HQET form factors for $B_s\to K\ell\nu$ decays beyond leading order

TL;DR

This paper calculates $B_s o K \, \ell \nu$ decay form factors using lattice HQET, including $1/m_b$ corrections, to improve the precision of theoretical predictions for semi-leptonic B decays.

Contribution

It extends previous static order calculations by incorporating $O(1/m_b)$ terms in lattice HQET for more accurate form factor determination.

Findings

Results for kinetic, spin, and current insertions calculated via the ratio method.

Form factors combined with non-perturbative HQET parameters for continuum extrapolation.

Form factors obtained up to $O(1/m_b^2)$ corrections without perturbative uncertainties.

Abstract

We compute semi-leptonic $B_s$ decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the $1/m_b$ expansion, one has to take into account not only the leading static order but also the terms arising at $O(1/m_b)$: kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to $O(1/m_b^2)$ corrections and without $O(\alpha_s(m_b)^n)$ corrections.