Measuring the running top-quark mass

We present the first direct determination of the running top-quark mass based on the total cross section of top-quark pair production as measured at the Tevatron. Our theory prediction for the cross section includes various next-to-next-to-leading order QCD contributions, in particular, all logarithmically enhanced terms near threshold, the Coulomb corrections at two loops and all explicitly scale-dependent terms at next-to-next-to-leading order accuracy. The result allows for an exact and independent variation of the renormalization and factorization scales. For Tevatron and LHC we study its dependence on all scales, on the parton luminosity and on the top-quark mass using both the conventional pole mass definition as well as the running mass in the $\overline{\mathrm{MS}}$ scheme. We extract for the top quark an $\overline{\mathrm{MS}}$ mass of $m(\mu =m)={160.0}_{-3.2}^{+3.3}\mathrm{GeV}$, which corresponds to a pole mass of $m_t={168.9}_{-3.4}^{+3.5}\mathrm{GeV}$.