresponds to the hypothesis with the highest confidence level. Photon candidates are required to have at least 25 and 50 MeV of energy in the EMC regions j cosj < 0:8 and 0:86 < j cosj < 0:92, respectively, and be separated from all charged tracks by more than 10.
For J=c ! þ0, the candidate events are re-quired to have two oppositely charged tracks identified as pions and at least three photon candidates. A four-constraint (4C) energy-momentum conserving kinematic fit is performed to the þ hypothesis, and 24C<
30 is required. For events with more than three photon candidates, the combination with the smallest 2 is
re-tained. To reject possible background events with two or four photons in the final state, the 4C-fit probability for an assignment of the J=c ! þ channel must be larger than that of the J=c ! þ and the J=c ! þ channels. The 0 candidates are selected by requiring jM m0j < 0:015 GeV=c2. Events with
jM0 m!j < 0:05 GeV=c2 are rejected to suppress the
background from J=c ! !þ.
For J=c ! 30, the candidate events are required to
have no charged track. The 0 ! candidates are formed from pairs of photon candidates that are kinemati-cally fit to the 0 mass, and the 2from the kinematic fit
with 1of freedom are required to be less than 25. True 0
mesons decay isotropically in the 0 rest frame, and their
decay distributions are flat, contrary to 0 candidates
originating from wrong photon combinations. To remove wrong photon combinations, the decay angle, defined as the polar angle of a photon in the 0rest frame, is required
to satisfyj cosdecayj < 0:95. Events with at least seven and less than nine photons, which form at least three distinct 0
candidates, are selected. A 7C kinematic fit is performed to the J=c ! 30 hypothesis (constraints are the 4-momentum of J=c and the three 0 masses), and 2
7C<
60 is required. If there is more than one combination, the combination with the smallest 2
7Cis retained. Events with
jM0 m!j < 0:05 GeV=c2 are rejected to suppress the
background from J=c ! !00.
The distributions of the selected events in the Mþ0 Mþ and M000 M00 planes are
shown in Figs. 1(a) and 1(b), respectively. The clusters corresponding to ! 3, 0! 3, and ð1405Þ ! f0ð980Þ0 can be clearly discerned; the ! signal is also
evident in Fig. 1(a), which mainly comes from the back-ground channel J=c ! !0, while it is not observed in the neutral channel, as expected from charge conjugation symmetry.
To confirm that the apparent signal for ð1405Þ ! f0ð980Þ0is not caused by background events, we perform
a study with an inclusive MC sample of 2:25 108 J=c events generated according to the Lund-Charm model [25] and the Particle Data Group (PDG) decay tables [26]. After the same event selection as above, neither ð1405Þ nor f0ð980Þ are seen in the mass spectra. Non-f0ð980Þ or
non-ð1405Þ processes are studied using the f0ð980Þ
sidebands (0:88 GeV=c2< M þð00Þ< 0:93 GeV=c2 and 1:05 GeV=c2< M þð00Þ< 1:10 GeV=c2) or the ð1405Þ sidebands (1:15 GeV=c2< M þ0ð000Þ<
1:25 GeV=c2 and 1:55 GeV=c2< M
þ0ð000Þ<
1:65 GeV=c2). No peaking structures are observed.
Figures 2(a) and 2(b) show the þ and 00
mass spectra with the requirement 1:3 GeV=c2<
Mþ0ð30Þ< 1:5 GeV=c2. A fit is performed to the
þ mass spectrum with the f0ð980Þ signal
parame-trized by a Breit-Wigner function convolved with a Gaussian mass resolution function plus a second-order Chebychev polynomial background function. The mass, width, and number of events of the f0ð980Þ
obtained from the fit are m ¼ 989:9 0:4 MeV=c2,
) 2 )(GeV/c -π + π M( 0.5 1.0 1.5 ) 2 )(GeV/c 0 π -π +π M( 0.5 1.0 1.5 (a) ) 2 )(GeV/c 0 π 0 π M( 0.5 1.0 1.5 ) 2 )( G eV/c 0 π 0 π 0 π M ( 0.5 1.0 1.5 (b)
FIG. 1. (a) Scatter plot of Mþ0versus Mþ. (b) Scatter plot of M000 versus M00 (3 entries per event).
¼ 9:5 1:1 MeV=c2, and N ¼ 706 41, respectively.
A fit to the 00 mass spectrum, shown in Fig. 2(b), is performed in a similar fashion. The mass, width, and number of events of the f0ð980Þ obtained from the fit are
m ¼ 987:0 1:4 MeV=c2, ¼ 4:6 5:1 MeV=c2 (less than 11:8 MeV=c2 at 90% C.L.) and N ¼ 190 30,
re-spectively. The measured width of the f0ð980Þ is much
narrower than the world average.
