Branching fraction measurement of and search for
Using a sample of events collected with the BESIII detector at the BEPCII collider, we study the decays of and . The branching fraction of is determined to be , which significantly improves on previous measurements. No clear signal is observed for the process, and the upper limit at the 95% confidence level for its branching fraction is determined to be , which improves on the previous searches by 2 orders in magnitude and reaches the order of the Einstein-Podolsky-Rosen expectation.
pacs:13.66.Bc, 13.25.Gv, 03.65.Vf
The charmonium state with a mass below the open charm threshold decays to light hadrons through the annihilation of into one virtual photon, three gluons or one photon and two gluons. The decaying to proceeds via the first two processes, thereby providing valuable information to understand the nature of decays. The available measurements of its branching fraction, , based on 57.7 million events collected at BESII ksklbes2 and 24.5 million events at CLEO kkcleo , are given by and respectively. Due to the discrepancy between these two measurements, the world average value in the particle data group (PDG) PDG2016 has quoted a relative precision of 19%, which limits the precise understanding of decay mechanisms.
In the -violating decay of to , the two identical bosons from the decay would need to form an antisymmetric state, and the process would be ruled out according to Bose-Einstein statistics. However, according to the Einstein-Podolsky-Rosen (EPR) epr paradox, the quantum state of a two-particle system cannot always be decomposed into the joint state of the two particles. Thus the spacelike separated coherent quantum system may also yield a sizable decay branching fraction of at the level roos . In this way, the system can be used to test the EPR paradox versus quantum theory. There also might be a small possibility to have a final state due to violation. In the oscillation model lihb , the violating branching fraction of is calculated to be . The MARKIII experiment searched for the decay with 2.7 million events, and the upper limit was determined to be at the 90% confidence level (C.L.) kkmark . Based on 57.7 million events collected at the BESII detector, the upper limit on the branching fraction was improved to be at the 95% C.L. ksksbes2 , which is still far from the expectations from EPR and oscillation.
The world’s largest sample with events was accumulated at BESIII during 2009 and 2012 jpsino . In this paper, we measure the branching fraction of , and also search for the violating decay .
Ii Apparatus and Monte Carlo simulation
The Beijing Spectrometer III (BESIII), located at the double-ring Beijing Electron Positron Collider (BEPCII), is a general purpose detector as described in Ref. Ablikim:2009vd . It covers 93% of in geometrical acceptance and consists of four main detectors. A 43-layer small-cell, helium gas based drift chamber, operating in a 1.0 (0.9) T solenoidal magnetic field in 2009 (2012), provides an average single-hit resolution of 135 m. A time-of-flight system, composed of 5 cm thick plastic scintillators with 176 bars of 2.4 m length, arranged in two layers in the barrel and 96 fan-shaped counters in the end caps, has a time resolution of 80 ps (100 ps) in the barrel (end caps) region providing 2 separation for momenta up to 1.0 GeV/. An electromagnetic calorimeter, which consists of 5280 CsI(Tl) crystals arranged in a cylindrical structure in the barrel and 480 crystals in each of the two end caps, provides an energy resolution for a 1.0 GeV/ photon of 2.5% in the barrel region and 5% in the end caps. The position resolution is 6 mm (9 mm) in the barrel (end caps). A muon counter system, which consists of resistive plate chambers arranged in nine barrel and eight end-cap layers, provides 2.0 cm position resolution.
The optimization of event selection criteria, the determination of detection efficiencies, and the estimation of background are performed by means of Monte Carlo (MC) simulations. The KKMC kkmc generator is used to simulate the process. The angular distribution of the or is generated to be proportional to , where is the polar angle in the laboratory system. In the MC simulation, the interference between the resonance decay and the continuum process is ignored. A GEANT4-based Agostinelli:2003hh ; Allison:2006ve detector simulation software, which includes the geometric and material description of the BESIII spectrometer, and the detector response, is used to generate the MC samples. The background is studied with a MC sample of inclusive decays, in which the known decays are generated with the EvtGen evtgen1 ; evtgen2 generator by setting the branching fraction to the values in the PDG PDG2016 and the remaining unknown decays are generated with the LUNDCHARM Chen:2000 .
