Triple (and quadruple) soft-gluon radiation in QCD hard scattering

Abstract

We consider the radiation of three soft gluons in a generic process for multiparton 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 $\mathcal{O}(1/N_c^2)$ to the eikonal formula for multiple soft-gluon radiation with strong energy ordering from two hard gluons.

60 pages, 2 figures (extended discussions, added one appendix, typo corrected at line 3 of Eq.(C.9))

References in corpus (10)

• Higgs boson gluon-fusion production in N3LO QCD
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Hard-Soft-Collinear Factorization to All Orders
• Webs in multiparton scattering using the replica trick
• Bootstrapping the QCD soft anomalous dimension
• Diagrammatic Exponentiation for Products of Wilson Lines
• Soft-gluon effective coupling and cusp anomalous dimension

Cited by in corpus (31)

• The Four Loop QCD Rapidity Anomalous Dimension
• Tree-level splitting amplitudes for a quark into four collinear partons
• Soft gluon emission at two loops in full color
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Multiparton webs beyond three loops
• NNLO subtraction for any massless final state: a complete analytic expression
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• A general algorithm to build real-radiation antenna functions for higher-order calculations
• Tree-level soft emission of a quark pair in association with a gluon
• Same-hemisphere three-gluon-emission contribution to the zero-jettiness soft function at N3LO QCD
• Cwebs beyond three loops in multiparton amplitudes
• Soft gluon-quark-antiquark emission in QCD hard scattering
• On phase-space integrals with Heaviside functions
• The parton-level structure of $e^{+}{e}^{-}$ to 2 jets at N${}^3$LO
• Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• Initial-Final and Initial-Initial antenna functions for real radiation at next-to-leading order
• Zero-jettiness soft function to third order in perturbative QCD
• Building blocks of Cwebs in multiparton scattering amplitudes
• Decomposition of Triple Collinear Splitting Functions
• The parton-level structure of Higgs decays to hadrons at N${}^3$LO
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• Eikonal amplitudes for three-hard legs processes at finite-N${}_c$
• Jet production at electron-positron colliders at next-to-next-to-next-to-leading order in QCD
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Catani's generalization of collinear factorization breaking
• Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle
• Non-abelian soft radiation data for a celestial theory