Top Quark Production and Decay at Next-to-leading Order in $e^+e^-$ Annihilation

TL;DR

This work develops a next-to-leading order QCD framework for $e^+e^- \to t\bar t + X$, including gluon radiation in both production and decay while preserving full angular correlations through a helicity-based formalism. A four-channel NLO Monte Carlo is constructed to isolate and combine virtual, soft, and real gluon contributions with infrared-safe cancellations, and to handle ambiguities in gluon assignment to production or decay. The study shows gluon emission is mainly from decay near $\sqrt{s}=400$ GeV with $m_t=175$ GeV, while higher energies require resummation of collinear logs as production-stage radiation becomes more important. The results quantify how QCD radiation distorts top-mass reconstructions and helicity distributions and guide experimental strategies for precise top-quark parameter extraction at future $e^+e^-$ colliders.

Abstract

We study the effects of QCD corrections to the process $e^+e^-\rightarrow t\bar t+X\rightarrow b\ell^+ν\bar b\ell^-\bar ν+X$ above threshold. We show how to treat consistently to ${\cal O}(α_s)$ the gluon radiation in both the production and the decay of the top quarks, while maintaining all angular correlations in the event. At this order there is an ambiguity in the event reconstruction whenever a real gluon occurs in the final state. We study the effects of this ambiguity on the top mass and helicity angle distributions. For a top mass of 175 GeV and collider energy of 400 GeV the gluon radiation is emitted predominantly in the decay of the top quarks.