Measurements of the branching fractions for and and
We report on a study of the isospin-violating and conserving decays of the and charmonium state to and , respectively. The data are based on 225 million and 106 million events that were collected with the BESIII detector. The most accurate measurement of the branching fraction of the isospin-violating process is obtained, and the isospin-conserving processes and are observed for the first time. The branching fractions are measured to be and . No significant signal events are observed for decay resulting in an upper limit of the branching fraction of at the 90% confidence level. The two-body decay of is searched for, and the upper limit is at the 90% confidence level.
pacs:13.25.Gv, 12.38.Qk, 14.20.Gk
The charmonium vector meson, , is usually interpreted as an SU(3) singlet bound states with an isospin =0. Systematic measurements of its decay rates into final states that are isospin violating are of particular interest, since these results will provide a sensitive probe to study symmetry-breaking effects in a controlled environment. In this paper, we present a systematic study of isospin-conserving and violating decays of charmonium vector mesons into baryonic decays accompanied by a light pseudoscalar meson, namely and , respectively.
This work is for a large part motivated by a controversial observation that was made in the past while studying the baryonic decay of the . Surprisingly, the average branching fraction of the isospin violating decay of measured by DM2 dm2 and by BESI bes1 was determined to be , while the isospin conserving decay mode was not reported by either experiment. In 2007, the decays of and to the final states with a pair plus a neutral pseudoscalar meson were studied using 58 million and 14 million events collected with the BESII detector xuxp . The new measurement suggested that the two previous studies of may have overlooked the sizable background contribution from . The BESII experiment removed this type of background contribution and only a few statistically insignificant signal events remained, resulting in an upper limit of . Moreover, the isospin conserving decay mode, , was observed for the first time with a significance of 4.8. However, signal events of the channels and were not observed by BESII, and resulted in upper limits of and .
In 2009, BESIII collected 225 million jpsinumber and 106 million psipnumber events. These samples provide a unique opportunity to revisit these isospin conserving and violating decays with improved sensitivity to confirm the previous observations in decays with BESII. The ambition is to investigate as well the same final states in decays with the new record in statistics, and look for possible anomalies. A measurement of these branching fractions would be a test of the “” rule rule . The data allow in addition a search for the two-body decays .
Ii Experimental details
BEPCII is a double-ring collider that has reached a peak luminosity of about at the center of mass energy of 3.77 GeV. 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 superconducting 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 for 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 detector is described in more detail in BESIII .
The optimization of the event selection criteria and the estimates of physics background sources are performed through Monte Carlo (MC) simulations. The BESIII detector is modeled with the geant4 toolkit geant4 ; geant42 . Signal events are generated according to a uniform phase-space distribution. Inclusive and decays are simulated with the kkmc kkmc generator. Known decays are modeled by the evtgen evt1 generator according to the branching fractions provided by the Particle Data Group (PDG) PDG , and the remaining unknown decay modes are generated with the lundcharm model evt2 .
Iii Event selection
The decay channels investigated in this paper are and . The final states include , and one neutral pseudoscalar meson ( or ), where () decays to (), while the and decay to . Candidate events are required to satisfy the following common selection criteria:
Only events with at least two positively charged and two negatively charged tracks are kept. No requirements are made on the impact parameters of the charged tracks as the tracks are supposed to originate from secondary vertices.
The transverse momenta of the proton and anti-proton are required to be larger than 0.2 GeV/. Tracks with smaller transverse momenta are removed since the MC simulation fails to describe such extremely soft tracks.
Photon candidates are identified from the reconstructed showers in the EMC. Photon energies are required to be larger than 25 MeV in the EMC barrel region () and larger than 50 MeV in the EMC end-cap (). The overlapping showers between the barrel and end-cap () are poorly reconstructed, therefore, excluded from the analysis. In addition, timing requirements are imposed on photon candidates to suppress electronic noise and energy deposits from uncorrelated events.
The and candidates are identified by a reconstruction of decay vertices from pairs of oppositely charged tracks and xum . At least one and one candidate are required to pass the () vertex fit successfully by looping over all the combinations of positive and negative charged tracks. In the case of multiple pair candidates, the one with the minimum value of is chosen, where () is the nominal mass of (), obtained from the PDG PDG .
