Abstract
We consider the radiation of three soft gluons in a generic process for multi- parton hard scattering in QCD. In the soft limit the corresponding scattering amplitude has a singular behaviour that is factorized and controlled by a colorful soft current. We compute the tree-level current for triple soft-gluon emission from both massless and massive hard partons. The three-gluon current is expressed in terms of maximally non-abelian irreducible correlations. We compute the soft behaviour of squared amplitudes and the colour correlations produced by the squared current. The radiation of one and two soft gluons leads to colour dipole correlations. Triple soft-gluon radiation produces in addition colour quadrupole correlations between the hard partons. We examine the soft and collinear singularities of the squared current in various energy ordered and angular ordered regions. We discuss some features of soft radiation to all-loop orders for processes with two and three hard partons. Considering triple soft-gluon radiation from three hard partons, colour quadrupole interactions break the Casimir scaling symmetry between quarks and gluons. We also present some results on the radiation of four soft gluons from two hard partons, and we discuss the colour monster contribution and its relation with the violation (and generalization) of Casimir scaling. We also compute the first correction of \U0001d4aa(1/ {N}_c^2 ) to the eikonal formula for multiple soft-gluon radiation with strong energy ordering from two hard gluons.
Highlights
The first two operational runs of proton-proton collisions at the LHC have produced a large amount of high-precision data on hard-scattering final states
We find that triple soft-gluon radiation produces non-abelian colour quadrupole correlations between the hard partons in generic processes with three or more hard partons
We consider soft-gluon radiation at the tree level, and we present the explicit expressions for emission of N = 1, 2 and 3 soft gluons from the scattering amplitude MABC with three hard partons
Summary
The first two operational runs of proton-proton collisions at the LHC have produced a large amount of high-precision data on hard-scattering final states. The explicit knowledge of soft/collinear factorization of scattering amplitudes at O(αS) has been essential to devise fully general (observable-independent and process-independent) methods to carry out next-to-leading order (NLO) QCD calculations The appendix C includes the large explicit expressions of the dipole and quadrupole correlation functions for triple soft-gluon radiation
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