We present the first study of the process using events accumulated with the BESIII detector at the BEPCII facility. The branching fraction for is measured to be . With a Bayesian approach, the upper limits of the branching fractions and are determined to be and at the 95% confidence level, respectively. All of these measurements are given for the first time.
pacs:11.30.Er, 13.20.Gd, 12.38.Qk
The nature of the lightest scalar meson nonet has been a hot topic in hadron physics for many years ref:pdg (). In particular, the nature of the isovector is still not understood. It is interpreted by theorists to be a state with a possible admixture of a bound-state component due to the proximity to the threshold ref:pdg (); ref:baru (); ref:a0f0 (). The mass is known to be about 980 MeV and the dominant decay mode is . The radiative decay of the to the enigmatic scalar meson will provide useful information on the nature of state jpsidecay:1989 (); ref:theory (). Especially, in Ref. ref:theory (), the predicted branching fraction is based on the factorization of mixing and effective coupling constants. Therefore, search for production of the neutral in the isospin-violating decay will discriminate between different models jpsidecay:1989 (); ref:theory ().
The radiative decays with the total isospin of the hadronic final state , such as or , have been studied by previous experiments ref:liucy (); ref:previous (); ref:zhuyc (); ref:bes1 (); ref:gpi0pi0 (), while only a few processes with isotriplet hadronic final states, such as and , have been measured ref:isospin1 (); ref:isospin11 (). It is therefore of interest to study the isospin violating decay , which can be used to test charmonium decay dynamics ref:theory ().
In this paper, we present the first study of the decay based on a sample of events ref:jpsitotnumber (), collected by the Beijing Spectrometer (BESIII) located at the Beijing Electron Positron Collider (BEPCII).
Ii Besiii Detector and Data Samples
The accelerator BEPCII and the BESIII detector bes3 () are major upgrades of the BESII experiment at the BEPC accelerator bes2 (); bes2-p2 () for studies of hadron spectroscopy, charmonium physics, and -charm physics bes3phys (). The BESIII detector with a geometrical acceptance of 93% of 4 consists of the following main components: (1) a small-cell main drift chamber (MDC) with 43 layers used to track charged particles. The average single-wire resolution is 135 m, and the momentum resolution for 1 GeV/ charged particles in a 1 T magnetic field is 0.5%. (2) a time-of-flight system (TOF) used for particle identification. It is composed of a barrel made of two layers, each consisting of 88 pieces of 5 cm thick and 2.4 m long plastic scintillators, as well as two end caps with 96 fan-shaped, 5 cm thick, plastic scintillators in each end cap. The time resolution is 80 ps in the barrel and 110 ps in the end caps, providing a separation of more than 2 for momenta up to about 1.0 GeV/. (3) an electro-magnetic calorimeter (EMC) used to measure photon energies. The EMC is made of 6240 CsI (Tl) crystals arranged in a cylindrical shape (barrel) plus two end caps. For 1.0 GeV photons, the energy resolution is 2.5% in the barrel and 5% in the end caps, and the position resolution is 6 mm in the barrel and 9 mm in the end caps. (4) a muon counter made of resistive plate chambers arranged in 9 layers in the barrel and 8 layers in the end caps, which is incorporated into the iron flux return yoke of the superconducting magnet. The position resolution is about 2 cm.
The event selection optimization, efficiency estimation, and background evaluation are performed are performed through Monte Carlo (MC) simulations, for which the GEANT4-based geant4 () MC simulation package BOOST sim-boost () is used. The BOOST software incorporates the geometric and material description of the BESIII detector components, the detector response and digitization models, and detector running conditions and performance. The production of the resonance is simulated with the MC event generator KKMC sim-kkmc (); sim-kkmc2 (), while known decay modes are generated with EVTGEN sim-evtgen (); ref:sim (), with branching fractions set to world average values from the Particle Data Group (PDG) ref:pdg (). The LUNDCHARM sim-lundcharm () model is used for the remaining, unknown decays. A sample of 200 generic decay events (named inclusive MC sample thereafter) is used to study potential backgrounds. A sample of exclusive MC signal events is generated uniformly in phase space. For additional signal studies, samples of exclusive and MC events are generated with angular dependence in the and distributions based on experimental information sim-evtgen (); ref:sim (). For further background studies, we use exclusive MC events for each of the following processes: , , or . All exclusive samples listed previously are generated without consideration of angular dependence in phase space.
Iii Event selection
The decays, with subsequent decays and , have a topology of five photons in the final state. To select signal candidates, we require at least five photons and no reconstructed charged particles in an event. The photon candidates are required to have at least 25 MeV deposited energy in barrel region () of the EMC, while 50 MeV are required in the end cap regions (), where is the polar angle of the electromagnetic shower. Timing information of the EMC is used to suppress electronic noise and energy depositions that are unrelated to the event. Photon candidates within 50 ns relative to the most energetic shower are selected.
A four-constraint (4C) kinematic fit imposing energy-momentum conservation under the hypothesis is performed, and is required. All further selections are based on the four-momenta updated by the 4C fit. The variable is used to identify which photons originate from the decays of and , respectively; here, is the invariant mass of two photons and () is the mass of () listed in PDG ref:pdg (). We try all possible combinations of the five selected photons, and the one with the minimum is selected. To suppress backgrounds with two in the final state (e.g., ), we define the variable . An event is rejected if any combination of photons satisfies GeV. The invariant mass spectra of the photon pairs from the and decays are shown in Fig. 1. We fit a Gaussian function plus a third order polynomial background to the mass spectra to obtain the mass resolution, which is determined to be 8 MeV for the meson and 5 MeV for the . The signal region is defined as GeV/. The signal region is defined as GeV/, and the sidebands are defined as GeV/ GeV/.
The scatter plot of the invariant mass of the candidate versus that of , obtained after applying above selection criteria, is shown in Fig. 2(a). A strong peak, which is associated with the background process from the production of mesons with the final state, is visible in Fig. 2(b). The signature of the decay is more evident from the invariant mass spectrum shown in Fig. 2(b), obtained after additionally selecting the and candidates. To reject backgrounds, we require GeV/, where is the nominal mass ref:pdg ().
Iv Branching fraction and yield measurements
After all selection criteria discussed in the previous section are applied, we obtain event candidates for the decay . The potential background contribution is studied using both data and MC samples. The background events from the data are selected using the sidebands, defined in Sec. III. In addition, the background events are studied with the inclusive MC sample; the background events with the same final state are found to be from the and decays. Apart from these two background channels, other background contributions are found to be represented by the sidebands.
To scale the background events from the sideband regions to the signal region, a normalization factor is defined as the ratio of the number of background events in the signal region and in the sideband regions. To obtain , we fit to the mass spectrum a combination of the signal shape, obtained from the exclusive signal MC, combined with a third order Chebychev polynomial to represent the background distribution. The polynomial background is integrated in the signal region () and in the sideband regions () and the normalization factor is found to be .
To obtain the number of events, an unbinned maximum likelihood fit is performed to the mass spectrum of the candidates, in the signal and sideband regions separately. The signals are parametrized by the shape obtained from the signal MC. The background shape is described by a third order Chebychev polynomial. The fit is shown in Fig. 3. The number of candidates obtained from the fit in the signal region is , while in the sideband regions the corresponding number is . The number of signal events is estimated to be .
The number of peaking background events from and is obtained from exclusive MC samples, and the corresponding background yields are given as and . The errors given here are the statistic errors from MC samples.
The branching fraction is calculated using the following expression:
where is the total number of events ref:jpsitotnumber (), and and are the branching fractions of the and decays to two photons, respectively ref:pdg (). The detection efficiency, , is obtained from the simulated signal events. The resulting branching fraction is calculated to be .
We also investigate the intermediate resonant process , where stands for or . The invariant mass spectrum in the and signal regions is shown in Fig. 4. We perform an unbinned maximum likelihood fit to determine the branching fractions of the radiative decays into these two mesons. For the signal shape, we use the formula ref:flatte () with the parameters from the model ref:WUjja0f0 (), while the signal shape is described by a Breit-Wigner (BW) function with the mass and width taken from PDG ref:pdg (). The and signal shapes are convoluted with corresponding resolution functions, and multiplied by the efficiency distribution. The resolution and efficiency as functions of the invariant mass are obtained using the signal MC sample. The resolution function is modeled by a sum of two Gaussians, with central values, widths and ratios fixed to the values obtained by analyzing the mass resolutions of the and resonances. The background shape consists of a third order Chebychev polynomial and two functions obtained from MC study for the background channels , and , .
The spectrum in Fig. 5 is obtained from the fit to the first region, [0.8, 2.0] GeV/. The event yields are for and for . The statistical significance is for and for . Using a Bayesian method ref:pdg (), we determine the upper limits for the and production, at the 95% confidence level (C.L.), by finding the value such that
where is the number of signal events, and is the value of the likelihood function of obtained in the fit. We find the upper limits at the 95% C.L. on the number of the and to be and .
We study the upper limits under different assumptions for the shapes of the and signal and non-resonant processes. For the non-resonant process, we replace the third-order Chebychev polynomial with a fourth-order Chebychev polynomial or the distribution from the signal MC. We also fit the signals of and together with background described above. All these variations are applied in three different mass regions: [0.8, 2.0] GeV/, [0.8, 1.92] GeV/ and [0.8, 2.08] GeV/. In addition, the fractions of the background channels are varied within one standard deviation due to the MC statistics and the used branching fractions. The signal shapes are varied by using different parameters of the and functions. In the formula for the , the parameters from the model are substituted by the model and model parameters ref:WUjja0f0 (); ref:prd90 (). In the case of the , the mass and width of the BW function are varied within the uncertainties of the quoted values ref:pdg (). We take the largest upper-limit number of signal events among different models as a conservative estimate, where we have the upper limits corresponding to the model, while corresponding to a variation in the width for the .
