Computation of the b-quark mass with perturbative matching at the next-to-next-to-leading order

We compute the two-loop term in the perturbation series for the quark-mass in the lattice Heavy Quark Effective Theory (HQET). This is an ingredient in the matching factor required to obtain the b-quark mass from lattice simulations of the HQET at first-order in the Heavy Quark Expansion. Combining our calculation with numerical results from quenched simulations by the APE collaboration, we find, at two-loop order, m-barb ≡ mbMS-bar(mbMS-bar = 4.38 ± 0.05 ± 0.10 GeV. It was expected that the two-loop term would have a significant effect, and this is indeed what we find. Depending on the choice of 'reasonable' coupling constant in the one-loop estimates, the result for m-barb can change by several hundred MeV when the two-loop terms are included