Light Quark Masses from Lattice QCD

We present estimates of the masses of light quarks using lattice data. Our main results are based on a global analysis of all the published data for Wilson and Staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. We find that the values of masses in the Wilson and Staggered formulations agree after extrapolation to the continuum limit for both the $n_f=0$ and $n_f=2$ theories. Our best estimates, in the \MSbar\ scheme at $\mu=2 \GeV$, are $\mbar=3.1(3) \MeV$ and $m_s = 90(20) \MeV$ in the quenched approximation, and $\mbar < 2.7 \MeV$ and $m_s = 55-70 \MeV$ for the $n_f=2$ theory. These estimates are significantly smaller than phenomenological estimates based on sum rules and chiral perturbation theory. Finally, using our high statistics study on $32^3 \times 64$ lattices at $\beta = 6.0$ with Wilson fermions we analyze the validity of the Ward identity for the axial current, and present results for the quark condensate.