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.

arXiv comment45 pages, 1 figure. Few comments and several references added. Published version

References in corpus (77)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Three-jet cross sections to next-to-leading order
• Invariant Operators in Collinear Effective Theory
• Multi-Parton Amplitudes in Gauge Theories
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Hard Scattering Factorization from Effective Field Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• Dimensionally Regulated Pentagon Integrals
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Multi-loop Amplitudes and Resummation
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• A general approach to jet cross sections in QCD
• Infrared factorization of tree-level QCD amplitudes at the next-to-next-to-leading order and beyond
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• One-Loop Splitting Amplitudes in Gauge Theory
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The soft-gluon current at one-loop order
• Double Unresolved Approximations to Multiparton Scattering Amplitudes
• The Infrared Behavior of One-Loop QCD Amplitudes at Next-to-Next-to-Leading Order
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Double-real radiation in hadronic top quark pair production as a proof of a certain concept
• Factorization in One-Loop Gauge Theory
• One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory
• Transverse-momentum-dependent parton distributions up to N${}^3$LL from Drell-Yan data
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• Fiducial distributions in Higgs and Drell-Yan production at N${}^3$LL+NNLO
• Collider Physics at the Precision Frontier
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Momentum-space resummation for transverse observables and the Higgs $p_{\perp }$ at N${}^3$LL+NNLO
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Hard-Soft-Collinear Factorization to All Orders
• The two-loop soft current in dimensional regularization
• Two-loop splitting functions in QCD
• Reduction formalism for dimensionally regulated one-loop N-point integrals
• 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
• Regularization Scheme Independence and Unitarity in QCD Cross Sections
• Perturbative generation of a strange-quark asymmetry in the nucleon
• Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N${}^3$LO
• Transverse momentum dependent PDFs at N${}^3$LO
• Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N${}^3$LL
• On the breaking of collinear factorization in QCD
• Precise QCD Description of the Higgs Boson Transverse Momentum Spectrum
• The transverse momentum spectrum of weak gauge bosons at N${}^3$LL+NNLO
• 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
• QCD resummation for hadronic final states
• The triple collinear limit of one-loop QCD amplitudes
• Fiducial $q_T$ resummation of color-singlet processes at N${}^3$LL+NNLO
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• Double collinear splitting amplitudes at next-to-leading order
• The $q_T$ and $\Delta \varphi$ spectra in W and Z production at the LHC at N${}^3$LL'+N${}^2$LO
• TMD Fragmentation Functions at N${}^3$LO
• 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
• N-jettiness beam functions at N3LO
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Triple collinear splitting functions at NLO for scattering processes with photons
• Polarized triple-collinear splitting functions at NLO for processes with photons
• Symmetry of anomalous dimension matrices explained
• A simplified expression for the one-loop soft-gluon current with massive fermions
• One-loop triple collinear splitting amplitudes in QCD
• The Diphoton $q_T$ spectrum at N${}^3$LL${}^{\prime }$+NNLO

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