ABSTRACT
All lattice-QCD calculations of the hadronic-vacuum-polarization contribution to the muon's anomalous magnetic moment to date have been performed with degenerate up- and down-quark masses. Here we calculate directly the strong-isospin-breaking correction to a_{µ}^{HVP} for the first time with physical values of m_{u} and m_{d} and dynamical u, d, s, and c quarks, thereby removing this important source of systematic uncertainty. We obtain a relative shift to be applied to lattice-QCD results obtained with degenerate light-quark masses of δa_{µ}^{HVP,m_{u}≠m_{d}}=+1.5(7)%, in agreement with estimates from phenomenology.
ABSTRACT
By using a single formalism to handle charm, strange, and light valence quarks in full lattice QCD for the first time, we are able to determine ratios of quark masses to 1%. For m(c)/m(s) we obtain 11.85(16), an order of magnitude more precise than the current PDG average. Combined with 1% determinations of the charm quark mass now possible this gives m(s)(2 GeV)=92.4(1.5) MeV. The MILC result for m(s)/m(l)=27.2(3) yields m(l)(2 GeV)=3.40(7) MeV for the average of u and d quark masses.