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_s energies in lattice QCD i
ncluding 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-beta simulation and automated lattice perturbation theory. Comparison with experiment enables the quark mass to be extracted: in the MS bar scheme we find m_b(m_b) = 4.166(43) GeV.
We present an algorithm to automatically derive Feynman rules for lattice perturbation theory in background field gauge. Vertices with an arbitrary number of both background and quantum legs can be derived automatically from both gluonic and fermioni
c actions. The algorithm is a generalisation of our earlier algorithm based on prior work by Luscher and Weisz. We also present techniques allowing for the parallelisation of the evaluation of the often rather complex lattice Feynman rules that should allow for efficient implementation on GPUs, but also give a significant speed-up when calculating the derivatives of Feynman diagrams with respect to external momenta.
