Effective heavy-light meson energies in small-volume quenched QCD

We study effective energies of heavy-light meson correlation functions in lattice QCD and a small volume of (0.2 fm)4 to non-perturbatively calculate their dependence on the heavy quark mass in the continuum limit. Our quenched results obtained here constitute an essential part of a first fully non-perturbative computation of the b-quark's mass in the static approximation that has recently been presented as an application of a new proposal to non-perturbatively renormalize the Heavy Quark Effective Theory. As an intermediate step, the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass are determined in the relevant parameter region at weak couplings, which allows to perform the numerical simulations at several, precisely fixed values of the renormalization group invariant heavy quark mass in a range from 3 GeV to 15 GeV. (author)