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) over bar(b) = m(b)(<(MS)over bar>) (m(b)(<(MS)over 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) over bar(b) can change by several hundred MeV when the two-loop terms are included. (C) 1999 Elsevier Science B.V. All rights reserved.