The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory

Abstract

We compute the symbol of the two-loop five-point scattering amplitude in $\mathcal{N}$ = 4 super-Yang-Mills theory, including its full color dependence. This requires constructing the symbol of all two-loop five-point nonplanar massless master integrals, for which we give explicit results.

6pages, 1 figure, 1 table; v2: references added, fixed typos, flipped overall sign of amplitude in ancillary files; v3: references and typos fixed

References in corpus (44)

• Multiloop integrals in dimensional regularization made simple
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• A novel approach to integration by parts reduction
• From polygons and symbols to polylogarithmic functions
• Bootstrapping the three-loop hexagon
• 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
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Towards a Basis for Planar Two-Loop Integrals
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Integration-by-parts reductions from unitarity cuts and algebraic geometry
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Pentagon functions for massless planar scattering amplitudes
• On the highest transcendentality in N=4 SUSY
• Pulling the straps of polygons
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A first look at two-loop five-gluon scattering in QCD
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Evidence for a Nonplanar Amplituhedron
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Bootstrapping pentagon functions
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• The high energy limit of QCD at two loops
• The Galois coaction on ${\varphi }^4$ periods
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Dual Conformal Structure Beyond the Planar Limit
• Infrared singularities of QCD scattering amplitudes in the Regge limit to all orders
• A tale of two Regge limits

Cited by in corpus (77)

• PolyLogTools - Polylogs for the masses
• Reconstructing Rational Functions with $\text{FireFly}$
• Collider Physics at the Precision Frontier
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• All master integrals for three-jet production at NNLO
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Pentagon Functions for Scattering of Five Massless Particles
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• NNLO QCD corrections to three-photon production at the LHC
• Analytic result for a two-loop five-particle amplitude
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Cluster algebras for Feynman integrals
• Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
• Leading-Color Two-Loop Amplitudes for Four Partons and a W Boson in QCD
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Duals of Feynman Integrals, I: Differential Equations
• Two-loop helicity amplitudes for diphoton plus jet production in full color
• Physical projectors for multi-leg helicity amplitudes
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
• Two-loop leading-color helicity amplitudes for three-photon production at the LHC
• Soft gluon emission at two loops in full color
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
• Multi-Quark Colour Decompositions from Unitarity
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• IBP reduction coefficients made simple
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Extracting analytical one-loop amplitudes from numerical evaluations
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• Bootstrapping a Two-Loop Four-Point Form Factor
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• One-loop hexagon integral to higher orders in the dimensional regulator
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Two-loop $N$-jettiness soft function for $pp\to 2j$ production
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• Illustrations of Integrand-Basis Building at Two Loops
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• pfd-parallel, a Singular/GPI-Space package for massively parallel multivariate partial fractioning
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• QCD and High Energy Interactions: MORIOND 2019 Theory Summary
• One-Loop QCD Corrections to $\bar{u}d\to t\bar{t}W$ at $\mathcal{O}({\epsilon }^2)$
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes
• Recent progress for five-particle two-loop scattering amplitudes with an off-shell leg
• The Hopf Algebra Structure of the Two Loop Three Mass Non-Planar Feynman Diagram
• NNLO soft function for threshold single inclusive jet production