Top Near Threshold: All QCD Radiative Corrections are Trivial

Abstract

We have calculated part of O($α_{S}$) QCD radiative correction to the total cross-section of top's threshold production in $ e^{+}e^{-} \to t\bar t \to W^{-} b W^{+} \bar b$ reaction. We found out a curious fact: there is no O($α_{S}$) correction to the total cross-section, originated from $b \bar b , t \bar b ,\bar t b $ gluon exchange and corresponding gluon emission. Thus, all O($α_{S}$) corrections which are non-zero, can be classified as: 1) corrections to $t \bar t$ nonrelativistic potential 2) corrections to the top's width 3) hard gluon correction to $γt \bar t$-vertex. These corrections are well-known and were described in the previous papers. We can conclude that similar situation takes place for all unstable particles threshold production. This result can be expressed in the form of a general statment: There is no O($α_{QED}$ or $α_{QCD}$) corrections for the total cross-section , originated from the "jet-jet" interection.