Search for the decays and measurements of the branching fractions
Using a sample of events collected with the BESIII detector at BEPCII, the decays and are searched for, where and are reconstructed in the decay chains , and , , respectively. No significant signals are observed. The upper limits of the product branching fractions are determined to be and at the 90% C.L.. The branching fractions for are also measured to be , which are the world’s most precise measurements.
pacs:13.25.Gv, 13.40.Hq, 14.40.Pq
Charmonium has been playing an important role in understanding the dynamics of QCD. Despite the success of QCD in many aspects of the strong interaction, the charmonium decay mechanism remains challenging and presents disagreement between experimental data and theoretical predictions Eich .
In massless QCD models, the processes are forbidden by the helicity selection rule helicity . However, the experimental observations of the decays PDG , as well as formed in the annihilation hc_first , indicate substantial contributions due to finite masses. These observations have stimulated many theoretical efforts pr2 ; pr1 ; pr3 . In Ref. zhaogd , it is pointed out that the branching fraction of with respect to that of may serve as a criterion to validate the helicity conservation theorem, and an anomalous decay in might imply the existence of a glueball. For the decay , possible large branching fractions are suggested. Authors of Ref. pr2 investigate the long distance contribution via charmed hadron loops and predict . In Ref. pr1 , a branching fraction of is predicted by “factorizing” the initial and the final states.
In this paper, we report on a search for and decays into , where is produced from the radiative transition, while is produced via the isospin-forbidden process . In addition, we measure the decays with J = 0, 1, and 2. The analysis is based on an annihilation sample of events taken at GeV psiNum . A 44 sample taken at GeV is used to estimate the background contribution from the continuum processes.
Ii Experiment and data sets
The BESIII detector, described in detail in Ref. BES , has an effective geometrical acceptance of 93% of . A helium-based main drift chamber (MDC) determines the momentum of charged particles measured in a 1 T magnetic field with a resolution 0.5% at 1 GeV/ (the resolutions mentioned in the paper are rms resolutions). The energy loss (E) is also measured with a resolution better than 6%. An electromagnetic calorimeter (EMC) measures energies and positions of electrons and photons. For 1.0 GeV photons and electrons, the energy resolution is 2.5% in the barrel and 5.0% in the end caps, and the position resolution is 6 mm in the barrel and 9 mm in the end caps. A time-of-flight system (TOF) with a time resolution of 80 ps (110 ps) in the barrel (end cap) is used for particle identification. A muon chamber based on resistive plate chambers with 2 cm position resolution provides information for muon identification.
An inclusive Monte Carlo (MC) sample of events is used for background studies. The resonance is produced by the event generator KKMC KKMC , and the decays are generated by EvtGen EvtGen with known branching fractions PDG , while the unmeasured decays are generated according to the Lundcharm model lundcharm . Exclusive signal MC samples are generated to determine the detection efficiency and to optimize selection criteria. The and decays are generated according to phase space distributions, and decays are generated with an angular distribution of protons following the form in the helicity frame, where is taken from measured data. GEANT4 is used to simulate events where the measured detector resolutions are taken into consideration geant .
Iii Event selection and background analysis
Each charged track is required to have its point of closest approach to the beam line within 1 cm of the beam line in the radial direction and within 10 cm from the interaction point along the beam direction and to lie within the polar angle coverage of the MDC, in laboratory frame. The information from the TOF is used to form a likelihood () with a proton (kaon/pion) hypothesis. To identify a track as a proton, the likelihood is required to be greater than and .
Photons are reconstructed from isolated showers in the EMC which are at least 15 (25) degrees away from the proton (antiproton) candidate. Photon candidates in the barrel () and in the end cap () must have an energy of at least 25 MeV. Electromagnetic showers close to the EMC boundaries are poorly reconstructed and excluded from this analysis. To suppress electronic noise and energy deposits unrelated to the event, the EMC timing of the photon candidate must be in coincidence with collision events (in units of 50 ns).
