On t anti-t threshold and top quark mass definition

In this talk we discuss the process e^+e^-\to t\bar t near threshold, calculated with NNLO accuracy as well as top quark mass definitions adequate for the threshold. As new definition we suggest the PS-bar mass which allows to calculate recoil corrections to the static PS mass. Using this result we calculate the cross section of e^+e^-\to t\bar 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 PS-bar mass. We demonstrate that perturbative predictions for the cross section become much more stable if we use the PS or the PS-bar 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 MeV.Comment: 4 pages, LaTeX, the contribution to the Linear Collider Workshop 2000, Fermilab, October 2000; the slides of the talk presented by O. Yakovlev are available here: http://conferences.fnal.gov/lcws2000/web/Yakovlev_P2