Improving methods and predictions at high-energy $e^+e^-$ colliders within collinear factorisation

TL;DR

This paper emphasizes the importance of using electron PDFs with next-to-leading collinear accuracy for precise predictions at high-energy $e^+e^-$ colliders, analyzing their evolution, uncertainties, and impact on key processes.

Contribution

It provides a detailed study of electron PDFs at next-to-leading order, including scheme dependence, mass thresholds, and their effect on collider observable predictions.

Findings

Electron PDFs significantly influence cross section predictions.

Uncertainties in PDFs affect precision estimates for collider processes.

Next-to-leading-order electroweak effects are incorporated into predictions.

Abstract

We illustrate how electron Parton Distribution Functions (PDFs) with next-to-leading collinear logarithmic accuracy must be employed in the context of perturbative predictions for high-energy $e^+e^-$-collision processes. In particular, we discuss how the renormalisation group equation evolution of such PDFs is affected by the presence of multiple fermion families and their respective mass thresholds, and by the dependences on the choices of the factorisation and renormalisation schemes. We study the impact of the uncertainties associated with the PDFs on physical cross sections, in order to arrive at realistic precision estimates for observables computed with collinear-factorisation formulae. We do so by presenting results for the production of a heavy neutral object as well as for $t\bar{t}$ and $W^+W^-$ pairs, including next-to-leading-order effects of electroweak origin.