A Measurement of the Branching Fractions of exclusive Decays in Events with a Fully Reconstructed Meson
We report a measurement of the branching fractions for decays based on 341.1 fb of data collected at the resonance with the BABAR detector at the PEP-II storage rings. Events are tagged by fully reconstructing one of the mesons in a hadronic decay mode. We obtain , , , , , , and .
The BABAR Collaboration
The determination of the individual exclusive branching fractions of decays ell () is important for the study of the semileptonic decays of the meson. Improvement in the knowledge of these branching fractions is also important to reduce the systematic uncertainty in the measurements of the Cabibbo-Kobayashi-Maskawa CKM () matrix elements and . For example, one of the leading sources of systematic uncertainty in the extraction of from the exclusive decay is the limited knowledge of the background due to . Improved measurements of decays will also benefit the accuracy of the extraction of , as analyses are extending into kinematic regions in which these decays represent a sizable background.
Based on current measurements aleph (); delphi (); babar-1 (); babar-2 (); belle () the rate of inclusive semileptonic decays exceeds the sum of the measured exclusive decay rates pdg (). While and decays account for about 70% of this total, the contribution of other states, including resonant and non-resonant (denoted by ), is not yet well measured and may help to explain the inclusive-exclusive discrepancy.
In this letter, we present measurements of the branching fractions for decays, separately for charged and neutral mesons.
The analysis is based on data collected with the BABAR detector detector () at the PEP-II asymmetric-energy storage rings. The data consist of a total of 341.1 fb recorded at the resonance, corresponding to 378 million pairs. An additional 36 fb off-peak data sample, taken at a center-of-mass (CM) energy 40 MeV below the resonance, is used to study background from events (continuum production). A detailed GEANT4-based Monte Carlo (MC) simulation Geant () of and continuum events is used to study the detector response, its acceptance, and to test the analysis techniques. The simulation models decays using calculations based on Heavy Quark Effective Theory HQETBaBar (), decays using the ISGW2 model ISGW (), and decays using the Goity-Roberts model Goity ().
We select semileptonic decays in events containing a fully reconstructed meson (), which allows us to constrain the kinematics, reduce the combinatorial background, and determine the charge and flavor of the signal meson.
We first reconstruct the semileptonic decay, selecting a lepton with momentum in the center-of-mass frame higher than 0.6 GeV/. Electrons from photon conversions and Dalitz decays are removed by searching for pairs of oppositely charged tracks that form a vertex with an invariant mass compatible with a photon conversion or a Dalitz decay. Candidate mesons, having the correct charge-flavor correlation with the lepton, are reconstructed in the , , , , , , , , and channels, and mesons in the , , , , , , and channels. In events with multiple candidates, the candidate with the best - vertex fit is selected. Candidate mesons are reconstructed by combining a candidate with a pion or a photon in the , , , and channels. In events with multiple candidates, we choose the candidate with the smallest based on the deviations from the nominal values of the invariant mass and the invariant mass difference between the and the , using the measured resolution.
We reconstruct decays of the type , where represents a collection of hadrons with a total charge of , composed of , where , , and . Using and as seeds for decays, we reconstruct about 1000 different decay chains.
The kinematic consistency of a candidate with a meson decay is evaluated using two variables: the beam-energy substituted mass , and the energy difference . Here refers to the total CM energy, and and denote the momentum and energy of the candidate in the CM frame. For correctly identified decays, the distribution peaks at the meson mass, while is consistent with zero. We select a candidate in the signal region defined as 5.27 GeV/ 5.29 GeV/, excluding candidates with daughter particles in common with the charm meson or the lepton from the semileptonic decay. In the case of multiple candidates in an event, we select the one with the smallest value. The and the candidates are required to have the correct charge-flavor correlation. Mixing effects in the sample are accounted for as described in BBmixing (). Cross-feed effects, , candidates erroneously reconstructed as a neutral (charged) , are subtracted using estimates from the simulation.
For decays, candidates are selected within 2 (1.5-2.5, depending on the decay mode) of the mass ( mass difference), with typically around 8 (1-7) MeV. We also require the cosine of the angle between the directions of the candidate and the lepton in the CM frame to be less than zero, to reduce background from non- semileptonic decays.
We reconstruct and decays starting from the corresponding samples and selecting events with only one additional reconstructed charged track that has not been used for the reconstruction of the , the signal , or the lepton. For the and the decays, we additionally require the invariant mass difference to be greater than 0.18 GeV/ to veto events. To reduce the combinatorial background in the mode, we also require the total extra energy in the event, obtained by summing the energy of all the showers in the electromagnetic calorimeter that have not been assigned to the or the candidates, to be less than 1 GeV.
The exclusive semileptonic decays are identified by the missing mass squared in the event, , defined in terms of the particle four-momenta in the CM frame of the reconstructed final states. For correctly reconstructed signal events, the only missing particle is the neutrino, and peaks at zero. Other semileptonic decays, where one particle is not reconstructed (feed-down) or is erroneously added (feed-up) to the charm candidate, exhibit higher or lower values in . To obtain the semileptonic signal yields, we perform a one-dimensional extended binned maximum likelihood fit Barlow () to the distributions. The fitted data samples are assumed to contain four different types of events: signal events, feed-down or feed-up from other semileptonic decays, combinatoric and continuum background, and hadronic decays (mainly due to hadrons misidentified as leptons). For the fit to the distributions of the channel, we also include a component corresponding to other misreconstructed decays. We use the MC predictions for the different semileptonic decay distributions to obtain the Probability Density Functions (PDFs). The combinatoric and continuum background shape is also estimated by the MC simulation, and we use the off-peak data to provide the continuum background normalization. The shape of the continuum background distribution predicted by the MC simulation is consistent with that obtained from the off-peak data.
The distributions are compared with the results of the fits in Fig. 1 for each of the channels. The fitted signal yields and the signal efficiencies, accounting for the reconstruction, are listed in Table 1.
To reduce the systematic uncertainty, the exclusive branching fractions relative to the inclusive semileptonic branching fraction are measured. A sample of events is selected by identifying a charged lepton with CM momentum greater than 0.6 GeV/ and the correct charge-flavor correlation with the candidate. In the case of multiple candidates in an event, we select the one reconstructed in the decay channel with the highest purity, defined as the fraction of signal events in the signal region. Background components peaking in the signal region include cascade meson decays (, the lepton does not come directly from the ) and hadronic decays, and are subtracted by using the corresponding MC distributions. The total yield for the inclusive decays is obtained from a maximum likelihood fit to the distribution of the candidates using an ARGUS function Argus () for the description of the combinatorial and continuum background, and a Crystal Ball function CrystallBall () for the signal. Additional Crystal Ball and ARGUS functions are used to model a broad-peaking component, included in the signal definition, due to real decays for which, in the reconstruction, neutral particles have not been identified or have been interchanged with the semileptonic decays. Fig. 2 shows the distribution of the candidates in the and sample. The fit yields 159896 1361 events for the sample and 96771 968 events for the sample.
The relative branching fractions are obtained by correcting the signal yields for the reconstruction efficiencies (estimated from MC events) and normalizing to the inclusive signal yield, following the relation . Here, is the number of signal events for the various modes, reported in Table 1 together with the corresponding reconstruction efficiencies , is the signal yield, and is the corresponding reconstruction efficiency including the reconstruction, equal to 0.36% and 0.23% for the and decays, respectively. The absolute branching fractions are then determined using the semileptonic branching fraction and the ratio of the and the lifetimes pdg ().
|Decay Mode||Decay Mode|
|1635 61||1.71 0.02||174 25||1.02 0.03|
|3050 73||1.27 0.01||306 27||1.26 0.03|
|852 40||0.94 0.02||107 20||0.60 0.03|
|2045 55||0.91 0.01||130 20||0.66 0.02|
Numerous sources of systematic uncertainties have been investigated. The uncertainties due to the detector simulation are established by varying, within bounds given by data control samples, the tracking efficiency of all charged tracks (resulting in 1.2-2.7% relative systematic uncertainty among the different decay modes), the calorimeter efficiency (0.5-1.8%), the lepton identification efficiency (0.4-3%), and the reconstruction efficiency for low momentum charged (1.2%) and neutral pions (1.3%). We evaluate the systematic uncertainties associated with the MC simulation of various signal and background processes: photon conversion and Dalitz decay (0.04-0.4%), cascade decay contamination (0.6-1%), and flavor cross-feed (0.2-0.3%). We vary the and form factors within their measured uncertainties HQETBaBar () (0.4-0.8%) and we include the uncertainty on the branching fractions of the reconstructed and modes (2.3-4.4%), and on the absolute branching fraction used for the normalization (1.9%). We also include a systematic uncertainty due to differences in the efficiency of the selection in the exclusive selection of decays and the inclusive reconstruction (0.9-5.6%), and the extraction of the (0.4-1.8%) and (0.5-0.9%) signal yields. The complete set of systematic uncertainties is given in Ref. epaps ().
We measure the following branching fractions:
The accuracy of the branching fraction measurements for the decays is comparable to that of the current world average pdg (). We compute the total branching fractions of the decays assuming isospin symmetry, , to estimate the branching fractions of final states, obtaining:
where we assume the systematic uncertainties on the and modes to be completely correlated. These results are consistent with, but have smaller uncertainties than, recent results from the Belle collaboration belle ().
By comparing the sum of the measured branching fractions for with the inclusive branching fraction pdg (), a discrepancy is observed, which is most likely due to decays with .
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.
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|Systematic uncertainty on|
|Soft particle efficiency||-||1.3||-||1.2|
|Monte Carlo corrections|
|Conversion and Dalitz decay background||0.04||0.07||0.06||0.05|
|Cascade decay background||0.6||0.6||1.0||1.0|
|Total systematic error||3.7||5.2||5.4||4.5|
|Systematic uncertainty on|
|Soft particle efficiency||-||1.2||-||1.3|
|Monte Carlo corrections|
|Conversion and Dalitz decay background||0.15||0.4||0.05||0.2|
|Cascade decay background||0.6||0.6||1.0||1.0|
|Total systematic error||7.7||7.3||6.4||8.4|