Three-Loop Leading Singularities and BDS Ansatz for Five Particles

Abstract

We use the leading singularity technique to determine the planar three-loop five-particle amplitude in N=4 super Yang-Mills in terms of a simple basis of integrals. We analytically compute the integral coefficients for both the parity-even and the parity-odd parts of the amplitude. The parity-even part involves only dual conformally invariant integrals. Using the method of obstructions we numerically evaluate two previously unfixed coefficients which appear in the three-loop BDS ansatz.

20 pages, 2 figures, v2: very minor changes

References in corpus (27)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Gluon scattering amplitudes at strong coupling
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Magic identities for conformal four-point integrals
• One-Loop Amplitudes for e^+ e^- to Four Partons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• On planar gluon amplitudes/Wilson loops duality
• Multi-loop Amplitudes and Resummation
• Comments on gluon scattering amplitudes via AdS/CFT
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Massive Loop Amplitudes from Unitarity
• Progress in One-Loop QCD Computations
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• One-Loop Self-Dual and N=4 Super Yang-Mills
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Hidden Beauty in Multiloop Amplitudes

Cited by in corpus (41)

• What is the Simplest Quantum Field Theory?
• Local Integrals for Planar Scattering Amplitudes
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Single soft gluon emission at two loops
• Generalized Unitarity and Six-Dimensional Helicity
• Two-Loop Polygon Wilson Loops in N=4 SYM
• Generic multiloop methods and application to N=4 super-Yang-Mills
• Bipartite Field Theories: from D-Brane Probes to Scattering Amplitudes
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• Simple loop integrals and amplitudes in N=4 SYM
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Iterated amplitudes in the high-energy limit
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Simplicity in the Structure of QED and Gravity Amplitudes
• Unraveling L_{n,k}: Grassmannian Kinematics
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Full-color three-loop three-point form factors in N=4 SYM
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Prescriptive Unitarity with Elliptic Leading Singularities
• An Elliptic Yangian-Invariant, `Leading Singularity'
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Hidden Simplicity of Gauge Theory Amplitudes
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• On the Classification of Residues of the Grassmannian
• Series Solution and Minimal Surfaces in AdS
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations