Continuum limit of the leading order HQET form factor in $B_s \to K\ell\nu$ decays

TL;DR

This paper demonstrates that lattice QCD calculations of B_s meson decay form factors can reliably reach the continuum limit after non-perturbative renormalization, aiding precise determination of the CKM matrix element V_ub.

Contribution

It provides a non-perturbative approach to compute B_s decay form factors and confirms the feasibility of continuum limit extrapolation in lattice QCD.

Findings

Continuum limit can be confidently taken after non-perturbative renormalization.

Precision of form factor calculations is suitable for V_ub extraction.

Estimated 1/m_b corrections are manageable and expected to be incorporated easily.

Abstract

We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the continuum limit can be taken with confidence. The resulting precision is of interest for extractions of $V_{\rm ub}$. The size of the corrections of order $1/m_{\rm b}$ is just estimated at present but it is expected that their inclusion does not pose significant difficulties.