Figures3(a) and3(b) show the þ0 and 000
mass spectra where þð00Þ is in the f
0ð980Þ mass
region (0:94 GeV=c2< M
þð00Þ< 1:04 GeV=c2). In
addition to the ð1405Þ, there is an enhancement at 1:3 GeV=c2. A fit is performed to the þ0 mass spectrum. The two peaks are parametrized by efficiency-corrected Breit-Wigner functions convolved with a Gaussian resolution function. The mass and width of the
small enhancement are fixed to PDG values of f1ð1285Þ
[26]. The background is described by a third-order Chebychev polynomial with shape parameters determined from a simultaneous fit to the þ0 mass spectrum
while the þ invariant mass is found in the f0ð980Þ
sidebands. The normalization of each component is al-lowed to float. The masses, widths, number of events, efficiencies, and the product branching ratios of the ð1405Þ and the possible f1ð1285Þ=ð1295Þ contribution
are listed in Table I. The statistical significance of the ð1405Þ is determined by the change of the fit likelihood -2 lnL obtained from the fits with and without the assump-tion of the ð1405Þ and is found to be well above 10. The significance of the potential f1ð1285Þ=ð1295Þ
con-tribution is determined to be 3:7. A fit to the 000 mass spectrum is performed in a similar fashion, shown in Fig.3(b). The significance of the ð1405Þ is determined to be larger than 10. For a possible f1ð1285Þ=ð1295Þ
con-tribution, the significance is only 1:2, and we derive an upper limit on the branching ratio at the 90% C.L. using the Bayesian method.
An angular-distribution analysis is performed with the selected J=c ! ð1405Þ ! f0ð980Þ0! þ0
events. Backgrounds are subtracted using the f0ð980Þ
side-band events. For radiative J=c decays to a JP¼ 0
me-son, the polar angle of the photon in the J=c
center-of-mass system should be distributed according to 1 þ cos2. In the case of a JP¼ 1þ meson, the distributions
d d cos 1 þ 2jj 2þ ð1 2jj2Þcos2 and d cosd f0ð980Þ 2 þ ðjj2 2Þsin2
f0ð980Þ are expected, where f0ð980Þ is
the polar angle of f0ð980Þ in the helicity frame of
ð1405Þ, is the ratio of helicity 1 to helicity 0. For the JP¼ 1þassumption,jj2is determined to be 2:10 0:26
from a fit to cosf0ð980Þ [Fig. 3(c)]. The fitting
2=number of degrees of freedom of Fig. 3(d) with
jj2 ¼ 2:10 is 59:4=15. For the JP¼ 0 assumption, the
fitting 2=number of degrees of freedom of Fig. 3(d) is
38:4=15. Comparing the probability of 1þhypothesis to 0 hypothesis, the ratio of the probabilities is 4:1 104. The fitting results favor the JP¼ 0 assignment of the ð1405Þ.
Figures 4(a)and 4(b)show the þ0 and 000
mass spectra in the 0 region. A fit is performed to the þ0mass spectrum, shown in Fig.4(a). The shape of
the 0 is obtained from MC simulation and the mass and width of the 0 are fixed to its PDG values [26]. The shape of the peaking backgrounds [J=c ! 0! 0ðþÞ and J=c ! 0! !ðþ0Þ] is from exclusive MC samples with predicted background levels of 361 32 and 32 6 events, normalized by branching ratios in the PDG [26] and fixed in the fit. The error on the number of events is estimated by changing the normalization by 1 standard deviation from the PDG value. A second-order Chebychev polynomial is used to describe the sum of other nonpeaking backgrounds.
