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

Abstract

We compute semi-leptonic $B_s$ decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the $1/m_b$ expansion, one has to take into account not only the leading static order but also the terms arising at $O(1/m_b)$: kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to $O(1/m_b^2)$ corrections and without $O({\alpha }_s(m_b{)}^n)$ corrections.

Comments: 7 pages, 4 figures. Proceedings of the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain; v2: small corrections, published version