Extrapolating semileptonic form factors using Bayesian-inference fits regulated by unitarity and analyticity

TL;DR

This paper introduces a Bayesian-inference based, model-independent framework for fitting hadronic form factors using unitarity and analyticity constraints, enabling accurate extrapolation across the physical range.

Contribution

It develops a novel, dispersive bound-regulated fitting method for hadronic form factors, applicable to semileptonic meson decays, with demonstrated applications to $B_s\to K\ell\nu$ and $B\to D^*\ell\nu$ decays.

Findings

Successfully applied to $B_s\to K\ell\nu$ decay data

First application to $B\to D^*\ell\nu$ decays

Provides model-independent predictions over the entire physical range

Abstract

We discuss our recently proposed model-independent framework for fitting hadronic form-factor data, which are often only available at discrete kinematical points, using parameterisations based on unitarity and analyticity. The accompanying dispersive bound on the form factors (unitarity constraint) is used to regulate the ill-posed fitting problem and allow model-independent predictions over the entire physical range. Kinematical constraints, for example for the vector and scalar form factors in semileptonic meson decays, can be imposed exactly. The core formulae are straight-forward to implement with standard math libraries. We demonstrate the method for the exclusive semileptonic decay $B_s\to K\ell\nu$, an example requiring one to use a generalisation of the original Boyd Grinstein Lebed (BGL) unitarity constraint. We further present a first application of the method to $B \to D^*\ell \nu$ decays.