Form factors for ${\mathrm{B}}_{\mathrm{s}}\to \mathrm{K}\ell \hat{I}½$ decays in Lattice QCD

Abstract

We present the current status of the computation of the form factor $f_{+}(q^2)$ for the semi-leptonic decay ${\mathrm{B}}_{\mathrm{s}}\to \mathrm{K}\ell \hat{I}½$ 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 $m_{\ddot{I}}€L\ge 4$. 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.

6 pages and 3 figures. Proceedings of the 8th International Workshop on the CKM Unitarity Triangle (CKM 2014), Vienna, Austria, September 8-12, 2014