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We re-examine the use of sum rules in the extraction of light quark massesand discuss a number of potential problems with existing analyses. The mostimportant issue is that of the overall normalization of the hadronic spectralfunctions should not be fixed by assuming complete resonance dominance of thecontinuum threshold region as it can overestimate the resonance contributionsto spectral integrals by factors as large as $\sim 5$. The second importantuncertainty comes from the assumed location, $s_0$, of the onset of dualitywith perturbative QCD, as the extracted quark masses depend very sensitively onthis parameter. The assumption of duality and the requirement of positivity of$\rho_5(s)$ imposes very severe constraints on the shape of the relevantspectral function in the dual region, and leads to rigorous lower bounds for$m_u+m_d$ as a function of $s_0$. In the extractions of $m_s$ we find that theconventional choice of the value of $s_0$ is not physical. For a morereasonable choice of $s_0$ we are not able to find a solution that is stablewith respect to variations of the Borel transform parameter. This problem canbe overcome only if the hadronic spectral function is determined up tosignificantly larger values of $s$ than is currently possible. Finally, we alsoestimate the error associated with the convergence of perturbative QCDexpressions used in the sum rule analyses. Our conclusion is that, taking allof 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 factor of 2.Comment: 28 pages. Published version. Modified "axis" source for figures also  include

Extraction of light quark masses from sum rule analyses of axial vector and vector current Ward identities