Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair

Abstract

We consider the radiation of two or more soft partons in QCD hard-scattering at one-loop order. The corresponding scattering amplitude is singular, and the singular behaviour is controlled by a process-independent soft current. Using regularization in $d=4-2\epsilon$ space-time dimensions, we explicitly evaluate the ultraviolet and infrared divergent ($\epsilon$-pole) terms of the one-loop soft current for emission of an arbitrary number of soft partons in a generic hard-scattering process. Then we consider the specific case of soft quark-antiquark ($q\bar{q}$) emission and we compute the one-loop current by including the finite terms. We find that the one-loop soft-$q\bar{q}$ current exhibits a new type of transverse-momentum singularity, which has a quantum (absorptive) origin and a purely non-abelian character. At the squared amplitude (cross section) level, this transverse-momentum singularity produces contributions to multijet production processes in hadron collisions. The one-loop squared current also leads to charge asymmetry terms, which are a distinctive features of soft-$q\bar{q}$ radiation. We also extend these results to the cases of QED and mixed QCD$\times$QED radiative corrections for soft fermion-antifermion emission.

45 pages, 1 figure. Few comments and several references added. Published version

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• 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
• Initial-Final and Initial-Initial antenna functions for real radiation at next-to-leading order
• Decomposition of Triple Collinear Splitting Functions
• The parton-level structure of Higgs decays to hadrons at N${}^3$LO
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
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• Measurements of Lund subjet multiplicities in 13 TeV proton-proton collisions with the ATLAS detector
• Catani's generalization of collinear factorization breaking