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 $\mathcal{O}({\hat{\alpha }}_s^3)$. 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 ${\hat{\alpha }}_s(M_Z)=0.1182$.

Comments: 28 pages, 6 figures