Catani's generalization of collinear factorization breaking

Abstract

We consider the most general form of soft and collinear factorization for hard-scattering amplitudes to all orders in perturbative Quantum Chromodynamics. Specifically, we present the generalization of collinear factorization to configurations with several collinear directions, where the most singular behaviour is encoded by generalized collinear splitting amplitudes that manifestly embed the breaking of strict collinear factorization in space-like collinear configurations. We also extend the analysis to the simultaneous soft-collinear factorization with multiple collinear directions where na\"ıve multiplicative factorization does not hold. As an illustrative example of factorization breaking, we present explicit results at the one-loop level in the soft-collinear limit.

8 pages, 5 figures, includes explicit perturbative results, journal version

References in corpus (33)

• Two-Loop g -> gg Splitting Amplitudes in QCD
• Super-leading logarithms in non-global observables in QCD?
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• Collider Physics at the Precision Frontier
• Hard-Soft-Collinear Factorization to All Orders
• The two-loop soft current in dimensional regularization
• Two-loop splitting functions in QCD
• Single soft gluon emission at two loops
• Drell-Yan lepton-pair production: $q_T$ resummation at N${}^3$LL accuracy and fiducial cross sections at N${}^3$LO
• Super-leading logarithms in non-global observables in QCD: Colour basis independent calculation
• On the breaking of collinear factorization in QCD
• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• The singular behavior of one-loop massive QCD amplitudes with one external soft gluon
• Multi-Gluon Collinear Limits from MHV diagrams
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• The triple collinear limit of one-loop QCD amplitudes
• Fiducial Drell-Yan production at the LHC improved by transverse-momentum resummation at N${}^4$LL+N${}^3$LO
• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• Double collinear splitting amplitudes at next-to-leading order
• Tree-level splitting amplitudes for a quark into four collinear partons
• Soft gluon emission at two loops in full color
• Collinear Limits in QCD from MHV Rules
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Super-leading logarithms in non-global observables in QCD: Fixed order calculation
• Triple collinear splitting functions at NLO for scattering processes with photons
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• Tree-level soft emission of a quark pair in association with a gluon
• Polarized triple-collinear splitting functions at NLO for processes with photons
• Soft gluon-quark-antiquark emission in QCD hard scattering
• 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
• Triple-collinear splittings with massive particles