Infrared Singularities of Scattering Amplitudes and N${}^3$LL Resummation for $n$-Jet Processes

Abstract

We revisit the multi-loop structure of the anomalous-dimension matrix governing the infrared divergences of massless $n$-particle scattering amplitudes in non-abelian gauge theories. In particular, we derive its most general form at four-loop order, significantly simplifying corresponding expressions given previously. By carefully reevaluating the constraints imposed by two-particle collinear limits, we find that at four-loop order color structures involving $d_R^{abcd}$, the symmetrized trace of four group generators, appear along with cusp logarithms $\ln [{\mu }^2/(-s_{ij})]$. As a consequence, naive Casimir scaling of the cusp anomalous dimensions associated with the quark and gluon form factors is violated, while a generalized form of Casimir scaling still holds. Our results provide an important ingredient for resummations of large logarithms in $n$-jet cross sections with next-to-next-to-next-to leading logarithmic (N${}^3$LL) accuracy.

31 pages, 3 figures. v2: journal version; note added with analytical result for k_1 from [73]; discussion of [42]

References in corpus (19)

• Gluon scattering amplitudes at strong coupling
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Comments on operators with large spin
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Path integral approach to eikonal and next-to-eikonal exponentiation
• Soft-/rapidity- anomalous dimensions correspondence
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• Webs in multiparton scattering using the replica trick
• Bootstrapping the QCD soft anomalous dimension
• Matter dependence of the four-loop cusp anomalous dimension
• Diagrammatic Exponentiation for Products of Wilson Lines
• General properties of multiparton webs: proofs from combinatorics
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop quark form factor with quartic fundamental colour factor
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Anomalous Dimensions from a Spinning D5-Brane
• Generating function for web diagrams

Cited by in corpus (36)

• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Collider Physics at the Precision Frontier
• The Four Loop QCD Rapidity Anomalous Dimension
• Fiducial $q_T$ resummation of color-singlet processes at N${}^3$LL+NNLO
• Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• Transverse-Energy-Energy Correlations in Deep Inelastic Scattering
• Non-abelian infrared divergences on the celestial sphere
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• The on-shell expansion: from Landau equations to the Newton polytope
• Precise predictions for photon pair production matched to parton showers in GENEVA
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Two-loop anomalous dimension for the resummation of non-global observables
• Multiparton webs beyond three loops
• The structure of IR divergences in celestial gluon amplitudes
• Factorization of Non-Global LHC Observables and Resummation of Super-Leading Logarithms
• Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour
• Cwebs beyond three loops in multiparton amplitudes
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Identifying regions in wide-angle scattering via graph-theoretical approaches
• EFT for Soft Drop Double Differential Cross Section
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• The Holographic Soft $S$-Matrix in QED and Gravity
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• Building blocks of Cwebs in multiparton scattering amplitudes
• Deciphering Colour Building Blocks of Massive Multiparton Amplitudes at 4-loops and beyond
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• The two-loop Higgs impact factor
• Two-Loop Four-Fermion Scattering Amplitude in QED
• Effective Field Theory for Heavy Vector Resonances Coupled to the Standard Model
• SUSY, Casimir scaling and probabilistic properties of gluon and quark jets evolution
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Non-abelian soft radiation data for a celestial theory
• Infrared Anomalous Dimensions at Three-Loop in the SM from Conserved Currents
• Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD