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We compute semi-leptonic $B_s$ decay form factors using Heavy Quark EffectiveTheory on the lattice. To obtain good control of the $1/m_b$ expansion, one hasto take into account not only the leading static order but also the termsarising at $O(1/m_b)$: kinetic, spin and current insertions. We show resultsfor these terms calculated through the ratio method, using our prior resultsfor the static order. After combining them with non-perturbative HQETparameters they can be continuum-extrapolated to give the QCD form factorcorrect up to $O(1/m_b^2)$ corrections and without $O(\alpha_s(m_b)^n)$corrections.

HQET form factors for $B_s\to K\ell\nu$ decays beyond leading order