In the and selection, the candidate events must have two oppositely charged tracks and at least one or two good photons, respectively. To suppress the nonproton backgrounds in selecting the final states, both tracks are required to be positively identified as protons, while for the final states only one track is required to be a proton. A four-constraint (4C) kinematic fit of () candidates is performed to the total initial four-momentum of the colliding beams in order to reduce background and to improve the mass resolution. If more photons than required exist in an event, the best one(s) is(are) selected by minimizing the of the 4C kinematic fit. Events with are accepted as () candidates. For candidates, the invariant mass of the two selected photons is further required to be in the range 0.11 GeV/0.15 GeV/.
For the channel, the main backgrounds in the signal region ( GeV/ GeV/) are decays combined with a fake photon, or with a photon from initial-state radiation or final-state radiation (FSR) and the continuum process. In the signal region ( GeV/ GeV/), the main backgrounds come from the decays or the nonresonant process . Since the energy of the transition photon from is only 50 MeV, events can easily fake signal events by combining with a fake photon. With a 4C kinematic fit, those events will produce a peak in the mass spectrum close to the expected mass. Therefore, a three-constraint (3C) kinematic fit, where the magnitude of the photon momentum is allowed to float, is used to determine signal yields. The 3C fit keeps the peak at the correct position as the photon momentum tends to zero, and it can separate this background from the signal efficiently as shown in Fig. 1 wangyq . The background from the continuum process is studied with the data taken at GeV. The contribution of the background is found to be negligible.
Background from is measured by selecting events from data. The selection is the same as that for , . A MC sample of is generated to determine the efficiencies of the selection () and the selection (). The selected events corrected by the efficiencies () are taken as the background in . The shape of this background can be described with a Novosibirsk function Novo as shown in Fig. 2.
For , the main background sources are the decays (where ) combined with a fake photon and the decay from or continuum process. The backgrounds are strongly suppressed by using the 3C kinematic fit, where the momentum of the photon with lower energy is allowed to float. For the backgrounds, the (where is the photon with higher energy) with 3C peaks at 3.686 GeV/, while for the signal, it is below 3.66 GeV/ as shown in Fig. 3 wangyq . A requirement is used to remove this background effectively. The background from the continuum process is studied with the data sample taken at GeV and is found not peaking in the signal region. The background having the same final state as signal events is irreducible. It is included in the fit to the spectrum.
Iv Determination of yields
Figure 4 shows the invariant-mass distribution for the selected candidates. There are clear , , and peaks. The signal for is not significant. An unbinned maximum likelihood fit to the distribution is used to determine the signal yields of and . The fitting function is composed of signal and background components, where the signal components include and , and the background components include , , and nonresonant background. The line shapes for and are obtained from MC simulation following , where is the invariant mass of , and are the mass and width of the Breit-Wigner line shape for and , and the values are fixed at the nominal values PDG . which equals to is the energy of the transition photon in the rest frame of , and is a function that damps the diverging tail originating from the dependence at the low mass side (corresponding to high energy of the radiative photon). The form of the damping factor was introduced by the KEDR collaboration and is kedr , where is the peak energy of the transition photon. The background is described with a Novosibirsk function with the fixed shape and amplitude as described earlier. The backgrounds from and are described with a shape based on a MC simulation, where the FSR photon is simulated with PHOTOS photo , and their magnitudes are allowed to float. The shape of the nonresonant background is determined from a MC simulation while its magnitude is allowed to float. To account for a possible difference in the mass resolution between data and MC simulation, a smearing Gaussian function is convolved with the line shape of , and the parameters of this function are free in the fit. Since we find that the discrepancy in the mass resolution decreases with increasing and is close to zero in the region, a MC-determined line shape is directly used for the in the fit to data. The fitting results are shown in Fig. 4. The signal yields of , , , and are , , and , respectively. The statistical significance of the signal is . The goodness of fit is , which indicates a reasonable fit.
Since signal is not significant, we determine the upper limit on the number of signal events. The probability density function (PDF) for the expected number of signal events is taken to be the likelihood in fitting the distribution while scanning the number of signal events from zero to a large number, where the signal yields of the are free. The 90% C.L. upper limit on the number of signal events , which corresponds to , is 54.
