Subleading Effects in Soft-Gluon Emission at One-Loop in Massless QCD

• DOI: 10.48550/arxiv.2307.02286
• Publication Date: 2023-12-18
• Authors: Michał Czakon; Felix Eschment; Tom Schellenberger
• Keywords: High Energy Physics - Theory; FOS: Physical sciences; QC770-798; 01 natural sciences; 530; High Energy Physics - Phenomenology; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Higher-Order Perturbative Calculations; Renormalization Group; Factorization; info:eu-repo/classification/ddc/530; Scattering Amplitudes

Abstract We elucidate the structure of the next-to-leading-power soft-gluon expansion of arbitrary one-loop massless-QCD amplitudes. The expansion is given in terms of universal colour-, spin- and flavour-dependent operators acting on process-dependent gauge-invariant amplitudes. The result is proven using the method of expansion-by-regions and tested numerically on non-trivial processes with up to six partons. In principle, collinear-region contributions are expressed in terms of convolutions of universal jet operators and process-dependent amplitudes with two collinear partons. However, we evaluate these convolutions exactly for arbitrary processes. This is achieved by deriving an expression for the next-to-leading power expansion of tree-level amplitudes in the collinear limit, which is a novel result as well. Compared to previous studies, our analysis, besides being more general, yields simpler formulae that avoid derivatives of process-dependent amplitudes in the collinear limit.