Analytical results for O(αs) radiative corrections to e+e- → t(t)over-bar↑ up to a given gluon energy cut

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(-) -> (t) over bart(G) and e(+)e(-) -> (t) over bart(up arrow)(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 cutoff dependence of the various polarized and unpolarized cross sections and discuss how the exact results numerically differ from the approximate soft-gluon results.