The upper limit on the product of branching fractions is determined by
where is corresponding number of signal events. The efficiency is 16.7% (20.1%) for the (), obtained from the () MC sample. is the total systematic uncertainty of the quantities in the denominator in Eq. (2). The upper limits on the branching fractions are and at the 95% C.L.
V Systematic uncertainties
To estimate systematic uncertainties in our measurement of the branching fractions, we consider the following effects: photon detection efficiency, photon energy scale, photon energy resolution, photon position reconstruction, the kinematic fit, and the fitting procedures. Uncertainties associated with our fitting procedures stem from the background shape, MC modeling of angular distributions, fitting region, background subtraction. External factors include the total number of events, branching fractions of the intermediate states and uncertainties in the branching fractions of the two background channels and .
The systematic uncertainty from the photon detection is studied by comparing the photon detection efficiency between MC simulation and a control sample consisting of the decays. The relative efficiency difference is about 1% for each photon ref:photon1 (). In this paper, 5% is taken as the systematic error for the efficiency of detecting five photons in the final state.
The uncertainty in the photon energy scale is determined to be 0.4% ref:bianjm (). After varying photon energy according to this factor, we obtain the difference in the branching fraction of 1.9%.
To estimate the uncertainty associated with the photon energy resolution, the photon energy is smeared by the Gaussian with energy dependent width, . This factor is determined from the difference in relative energy resolution between data and MC of 4% ref:bianjm (). With this smearing applied to the exclusive signal MC, we determine the corresponding efficiency and find that the systematic error associated with the photon energy resolution is 0.9%.
The difference in energy resolution between data and MC also affects the kinematic fit. When we adjust the energy error in the reconstructed photon error matrix by 4% ref:bianjm (), we obtain a 1.1% difference in the branching fraction measurement.
The uncertainty in photon position reconstruction is studied by changing the position parameter of each photon in the signal MC and the difference is found to be negligible (less than 0.1%).
When fitting two photons invariant mass distributions of the and candidate, we vary the background shape by replacing a third order Chebychev polynomial with a second or fourth order polynomial. The difference of 2.4% with respect to our nominal result is associated with these effects.
The angular distributions of the and in the signal MC are based on the phase space model. To obtain the uncertainty associated with this assumption, we change the angular distributions for the and by assuming a form: . We find the difference in the branching fraction of 9.2% from this effect.
In the nominal fit, the mass spectrum of the is fitted in the range from 0.45 GeV/ to 0.65 GeV/. Alternative fits within ranges from 0.43 GeV/ to 0.67 GeV/ and from 0.47 GeV/ to 0.63 GeV/ are performed, and the difference in the branching fraction of 1.6% is taken as the systematic uncertainty.
The uncertainty due to background subtraction is obtained by changing the sidebands from GeV/ GeV/ to GeV/ GeV/, which corresponds to a 1 change in sideband separation from the mass peak. The difference is found to be 2.0%, which is taken as the uncertainty from the background subtraction.
The number of events is determined from an inclusive analysis of the hadronic decays, and has an uncertainty of 0.6% ref:jpsitotnumber (). The uncertainties due to the branching fractions of and are taken from PDG ref:pdg (). The uncertainties due to the branching fractions of the background channels and are obtained by varying the respective values within ref:pdg (). The uncertainty associated with the branching fractions of background channels is determined to be 3.2%.
All the contributions are summarized in Table 1. The total systematic uncertainty is given by the quadratic sum of the individual errors, assuming all sources to be independent.
|Photon energy scale||1.9||3.6||3.8|
|Photon energy resolution||0.9||0.6||0.5|
|Number of events||0.6||0.6||0.6|
Based on 223.7 million events collected with the BESIII detector, the decay has been firstly observed. The branching fraction of the process is measured to be . With the Bayesian approach, upper limits for the intermediate production of and have been obtained at the 95% C.L. The upper limits are and , including systematic uncertainties.
For comparison, the branching fraction for the process is ref:zhuyc (), while for it is ref:zhuyc (). This study shows that the suppression rates for isospin-one processes in radiative decays, compared to isospin-zero decays, are consistent with naive theoretical expectations jpsidecay:1989 (), i.e., at least one order of magnitude. It is noticed that the upper limit on is much lower than the theoretical calculation in Ref. ref:theory (). The result in this paper indicates that the decay mechanism of may be totally different from , so the factorization method may not work for the decay ref:theory (). Our measurement provides important constraints on theoretical calculations.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11125525, 11235011, 11322544, 11335008, 11425524; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); the Collaborative Innovation Center for Particles and Interactions (CICPI); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts Nos. 11179007, U1232201, U1332201; CAS under Contracts Nos. KJCX2-YW-N29, KJCX2-YW-N45; 100 Talents Program of CAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) under Contract No. 530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Natural Science Foundation of China (NSFC) under Contracts Nos. 11405046, U1332103; Russian Foundation for Basic Research under Contract No. 14-07-91152; The Swedish Resarch Council; U. S. Department of Energy under Contracts Nos. DE-FG02-04ER41291, DE-FG02-05ER41374, DE-SC0012069, DESC0010118; U.S. National Science Foundation; 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.
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