Estimating form factors ofB_s→D_s^(*)and their applications to semi-leptonic and non-leptonic decays

Abstract

B 0 s → D − s and B 0 s → D * − s weak transition form factors are estimated for the whole physical region with a method based on an instantaneous approximated Mandelstam formulation of transition matrix elements and the instantaneous Bethe-Salpeter equation. We apply the estimated form factors to branching ratios, CP asymmetries and polarization fractions of nonleptonic decays within the factorization approximation. And we study the non-factorizable effects and annihilation contributions with the perturbative QCD approach. The branching ratios of semi-leptonic B 0 s → D ( * )− s l + ν l decays are also evaluated. We show that the calculated decay rates agree well with the available experimental data. The longitudinal polarization fraction of B s → D * s V (A) decays are ∼ 0.8 when V (A) denotes a light meson, and are ∼ 0.5 when V (A) denotes a D q (q = d, s) 1 adopted QCDSR for the calculation. In [14], the form factors are estimated within the covariant light-front quark model (CLFQM). Authors of [15] used the so called light cone sum rules (LCSR) to investigate form factors at large recoil, and heavy quark effective theory (HQET) to describe them at small recoil region. Each of these methods sketches one or another profile of non-perturbative QCD, and each has advantages as well as shortcomings. So it is worthy to estimate the B s → D ( * ) s form factors in another method which is based on the B-S equation [16] and the Mandelstam formulation [17] of the transition matrix element. To make predictions on non-leptonic decays, there is another task, that is how to evaluate the decay amplitudes with form factors available. It is well known that factorization approximation (FA) [11] has been extensively applied in non-leptonic weak decays and has been justified to success in explaining the branching ratios of several color-allowed B q decays [18]. The works mentioned before all adopted the FA to evaluate non-leptonic decay amplitudes. However, estimations based on the FA still suffer uncertainties from the non-factorizable effects and annihilation diagrams contributions, especially for the CP asymmetries (CPAs). Thus approaches beyond the FA are in need. Till now several approaches which can cover the non-factorizable effects have been developed, such as the perturbative QCD (pQCD) approach [19], the QCD improved factorization (QCDF) approach [20] and SCET approach [21]. Studies on B s decays into charmed particles with the perturbative QCD approach have been carried out in [22]. In this work, we evaluate non-leptonic decay amplitudes under FA, as well as estimate non-factorizable and annihilation contributions in the pQCD approach. Besides these direct calculation in the FA or pQCD, the authors in [23] used SU(3) F symmetry to estimate the widths of a class of two-body B s decays with the help of experimental data of corresponding B decays. There have been some studies on semi-leptonic B 0 s → D ( * )− s l + ν l decays with the approaches such as QCDSR [13], LCSR [15], CLFQM [14] and constituent quark meson mod...

Weak decays ofB¯smesons

“…In Table XI, we present our values as branching fractions, and compare with other results, in the case of decays with two D ( * ) s mesons in the final state. We have found a fair agreement with the branching fractions calculated in [28] and [36], and larger differences with the values given in [32], [33] and [51]. Most of the values calculated here and those found in the literature differ from the experimental results by a factor around 2.…”

“…[28] and [36] in which relativistic CQM and QCD sum rules techniques were used, respectively. Our results for decays with a vector D * s in the final state also agree finely with those from [32], although our values for final states with a pseudoscalar D s meson in the final state are about a factor 2 larger than those from [32], who also works in the context of nonrelativistic constituent quark models. The values calculated in this work are larger by a factor 2 or more than the results from Refs.…”

“…Our results also compare well to the sum-rules calculation of [34,35], while the result of [36] is lower by about one half. The same happens if we compare with the results of [32] or [33].…”

“…[28] the authors adopt the relativistic quark model. Chen et al solve the instantaneous Bethe-Salpeter equation in [32] to estimate the weak transition form factors. In [33] the authors work out the form factors within the covariant light front quark model.…”

“…Some of the decay modes of B s orB s mesons have been studied within the framework of relativistic constituent quark model [28,29], perturbative QCD [30,31], Bethe-Salpeter techniques [32], light front quark model [33], sum rules [34][35][36] or non relativistic constituent quark model [37] for instance. In this paper we study the semileptonic and nonleptonic decay ofB s in the context of nonrelativistic constituent quark model.…”