Charm and Bottom Quark Masses from Perturbative QCD

Using a new result for the first moment of the hadronic production cross section at order ${\cal O}(\alpha_s^3)$, and new data on the $J/\psi$ and $\psi'$ resonances for the charm quark, we determine the \msb masses of the charm and bottom quarks to be $m_c(m_c) = 1.295 \pm 0.015$ GeV and $m_b(m_b) = 4.205 \pm 0.058$ GeV. While we observe a large reduction of the perturbative error, the shifts induced by the theoretical input are very small. The main change in the central value of $m_c$ is related to the experimental data. On the other hand, the value of $m_b$ is not changed by our calculation to the assumed precision.