Nonperturbative Determination of Quark Masses in Quenched Lattice QCD with the Kogut-Susskind Fermion Action

We report results of quark masses in quenched lattice QCD with the Kogut-Susskind fermion action, employing the regularization independent scheme of Martinelli et al. to nonperturbatively evaluate the renormalization factor relating the bare quark mass on the lattice to that in the continuum. Calculations are carried out at $\beta =6.0\mathrm{}$, $6.2$, and $6.4$, from which we find $m_{\mathrm{ud}}^{\overline{\mathrm{MS}}}\left(2\mathrm{GeV}\right)=4.23\mathrm{}\left(29\right)\mathrm{MeV}$ for the average up and down quark mass and, with the $\phi$ meson mass as input, $m_s^{\overline{\mathrm{MS}}}\left(2\mathrm{GeV}\right)=129\mathrm{}\left(12\right)\mathrm{MeV}$ for the strange mass in the continuum limit. These values are about 20% larger than those obtained with the one-loop perturbative renormalization factor.