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We explain how the strategy of solving renormalization problems in HQET non-perturbatively by a matching to QCD in finite volume can be implemented to includ e dynamical fermions. As a primary application, some elements of an HQET computation of the mass of the b-quark beyond the leading order with Nf = 2 are outlined. In particular, the matching of HQET and QCD requires relativistic QCD simulations in a volume with L¼ 0.5 fm, which will serve to quantitatively determine the heavy quark mass dependence of heavy-light meson observables in the continuum limit of finite-volume two-flavour lattice QCD. As a preparation fo r the latter, we report on our determination of the renormalization constants and improvement coefficients relating the renormalized current and subtracted bare quark mass in the relevant weak coupling region. The calculation of these coefficients employs a constant physics condition in t he Schrodinger functional scheme, where the box size L is fixed by working at a prescribed value of the renormalized c oupling.

Towards a non-perturbative matching of HQET and QCD with dynamical light quarks