Form factors for $\mathrm B_\mathrm s \to \mathrm K \ell \nu$ decays in Lattice QCD

TL;DR

This paper reports on the lattice QCD calculation of the form factor for the semileptonic decay B_s to K, using improved Wilson fermions and HQET, providing preliminary results relevant for understanding this decay process.

Contribution

The study presents the current status and preliminary results of computing the B_s to K form factor using lattice QCD with non-perturbative HQET and improved Wilson fermions.

Findings

First results for the form factor at q^2 = 21.23 GeV^2

Use of gauge configurations from CLS with pion masses down to 250 MeV

Continuum extrapolation of the form factor is performed

Abstract

We present the current status of the computation of the form factor $f_+ (q^2)$ for the semi-leptonic decay $\mathrm B_\mathrm s \to \mathrm K \ell \nu$ by the ALPHA collaboration. We use gauge configurations which were generated as part of the Coordinated Lattice Simulations (CLS) effort. They have $N_\mathrm f=2$ non-perturbatively $O(a)$ improved Wilson fermions, and pion masses down to $\approx 250 \,\mathrm {MeV}$ with $m_\pi L \geq 4$. The heavy quark is treated in non-perturbative Heavy Quark Effective Theory (HQET). We discuss how to extract the form factors from the correlation functions and present first results for the form factor at $q^2 = 21.23\,\mathrm{GeV}^2$ extrapolated to the continuum. Next-to-leading order terms in HQET and the chiral extrapolation still need to be included in the analysis.