Precise charm- and bottom-quark masses: Theoretical and experimental uncertainties

We consider recent theoretical and experimental improvements in determining charm- and bottom-quark masses. We present a new, improved evaluation of the contribution of the gluon condensate $\langle\alpha_{\mathrm s}G^2/\pi\rangle$ to the charm mass determination and a detailed study of potential uncertainties in the continuum cross section for $b\bar b$ production, together with a study of the parametric uncertainty from the $\alpha_{\mathrm s}$-dependence of our results. The final results, $m_c(3\text{\,GeV})=986(13)\text{\,MeV}$ and $m_b(m_b)= 4163(16)\text{\,MeV}$, together with the closely related lattice determination $m_c(3\text{\,GeV})=986(6)\text{\,MeV}$, currently represent the most precise determinations of these two fundamental standard-model parameters. We critically analyze the theoretical and experimental uncertainties.