Analytic results for $$e^ + e^ - \to \overline {tt} $$ and $$\gamma \gamma \to \overline {tt} $$ observables near the threshold up to the next-to-next-to-leading order of NRQCD

We present an analytic description of top-antitop pair production near the threshold in e⁺e⁻ annihilation and γγ collisions. A set of basic observables being considered includes total cross sections, forward-backward asymmetry, and top-quark polarization. Threshold effects relevant to 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 \(e^ + e^ - \to \overline {tt} \) cross section near the threshold is obtained in the next-to-next-to-leading order in a closed form including the contribution originating from the axial coupling of top quarks that is mediated by the Z boson. The effects of the running of the strong coupling constant and the finite top-quark width are taken into account analytically for the P-wave production and S-P wave interference.