Top and bottom quark forward-backward asymmetries at next-to-next-to-leading order QCD in (un)polarized electron positron collisions

TL;DR

This paper calculates next-to-next-to-leading order QCD corrections to forward-backward asymmetries in top and bottom quark production in electron-positron collisions, including polarization effects, providing precise theoretical predictions for collider experiments.

Contribution

It provides the first NNLO QCD calculations of forward-backward asymmetries for top and bottom quarks, incorporating polarization and different jet definitions, enhancing precision in theoretical predictions.

Findings

QCD corrections to top-quark asymmetry are significant and polarization-dependent.

QCD corrections to bottom-quark asymmetry at the Z peak are small, making it a precise observable.

Different jet algorithms affect the definition and calculation of bottom-quark asymmetries.

Abstract

We consider, at order $\alpha_s^2$ in the QCD coupling, top-quark pair production in the continuum at various center-of-mass energies and $b$-quark pair production at the $Z$ resonance by (un)polarized electron and positron beams. For top quarks we compute the forward-backward asymmetry with respect to the top-quark direction of flight, the associated polar angle distribution, and we analyze the effect of beam polarization on the QCD corrections to the leading-order asymmetry. We calculate also the polarized forward-backward asymmetry. For $b$-quark production at the $Z$ peak we explore different definitions of $A_{\rm FB}$. In particular, we analyze $b$ jets defined by the Durham and the flavor-$k_T$ clustering algorithms. We compute the inclusive $b$-jet and two-jet asymmetry with respect to the $b$-jet direction. For the latter asymmetry the QCD corrections to order $\alpha_s^2$ are small. That predestines it to act as a precision observable.