The b quark mass from lattice nonrelativistic QCD
Abstract
We present the first two-loop calculation of the heavy quark energy shift in lattice nonrelativistic QCD (NRQCD). This calculation allow us to extract a preliminary prediction of mb(mb, nf = 5) = 4.25(12) GeV for the mass of the b quark from lattice NRQCD simulations performed with a lattice of spacing a=0.12fm. Our result is an improvement on a previous determination of the b quark mass from unquenched lattice NRQCD simulations, which was limited by the use of one-loop expressions for the energy shift. Our value is in good agreement with recent results of mb(mb) = 4.163(16) GeV from QCD sum rules and mb(mb, nf = 5) = 4.170(25) GeV from realistic lattice simulations using highly-improved staggered quarks. We employ a mixed strategy to simplify our calculation. Ghost, gluon and counterterm contributions to the energy shift and mass renormalisation are extracted from quenched high-beta simulations whilst fermionic contributions are calculated using automated lattice perturbation theory. Our results demonstrate the effectiveness of such a strategy.
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