Massive quark-antiquark production with gluon radiative effects in high-energy spin-polarized electron-positron collisions

Abstract

The quark-antiquark production cross section, including gluon radiative corrections to order ${\ensuremath{\alpha}}_{s}$, for high-energy spin-polarized electron-positron collisions is obtained. The gluon radiative corrections are functions of the maximum recorded scaled gluon momentum ${X}_{g}=\frac{{E}_{g}}{E}$ and are expressed by gluon form factors ${F}_{i}({\overline{m}}_{f}, {X}_{g})$. Formulas for form factors are given for all values of ${X}_{g}$, $0<{X}_{g}<~1\ensuremath{-}{m}_{f}^{\ensuremath{-}2}$, where ${\overline{m}}_{f}$ is the scaled quark mass for flavor $f$, ${\overline{m}}_{f}=\frac{{m}_{f}}{E}$. Exact formulas in terms of the form factors are given for the radiative corrections to the cross section, the forward-backward asymmetry, the left-right asymmetry, and the forward-backward, left-right asymmetry. Explicit analytic formulas for ${\overline{m}}_{f}<~0.2$ are given for the radiative corrections to the cross section and the asymmetries for elastic quark-antiquark production, small values of ${X}_{g}$, and for the case that almost all gluons are recorded, $1\ensuremath{-}{X}_{g}\ensuremath{\ll}1$.