EXTRACTION OF LIGHT-QUARK MASSES FROM SUM-RULE ANALYSES OF AXIAL-VECTOR AND VECTOR CURRENT WARD IDENTITIES

In light of recent lattice results for the light quark masses m(s) and m(u)+ m(d), we reexamine the use of sum rules in the extraction of th ese quantities, and discuss a number of potential problems with existi ng analyses. The most important issue is that of the overall normaliza tion of the hadronic spectral functions relevant to the sum rule analy ses. We explain why previous treatments, which fix this normalization by assuming complete resonance dominance of the continuum threshold re gion, can potentially overestimate the resonance contributions to spec tral integrals by factors as large as similar to 5. We propose an alte rnate method of normalization based on an understanding of the role of resonances in chiral perturbation theory which avoids this problem. T he second important uncertainty we consider relates to the physical co ntent of the assumed location s(0) of the onset of duality with pertur bative QCD. We find that the extracted quark masses depend very sensit ively on this parameter. We show that the assumption of duality impose s very severe constraints on the shape of the relevant spectral functi on in the dual region and present rigorous lower bounds for m(u) + m(d ) as a function of so based on a combination of these constraints and the requirement of positivity of rho(5)(s). In the extractions of m(s) , we find that the conventional choice of the value of s(0) is not phy sical. For a more reasonable choice of s(0), we are not able to find a solution that is stable with respect to variations of the Borel trans form parameter. This problem can, unfortunately, be overcome only if t he hadronic spectral function is determined up to significantly larger values of s than is currently possible. Finally, we also estimate the error associated with the convergence of perturbative QCD expressions used in the sum rule analyses. Our conclusion is that, taking all of these issues into account, the resulting sum rule estimates for both m (u) + m(d) and m(s) could easily have uncertainties as large as a fact or of 2, which would make them compatible with the low estimates obtai ned from lattice QCD.