Analytical results for $e^{+}{e}^{-}\to t\bar{t}$ and $\gamma \gamma \to t\bar{t}$ observables near the threshold up to the next-to-next-to-leading order of NRQCD

Abstract

We present an analytical description of top-antitop pair production near the threshold in $e^{+}{e}^{-}$ annihilation and $\text{g}\text{g}$ collisions. A set of basic observables considered includes the total cross sections, forward-backward asymmetry and top quark polarization. The threshold effects relevant for the basic observables are described by three universal functions related to S wave production, P wave production and S-P interference. These functions are computed analytically up to the next-to-next-to-leading order of NRQCD. The total $e^{+}{e}^{-}\to t\bar{t}$ cross section near the threshold is obtained in the next-to-next-to-leading order in the closed form including the contribution due to the axial coupling of top quark and mediated by the Z-boson. The effects of the running of the strong coupling constant and of the finite top quark width are taken into account analytically for the P wave production and S-P wave interference.

Comments: 46 pages LaTeX, editorial changes