The $B\to K^{\ast }$ form factors on the lattice

Abstract

The extraction of the $B\to K^{\ast }$ 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-Lüscher formula is reproduced. Due to the resonance nature of the $K^{\ast }$, 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

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