Iii Branching fraction measurement of
The candidate is reconstructed from its charged final state, while the is assumed not to decay in the detector leaving only the signature of missing energy. The candidates are reconstructed with vertex-constrained fits to pairs of oppositely charged tracks, assumed to be pions, whose polar angles satisfy the condition . Only one candidate is accepted in each event. The candidates are required to satisfy 1 cm and , where is the distance between the common vertex of the pair and the interaction point and is its uncertainty. The invariant mass of the pair, , shown in Fig. 1, is required to satisfy MeV/, where is the nominal mass PDG2016 . There should be no extra tracks satisfying , within 1 cm of the interaction point in the transverse direction to the beam line and 10 cm of the interaction point along the beam axis. In order to suppress conversion background, the angle between the two charged tracks, , is required to satisfy .
The same event selection criteria are applied to the inclusive MC sample. The major potential backgrounds are and events, but the leakage of their momentum () spectra into the signal region is smooth and tiny.
The signal yield is determined from a maximum likelihood fit to the distribution, as shown in Fig. 2. In the fit, the signal shape is described by a double Gaussian function with a common mean value and two different widths. The background shape is represented by a second-order Chebychev polynomial function.
The continuum process is studied with a data set of 30.0 pb taken at 3.080 GeV. The same selection criteria are applied. The result of the maximum likelihood fit to the distribution is shown in Fig. 3. In the fit, the signal function is the same as that used in the fit of data. The background shape is represented by a first-order Chebychev polynomial function.
The event selection efficiencies are assumed to be the same at 3.080 GeV and the resonance. The continuum contribution to the resonance region is estimated from
where is the signal yield at 3.080 GeV, and are the luminosities collected at the and at 3.080 GeV, determined with events jpsino , while and correspond to the squares of center-of-mass energies of and 3.080 GeV. The power law of the center-of-mass energy follows the cross section slope measured by BABAR babarkk .
Assuming no interference between the decay and the continuum process, the branching fraction is determined from
where is the number of signal events obtained in the sample, is the event selection efficiency, is the number of events jpsino and is the branching fraction of . Table 1 summarizes the values used in the calculation, and is determined to be , where the quoted uncertainty is purely statistical.
|3.097 GeV ()||3.080 GeV|
The systematic uncertainties for the measurement include those due to reconstruction, the requirement on , the fit to the spectrum, the branching fraction of the decay, and the number of events.
The reconstruction involves the charged track reconstruction of the pair, the vertex fit and the mass window requirement. The corresponding systematic uncertainty is estimated using a control sample of events, where . The momentum of the , in decay is around 1.46 GeV/; thus only candidates with momentum larger than 1 GeV/ in the control sample are considered. The ratio of the reconstruction efficiency of the data over that in the MC is taken as a correction factor to the selection efficiency, while the uncertainty of the ratio, 1.4%, is taken as the systematic uncertainty.
The uncertainty from the requirement is estimated by varying the selection range. The range is expanded and contracted by , and the largest change in the branching fraction with respect to the nominal value is taken as the systematic uncertainty.
The systematic uncertainty related to the fit method is estimated by varying the fit range and the background shape simultaneously. The fit range is expanded and contracted by 8 MeV/. For the data sample, the background shape is varied from a second-order Chebyshev polynomial function to a third-order Chebyshev polynomial function and an exponential function. For the continuum data sample, the background is replaced by a second-order Chebychev polynomial function. The largest change in the branching fraction is treated as the systematic uncertainty.
The summary of all individual systematic uncertainties is shown in Table 2, where the total uncertainty is obtained by adding the individual contributions in quadrature.
