Non-perturbatively renormalized light-quark masses with the alpha action

We have computed the light quark masses using the O(a(2)) improved Alpha ac tion, in the quenched approximation. The renormalized masses have been obta ined non-perturbatively. By eliminating the systematic error coming from th e truncation of the perturbative series, our procedure removes the discrepa ncies, observed in previous calculations, between the results obtained usin g the vector and the axial-vector Ward identities. It also gives values of the quark masses larger than those obtained by computing the renormalizatio n constants using (boosted) perturbation theory. Our main results, in the R I (MOM) scheme and at a renormalization scale mu = 2 GeV, are m(s)(RI) = 13 8(15) MeV and m(i)(RI) = 5.6(5) MeV, where m(s)(RI) is the mass of the stra nge quark and m(l)(RI) = (m(u)(RI) + m(d)(RI))/2 the average mass of the up -down quarks. From these results, which have been obtained non-perturbative ly, by using continuum perturbation theory we derive the MS masses, at the same scale, and the renormalization group invariant (m(RGI)) masses. We fin d m(s)(NLO MS) = 121(13) MeV and m(l)(NLO MS) = 4.9(4) MeV at the next-to-l eading order; m(s)(N2 LO MS) = 111(12) MeV, m(l)(N2) (LO) (MS) = 4.5(4) MeV , m(s)(RGI) = 177(19) MeV and m(l)(RGI) = 7.2(6) MeV at the next-to-next-to -leading order. (C) 1998 Published by Elsevier Science B.V. All rights rese rved.