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

Abstract

We discuss the computation of form factors for semi-leptonic decays of $\mathrm{B}$-, ${\mathrm{B}}_{\mathrm{s}}$- mesons in lattice QCD. Considering in particular the example of the static ${\mathrm{B}}_{\mathrm{s}}$ 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 $V_{\mathrm{ub}}$. The size of the corrections of order $1/m_{\mathrm{b}}$ is just estimated at present but it is expected that their inclusion does not pose significant difficulties.

Comments: 16 pages, 3 figures; minor corrections and typo fixes, published version