Corrections of Order \alpha_s^2 to the Forward-Backward Asymmetry

TL;DR

This paper computes second-order QCD corrections to the forward-backward asymmetry in electron-positron annihilation, highlighting the impact of quark mass logarithms and the non-perturbative effects on the asymmetry calculations.

Contribution

It provides new second-order QCD correction calculations using the thrust axis and clarifies discrepancies with previous results, emphasizing the role of quark mass effects.

Findings

Second-order corrections differ slightly from previous calculations but are well-understood.

Massive quark asymmetry is enhanced by mass logarithms, affecting theoretical predictions.

Asymmetry for massless quarks is non-perturbative and not fully computable in QCD.

Abstract

We calculate the second-order QCD corrections to the forward-backward asymmetry in $e^+e^-$ annihilation. Using the quark axis definition, we do not agree with either existing calculation, but the difference relative to one of them is small and understood. In particular, we point out that the forward-backward asymmetry of massive quarks is enhanced by logarithms of the quark mass. This implies that the forward-backward asymmetry of massless quarks is not computable in QCD perturbation theory and affected by non-power-suppressed corrections coming from the non-perturbative fragmentation functions. We also calculate the second-order corrections using the experimentally-preferred thrust axis definition for the first time.