Ward identities, $\mathbf{B}\to \mathbf{V}$ transition form factors and applications

Abstract

Long distance effects are studied in the rare exclusive semileptonic $B_{(d,s)}\to V{\ell }^{+}{\ell }^{-}$ decays, where $V$ denotes a $K^{\ast }$ or $\varphi$ meson. The form factors, which describe the meson transition amplitudes in the effective Hamiltonian approach, are calculated by means of Ward identities, experimental constraints and extrapolated within a general vector meson dominance framework. These form factors are then compared to the ones obtained in Lattice QCD simulations, with Light Cone Sum Rules and a Dyson-Schwinger equation approach. Additionally, the $B_d\to K^{\ast }{\ell }^{+}{\ell }^{-}$ and $B_s\to \varphi {\ell }^{+}{\ell }^{-}$ branching ratios are computed and the differential branching fractions are given as a function of the squared-momentum transfer.

10 pages, 3 figures