Pure QCD bounds and estimates for light quark masses

We consider bounds on light quark masses that follow from positivity of the pseudoscalar correlator spectral function plus the assumption that perturbative QCD is valid for the correlator and its derivatives up to order N for momenta t greater than or equal to (t) over cap. We find that the bounds vary a lot depending on the assumed value of (t) over cap and even, if it is too small ((t) over cap similar or equal to 1.5, 1.6, 2.1 GeV2 for respectively N = 0, 1, 2), that there is incompatibility between the assumption of validity of perturbative QCD and positivity. This allows us to establish a criterion for the values of (t) over cap admissible, and to get upper and lower bounds for m(s) and upper bounds for m(d) + m(u), m(d) - m(u). The upper bounds are not particularly interesting, but the lower ones are very tight; specifically we find 240 MeV less than or equal to m(s); 16 MeV less than or equal to m(d) + m(u) if we assume perturbative QCD to give a valid description of the correlator for t greater than or equal to 2.2 GeV2; or, if it only holds for t greater than or equal to 4.5 GeV2, then 150 MeV less than or equal to m(s); 10 MeV less than or equal to m(d) + m(u). Here the masses are running masses defined at 1 GeV. We also show reasonable models where the bounds are saturated. The results suggest that some of the current estimates of the light quark masses are less precise than usually claimed, which is the main outcome of this work. (C) 1998 Elsevier Science B.V.