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

TL;DR

This paper investigates long-distance effects in rare semileptonic B decays, calculating transition form factors using Ward identities and comparing them with various theoretical approaches, to improve understanding of these processes.

Contribution

It introduces a novel method for calculating B to V transition form factors using Ward identities, experimental data, and vector meson dominance, and compares results with lattice QCD and other models.

Findings

Form factors are consistent with lattice QCD and sum rule results.

Branching ratios and differential decay rates are computed for B to V transitions.

The approach enhances the understanding of long-distance effects in rare B decays.

Abstract

Long distance effects are studied in the rare exclusive semileptonic $B_{(d,s)}\to V \ell^+ \ell^-$ decays, where $V$ denotes a $K^*$ or $\phi$ 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 $B_d\to K^* \ell^+ \ell^-$ and $B_s\to \phi \ell^+ \ell^- $ branching ratios are computed and the differential branching fractions are given as a function of the squared-momentum transfer.