Lattice quark masses: a non-perturbative measurement

We discuss the renormalization of different definitions of quark masses in the Wilson and the tree-level improved SW-Clover fermionic action. For the improved case we give the correct relationship between the quark mass and the hopping parameter. Using perturbative and non-perturbative renormalization constants, we extract quark masses in the $\MSbar$ scheme from Lattice QCD in the quenched approximation at $\beta=6.0$, $\beta=6.2$ and $\beta=6.4$ for both actions. We find: $\bar{m}^{\MSbar}(2 GeV)=5.7 \pm 0.1 \pm 0.8$ MeV, $m_s^{\MSbar}(2GeV)= 130 \pm 2 \pm 18$ MeV and $m_c^{\MSbar}(2 GeV) = 1662\pm 30\pm 230$ MeV.