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.
Highlights
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 starting point will be a factorisation formula for NLP effects at amplitude level recently derived in refs. [23, 24], which expresses the effect of adding an additional gluon to an arbitrary hard process with an electroweak final state in terms of universal functions
We have considered the hadro-production of an arbitrary heavy colourless system, in both the gluon-fusion and quark-antiquark-annihilation channels, near partonic threshold for the production of the selected final state
Summary
We briefly review the results of refs. [23, 24], which derive a factorisation formula for QCD radiation up to NLP level, and we provide a generalisation of these results to the case of external incoming gluons. The next-to-eikonal jet J(pi, ni) corrects for the double counting of contributions from gluons which are both (next-to-)soft and collinear, and the hard function H ({pi}, n1, n2) is defined by matching to the amplitude on the left-hand side of eq (2.1), so that all dependence on the auxiliary vectors {ni} cancels out. Eq (2.2) includes a radiative jet function Jμa collecting all contributions associated with the emission of a gluon from the ith parton, and enhanced by virtual collinear poles This function was first introduced in the context of abelian gauge theory in ref. Equation (2.12) is recognisable as the recently derived next-to-soft theorem [44], which mirrors a similar result derived in gravity [45, 46] As noted, this formula encompasses both the quark and gluon cases, provided the spin operator is interpreted appropriately, validating our diagrammatic definition for the leading order gluon radiative jet function. For the NLO analysis performed in this paper, we could have adopted eq (2.12) as the starting point for our following analysis; note, that eq (2.2) and eq (2.5) are much more general results, applicable in principle to any order in perturbation theory
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