One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits

Abstract

We present a technique which utilizes unitarity and collinear limits to construct ansatze for one-loop amplitudes in gauge theory. As an example, we obtain the one-loop contribution to amplitudes for $n$ gluon scattering in $N=4$ supersymmetric Yang-Mills theory with the helicity configuration of the Parke-Taylor tree amplitudes. We prove that our $N=4$ ansatz is correct using general properties of the relevant one-loop $n$-point integrals. We also give the ``splitting amplitudes'' which govern the collinear behavior of one-loop helicity amplitudes in gauge theories.

52 pages (including figures), minor typographical errors corrected, SLAC-PUB-6415

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• Two loop correction to interference in $gg\to ZZ$
• Towards pp -> VVjj at NLO QCD: Bosonic contributions to triple vector boson production plus jet
• Analytic results for the one-loop NMHV Hqqgg amplitude
• Iterated amplitudes in the high-energy limit
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• Direct Solution of Integration-by-Parts Systems
• Explicit Action of E7(7) on N=8 Supergravity Fields
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Helicity amplitudes for QCD with massive quarks
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Six-Photon Amplitudes
• Gravity On-shell Diagrams
• On super form factors of half-BPS operators in N=4 super Yang-Mills
• Analytic Results for MHV Wilson Loops
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• A complete algebraic reduction of one-loop tensor Feynman integrals
• Constructing Amplitudes from Their Soft Limits
• Two-loop six gluon all plus helicity amplitude
• A Theory of Spinning Particles for Large N_extended Supersymmetry (II)
• An Introduction to On-shell Recursion Relations
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Landau Singularities from the Amplituhedron
• Loops in exceptional field theory
• A comparison of efficient methods for the computation of Born gluon amplitudes
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• A prescription for projectors to compute helicity amplitudes in D dimensions
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• One-loop helicity amplitudes for H -> gluons: the all-minus configuration
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• The one-loop amplitude for six-gluon scattering
• Compact multigluonic scattering amplitudes with heavy scalars and fermions
• The large $N_c$ limit of four-point functions in N=4 super-Yang-Mills theory from anti-de Sitter Supergravity
• A Two-Loop Octagon Wilson Loop in N = 4 SYM
• All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD
• Lifting Heptagon Symbols to Functions
• Tropical Feynman integration in the Minkowski regime
• Caravel: A C++ Framework for the Computation of Multi-Loop Amplitudes with Numerical Unitarity
• The rational parts of one-loop QCD amplitudes I: The general formalism
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• New Dual Conformally Invariant Off-Shell Integrals
• Star Integrals, Convolutions and Simplices
• One-loop MHV Rules and Pure Yang-Mills
• Form factors and scattering amplitudes in N=4 SYM in dimensional and massive regularizations
• Factorization and Resummation for Generic Hierarchies between Jets
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• New Relations for Gauge-Theory Amplitudes with Matter
• Multigluonic scattering amplitudes of heavy quarks
• Simplicity in the Structure of QED and Gravity Amplitudes
• Next-to-leading order QCD corrections to diphoton-plus-jet production through gluon fusion at the LHC
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Elliptic Functions and Maximal Unitarity
• Generalised ladders and single-valued polylogarithms
• Real-Virtual corrections for gluon scattering at NNLO
• Unraveling L_{n,k}: Grassmannian Kinematics
• Dual conformal symmetry of 1-loop NMHV amplitudes in N=4 SYM theory
• MHV Techniques for QED Processes
• Loop-Level Double-Copy for Massive Quantum Particles
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Double collinear splitting amplitudes at next-to-leading order
• Dual conformal symmetry at loop level; massive regularization
• The SU(2|3) dynamic two-loop form factors
• Unitarity bounds on charged/neutral state mass ratio
• Scattering Amplitudes in Quantum Field Theory
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• Gravitational Faraday effect from on-shell amplitudes
• Tree-level splitting amplitudes for a quark into four collinear partons
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• One-loop Correlators and BCJ Numerators from Forward Limits
• Susy Theories and QCD: Numerical Approaches
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• Two-Loop SL(2) Form Factors and Maximal Transcendentality
• Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams
• Soft gluon emission at two loops in full color
• Analytic Structure of Three-Mass Triangle Coefficients
• The Dimensional Recurrence and Analyticity Method for Multicomponent Master Integrals: Using Unitarity Cuts to Construct Homogeneous Solutions
• Amplitudes in Pure Yang-Mills and MHV Diagrams
• Duality between Wilson loops and gluon amplitudes
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• Virtual Next-to-Leading Corrections to the Lipatov Vertex
• Graphs, determinants and gravity amplitudes
• Collinear Limits in QCD from MHV Rules
• NNLO QCD subtraction for top-antitop production in the $q\bar{q}$ channel
• An Integrand Reconstruction Method for Three-Loop Amplitudes
• Yukawa Couplings for the Spinning Particle and the World Line Formalism
