A factorization approach to next-to-leading-power threshold logarithms

TL;DR

This work extends soft–collinear factorization to next-to-leading power in threshold logarithms by introducing a universal radiative jet function within the Low-Burnett-Kroll-Del Duca (LBKD) framework and carefully removing double counting of soft–collinear regions. The authors compute the one-loop radiative jet function and validate the formalism by reproducing all abelian-like NLP threshold logarithms in the NNLO Drell–Yan real–virtual K-factor, demonstrating the practical viability of NLP resummation techniques. The results illuminate how NLP corrections can be organized at the amplitude level and connected to phase-space expansions, and they reveal a loop-induced breaking of strict next-to-soft theorems due to collinear effects. This work provides a concrete step toward a general NLP resummation formalism with clear paths to non-abelian generalizations and phenomenological applications such as Higgs production via gluon fusion and multi-gluon final states.

Abstract

Threshold logarithms become dominant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear. Such radiation factorizes at the level of scattering amplitudes, and this leads to the resummation of threshold logarithms which appear at leading power in the threshold variable. In this paper, we consider the extension of this factorization to include effects suppressed by a single power of the threshold variable. Building upon the Low-Burnett-Kroll-Del Duca (LBKD) theorem, we propose a decomposition of radiative amplitudes into universal building blocks, which contain all effects ultimately responsible for next-to-leading power (NLP) threshold logarithms in hadronic cross sections for electroweak annihilation processes. In particular, we provide a NLO evaluation of the "radiative jet function", responsible for the interference of next-to-soft and collinear effects in these cross sections. As a test, using our expression for the amplitude, we reproduce all abelian-like NLP threshold logarithms in the NNLO Drell-Yan cross section, including the interplay of real and virtual emissions. Our results are a significant step towards developing a generally applicable resummation formalism for NLP threshold effects, and illustrate the breakdown of next-to-soft theorems for gauge theory amplitudes at loop level.

Figures (4)

• Figure 1: Schematic depiction of the factorization of the amplitude into the non-collinear function $H$ of Eq. (\ref{['Hdef']}) and external jet functions: (a) portrays the non-radiative amplitude, while (b) and (c) contribute to the radiation of an extra gluon.
• Figure 2: Feynman diagrams contributing to the one-loop jet function. Here $J_{V,_{CT}}^{(1)}$ denotes the counterterm associated with the vertex graph, $J_V^{(1)}$, while counterterms associated with external leg corrections have been omitted.
• Figure 3: Contributions to the QED-like terms in the one-loop bare radiative jet function.
• Figure 4: Feynman diagrams for the matrix element squared contributing to Drell-Yan production at NNLO, and involving one real and one virtual emission. Diagrams obtained by interchanging $p\leftrightarrow \bar{p}$ and/or complex conjugation are not shown.