O ( α s ) longitudinal spin polarization in heavy-quark production

We present the massive one-loop QCD corrections to the production cross sections of polarized quarks in the annihilation process ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}qq\ifmmode\bar\else\textasciimacron\fi{}(g) for bottom, top, and charm quarks. From the full analytical expressions for the production cross sections, Schwinger-type interpolation formulas for all parity-parity combinations (VV, VA, AA) are derived. The parity-odd interpolation formula contains the correct limit for vanishing quark masses taking into account a residual coupling of left- and right-chiral states in the massless theory. Numerical results for the total cross section and the longitudinal spin polarization demonstrate the accuracy of the interpolation formulas.