Form factors for Bₛ → K ℓ ν decays in Lattice QCD

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We present the current status of the computation of the form factor f+ (q²) for the semi-leptonic decay Bₛ → K ℓ ν by the ALPHA collaboration. We use gauge configurations which were generated as part of the Coordinated Lattice Simulations (CLS) effort. They have Nf=2 non-perturbatively O(a) improved Wilson fermions, and pion masses down to ≈ 250 MeV with mπL ≥ 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 q² = 21.23GeV² extrapolated to the continuum. Next-to-leading order terms in HQET and the chiral extrapolation still need to be included in the analysis.