overlineMS charm mass from charmonium sum rules with contour improvement

A detailed error analysis is carried out for the determination of the overlineMS charm quark mass m¯_c(m¯_c) from moments at order α_s² of the charm cross section in e⁺e^- annihilation. To estimate the theoretical uncertainties the renormalization scale is implemented in various ways including energy-dependent functions, which lead to "contour-improved" predictions. We obtain m¯_c(m¯_c)=1.29±0.07 GeV which contains a substantial theoretical uncertainty.