出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：The HPQCD collaboration has a program for determining the fundamental constants of the Standard
Model Lagrangian from lattice QCD. The most accurate method of doing this uses the
nf = 2+1 improved staggered MILC ensembles with chiral fitting and multi-loop perturbative
renormalisation to connect to the continuumMS scheme. This programhas already been very successful
with the recent strong coupling constant determination at three-loops from 28 observables
at three lattice spacings, and the one-loop light quark mass calculation last year. Here a preliminary
result is presented for the first-ever lattice determination of the two-loop multiplicative quark
mass renormalisation. The perturbative calculation involved was automated in the generation of
the Feynman rules, and the generation and coding of all of the roughly 30 Feynman diagrams. The
full formal framework for lattice quark mass renormalisation is given, including the cancellation
of infrared divergences in intermediate diagrams. The result was checked by evaluation in three
separate gauges and by two authors independently, showing the incredible flexibility and power
of this perturbative methodology. Our preliminary result for the two-loop perturbative matching
factor, and of systematic errors associated with higher-orders, gives MS masses at a 2 GeV scale
of ms = 87(0)(4)(4)(0) MeV, and 1
2 (mu +md) = 3.3(0)(2)(2)(0) MeV, where the respective uncertainties
are from lattice statistical, lattice systematic, perturbative, and electromagnetic and
isospin effects. The perturbative errors are a factor of two smaller than in our previous study, and
we anticipate reducing this somewhat further from additional analysis of the systematics.
