Three-loop helicity amplitudes for four-quark scattering in massless QCD

Abstract

We compute the three-loop corrections to the helicity amplitudes for $q\bar{q}\to Q\bar{Q}$ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.

33 pages, 5 figures, 3 tables; electronic files with analytical results. v2: added references, fixed typos, fixed analytic continuation. v3: fixed error in ancillary files

References in corpus (108)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Scattering Amplitudes with Open Loops
• Multiloop integrals in dimensional regularization made simple
• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Higgs boson gluon-fusion production in N3LO QCD
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Antenna Subtraction at NNLO
• OpenLoops 2
• Numerical evaluation of multiple polylogarithms
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Reduze - Feynman Integral Reduction in C++
• A novel subtraction scheme for double-real radiation at NNLO
• Multi-loop Amplitudes and Resummation
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD
• Multiple polylogarithms and mixed Tate motives
• Fully differential VBF Higgs production at NNLO
• A novel approach to integration by parts reduction
• From polygons and symbols to polylogarithmic functions
• Higgs boson production in association with a jet at next-to-next-to-leading order
• PolyLogTools - Polylogs for the masses
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Three-Loop Results for Quark and Gluon Form Factors
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Towards a Basis for Planar Two-Loop Integrals
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• The Quark Form Factor at Higher Orders
• Vector-boson fusion Higgs production at N${}^3$LO in QCD
• Two-loop QCD corrections to gluon-gluon scattering
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• The massless higher-loop two-point function
• Three-loop corrections to the soft anomalous dimension in multi-leg scattering
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms
• Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions
• Nested soft-collinear subtractions in NNLO QCD computations
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• On the maximal cut of Feynman integrals and the solution of their differential equations
• Super-leading logarithms in non-global observables in QCD?
• Pentagon functions for massless planar scattering amplitudes
• 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 five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations
• A first look at two-loop five-gluon scattering in QCD
• Pentagon Functions for Scattering of Five Massless Particles
• The three-loop cusp anomalous dimension in QCD
• Two-loop corrections to Higgs boson production
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory
• A first next-to-next-to-leading order study of three-jet production at the LHC
• Triphoton production at hadron colliders in NNLO QCD
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• NNLO QCD corrections to three-photon production at the LHC
• Analytic result for a two-loop five-particle amplitude
• Four-gluon scattering at three loops, infrared structure and Regge limit
• On the breaking of collinear factorization in QCD
• Precision Predictions at N${}^3$LO for the Higgs Boson Rapidity Distribution at the LHC
• Higgs production in bottom-quark fusion to third order in the strong coupling
• Analytic result for the nonplanar hexa-box integrals
• spinney: A Form Library for Helicity Spinors
• Higgs $p_T$ Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD
• Local Analytic Sector Subtraction at NNLO
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Tensor decomposition for bosonic and fermionic scattering amplitudes
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Physical projectors for multi-leg helicity amplitudes
• Geometric IR subtraction for real radiation
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• Simplified differential equations approach for Master Integrals
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Two-loop leading colour QCD corrections to $q\bar{q}\to \gamma \gamma g$ and $qg\to \gamma \gamma q$
• Caravel: A C++ Framework for the Computation of Multi-Loop Amplitudes with Numerical Unitarity
• Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Two-loop leading-color helicity amplitudes for three-photon production at the LHC
• Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
• Two-loop five-point massless QCD amplitudes within the IBP approach
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Two-loop helicity amplitudes for $gg\to ZZ$ with full top-quark mass effects
• Triphoton production at hadron colliders
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• Automating QCD amplitudes with on-shell methods
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator

Cited by in corpus (1)

• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist