# Measurements of Branching Fractions and Time-dependent Violating Asymmetries in Decays

###### Abstract

We report measurements of branching fractions and time-dependent asymmetries in and decays using a data sample that contains pairs collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider. We determine the branching fractions to be and . We measure asymmetry parameters and in and , , , and in , where the first uncertainty is statistical and the second is systematic. We exclude the conservation of symmetry in both decays at equal to or greater than significance.

###### pacs:

13.25.Hw, 11.30.Er, 12.15.FfThe Belle Collaboration

In the standard model (SM) of electroweak interactions, the effect of violation is explained by a single complex phase in the three-family Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix CabibboKobayashiMaskawa . Both the Belle and BaBar Collaborations experimentally established this effect CPV_observation_Belle ; CPV_observation_BaBar and precisely determined the parameter by measurements of mixing-induced asymmetries in transitions, where BaBar_btoccs ; Belle_btoccs ; phione .

In transitions such as decays, the dominant contributions are Cabibbo-disfavored but color-allowed tree-level diagrams and the corresponding mixing-induced asymmetries are directly related to . In addition, penguin diagrams that may have different weak phases can contribute to these decays. Theoretical considerations based on models using factorization approximations and heavy quark symmetry predict the corrections to mixing-induced violation to be a few percent and possible direct violation to be negligibly small Xing1998Xing1999 .

violation in transitions has been studied previously by the Belle and BaBar Collaborations. In decays using a data sample of pairs, Belle found evidence of a large direct violation: corresponding to a deviation from zero Fratina2007 ; directCPV_A_or_C , in contradiction to theoretical expectations Xing1998Xing1999 . This deviation was not confirmed by BaBar and has not been observed in other decay modes Aushev2004 ; Vervink2009 ; Aubert2009_btodd .

In this article we present measurements of branching fractions and violating asymmetries in the decays and using the final data sample of the Belle experiment.

The decay rate of a neutral meson decaying to a eigenstate such as is given by

(1) |

where represents the -flavor charge when the accompanying meson is tagged as a (), and represents the proper time interval between the two neutral decays in an event. The lifetime is denoted by and the mass difference between the two neutral mass eigenstates by . The parameters and measure mixing-induced and direct violation, respectively directCPV_A_or_C .

Unlike , and are not eigenstates. The decay rate of neutral mesons decaying to these states has four flavor-charge configurations and can be expressed as Aleksan1991 ; Aubert2003_b_to_rhopi_parametrisation

(2) |

where the () sign represents the () final state. The time- and flavor-integrated charge asymmetry measures direct violation. The quantity parameterizes mixing-induced violation and parameterizes flavor-dependent direct violation. The quantities and are not sensitive to violation. The parameter describes the asymmetry between the rates and . The parameter is related to the relative strong phase between the amplitudes contributing to the decays.

This analysis is based on a data sample containing pairs collected at the resonance with the Belle detector at the KEKB asymmetric-energy collider KEKB . The is produced with a Lorentz boost of close to an axis along the beam, which allows the determination of from the displacement of decay vertices of both mesons.

The Belle detector is a large-solid-angle magnetic spectrometer that is described in detail in Ref. Belle . The present analysis uses for track reconstruction and particle identification a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter composed of CsI(Tl) crystals (ECL) located inside a superconducting solenoid coil that provides a 1.5 T magnetic field.

Reconstructed charged tracks are required to have a transverse (longitudinal) distance of closest approach to the interaction point (IP) of less than () cm. For identification of charged particles (PID), measurements of specific energy loss in the CDC and measurements from the ACC and TOF are combined in an likelihood-ratio approach. The selection requirement on the combined PID quantity has a kaon (pion) identification efficiency of () with an associated pion (kaon) misidentification rate of (). Charged tracks are also required to be not positively identified as electrons by measurements of shower shapes and energy deposited in the ECL. Neutral pions are reconstructed from two photons detected in the ECL with each photon having an energy greater than . The invariant mass of the photon pair is required to be within of the nominal mass (corresponding to a width of ). For candidates a kinematic fit to the IP profile with a mass constraint is performed. Neutral kaons are reconstructed in the decay mode . The invariant mass of the pair is required to be within of the nominal mass (). Additional momentum-dependent selection requirements consider the possible displacement of the decay vertices from the IP Kshortselection .

Charged mesons are reconstructed in the decay modes and CC . The invariant mass of candidates is required to be within of the nominal mass ( in and in ). Neutral mesons are reconstructed in the decay modes , , and . The invariant mass of candidates is required to be within () of the nominal mass, except for the decay mode where a requirement of () is applied. We reconstruct mesons in the decay modes and . The momentum resolution of charged low momentum pions from decays, referred to as soft pions, is improved by a kinematic fit in which the soft pion is constrained to the decay vertex determined from a kinematic fit of candidates constrained to originate from the IP profile. The difference of invariant masses of the and () candidates is required to be within () () of the nominal mass difference, except for modes involving and decays where a requirement of ( and ) is applied.

Neutral B mesons are reconstructed by combining and candidates, and selected by the beam-energy-constrained mass and the energy difference , where is the energy of the beam and and are the momentum and energy of the candidates in the center-of-mass frame (c.m.). The selected regions are and . The lower boundary in was chosen to exclude reflections from misidentified decays that populate the signal region at .

In (), after applying the above selection requirements, 12% (16%) of the signal events contain more than one candidate. In this case the candidate with the smallest quadratic sum of deviations of reconstructed invariant masses of daughters (and mass differences of daughters) from nominal values, divided by the width of corresponding signal peaks, is selected. This requirement selects the correct candidate with a probability of 96% (92%).

In unlike in the major source of background arises from continuum events. This background is suppressed by a neural network (NN) implemented by the NeuroBayes package Neurobayes that combines information about the event topology. Observables included in the NN are , where is the polar angle of the candidate with respect to the beam direction in the c.m. frame, a combination of 16 modified Fox-Wolfram moments FWmoments , and the momentum flow in nine concentric cones around the thrust axis of the candidate CLEOcones . The requirement on the NN selection rejects 64% of the background while retaining 92% of the signal.

The signal yields are obtained by two-dimensional unbinned extended maximum likelihood fits to the and distributions. The distributions are parameterized by a Gaussian function for the signal component and by an empirically determined threshold function introduced by the ARGUS Collaboration ARGUSfunction for the background component. The distributions are parameterized by the sum of two Gaussian functions (the sum of a Gaussian function and an empirically determined function introduced by the Crystal Ball Collaboration CBfunction ) with common mean for the signal component in () and by a linear function for the background component. The shape parameters of signal components in () are fixed to values obtained from () data distributions, where the relative widths and fractions of the signal components in are fixed to values obtained from Monte Carlo (MC) simulation studies. The and distributions and fit projections are shown in Fig. 1. For the obtained yields are signal events in the final state and signal events in the final state.

For , we obtain a yield of signal events in all reconstructed modes combined. Of these, the yield in modes involving decays only is signal events.

Decays such as , and have the same final states as the reconstructed decay modes and can possibly populate the and signal region. The contributions of such decays, referred to as peaking background, are estimated from mass sidebands and subtracted in the signal yields given above. For (), we find a contribution of () peaking background events from fits to mass sidebands. The mass sidebands are considered to be free of peaking background and no background subtraction is performed. This assumption has been tested by MC simulations and no peaking background is found in the data sidebands.

The reconstruction efficiencies are obtained from MC simulations of signal decays and have been corrected to account for PID selection efficiency differences between MC simulations and data. To exclude systematic effects in the determination of reconstruction efficiencies associated with soft neutral pions, only modes involving decays are used in the branching fraction measurement.

The branching fractions are calculated from signal yields, reconstruction efficiencies, the number of events and current world averages of , and branching fractions PDG . The branching fraction for decays is calculated as the weighted average of the branching fractions determined for each of both reconstructed decay modes separately. The branching fraction for decays is determined by the signal yield in all modes and the average reconstruction efficiency weighted by the branching fractions. The determined branching fractions are and .

Source | ||
---|---|---|

Track reconstruction efficiency | ||

reconstruction efficiency | ||

reconstruction efficiency | - | |

selection efficiency | ||

Event reconstruction efficiency | ||

Continuum suppression | - | |

Fit models | ||

branching fractions | ||

Number of events | ||

Total |

The systematic uncertainties of the measured branching fractions are summarized in Table 1. The uncertainties due to track, and reconstruction efficiency and the uncertainty due to the selection efficiency have been estimated using studies of decays with MC simulations and data. The effect on the event reconstruction efficiencies due to broader mass distributions for data and the corresponding selection is studied by a MC/data comparison and assigned as a systematic uncertainty. As the systematic uncertainty of the applied continuum suppression in , the maximum variation of signal yields in a MC/data comparison of the neural networks using decays is assigned. The contributions due to the fit models are estimated by varying the fixed parameters within their uncertainties. The contributions due to uncertainties of the , and branching fractions and of the number of events are obtained by propagation of the appropriate uncertainties. The total systematic uncertainties are obtained by adding all contributions in quadrature.

Source | |||||||
---|---|---|---|---|---|---|---|

Vertex reconstruction | |||||||

resolution function | |||||||

Background PDFs | |||||||

Signal purity | |||||||

Physics parameters | |||||||

Flavor tagging | |||||||

Possible fit bias | |||||||

Peaking background | |||||||

Tag-side interference | |||||||

Total |

The technique used to determine the asymmetry parameters from distributions is described in detail in Ref. Belle_btoccs . The decay vertex of the signal meson is reconstructed from a kinematic fit of the two mesons to a common vertex including information about the IP profile. No information about soft pions is used in the vertex reconstruction. The decay vertex and the flavor of the accompanying meson is obtained by an inclusive approach using the remaining charged tracks that are not used in the signal reconstruction. Requirements on the quality of reconstructed vertices and on the number of hits in the silicon vertex detector are applied. The algorithms applied to obtain the -flavor charge and a tagging quality variable are described in detail in Ref. TaggingNIM . The variable is related to the mistag fractions determined from control samples and ranges from (no flavor discrimination) to (unambiguous flavor assignment). The data is divided into seven intervals.

The asymmetry parameters are determined by unbinned maximum likelihood fits to the distributions. The probability density function used to describe the distributions is given by

(3) |

where the index denotes signal and background components and the fraction depends on the interval and is evaluated on an event-by-event basis as a function of and . The signal component consists of the convolution of distributions given by modifications of Eq. 1 and 2 that include the effect of incorrect flavor assignments and of a resolution function to account for the finite resolution of the vertex reconstruction vertexres . The background component is parameterized by the convolution of the sum of a prompt and an exponential distribution allowing for effective lifetimes and a resolution function composed of the sum of two Gaussian functions. The parameters of the background components are fixed to values determined by fits to sidebands. A Gaussian function with a broad width of about ps and a small fraction of about is added to account for outlier events with large .

The free parameters in the fit are and and the free parameters in the fit are , , , and . The lifetime and mass difference are fixed to current world averages PDG . The fits are performed in a signal region defined by and . The signal purity is 62% (59%) for (). For the results are

(4) |

and for

(5) |

where the first uncertainty is statistical and the second systematic. The distributions and projections of the fits are shown in Fig. 2.

The systematic uncertainties in the asymmetry parameters are evaluated for each decay mode and are summarized in Table 2. Sources of systematic uncertainties on the vertex reconstruction are the IP profile constraint, requirements on the vertex fit quality for signal and tagging mesons, requirements on impact parameters of tracks in the reconstruction of the tagging meson and the fit range. These contributions are estimated by variations of each of the applied requirements. Further contributions to the vertex reconstruction are a global SVD misalignment and a bias, which are both estimated by MC simulations. The contributions due to the resolution functions, the parameterization of background components, the calculation of the signal purity and the physics parameters and are estimated by varying the fixed parameters within their uncertainties. The systematic uncertainty due to flavor tagging is estimated by varying the mistag fractions in each interval within their uncertainties. A possible fit bias is estimated from a large sample of MC simulated signal decays. The effect of the peaking background is studied using MC simulations allowing for violation in non-resonant decays. The possible interference between Cabibbo-favored and suppressed amplitudes in the decay of the tagging meson, referred to as tag-side interference Long2003_tagside_interference , is studied using MC simulations with inputs obtained from control samples. The largest deviations in the above MC studies are assigned as systematic uncertainties. The total systematic uncertainty is obtained by adding all contributions in quadrature.

The significance of the results is studied by a likelihood-ratio approach. For we exclude the conservation of symmetry () at a confidence level of corresponding to . For the conservation of symmetry () is excluded at a confidence level of corresponding to . These results account for both the statistical and the systematic uncertainties.

The fit procedure was validated by various cross-checks. The same analysis was performed for decays. The results are , , , and in and , , , and in , where the uncertainties are statistical only. The results are consistent with the assumption of no violation in decays. The lifetimes determined by fits to untagged and samples are consistent with the world average PDG .

In summary we report measurements of the branching fractions and time-dependent violating asymmetries in and decays using the final Belle data sample of pairs. We measure the branching fractions and . The measured asymmetry parameters are and in and , , , and in . For , the asymmetries are approximately outside of the physical parameter space defined by and the direct asymmetry deviates from zero by approximately . For , if the contribution of penguin diagrams is negligible and if the hadronic phase between and amplitudes is zero and their magnitudes are the same, then , , and vanish and is equal to . Our result is consistent with the above and we measure . The asymmetries obtained in and decays are both in agreement with measurements of decays involving transitions BaBar_btoccs ; Belle_btoccs and with previous measurements of decays Aushev2004 ; Fratina2007 ; Vervink2009 ; Aubert2009_btodd . We find evidence for violation in both decay channels with a significance of 4. These results supersede previous measurements of branching fractions and time-dependent asymmetries in and by the Belle Collaboration Fratina2007 ; Aushev2004 ; BF_DstarD_Belle .

We thank the KEKB group for excellent operation of the accelerator; the KEK cryogenics group for efficient solenoid operations; and the KEK computer group, the NII, and PNNL/EMSL for valuable computing and SINET4 network support. We acknowledge support from MEXT, JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR (Australia); NSFC (China); MSMT (Czechia); DST (India); INFN (Italy); MEST, NRF, GSDC of KISTI, and WCU (Korea); MNiSW (Poland); MES and RFAAE (Russia); ARRS (Slovenia); SNSF (Switzerland); NSC and MOE (Taiwan); and DOE and NSF (USA).

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