Charm Quark Mass with Calibrated Uncertainty

Abstract

We determine the charm quark mass $\hat{m}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${\cal O} (\hat\alpha_s^3)$. Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result is $\hat{m}_c(\hat{m}_c) = 1272 \pm 8$~MeV for $\hat\alpha_s(M_Z) = 0.1182$.