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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 aspart of the Coordinated Lattice Simulations (CLS) effort. They have $N_\mathrmf=2$ non-perturbatively $O(a)$ improved Wilson fermions, and pion masses downto $\approx 250 \,\mathrm {MeV}$ with $m_\pi L \geq 4$. The heavy quark istreated in non-perturbative Heavy Quark Effective Theory (HQET).  We discuss how to extract the form factors from the correlation functions andpresent 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 thechiral extrapolation still need to be included in the analysis.

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