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

TL;DR

The paper develops an analytic NNLO NRQCD treatment of top-antitop threshold production in $e^+e^-$ and $\gamma\gamma$ collisions.Observables are expressed via three universal threshold functions: the $S$-wave Green function at the origin, the $P$-wave derivative at the origin, and the $S$-$P$ interference function $\Phi(k)$.It provides closed-form NNLO soft corrections for the total cross section in $e^+e^-$ including axial coupling and analyzes width and scale choices; it also treats $P$-wave and interference in $\gamma\gamma$ and computes forward-backward asymmetry and polarization at NLO.Numerical results indicate sizable NNLO corrections and show how these observables can constrain $\alpha_s$, $m_t$, and $\Gamma_t$.

Abstract

We present an analytical description of top-antitop pair production near the threshold in $e^+e^-$ annihilation and $\g\g$ 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.