Precision computation of the strange quark's mass in quenched QCD

We determine the renormalization group invariant quark mass corresponding t o the sum of the strange and the average light quark mass in the quenched a pproximation of QCD, using as essential input the mass of the K-mesons. In the continuum limit we find (M-s + (M) over cap)/F-K = 0.874(29), which inc ludes systematic errors. Translating this non-perturbative result into the running quark masses in the (M) over bar (S) over bar scheme at mu = 2 GeV and using the quark mass ratios from chiral perturbation theory, we obtain (m) over bar(s)(2 GeV) = 97(4)MeV. With the help of recent results by the C P-PACS Collaboration, we estimate that a 10% higher value would be obtained if one replaced F-K by the nucleon mass to set the scale. This is a typica l ambiguity in the quenched approximation. (C) 2000 Elsevier Science B.V. A ll rights reserved.