Iv Search for
For with , the final state is . The candidate events are required to have at least four charged tracks whose polar angles satisfy . The candidates are reconstructed by secondary vertex fits to all oppositely charged track pairs assuming them to be pions, and the invariant mass must be within 18 MeV/ from the nominal mass. The candidates must have a momentum within the range of [1.40, 1.60] GeV/. In order to suppress the non- backgrounds, the decay length over its uncertainty () has to be larger than 2.0. Each event must have at least two candidates. If there are more than two candidates, the combination with the smallest sum of of the secondary vertex fits is selected.
The candidates are then combined in a 4C kinematic fit, where the constraints are provided by energy and momentum conservation. Only events with are retained. The distribution of the momentum in the rest frame is shown in Fig. 4. The momentum resolution is determined from the signal MC sample as 1.3 MeV/, which is the weighted average of the standard deviations of two Gaussians with common mean. The number of signal events is obtained by counting the remaining events within of the expected momentum. After all requirements have been imposed, two events remain in this region.
The same selection criteria are applied to the inclusive MC sample, which shows that the background mainly comes from the processes and . Their contributions are estimated from the corresponding MC samples using
where represents the corresponding channels or (), and is the expected number of events from channel . is the product branching fractions of the cascade decay, where is taken from the PDG PDG2016 , is set to the value obtained in this paper, and is the selection efficiency for a sample of events. The efficiencies of and channels are and , respectively. The expected background numbers are calculated to be and , where the uncertainties are from propagation of the items in Eq.(3). Some other exclusive processes, such as , are also studied with high statistics MC samples, but none of them survive the event selection.
Table 3 summarizes the systematic uncertainties in the search for . Common uncertainties including those from the number of decays and the branching fraction are the same as described in Sec. III. The uncertainty from reconstruction is evaluated according to the selection criteria used in this channel, with a method similar to that in Sec. III, and is determined to be 1.5% per . The uncertainty from the 4C kinematic fit is investigated using the control sample of , and the difference of the efficiency between the data and MC samples is taken as the systematic uncertainty associated with the kinematic fit.
|4C kinematic fit||1.1|
Since we have not observed a significant signal, an upper limit for is set at the 95% C.L. The upper limit is calculated using the relation
where is the upper limit on the number of signal events estimated with and using a frequentist approach with the profile likelihood method, as implemented in the ROOT framework trolke , and is the detection efficiency. The calculation includes statistical fluctuations and systematic uncertainties. The signal and background fluctuations are assumed to follow Poisson distributions, while the systematic uncertainty is taken to be a Gaussian distribution. The branching fraction of is included in the event selection efficiency . The values of variables used to calculate the upper limit on the branching fraction and the final result are summarized in Table 4, where the is the sum of and .
Based on a data sample of events collected with the BESIII detector, the measurements of and have been performed. The branching fraction of is determined to be , which agrees with the BESII measurement ksklbes2 while discrepancy with the CLEO data kkcleo persists. Compared with the world average value listed in the PDG PDG2016 , the relative precision is greatly improved, while the central value is consistent. With regard to the search for the and Bose-Einstein statistics violating process , an upper limit on its branching fraction is set at the 95% C.L. to be , which is an improvement by 2 orders in magnitude compared to the best previous searches kkmark ; ksksbes2 . The upper limit reaches the order of the EPR expectationsroos .
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 No. 11235011, No. 11335008, No. 11425524, No. 11625523, No. 11635010; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for Excellence in Particle Physics (CCEPP); Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts No. U1232105, No. U1332201, No. U1532257, No. U1532258; CAS under Contracts No. KJCX2-YW-N29, No. KJCX2-YW-N45, No. QYZDJ-SSW-SLH003; 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 Contracts No. Collaborative Research Center CRC 1044, No. FOR 2359; Istituto Nazionale di Fisica Nucleare, Italy; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS; 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 Contract No. 11505010; National Science and Technology fund; The Swedish Resarch Council; U. S. Department of Energy under Contracts No. DE-FG02-05ER41374, No. DE-SC-0010118, No. DE-SC-0010504, No. DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum für 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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