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Top quark production near threshold and the top quark mass

We consider top-anti-top production near threshold in $e^+ e^-$ collisions, resumming Coulomb-enhanced corrections at next-to-next-to-leading order (NNLO). We also sum potentially large logarithms of the small top quark velocity at the next-to-leading logarithmic level using the renormalization group. The NNLO correction to the cross section is large, and it leads to a significant modification of the peak position and normalization. We demonstrate that an accurate top quark mass determination is feasible if one abandons the conventional pole mass scheme and if one uses a subtracted potential and the corresponding mass definition. Significant uncertainties in the normalization of the $t\bar{t}$ cross section, however, remain.