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We present a determination of the b-quark mass accurate through O(\alpha_s^2)in perturbation theory and including partial contributions at O(\alpha_s^3).Nonperturbative input comes from the calculation of the Upsilon and B_senergies in lattice QCD including the effect of u, d and s sea quarks. We usean improved NRQCD action for the b-quark. This is combined with the heavy quarkenergy shift in NRQCD determined using a mixed approach of high-beta simulationand automated lattice perturbation theory. Comparison with experiment enablesthe quark mass to be extracted: in the MS bar scheme we find m_b(m_b) =4.166(43) GeV.

The mass of the b-quark from lattice NRQCD and lattice perturbation theory