The double-soft integral for an arbitrary angle between hard radiators

Abstract

We consider the double-soft limit of a generic QCD process involving massless partons and integrate analytically the double-soft eikonal functions over the phase-space of soft partons (gluons or quarks) allowing for an arbitrary relative angle between the three-momenta of two hard massless radiators. This result provides one of the missing ingredients for a fully analytic formulation of the nested soft-collinear subtraction scheme recently proposed by some of us.

arXiv comment24 pages, 1 appendix

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• Collider Physics at the Precision Frontier
• May the four be with you: Novel IR-subtraction methods to tackle NNLO calculations
• Analytic results for color-singlet production at NNLO QCD with the nested soft-collinear subtraction scheme
• Mixed QCD$\otimes$QED corrections to on-shell $Z$ boson production at the LHC
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Factorisation and Subtraction beyond NLO
• Tree-level splitting amplitudes for a quark into four collinear partons
• Integrated triple-collinear counter-terms for the nested soft-collinear subtraction scheme
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Bottom quark mass effects in associated $WH$ production with $H\to b\bar{b}$ decay through NNLO QCD
• Analytic results for deep-inelastic scattering at NNLO QCD with the nested soft-collinear subtraction scheme
• Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO
• Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD
• On phase-space integrals with Heaviside functions
• NNLO QCD corrections to weak boson fusion Higgs boson production in the $H\to b\bar{b}$ and $H\to W{W}^{\ast }\to 4l$ decay channels
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Momentum mappings for subtractions at higher orders in QCD
• Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
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• Monte Carlo Event Generators
• Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle