Charm- and bottom-quark masses from perturbative QCD

Using a new result for the first moment of the hadronic production cross section at order $\mathcal{O}({\alpha }_s^3)$, and new data on the $J/\psi$ and ${\psi }^{\prime }$ resonances for the charm quark, we determine the $\overline{\mathrm{MS}}$ masses of the charm and bottom quarks to be ${\overline{m}}_c({\overline{m}}_c)=1.295\pm 0.015\mathrm{GeV}$ and ${\overline{m}}_b({\overline{m}}_b)=4.205\pm 0.058\mathrm{GeV}$. We assume that the continuum contribution to the sum rules is adequately described by pQCD. 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.