Tree-level soft emission of a quark pair in association with a gluon

Abstract

We compute the tree-level current for the emission of a soft quark-antiquark pair in association with a gluon. This soft current is the last missing ingredient to understand the infrared singularities that can arise in next-to-next-to-next-to-leading-order (N${}^3$LO) computations in QCD. Its square allows us to understand for the first time the colour correlations induced by the soft emission of a quark pair and a gluon. We find that there are three types of correlations: Besides dipole-type correlations that have already appeared in soft limits of tree-level amplitudes, we uncover for the first time also a three-parton correlation involving a totally symmetric structure constant. We also study the behaviour of collinear splitting amplitudes in the triple-soft limit, and we derive the corresponding factorisation formula.

arXiv comment35 pages, 1 figure, 9 ancillary files

References in corpus (37)

• A General Algorithm for Calculating Jet Cross Sections in NLO QCD
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• The Dipole Formalism for the Calculation of QCD Jet Cross Sections at Next-to-Leading Order
• 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 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
• Double-real radiation in hadronic top quark pair production as a proof of a certain concept
• Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations
• Space-like (vs. time-like) collinear limits in QCD: is factorization violated?
• Vector-Boson Fusion Higgs Pair Production at N${}^3$LO
• The two-loop soft current in dimensional regularization
• Matching of Singly- and Doubly-Unresolved Limits of Tree-level QCD Squared Matrix Elements
• Multiple Singular Emission in Gauge Theories
• Single soft gluon emission at two loops
• Higgs boson pair production via gluon fusion at N${}^3$LO in QCD
• Precision Predictions at N${}^3$LO for the Higgs Boson Rapidity Distribution at the LHC
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• Di-lepton Rapidity Distribution in Drell-Yan Production to Third Order in QCD
• Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD
• The triple collinear limit of one-loop QCD amplitudes
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Third order fiducial predictions for Drell-Yan at the LHC
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Triple (and quadruple) soft-gluon radiation in QCD hard scattering
• Tree-level splitting amplitudes for a quark into four collinear partons
• Soft gluon emission at two loops in full color
• Three-loop helicity amplitudes for diphoton production in gluon fusion
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• Multiple soft radiation at one-loop order and the emission of a soft quark-antiquark pair
• Decomposition of Triple Collinear Splitting Functions

Cited by in corpus (12)

• 50 Years of Quantum Chromodynamics
• NNLO subtraction for any massless final state: a complete analytic expression
• A general algorithm to build real-radiation antenna functions for higher-order calculations
• 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
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• 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
• Zero-jettiness soft function to third order in perturbative QCD
• The parton-level structure of Higgs decays to hadrons at N${}^3$LO
• Jet production at electron-positron colliders at next-to-next-to-next-to-leading order in QCD
• Catani's generalization of collinear factorization breaking