Factorisation schemes for proton PDFs

TL;DR

This paper compares various factorisation schemes for proton PDFs in perturbative QCD, analyzing their features and uncertainties to improve LHC phenomenology accuracy.

Contribution

It systematically assembles and compares different factorisation schemes in a unified notation, providing insights into their differences and uncertainties.

Findings

Analytical and numerical comparison of schemes

Estimation of factorisation-scheme uncertainties for LHC

Identification of schemes' suitability for specific purposes

Abstract

Beyond leading-order, perturbative QCD requires a choice of factorisation scheme to define the parton distribution functions (PDFs) and hard-process cross-section. The modified minimal-subtraction ($\overline{\mathrm{MS}}$) scheme has long been adopted as the default choice due to its simplicity. Alternative schemes have been proposed with specific purposes, including, recently, PDF positivity and NLO parton-shower matching. In this paper we assemble these schemes in a common notation for the first time. We perform a detailed comparison of their features, both analytically and numerically, and estimate the resulting factorisation-scheme uncertainty for LHC phenomenology.