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

We determine the renormalization group invariant quark mass corresponding to the sum of the strange and the average light quark mass in the quenched approximation 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 includes 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 CP-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 typical ambiguity in the quenched approximation. (C) 2000 Elsevier Science B.V. All rights reserved.