Elastic s-wave scattering phase shifts and |Vub| from lattice calculations of form factors for exclusive semileptonic decays

Abstract

Omnes dispersion relations make a connection between form factors for exclusive semileptonic decays and phase shifts in the corresponding elastic scattering channels. We describe two applications. In the first, we use lattice form factor calculations to learn about phase shifts in elastic s-wave isospin-1/2 channels for K pi, B pi, D pi and D K scattering. The aim of the second application is to make the determination of the CKM matrix element magnitude |Vub| from exclusive semileptonic B to pi decays competitive with that from inclusive decays. Here we use many subtractions in an Omnes dispersion relation to motivate a simple fitting function, allowing data to constrain the q^2 shape of the differential decay rate and theory, primarily lattice results, to provide normalisation via form factor values.