Abstract
A fully nonperturbative lattice determination of the up or down and strange quark masses is given for quenched QCD using both $O(a)$ improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$ improved fermions we obtain ${m}_{s}^{\overline{\mathrm{MS}}}(\ensuremath{\mu}=2\mathrm{GeV})=105(4)\mathrm{MeV},$ using the interquark force scale ${r}_{0}.$ Because of quenching problems, fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up or down quark mass we find for the average mass ${m}_{l}^{\overline{\mathrm{MS}}}(\ensuremath{\mu}=2\mathrm{GeV})=4.4(2)\mathrm{MeV}.$
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