Vertex renormalization and hard scattering symmetry breaking corrections to $B$ to axial vector meson form factors at large recoil

TL;DR

This paper calculates symmetry-breaking corrections to $B$ to axial-vector meson form factors at large recoil, analyzing their impact on observables like the forward-backward asymmetry and lepton polarization in semileptonic $B$ decays.

Contribution

It provides a detailed computation of vertex renormalization and hard-spectator scattering effects on form factors, improving the understanding of symmetry breaking in heavy-to-light $B$ decays.

Findings

The zero-position of the forward-backward asymmetry shifts by 10% due to corrections.

Effects on lepton polarization asymmetry are negligible.

Form factor corrections significantly influence certain decay observables.

Abstract

The symmetries arise due to heavy quark and large energy limit help us to reduce the number of independent form factors in the heavy-to-light $B$-meson decays. It is expected that these symmetry relations are not exact and are broken by the perturbative effects, namely, the vertex corrections and the hard-spectator scatterings. The former are included in the form factors via vertex renormalization whereas the later are calculated through light-cone distribution amplitudes. We first calculate these symmetry breaking corrections to the form factors involved in semileptonic $B$-meson to an axial-vector $(K_{1})$-meson decay. Later, by using these form factors we see their effect on the physical observables such as the zero-position of the forward-backward $(\mathcal{A}_{FB})$ asymmetry and the longitudinal lepton polarization ($P_L$) asymmetry in $B\rightarrow K_1(1270) \mu^+\mu^-$ decay. We find that as a result of these corrections to the form factors, the zero-position of the forward-backward asymmetry is shifted by $10\%$ from its SM value while the effects on $P_L$ are rather insignificant.