Figure 5 shows the invariant-mass distribution for the selected candidates. There is no obvious signal. The signal yield of is determined from an unbinned maximum-likelihood fit to the distribution in with the signal and the background components. The signal is described by the MC determined shape convolved with a smearing Gaussian. In the MC simulation, the mass and width of are set to the measured values PDG . The smearing Gaussian is used to account for the difference in the mass resolution between data and MC simulation. The parameters of the Gaussian function are determined from . The background is described by an ARGUS function argus with the magnitude and shape parameters floated. No obvious signal event is observed. The upper limit at the 90% C.L. on the signal events, calculated with the same method as was applied for the , is 4.4. Figure 5 shows the fitting result with the background shape, and the goodness of fit is .
V systematic uncertainties
In the branching-fraction measurements, there are systematic uncertainties from MDC tracking (1% per track) eff-track , particle identification (1% per track) eff-track , photon reconstruction (1% per photon) eff-photon , the total number of events (0.8%) psiNum , the kinematic fit, and the simulation of helicity angular distribution of the proton and antiproton. The uncertainty in the kinematic fit comes from the inconsistency between the data and MC simulation of the track-helix parameters. We make corrections to the helix parameters according to the procedure described in Ref. guoyp , and take the difference between the efficiencies with and without the correction as the systematic error. The helicity angular distribution of protons from is taken from measured data and fitted by the formula . The values for and are , and , respectively. The selection efficiencies are determined from MC where the values are set to the mean values. The change in efficiency by varying the value by is taken as the uncertainty in the proton angular distribution. For , the differences in efficiencies for MC samples simulated with phase space and , 0.8% and 0.5% for and , respectively, are taken as the systematic errors.
For the measurement, the uncertainties in the fitting procedure include the damping factor, fitting range, the description of the background, and the mass resolution of . An alternative damping function was used by CLEO cleo-damp , where , and MeV for and , respectively guoyp . The difference in the final results caused by the two damping factors is taken as the systematic uncertainty. The uncertainty caused by the fitting range is obtained by varying the limits of the fitting range by GeV/. The uncertainty of the background is estimated by varying the parameters of the shape and magnitude by . The uncertainty from the resolution of is found to be negligible.
|Total number of||0.8||0.8||0.8||0.8||0.8|
|Proton angle distribution||0.8||0.6||0.3||0.8||0.5|
|mass region cut||-||-||-||-||3.0|
For , additional uncertainties are caused by the mass resolution of , the fitting range, the mass requirement and the background shape. The uncertainty from the mass resolution of is estimated by varying the resolution by . The uncertainty due to the fitting range is estimated by allowing the fitting range to vary within GeV/. The difference in the number of signal events is taken as the systematic error. The uncertainty due to the mass requirement is studied using the decay bes3-bian , and 3% is quoted as the systematic uncertainty. The uncertainty from the background shape (12.5%) is estimated by changing the background shape from an ARGUS function to a second-order polynomial. Table 1 summarizes all the systematic uncertainties. The overall systematic uncertainties are obtained by summing all the sources of systematic uncertainties in quadrature, assuming they are independent.
Vi results and discussion
We use MC-determined efficiencies to calculate the product branching fractions . By combining the measurements of PDG , the branching fractions for are obtained. The results are summarized in Table 2. The upper limits on the product branching fractions of the and are calculated with the formula . Here is the upper limit of signal events, is the number of events, is the MC-determined efficiency (45.6% for , and 37.7% for ), and is the overall systematic error. We obtain and at the 90% C.L..
The branching fraction for is determined by multiplying the ratio of the product branching fractions and . Here the product branching fraction is taken from the recent BESIII measurement bes3-wangll , and was measured by BABAR BaBar . This allows some systematic errors, such as errors in the tracking efficiency and the damping factor, to cancel out. The result is inflated by a factor , where the fractional systematic error is dominated by the measurement. The 90% C.L. upper limit is determined to be . By combining the BESIII measurement of bes3-bian , the upper limit of the branching fraction is obtained to be at the 90% C.L., where the errors are treated with the same method as in .
