Top quark mass definition andtt¯production near threshold at the Next Linear Collider

We suggest an infrared-insensitive quark mass, defined by subtracting the soft part of the quark self-energy from the pole mass. We demonstrate the deep relation of this definition with the static quark-antiquark potential. At leading order in $1/m$ this mass coincides with the PS mass which is defined in a completely different manner. Going beyond the static limit, the small normalization point introduces recoil corrections which are calculated here as well. Using this mass concept and other concepts for the quark mass we calculate the cross section of $e^{+}{e}^{-}\to t\overline{t}$ near threshold at NNLO accuracy adopting three alternative approaches; namely, (1) fixing the pole mass, (2) fixing the PS mass, and (3) fixing the new mass which we call the $\overline{\mathrm{PS}}$ mass. We demonstrate that perturbative predictions for the cross section become much more stable if we use the PS or the $\overline{\mathrm{PS}}$ mass for the calculations. A careful analysis suggests that the top quark mass can be extracted from a threshold scan at NLC with an accuracy of about 100–200 MeV.