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

- Authors
- Type
- Published Article
- Publication Date
- Sep 10, 2019
- Submission Date
- Sep 10, 2019
- Identifiers
- DOI: 10.1103/PhysRevD.100.056013
- Source
- arXiv
- License
- Yellow
- External links

## 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.