Analytical results for O(\alpha_s) radiative corrections to e+ e- -> tbar t(pol.) up to a given gluon energy cut

TL;DR

This paper provides analytical calculations of O(α_s) radiative corrections to polarized top quark pair production in e+ e- annihilations with a gluon energy cut, comparing exact results with soft-gluon approximations.

Contribution

It presents fully analytical expressions for polarized and unpolarized cross sections including gluon energy cuts, extending previous soft-gluon approximation results.

Findings

Exact results differ numerically from soft-gluon approximations.

The analytical formulas recover known limits for soft gluon and inclusive cases.

Numerical analysis shows the impact of the energy cut on cross sections.

Abstract

We determine the O(\alpha_s) radiative corrections to polarized top quark pair production in e+ e- -annihilations with a specified gluon energy cut. We write down fully analytical results for the unpolarized and polarized O(\alpha_s) cross sections e+ e- -> tbar t (G) and e+ e- -> tbar t(pol.) (G) including their polar orientation dependence relative to the beam direction. In the soft gluon limit we recover the usual factorizing form known from the soft gluon approximation. In the limit when the gluon energy cut takes its maximum value we recover the totally inclusive unpolarized and polarized cross sections calculated previously. We provide some numerical results on the cut-off dependence of the various polarized and unpolarized cross sections and discuss how the exact results numerically differ from the approximate soft-gluon results.