0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 140 160 180 200 220 ) 2 )(GeV/c -π + π M(π+π-)(GeV/c2) M( 0.9 1.0 1.1 1.2 ) 2 Events/(0.005GeV/c ) 2 Events/(0.005GeV/c 0 20 40 60 80 100 120 140 160 180 200 220 (a) 0.9 1.0 1.1 1.2 0 50 100 ) 2 )(GeV/c 0 π 0 π M(π0π0)(GeV/c2) M( 0.9 1.0 1.1 1.2 ) 2 Even ts/(0.01GeV/c ) 2 Even ts/(0.01GeV/c 0 50 100 (b)
FIG. 2 (color online). The þ and 00 invariant mass spectra with þ0ð30Þ in the ð1405Þ mass region. The solid curve is the result of the fit described in the text. The dotted curve is the f0ð980Þ signal. The dashed curve denotes the background polynomial. 1 .2 1.4 1.6 1.8 0 50 100 150 200 250 ) 2 )(GeV/c 0 π (980) 0 M(f(980)π0)(GeV/c2) 0 M(f 1 .2 1.4 1.6 1.8 ) 2 Events/(0.02GeV/c ) 2 Events/(0.02GeV/c 0 50 100 150 200 250 (a) 1 .2 1.4 1.6 1.8 0 10 20 30 40 50 60 ) 2 )(GeV/c 0 π (980) 0 M(f(980)π0)(GeV/c2) 0 M(f 1 .2 1.4 1.6 1.8 ) 2 Eve nt s/(0.02G e V/ c ) 2 Eve nt s/(0.02G e V/ c 0 10 20 30 40 50 60 (b) -0.5 0.0 0.5 0 50 100 150 200 250 para1 = 2.10 ± 0.26 (980) 0 f θ cos (980) 0 f θ cos -0.5 0.0 0.5 (980 ) 0 f θ dN/dco s (980 ) 0 f θ dN/dco s 0 50 100 150 200 250 (c) -0.5 0.0 0.5 0 50 100 150 200 250 γ θ cosθγ cos -0.5 0.0 0.5 γ θ dN/dcos γ θ dN/dcos 0 50 100 150 200 250 -0 + 1 (d)
FIG. 3 (color online). Results of the fit to (a) the f0ð980Þ ðþÞ0 and (b) f
0ð980Þð00Þ0 invariant mass spectra. The solid curve is the result of the fit described in the text. The dotted curve is the f1ð1285Þ=ð1295Þ and ð1405Þ signal. The dashed curves denote the background polynomial. Angular distributions of the signal include efficiency corrections. (c) The cosf0ð980Þdistribution. The fitting result of cosf0ð980Þisjj
2¼ 2:10 0:26. (d) The cos distribution. The solid line is the prediction for the JP¼ 0hypothesis, and the dashed line is the prediction for the JP¼ 1þhypothesis withjj2¼ 2:10.
For 0 ! 000, 2ð000Þ < 2ð00Þ and
jM mj > 0:03 GeV=c2 are additionally required to
remove background events from 0 ! 00. A fit to the
000mass spectrum is performed as shown in Fig.4(b).
The shapes of the 0 and nonpeaking backgrounds are described analogously to the charged mode. The efficien-cies and the product branching ratios for the 0 obtained from the fit are also listed in TableI. From our measure-ment and the world average values for branching ratios of 0! [26], we determine r¼ ð8:87 0:98Þ
103and r0¼ ð16:41 1:94Þ 103.
The systematic uncertainties on the signal yield arise from fit ranges, signal shapes, and background estimation. In detail, for the ð1405Þ signal, the signal shape is given by a Breit-Wigner function with floating mass and width. Its uncertainties are estimated by fixing the mass and width of the ð1405Þ to the world average values. For the pos-sible f1ð1285Þ=ð1295Þ contribution and 0signal,
uncer-tainties are estimated by changing their mass and width by 1 standard deviation from the PDG values. The uncertainty due to the assumed background shape for the ð1405Þ and the f1ð1285Þ=ð1295Þ has been estimated using different
f0ð980Þ sidebands, while that of the 0 is studied using
different order polynomials. For 0 ! þ0, the
un-certainty of the peaking background is estimated by using the shape from the 0sidebands instead of using the shape
from exclusive MC samples. The systematic errors on the branching ratio measurements are also subject to
system-atic uncertainties in the number of J=c events [20], the intermediate branching ratios [26], the data-MC difference in the tracking efficiency, the photon detection effi-ciency, particle identification, the kinematic fit, and the 0selection. Combined in quadrature with the uncertainty
from the mass spectrum fitting, the systematic errors on the product branching ratios of the ð1405Þ, f1ð1285Þ=ð1295Þ, and 0are summarized in TableI.
The ð1405Þ ! f0ð980Þ0 signal could arise via
ð1405Þ ! a0
0ð980Þ0 and a00ð980Þ f0ð980Þ mixing.
Using the branching ratio of J=c ! ð1405Þ ! þ and the largest PDG value of ðð1405Þ ! a0ð980ÞÞ=ðð1405Þ ! Þ, BrðJ=c ! ð1405Þ !
a00ð980Þ0! 00Þ ¼ ð8:40 1:75Þ 105. The
a0
0ð980Þ f0ð980Þ mixing intensity [ af¼ Brðc1!
f0ð980Þ0! þ0Þ=Brðc1! a00ð980Þ0! 00Þ]
measured at BESIII is less than 1% (90% C.L.) [27]. The branching ratio of J=c ! ð1405Þ ! a0
0ð980Þ0!
f0ð980Þ0 ! þ0 is thus expected to be less
than ð8:40 1:75Þ 107, which is much smaller than the result that we measure. Therefore, a0
0ð980Þ f0ð980Þ
mixing alone can not explain the observed branching ratio of ð1405Þ ! f0ð980Þ0.
