The $B\to K^*$ form factors on the lattice

TL;DR

This paper develops a lattice QCD method to extract $B\to K^*$ transition form factors, accounting for resonance effects and multi-channel mixing, providing a process-independent way to determine form factors at the pole.

Contribution

It introduces a novel approach using non-relativistic effective field theory and a two-channel Lellouch-L"uscher formula to extract form factors at the resonance pole from lattice data.

Findings

Derived an equation for form factors at the $K^*$ resonance pole.

Reproduced the two-channel Lellouch-L"uscher formula.

Discussed the narrow width approximation implications.

Abstract

The extraction of the $B\to K^*$ transition form factors from lattice data is studied, applying non-relativistic effective field theory in a finite volume. The possible mixing of $\pi K$ and $\eta K$ states is taken into account. The two-channel analogue of the Lellouch-L\"uscher formula is reproduced. Due to the resonance nature of the $K^*$, an equation is derived, which allows to determine the form factors at the pole position in a process-independent manner. The infinitely-narrow width approximation of the results is discussed.