Mass of the charm-quark from QCD sum rules

Relativistic and non-relativistic ratios of Laplace transform QCD moment sum rules for charmonium are used in order to determine the value of the on-shell charm-quark mass. The validity of the non-relativistic version of QCD sum rules in this particular application is discussed. After using current values of the perturbative and non-perturbative QCD parameters, as well as experimental data on the $J/\psi$ system, we obtain $m_{c}(Q^{2}=m_{c}^{2}) = 1.46 \pm 0.07 \;\mbox{GeV}$.