The Light Quark Masses from Lattice Gauge Theory

We investigate the masses of the light quarks with lattice QCD. We show that most of the large dependence on the lattice spacing, a, observed in previous determinations using Wilson fermions is removed with the use of an O(a) corrected action. In the quenched approximation, we obtain for the strange quark MS bar mass m_s(2 GeV) = 95 (16) MeV, and for the average of the up and down quark masses m_l(2 GeV) = 3.6 (6) MeV. Short distance arguments and existing staggered fermion calculations make it likely that the answers including the effects of quark loops lie 20 % to 40 % below this: m_s(2 GeV) in the range 54-92 MeV, and m_l(2 GeV) in the range 2.1-3.5 MeV. We argue that almost all lattice determinations of the light quark masses are consistent with these values. These low values are outside the range usually given by conventional phenomenology.