Charm- and Bottom-Quark Masses: Recent Sum Rule Results

Recent experimental results on the cross section for electron-positron annihilation into hadrons in the low energy region between roughly 3 GeV and 10 GeV, combined with an improved determination of the strong coupling and increasingly precise theory results on sum rules have lead to determinations of charm- and bottom-quark masses with accuracies of around 10 MeV. The final results, expressed in the MS scheme, have lead to $m_{c}$ (3 GeV) = 993(8) MeV and $m_{b}$ $(m_{b})$ = 4163(16) MeV, and are thus among the most precise determinations of these standard model parameters. These results are, furthermore, nicely consistent with completely independent lattice results and allow precise predictions for a number of experimental observables like Higgs decays into charm- or bottom-quarks. A critical analysis of the theoretical and experimental un- certainties of this analysis is presented in the following.