Heavy-Quark expansion for {{bar{B}}_srightarrow D^{(*)}_s} form factors and unitarity bounds beyond the {SU(3)_F} limit

Abstract

We carry out a comprehensive analysis of the full set of {bar{B}}_q rightarrow D_q^{(*)} form factors for spectator quarks q=u,d,s within the framework of the Heavy-Quark expansion (HQE) to order {mathcal {O}}left( alpha _s, 1/m_b, 1/m_c^2right) . In addition to the available lattice QCD calculations we make use of two new sets of theoretical constraints: we produce for the first time numerical predictions for the full set of {bar{B}}_s rightarrow D_s^{(*)} form factors using Light-Cone sum rules with B_s-meson distribution amplitudes. Furthermore, we reassess the QCD three-point sum rule results for the Isgur-Wise functions entering all our form factors for both q=u,d and q=s spectator quarks. These additional constraints allow us to go beyond the commonly used assumption of SU(3)_F symmetry for the {{bar{B}}}_srightarrow D_s^{(*)} form factors, especially in the unitarity constraints which we impose throughout our analysis. We find the coefficients of the IW functions emerging at {mathcal {O}}left( 1/m_c^2right) to be consistent with the naive {mathcal {O}}left( 1right) expectation, indicating a good convergence of the HQE. While we do not find significant SU(3) breaking, the explicit treatment of q=s as compared to a simple symmetry assumption renders the unitarity constraints more effective. We find that the (pseudo)scalar bounds are saturated to a large degree, which affects our theory predictions. We analyze the phenomenological consequences of our improved form factors by extracting |V_{cb}| from {bar{B}}rightarrow D^{(*)}ell nu decays and producing theoretical predictions for the lepton-flavour universality ratios R(D), R(D^*), R(D_s) and R(D_s^*), as well as the tau - and D_q^* polarization fractions for the {bar{B}}_qrightarrow D_q^{(*)}tau nu modes.