MSbar Charm Mass from Charmonium Sum Rules with Contour Improvement

A detailed error analysis is carried out for the determination of the MSbar charm quark mass $\bar m_c(\bar m_c)$ from moments at order alpha_s^2 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 $\bar m_c(\bar m_c)=1.29\pm 0.07$ GeV which contains a substantial theoretical uncertainty.