Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills

Abstract

After reduction techniques, two-loop amplitudes in N=4 super Yang-Mills theory can be written in a basis of integrals containing scalar double-box integrals with rational coefficients, though the complete basis is unknown. Generically, at two loops, the leading singular behavior of a scalar double box integral with seven propagators is captured by a hepta-cut. However, it turns out that a certain class of such integrals has an additional propagator-like singularity. One can then formally cut the new propagator to obtain an octa-cut which localizes the cut integral just as a quadruple cut does at one-loop. This immediately gives the coefficient of the scalar double box integral as a product of six tree-level amplitudes. We compute, as examples, several coefficients of the five- and six-gluon non-MHV two-loop amplitudes. We also discuss possible generalizations to higher loops.

arXiv comment38 pages, 23 figures, harvmac; minor corrections, references added

References in corpus (52)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Multi-Parton Amplitudes in Gauge Theories
• 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
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• Calculating Scattering Amplitudes Efficiently
• Massive Loop Amplitudes from Unitarity
• Progress in One-Loop QCD Computations
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• MHV Rules for Higgs Plus Multi-Gluon Amplitudes
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• One-Loop Amplitudes Of Gluons In SQCD
• All-Order Collinear Behavior in Gauge Theories
• Tree Amplitudes in Gauge Theory as Scalar MHV Diagrams
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Non-Supersymmetric Loop Amplitudes and MHV Vertices
• Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
• Non-MHV Tree Amplitudes in Gauge Theory
• MHV Vertices and Fermionic Scattering Amplitudes in Gauge Theory with Quarks and Gluinos
• The Last of the Finite Loop Amplitudes in QCD
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• The Googly Amplitudes in Gauge Theory
• One-Loop MHV Amplitudes in Supersymmetric Gauge Theories
• Lectures on Twistor Strings and Perturbative Yang-Mills Theory
• One-Loop Gluon Scattering Amplitudes in Theories with $N<4$ Supersymmetries
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• N=1 Supersymmetric One-loop Amplitudes and the Holomorphic Anomaly of Unitarity Cuts
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• MHV Rules for Higgs Plus Multi-Parton Amplitudes
• Twistor-Inspired Construction of Electroweak Vector Boson Currents
• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• All Split Helicity Tree-Level Gluon Amplitudes
• Compact Formulas for Tree Amplitudes of Six Partons
• Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes
• Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell
• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model
• Unitarity-based Techniques for One-Loop Calculations in QCD
• Cross-Order Relations in N=4 Supersymmetric Gauge Theories

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