To further reduce the background and to improve the resolution of the reconstructed particle momenta, candidate signal events are subjected to a four constraint energy-momentum conservation (4C) kinematic fit under the hypothesis of . In the case of several combinations due to additional photons, the one with the best value is chosen. In addition, a selection is made on the . Its value is determined by optimizing the signal significance , where is the number of signal (background) events in the signal region. This requirement is effective against background with one or several additional photons like or decays (for instance , , etc.). For , backgrounds are suppressed by requiring (see Fig. 1(a)). For , the requirement is set to (see Fig. 1(b)). For , due to the peaking background the is required to be less than 15 (see Fig. 1(c)). For , we select events with (see Fig. 1(d)).
Followed by the common selection criteria, a further background reduction is obtained by applying various mass constraints depending on the channel of interest. To select a clean sample of and signal events, the invariant masses of and are required to be within the mass window of 5 MeV/. Here, the invariant mass is reconstructed with improved momenta from the 4C kinematic fit. The mass resolutions of and are about 1.0 MeV/. For , a mass selection of 10 MeV/ is used to exclude background from which can form a peak near the mass. The background from is removed by selecting events with GeV/ as shown in Fig. 2(a). For , a selection of events with GeV/ rejects all background contributions from decays as shown in Fig. 2(b). For and , events must satisfy the condition 8 MeV/ to remove the background from and . The background from and is rejected by the requirement 3.08 GeV/. The invariant-mass distributions for data and MC events from , and are shown in Fig. 3. The scatter plot of versus after applying all selection criteria is shown in Fig. 4. No visible signal of is observed.
Iv Background study
Backgrounds that have the same final states as the signal channels such as are either suppressed to a negligible level or completely removed. Background channels that contain one or more photons than the signal channels like have very few events passing event selection. The line shape of the peaking background sources, , is used in the fitting procedure to estimate their contributions. The contribution of remaining backgrounds from non- decays including is estimated using sideband studies as illustrated in Fig. 4. The square with a width of MeV/ around the nominal mass of the and is taken as the signal region. The eight squares surrounding the signal region are taken as sideband regions. The area of all the squares is equal. The sum of events in the sideband squares, , times a normalization factor is taken as the background contribution in the signal region. The normalization factor is defined as
The normalization factor is obtained from phase-space MC simulations of or with as the number of MC events in the signal region and as the sum of MC events in the sideband regions.
With 44 pb of data collected at a center-of-mass energy of GeV, the contribution from the continuum background is determined. From this data sample, no events survive in the or mass region in the two-photon invariant-mass, , distribution after applying all selection criteria. Therefore, we neglect this background.
V Signal yields and Dalitz analyses
The invariant-mass spectra of , and of the remaining events after the previously described signal selection procedure are shown in Fig. 5. A clear and signal can be observed in the data. The data set shows a significant signal, but lacks a pronounced peak near the mass.
The number of signal events are extracted by fitting the distributions with the parameterized signal shape from MC simulations. For , the dominant peaking backgrounds from are estimated by MC simulation. The fit also accounts for background estimates from a normalized sideband analysis. Other background sources are described by a Chebychev polynomial for all channels except where there are too few events surviving. The fit yields events, events in data and events in data. For , the upper limit on is 9 at the 90% confidence level (C.L.) and is determined with a Bayesian method bayes . For , the change in log likelihood value in the fit with and without the signal function is used to determine the signal significance, which is estimated to be 10.5.
To study the existence of intermediate resonance states in the decay of , and and to validate the phase-space assumption that was used in the MC simulations, we have performed a Dalitz plot analysis of the invariant masses involved in the three-body decay. These results are shown in Fig. 6. For these plots, and candidates are selected within mass windows of 0.12 GeV/0.14 GeV/ and 0.532 GeV/ GeV/, respectively. In all the Dalitz plots, no clear structures are observed. A test is performed to confirm the consistency between data and the phase-space distributed MC events. The is determined as follows:
where is the scaling factor between data and MC , refers to the number of data/MC events in a particular bin in the Dalitz plot, and the sum runs over all bins. We divide the Dalitz plots into 8 bins. Boxes with very few events are combined into an adjacent bin. The are equal to 1.1 and 2.1 for and , respectively, which validates the usage of a phase-space assumption in the MC simulations.
We have studied the branching fraction of the decay by combining and analyzing the invariant-mass spectra of and pairs as depicted in Fig. 7. For this analysis, events are selected by applying a two-photon invariant-mass selection of 0.12 GeV/0.14 GeV/. For the fit, the signal function is taken from a MC simulation of , and the background function is taken from a MC simulation of . A Bayesian analysis gives an upper limit on the number of events of 37 at the 90% C.L..
Vi Systematic errors
To estimate the systematic errors in the measured branching fractions of the channels of interest, we include uncertainties in the efficiency determination of charged and photon tracks, in the vertex and 4C kinematic fits, in the selection criteria for the signal and sideband region, and in the fit range. The uncertainties in the total number of and events and in the branching fractions of intermediate state are considered as well. Below we discuss briefly the analysis that is used to determine the various sources of systematic uncertainties.
Tracking efficiency. We estimate this type of systematic uncertainty by taking the difference between the tracking efficiency obtained via a control channel from data with the efficiency obtained from MC simulations. The control sample is employed to study the systematic error of the tracking efficiency from the decay. For example, to determine the tracking efficiency of the tracks, we select events with at least three charged tracks, the proton, kaon and anti-proton. The total number of tracks, , can be determined by fitting the recoiling mass distribution of the system, . In addition, one obtains the number of detected tracks, , by fitting , after requiring all four charged tracks be reconstructed. The tracking efficiency is simply . Similarly, we obtained the tracking efficiencies for , and . With inclusive MC events, we obtained the corresponding tracking efficiency for the MC simulation. The tracking efficiency difference between data and MC simulation is about 1.0% for each pion track. This difference is also about 1.0% for a proton (anti-proton) if its transverse momentum, , is larger than 0.3 GeV/. The difference increases to about 10% for the range GeV/ GeV/. Conservatively, we take a systematic error due to tracking of 1% for each pion. For the proton (anti-proton), we use weighted systematic errors, namely 2% in , 3.5% in , 1.5% in , and 2% in .
Vertex fit. The uncertainties due to the and vertex fits are determined to be 1.0% for each by using the same control samples and a similar procedure as described for the tracking efficiency.
Photon efficiency. The photon detection efficiency was studied by comparing the photon efficiency between MC simulation and the control sample . The relative efficiency difference is about 1% for each photon bianjm , which value was used as a systematic uncertainty.
Efficiency of the kinematic fit. The control sample of is used to study the efficiency of the 4C kinematic fit since its final state is the same as our signal. The event selection criteria for charged tracks and photons and the reconstruction of are the same as in our analysis. If there are more than two photon candidates in an event, we loop over all possible combinations and keep the one with the smallest value for . Furthermore, the remaining backgrounds are suppressed by limiting the momentum windows of and , i.e., MeV/ and MeV/. Figure 8 shows the scatter plot of versus for the inclusive MC events and data after applying all event selection criteria. The square in the center with a width of 10 MeV/ is taken as the signal region. Almost no background is found according to the topology analysis from inclusive MC events. The candidate signal events for both data and MC events are subjected to the same 4C kinematic fit as that in our analysis. The efficiency of the 4C kinematic fit is defined as the ratio of the number of signal events with and without a 4C kinematic fit. A correction factor, , can be obtained by comparing the efficiency of the 4C kinematic fit between data and MC simulation. i.e., . The efficiency corrections corresponding to are %, % and %, respectively. The errors in the efficiency corrections are taken as a systematic uncertainty.
Figure 8: The scatter plot of versus for for (left) data and (right) inclusive MC events.
Fit range. The , , and yields are obtained by fitting the data around the corresponding mass value. By changing the mass ranges for the fits, the number of signal events changes slightly. These differences are taken as the errors due to the uncertainty of the fit range.
Signal and sideband regions. By changing the signal and sideband region from 5 MeV/ MeV/ to 6 MeV/ MeV/, the number of fitted and events changes slightly for data and MC. The differences in yield between the two region sizes are taken as systematic errors.
Background shape. A part of the background depicted in Fig. 5 is estimated by a fit with a third-order Chebychev polynomial. The differences in signal yield with a background function that is changed to a second-order polynomial, are taken as a systematic error due to the uncertainty in the description of the background shape.
All the sources of systematic errors are summarized in Table 1. The total systematic error is calculated as the quadratic sum of all individual terms.
|Correction factor of 4C fit||0.6||0.3||0.6||0.8||0.6|
|Signal and sidebands||3.6||1.7||negligible||9.1||2.0|
The branching fraction of is determined by the relation
and if the signal is not significant, the corresponding upper limit of the branching fraction is obtained by
where, is the number of observed signal events or its upper limit , is the final state, is the intermediate state, is the detection efficiency, and is the systematic error. The branching fraction of is taken from the PDG PDG . Table 2 lists the various numbers that were used in the calculation of the branching fractions.
|Number of events /||323||454||60.4|
With these, we obtain