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

TL;DR

This paper uses lattice calculations and dispersion relations to connect form factors with phase shifts in elastic scattering, aiming to improve the determination of |Vub| from B to pi decays.

Contribution

It introduces a novel approach combining lattice form factors and Omnes relations to extract phase shifts and refine |Vub| measurements from exclusive semileptonic decays.

Findings

Estimated phase shifts for K pi, B pi, D pi, D K scattering.

A new fitting method for B to pi decay form factors.

Potential for more precise |Vub| determination.

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.