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

TL;DR

This paper provides an analytical, next-to-next-to-leading order (NNLO) NRQCD calculation of top-antitop production observables near threshold in $e^+e^-$ and $ ext{γγ}$ collisions, including cross sections, asymmetries, and polarization.

Contribution

It introduces a set of universal functions for threshold effects and computes them analytically up to NNLO, incorporating top width and running coupling effects.

Findings

Analytical NNLO expressions for total cross sections and asymmetries.

Universal functions for S wave, P wave, and S-P interference computed analytically.

Inclusion of top width and running coupling effects in the threshold region.

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.