Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills

Abstract

One-loop amplitudes of gluons in N=4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature (--++) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.

36 pages, harvmac. 13 figures. v3: References added, typos fixed. Figure 4 added. New n-gluon example with internal fermions and scalars. v4: Footnotes 2, 4 and 6 added, acknowledgments added, minor corrections

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• Hidden Simplicity of Gauge Theory Amplitudes
• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• Scattering Amplitudes and Toric Geometry
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Scattering in the static patch of de Sitter space
• Determination of Boundary Contributions in Recursion Relation
• EFT matching from analyticity and unitarity
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Complex Factorisation and Recursion for One-Loop Amplitudes
• Scattering on the Moduli Space of N=4 Super Yang-Mills
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• An $n$-point QCD two-loop amplitude
• NLO QCD calculations with HELAC-NLO
• Analytic Tadpole Coefficients of One-loop Integrals
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• External leg corrections in the unitarity method
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• R2 vertices for the effective ggH theory
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• One-loop Feynman Integral Reduction by Differential Operators
• Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
• Generation Function For One-loop Tensor Reduction
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• Cutting-Edge Tools for Cutting Edges
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Generalised Unitarity At One-Loop With Massive Fermions
• Form Factor and Boundary Contribution of Amplitude
• The BlackHat Library for One-Loop Amplitudes
• First-quantized N=4 Yang-Mills
• Consistency conditions from generalized-unitarity
• Imaginary parts and discontinuities of Wilson line correlators
• Dual-Conformal Regularization of Infrared Loop Divergences and the Chiral Box Expansion
• Next-to-leading order predictions for WW+jet production
• PV-Reduction of Sunset Topology with Auxiliary Vector
• Integrability and unitarity
• Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM
• Gravity loop integrands from the ultraviolet
• Reduction of General One-loop Integrals Using Auxiliary Vector
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• Massive Nonplanar Two-Loop Maximal Unitarity
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Reduction with Degenerate Gram matrix for One-loop Integrals
• Tree amplitudes of noncommutative U(N) Yang-Mills Theory
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Tree-level amplitudes and dual superconformal symmetry
• Positivity Sectors and the Amplituhedron
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
• Top-quark loop corrections in Z+jet and Z+2 jet production
• The $pp\to W(\to l\nu )+\gamma$ process at next-to-next-to-leading order
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• Recursion relations, Helicity Amplitudes and Dimensional Regularization
• On-Shell Unitarity Bootstrap for QCD Amplitudes
• BCJ Relations for One-Loop QCD Integral Coefficients
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Scattering amplitudes at strong coupling for 4K gluons
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• Natural Boundaries for Scattering Amplitudes
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Multi-loop Integrand Reduction with Computational Algebraic Geometry
• $W^{+}{W}^{-}$ + 3 Jet Production at the Large Hadron Collider in NLO QCD
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Position-space cuts for Wilson line correlators
• Testing and improving the numerical accuracy of the NLO predictions
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• $\Delta$-Algebra and Scattering Amplitudes
• Particle Physics at the LHC Start
• Gauged Linear Sigma Model on Supermanifold
• The recursive structure of Baikov representations II: the top-down reduction with intersection theory
• FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• Universal Treatment of Reduction for One-Loop Integrals in Projective Space
• Vector boson pair production at one loop: analytic results for the process $q\bar{q}\ell \bar{\ell }{\ell }^{\prime }{\bar{\ell }}^{\prime }g$
• Emergent unitarity from the amplituhedron
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
• Recursion relations for the general tree-level amplitudes in QCD with massive dirac fields
• From lightcone actions to maximally supersymmetric amplitudes
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Integration-by-parts identities from the viewpoint of differential geometry
• The dimension-shift conjecture for one-loop amplitudes
• Anatomy of the Amplituhedron
• Roots of Amplitudes
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
• Nontrivial One-loop Recursive Reduction Relation
• ALPs, the on-shell way
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• One-Loop N = 4 Super Yang-Mills Scattering Amplitudes to All Orders in the Dimensional Regularization Parameter
