Heavy quark effective theory computation of the mass of the bottom quark

We present a fully non-perturbative computation of the mass of the b-quark in the quenched approximation. Our strategy starts from the matching of HQET to QCD in a finite volume and finally relates the quark mass to the spin averaged mass of the Bs meson in HQET. All steps include the terms of order Λ2/mb. Expanding on [1], we discuss the computation and renormalization of correlation functions at order 1/mb. With the strange quark mass fixed from the Kaon mass and the QCD scale set through r0 = 0.5 fm, we obtain a renormalization group invariant mass Mb = 6.758(86) GeV or m-bar b( m-bar b) = 4.347(48)GeV in the M-bar S-bar scheme. The uncertainty in the computed Λ2/mb terms contributes little to the total error and Λ3/mb2 terms are negligible. The strategy is promising for full QCD as well as for other B-physics observables