In summary, with a sample of events, we search for the decays and , but no significant signals are observed. The 90% C.L. upper limits of the branching fractions for and are determined. The current upper limit of , which is larger than the measurement of bes3-guoaq , cannot directly test the conjecture of Ref. zhaogd to validate the helicity theorem. The upper limit on obtained from this work is consistent with the earlier experimental results hc_first and is lower than the predictions pr1 ; pr2 , where model parameters may need to be tuned. The branching fractions of are measured with improved precision, consistent with the most recent measurement by CLEO-c ppbar-cleo , and the results are also compatible with theoretical calculation of by including the color octet contribution com . The results presented in this paper will be of interest for future experiments like PANDA in their search for hadronic resonances panda .
The BESIII collaboration thanks the staff of BEPCII and the computing center for their strong support. 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, and No. 11235011; Joint Funds of the National Natural Science Foundation of China under Contracts No. 11079008 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; German Research Foundation DFG under Collaborative Research Center Contract No. CRC-1044; 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-FG02-05ER41374, No. DE-FG02-94ER40823, and No. DESC0010118; 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.
- (1) E. Eichten, S. Godfrey, H. Mahlke and J. L. Rosner, Rev. Mod. Phys. 80, 1161 (2008).
- (2) S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848 (1981).
- (3) J. Beringer et al. (Particle Data Group), Phys. Rev D 86, 010001 (2012).
- (4) M. Andreotti et al. Phys. Rev. D 72, 032001 (2005).
- (5) X. H. Liu and Q. Zhao, J. Phys. G 38, 035007 (2011).
- (6) S. Barsuk, J. He, E. Kou and B. Viaud, Phys. Rev. D 86, 034011 (2012).
- (7) F. Murgia, Phys. Rev. D 54, 3365 (1996).
- (8) K. -T. Chao, Y. -F. Gu and S. F. Tuan, Commun. Theor. Phys. 25, 471 (1996).
- (9) M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C 37 063001 (2013).
- (10) M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Meth. A 614, 345 (2010).
- (11) S. Jadach, B. F. L. Ward and Z. Was, Comp. Phys. Commu. 130, 260 (2000); Phys. Rev. D 63, 113009 (2001).
- (12) http://www.slac.stanford.edu/ lange/EvtGen; R. G. Ping et al., Chinese Physics C 32, 599 (2008).
- (13) J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang and Y. S. Zhu, Phys. Rev. D 62, 034003 (2000).
- (14) S. Agostinelli et al. (geant4 Collaboration), Nucl. Instrum. Meth. A 506, 250 (2003).
- (15) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 84, 091102 (2011).
- (16) The Novosibirsk function is defined as , where , the peak position is , the width is , and is the tail parameter.
- (17) H. Albrecht et al. (ARGUS Collaboration), Phys. Lett. B 241 (1990) 278.
- (18) V. V. Anashin et al. Int. J. Mod. Phys. Conf. Ser. 02, 188 (2011).
- (19) E. Barberio and Z. Was, Comput. Phys. Commun. 79, 291 (1994).
- (20) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 86, 032014 (2012)
- (21) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 83, 112005 (2011)
- (22) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 87, 012002 (2013)
- (23) R. E. Mitchell et al. (CLEO Collaboration), Phys. Rev. Lett. 102, 011801 (2009).
- (24) M. Ablikim et al. (BESIII Collobration), Phys. Rev. Lett. 109, 042003 (2012).
- (25) B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 78, 012006 (2008).
- (26) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 86, 092009 (2012).
- (27) M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 104, 132002 (2010).
- (28) P. Naik et al. (CLEO Collaboration), Phys. Rev. D 78, 031101(R) (2008).
- (29) S. M. H. Wong, Eur. Phys. J. C14, 643 (2000).
- (30) A. Lundborg, T. Barnes and U. Wiedner, Phys. Rev. D 73, 096003 (2006).