Non-Perturbative Bounds for Semileptonic Decays in Lattice QCD

TL;DR

This paper introduces a non-perturbative, model-independent method to determine form factors in semileptonic decays across all momentum transfers using lattice QCD data and unitarity constraints, demonstrated on D to K decays.

Contribution

The authors develop an extension of existing methods to accurately determine form factors at low and high momentum transfer without model assumptions, applicable to B decays.

Findings

Form factors can be precisely determined across the full kinematic range.

The method shows remarkable agreement with direct lattice calculations.

It enables non-perturbative analysis of semileptonic B decays.

Abstract

We present a new method aiming at a non-perturbative, model-independent determination of the momentum dependence of the form factors entering semileptonic decays using unitarity and analyticity constraints. We extend the original proposal and, using suitable two-point functions computed non-perturbatively, we determine the form factors at low-momentum transfer $q^2$ from those computed explicitly on the lattice at large $q^2$, without making any assumption about their $q^2$ dependence. As a training ground we apply the new method to the analysis of the lattice data of the semileptonic $D \rightarrow K \ell \nu_{\ell}$ decays obtained both at finite values of the lattice spacing and at the physical pion point in the continuum limit. We show that, starting from a limited set of data at large $q^2$, it is possible to determine quite precisely the form factors in a model independent way in the full kinematical range, obtaining a remarkable agreement with the direct calculation of the form factors. This finding opens the possibility to obtain non-perturbatively the form factors entering the semileptonic B decays in the full kinematical range.