To interpret the anomalously narrow width of f0ð980Þ
and large isospin violation observed in this channel, Wu et al. recently proposed that a novel scenario of triangle singularity would play a crucial role in this process [28]. Further theoretical and experimental studies are needed for a better understanding of the underlying dynamics.
In summary, we have studied J=c ! 3 decays. The isospin violating decay ð1405Þ ! f0ð980Þ0 is observed
for the first time with a statistical significance larger than 10 in both the charged and neutral modes. According to our measurement, the ratio of Brðð1405Þ ! f0ð980Þ0!
þ0Þ to Brðð1405Þ ! a0
0ð980Þ0! 00Þ is
ð17:9 4:2Þ% [26,29], which is 1 order of magnitude larger than the a0
0ð980Þ f0ð980Þ mixing intensity (less
than 1%) determined at BESIII previously [27]. The mea-sured width of the f0ð980Þ is anomalously narrower than
the world average. There is also evidence for an enhance-ment at around 1:3 GeV=c2 [potentially from the f1ð1285Þ=ð1295Þ] seen with a significance of 3:7 in
TABLE I. Summary of measurements of the masses, widths, number of events, the MC efficiencies () and the product branching ratios of BrðJ=c ! XÞ BrðX ! 0f
0ð980ÞÞ Brðf0ð980Þ ! Þ and the decay branching ratios of BrðY ! 3Þ for the þ0 and 000 channels, where X represents ð1405Þ and the possible f
1ð1285Þ=ð1295Þ contribution, Y represents 0. Here for the branching ratios, the first errors are statistical and the second ones are systematic.
Resonance MðMeV=c2Þ ðMeV=c2Þ N
event ð%Þ Branching ratios
ð1405Þðþ0Þ 1409:0 1:7 48:3 5:2 743 56 22:20 0:21 ð1:50 0:11 0:11Þ 105 ð1405Þð000Þ 1407:0 3:5 55:0 11:0 198 23 12:83 0:11 ð7:10 0:82 0:72Þ 106 f1ð1285Þ=ð1295Þðþ0Þ fixed fixed 60 18 26:99 0:23 ð9:99 3:00 1:03Þ 107 f1ð1285Þ=ð1295Þð000Þ fixed fixed 23 16:75 0:13 <7:11 107 0ðþ0Þ fixed fixed 1014 39 22:52 0:19 ð3:83 0:15 0:39Þ 103 0ð000Þ fixed fixed 309 19 7:57 0:08 ð3:56 0:22 0:34Þ 103 0.85 0.9 0.95 1 1.05 1.1 0 200 400 600 800 ) 2 )(GeV/c 0 π -π + π M(π+π-π0)(GeV/c2) M( 0.85 0.9 0.95 1 1.05 1.1 ) 2 Events/(0.01GeV/c ) 2 Events/(0.01GeV/c 0 200 400 600 800 (a) 0.850 0.9 0.95 1 1.05 50 100 150 ) 2 )(GeV/c 0 π 0 π 0 π M(π0π0π0)(GeV/c2) M( 0.85 0.9 0.95 1 1.05 ) 2 Event s /(0.01Ge V /c ) 2 Event s /(0.01Ge V /c 0 50 100 150 (b)
FIG. 4 (color online). Results of the fit to (a) the þ0and (b) 30invariant mass spectra. The solid curve is the result of the fit described in the text. The dotted curve is the 0signal. The dashed curves denote the background polynomial. The dash-dotted curve in (a) describes the peaking background.
the charged mode and 1:2 in the neutral mode. For the decay 0! þ0, the branching ratio that we measure
is consistent with the CLEO-c measurement [30], and the precision is improved by a factor of 4. For the decay 0! 30, it is 2 times larger than the world average value
[26]. Using our new measurement of the decay rates for 0! 3, the values of rand r0are more than 4 standard
deviations away from both 0 mixing prediction and
the chiral unitary framework prediction [19].
The BESIII Collaboration thanks the staff of BEPCII and the computing center for their hard efforts. Useful discus-sions with K. T. Chao, S. L. Zhu, and J. J. Wu are acknowl-edged. 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; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts No. KJCX2-YW-N29, No. KJCX2-YW-N45; 100 Talents Program of CAS; Istituto Nazionale di Fisica Nucleare, Italy; Siberian Branch of Russian Academy of Science, joint project No 32 with CAS; U.S. Department of Energy under Contracts No. 04ER41291, No. DE-FG02-91ER40682, No. DE-FG02-94ER40823; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
*Also at the Moscow Institute of Physics and Technology, Moscow, Russia.
†On leave from the Bogolyubov Institute for Theoretical
Physics, Kiev, Ukraine.
‡Present address: University of Perugia and INFN, Perugia,
Italy.
§Also at the PNPI, Gatchina, Russia.
kPresent address: Nagoya University, Nagoya, Japan.
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