HOW SMALL CAN THE LIGHT-QUARK MASSES BE

We derive lower bounds for the combination of Light quark masses m(s) + m(u) and m(d) + m(u). The derivation is based on first principles: t he analyticity properties of two-point functions of local current oper ators and the positivity of the corresponding hadronic spectral functi ons. The bounds follow from the restriction of the sum over all possib le hadronic states which can contribute to the hadronic spectral funct ions to those with the lowest invariant mass. These hadronic contribut ions are well known phenomenologically, either from experiment or from chiral perturbation theory calculations. The results we find cast ser ious doubts on the reliability of some of the lattice QCD determinatio ns which have been recently reported. (C) 1997 Elsevier Science B.V.