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

We have computed the light quark masses using the O(a2) improved Alpha action, in the quenched approximation. The renormalized masses have been obtained non-perturbatively. By eliminating the systematic error coming from the truncation of the perturbative series, our procedure removes the discrepancies, observed in previous calculations, between the results obtained using the vector and the axial-vector Ward identities. It also gives values of the quark masses larger than those obtained by computing the renormalization constants using (boosted) perturbation theory. Our main results, in the RI (MOM) scheme and at a renormalization scale μ=2 GeV, are mRIs=138(15) MeV and mRIl=5.6(5) MeV, where mRIs is the mass of the strange quark and mRIl=(mRIu+mRId)/2 the average mass of the up-down quarks. From these results, which have been obtained non-perturbatively, by using continuum perturbation theory we derive the MS masses, at the same scale, and the renormalization group invariant (mRGI) masses. We find msNLO MS=121(13) MeV and mlNLO MS=4.9(4) MeV at the next-to-leading order; msN2LO MS=111(12) MeV, mlN2LO MS=4.5(4) MeV, msRGI=177(19) MeV and mRGIl=7.2(6) MeV at the next-to-next-to-leading order.