Dynamical Quark Effects on Light Quark Masses

Light quark masses are calculated in lattice QCD with two degenerate flavors of dynamical quarks. The calculations are made with improved actions with lattice spacing $a=0.22\mathrm{}$–0.11 fm. In the continuum limit we find $m_{\mathrm{ud}}^{\overline{\mathrm{MS}}}\left(2\mathrm{GeV}\right){=3.44\mathrm{}}_{-0.22\mathrm{}}^{+0.14\mathrm{}}\mathrm{MeV}$ using the $\pi$ and $\rho$ meson masses as physical input, and $m_s^{\overline{\mathrm{MS}}}\left(2\mathrm{GeV}\right){=88\mathrm{}}_{-6\mathrm{}}^{+4\mathrm{}}\mathrm{MeV}$ or ${90}_{-11\mathrm{}}^{+5\mathrm{}}\mathrm{MeV}$ with the $K$ or $\phi$ meson mass as additional input. The quoted errors represent statistical and systematic combined, the latter including those from continuum and chiral extrapolations, and from renormalization factors. Compared to quenched results, two flavors of dynamical quarks reduce quark masses by about $25\%$.