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

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 $πK$ and $ηK$ states is taken into account. The two-channel analogue of the Lellouch-Lüscher 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.

29 pages, 4 figures