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Summary of Lepton Photon 2011
• Reduction of one-loop integrals with higher poles by unitarity cut method
• Next-to-Leading-Order Corrections to Weak Boson Production with a Massive Quark Jet Pair at Hadron Colliders
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Automated calculations for multi-leg processes
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Illustrations of Integrand-Basis Building at Two Loops
• Stable One-Dimensional Integral Representations of One-Loop N-Point Functions in the General Massive Case: I - Three Point Functions
• Spinor formalism for massive fields with half-integral spin
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Hard QCD at hadron colliders
• Gluonic evanescent operators: two-loop anomalous dimensions
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• Analytic Computations of Massive One-Loop Amplitudes
• Interactions as conformal intertwiners in 4D QFT
• Four photon production at the LHC: an application of 2->4 analytic unitarity
• Unitarity-Cuts and Berry's Phase
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Generalized unitarity method for unstable particles
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• Quantum Effects for Black Holes with On-Shell Amplitudes
• Generating MHV super-vertices in light-cone gauge
• Augmented Recursion For One-loop Amplitudes
• Recent theoretical progress in perturbative QCD
• Scrambling and Entangling Spinning Particles
• Locally Finite Observables in sYM
• Note on solutions of scattering equations
• The MHV lagrangian vertices and the Parke-Taylor formula
• A Note on Loop Amplitudes in QED
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Minimally helicity violating, maximally simple scalar amplitudes in N=4 SYM
• Analytic structure of one-loop coefficients
• Boundary Behaviors for General Off-shell Amplitudes in Yang-Mills Theory
• MHV Lagrangians for Yang--Mills and QCD
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• All one-loop NMHV gluon amplitudes in N=1 SYM
• Light-by-light scattering amplitudes from generalized unitarity in massive QED
• Generalised unitarity for dimensionally regulated amplitudes within FDF
• Five-Point Two-Loop Amplitudes from Numerical Unitarity
• On Higgs boson plus gluon amplitudes at one loop
• Numerical evaluation of one-loop QCD amplitudes
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• Massive particles and unitarity cuts
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Cuts and coproducts of massive triangle diagrams
• EERAD3 version 2: QCD corrections in hadronic colour-singlet decays
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Perturbative Gravity and Gauge Theory Relations -- A Review
• On perturbative field theory and twistor string theory
• Ward Identity implied recursion relations in Yang-Mills theory
• Automated computation of scattering amplitudes
• Particle Physics in the LHC Era and beyond
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• MultivariateResidues - a Mathematica package for computing multivariate residues
• Precise evaluation of the Cut Constructible part of one loop amplitudes within D-dimensional unitarity
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• Scattering amplitudes in gauge theories with and without supersymmetry
• Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
• Integrated Unitarity for Scattering Amplitudes
• Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• Supersums for all supersymmetric amplitudes
• Generalised Unitarity for Dimensionally Regulated Amplitudes
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Scattering Amplitudes in Gauge Theories
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• Ward Identity Implies Recursion Relation at Tree and Loop Level
• Extended Projection Method for Massive Fermion
• NLO automated tools for QCD and beyond
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Quantum point particle approximation of spinning black holes and compact stars
• On-shell recursion relations for generic integrands
• Equivalence of Coefficients Extraction of One-loop Master Integrals
• Recent Developments in Higher-Order Calculations: Hard Functions at NLO with GoSam
• Forward scattering amplitudes in the imaginary time formalism
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
• Feynman diagrams in terms of on-shell propagators
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Complexified Ward Identity in pure Yang-Mills theory at tree-level
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Co-homology of Differential Forms and Feynman diagrams
• On the Cuts of Scattering Amplitudes
• General One-loop Reduction in Generalized Feynman Parametrization Form
• Constructing QCD one-loop amplitudes
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Approximate Universality of N=4 Super-Yang--Mills One-Loop Amplitudes
• Analytic results for scalar-mediated Higgs boson production in association with two jets
• Constructing the general partial waves and renormalization in EFT
• A Tale Of Two Amplitudes In High Energy Physics
• Reduction of one-massless-loop with scalar boxes in $n+2$ dimensions
• Next-to-leading order QCD corrections to ttbb production at the LHC