Factorisation schemes for proton PDFs

• DOI: 10.48550/arxiv.2501.18289
• Publication Date: 2025-01-01
• Authors: Delorme, Stéphane; Kusina, Aleksander; Siódmok, Andrzej; Whitehead, James
• Keywords: High Energy Physics - Theory; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); FOS: Physical sciences

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.<br/>53 pages, 31 figures, 9 tables<br/>