Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions

TL;DR

The paper shows that next-to-leading power threshold effects for colourless final states in hadronic collisions admit a universal factorisation at NLO: the NLP corrections collapse into a simple K-factor multiplying the Born cross section with shifted partonic kinematics, independently of the emitter spin and with trivial color-factor replacements between gluon- and quark-initiated channels. This universality, grounded in next-to-soft amplitude factorisation, yields fully differential results for arbitrary colour-singlet final states and reproduces known Higgs production results while providing new analytic NLP expressions with exact top-mass dependence for Higgs pair production. The findings offer practical analytic approximations for loop-induced processes and a pathway to higher-order (NNLO) NLP resummation via radiative functions, with potential applications to beyond-Standard-Model scenarios. Overall, the work significantly simplifies and unifies NLP threshold predictions across a broad class of hadronic processes.

Abstract

We consider the production of an arbitrary number of colour-singlet particles near partonic threshold, and show that next-to-leading order cross sections for this class of processes have a simple universal form at next-to-leading power (NLP) in the energy of the emitted gluon radiation. Our analysis relies on a recently derived factorisation formula for NLP threshold effects at amplitude level, and therefore applies both if the leading-order process is tree-level and if it is loop-induced. It holds for differential distributions as well. The results can furthermore be seen as applications of recently derived next-to-soft theorems for gauge theory amplitudes. We use our universal expression to re-derive known results for the production of up to three Higgs bosons at NLO in the large top mass limit, and for the hadro-production of a pair of electroweak gauge bosons. Finally, we present new analytic results for Higgs boson pair production at NLO and NLP, with exact top-mass dependence.

Figures (6)

• Figure 1: Tree-level contribution to the radiative jet function for (a) an external quark; (b) an external gluon.
• Figure 2: The amplitude for the production of $N$ colour-singlet particles from a pair of gluons, without final state QCD radiation.
• Figure 3: The amplitude for the production of $N$ colour-singlet particles from a quark-antiquark pair, without final state QCD radiation.
• Figure 4: Diagrams contributing to the spin-dependent part of the NLO cross-section, where $\bullet$ denotes the magnetic moment coupling of the gluon to the spin of the quark.
• Figure 5: (a) Leading order diagram for the production of a Higgs boson via gluon fusion; (b) Contact interaction in the large top mass limit; (c) Contact interaction for radiation of an extra gluon.