Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions

摘要

We determine the light quark masses from lattice QCD simulationsincorporating the electromagnetic interaction of valence quarks. The mesonmasses are calculated on lattice QCD configurations generated by the RBCCollaboration for two flavors of dynamical domain wall fermions, which arecombined with QED configurations generated via quenched non-compact latticeQED. The electromagnetic part of the pion mass splitting is found to be$m_{\pi^+}-m_{\pi^0}=4.12(21)$ MeV, where only the statistical error is quoted,and similarly for the kaon, 1.443(55) MeV. Our results for the light quarkmasses are $m_u^{\rm\bar{MS}}$(2 GeV)=$3.02(27)(19)$ MeV, $m_d^{\rm\bar{MS}}$(2GeV)=$5.49(20)(34)$ MeV, and $m_s^{\rm\bar{MS}}$(2 GeV)=$119.5(56)(74)$ MeV,where the first error is statistical and the second systematic. By averagingover $\pm e$ to cancel ${\cal O}(e)$ noise exactly on each combined gauge fieldconfiguration, we are able to work at physical $\alpha=1/137$ and obtain verysmall statistical errors. In our calculation, several sources of systematicerror remain, including finite volume, non-zero lattice spacing, chiralextrapolation, quenched QED, and quenched strange quark, which may be moresignificant than the errors quoted above.