Mass of the b quark from lattice NRQCD and lattice perturbation theory

We present a determination of the b-quark mass accurate through O(α2s) in perturbation theory and including partial contributions at O(α3s). Nonperturbative input comes from the calculation of the Υ and Bs energies in lattice QCD, including the effect of u, d and s sea quarks. We use an improved NRQCD action for the b quark. This is combined with the heavy quark energy shift in NRQCD determined using a mixed approach of high-β simulation and automated lattice perturbation theory. Comparison with experiment enables the quark mass to be extracted: in the MS scheme we find mb(mb)=4.166(43) GeV