  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: the analyticity
properties of two-point functions of local current operators and the positivity
of the corresponding hadronic spectral functions. The bounds follow from the
restriction of the sum over all possible hadronic states which can contribute
to the hadronic spectral functions to those with the lowest invariant mass.
These hadronic contributions are well known phenomenologically, either from
experiment or from chiral perturbation theory calculations. The results we find
cast serious doubts on the reliability of some of the lattice QCD
determinations which have been recently reported.