• New relations for scattering amplitudes in Yang-Mills theory at loop level
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• Simplicity of Polygon Wilson Loops in N=4 SYM
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• A note on the absence of $R^2$ corrections to Newton's potential
• Cosmological Scattering Equations at Tree-level and One-loop
• The classification of two-loop integrand basis in pure four-dimension
• Coplanarity In Twistor Space Of N=4 Next-To-MHV One-Loop Amplitude Coefficients
• Unitarity-based Techniques for One-Loop Calculations in QCD
• Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge
• Multi-Quark Colour Decompositions from Unitarity
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• One-Loop Helicity Amplitudes for ttbar Production at Hadron Colliders
• All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• The Two-Loop Four-Graviton Scattering Amplitudes
• Multivariate Residues and Maximal Unitarity
• Loop Amplitudes and Quantum Homotopy Algebras
• Analytic all-plus-helicity gluon amplitudes in QCD
• Efficient Color-Dressed Calculation of Virtual Corrections
• New structures in scattering amplitudes: a review
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Two-loop Master Integrals with the Simplified Differential Equations approach
• Amplitudes for Multiple M5 Branes
• Feynman Rules for the Rational Part of the Standard Model One-loop Amplitudes in the 't Hooft-Veltman ${\gamma }_5$ Scheme
• Tree-Level Formalism
• Employing Helicity Amplitudes for Resummation
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Getting more flavour out of one-flavour QCD
• Scattering amplitudes with massive fermions using BCFW recursion
• Amplitude bases in generic EFTs
• Monodromy relations from twisted homology
• $n$-point amplitudes with a single negative-helicity graviton
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• An on-shell approach to factorization
• Tree-level splitting amplitudes for a gluon into four collinear partons
• Colour Decompositions of Multi-quark One-loop QCD Amplitudes
• Proof of the Dual Conformal Anomaly of One-Loop Amplitudes in N=4 SYM
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Automating QCD amplitudes with on-shell methods
• Monodromy--like Relations for Finite Loop Amplitudes
• N=8 Supergravity 4-point Amplitudes
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• The one-loop pentagon to higher orders in epsilon
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• N=8 Supergravity on the Light Cone
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• One-loop Amplitudes in Six-Dimensional (1,1) Theories from Generalised Unitarity
• Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
• Next-to-Leading Order Gamma Gamma + 2-Jet Production at the LHC
• One-Loop Gluonic Amplitudes from Single Unitarity Cuts
• Loop-level gluon OPEs in celestial holography
• KLT and New Relations for N=8 SUGRA and N=4 SYM
• Amplitudes at Infinity
• The two-loop n-point all-plus helicity amplitude
• Graviton Bending in Quantum Gravity from One-Loop Amplitudes
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Six-Photon Amplitudes in Scalar QED
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• One-loop monodromy relations on single cuts
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Manifestly Dual-Conformal Loop Integration
• The role of colour flows in matrix element computations and Monte Carlo simulations
• Extracting analytical one-loop amplitudes from numerical evaluations
• Amplitudes at Weak Coupling as Polytopes in AdS_5
• Simplifying Algebra in Feynman Graphs, Part I:Spinors
• The Next-to-Simplest Quantum Field Theories
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Single Cut Integration
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Symbol Alphabets from Tensor Diagrams
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Some properties of the Alday-Maldacena minimum
• $H\to b\overline{b}j$ at Next-to-Next-to-Leading Order Accuracy
• Maximal Unitarity for the Four-Mass Double Box
• Exact Superconformal and Yangian Symmetry of Scattering Amplitudes
• Double Virtual corrections for gluon scattering at NNLO
• Amplitudes of 3d Yang Mills Theory
• All-Helicity Symbol Alphabets from Unwound Amplituhedra
• Numerical multi-loop integrals and applications
• Dual-color decompositions at one-loop level in Yang-Mills theory
• Next-to-leading-order QCD Corrections to Higgs Production in association with a Jet
• Loop amplitudes monodromy relations and color-kinematics duality
• SUSY Ward identities, Superamplitudes, and Counterterms
• The six-point remainder function to all loop orders in the multi-Regge limit
• Counting to one: reducibility of one- and two-loop amplitudes at the integrand level
• Helicity Methods for High Multiplicity Subleading Soft and Collinear Limits
• Jet Veto Clustering Logarithms Beyond Leading Order
• Quark scattering amplitudes at strong coupling
• Simplifying $D$-Dimensional Physical-State Sums in Gauge Theory and Gravity
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Unitarity Cuts of Integrals with Doubled Propagators
• Full-color three-loop three-point form factors in N=4 SYM
• Evolution Kernels from Splitting Amplitudes
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• One-Loop Maximal Helicity Violating Amplitudes in N=4 Super Yang-Mills Theories
• Spinor helicity structures in higher spin theories
• One-loop matrix element emulation with factorisation awareness
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude
• Building Bases of Loop Integrands
• Solving for tadpole coefficients in one-loop amplitudes
• Comments on gluon 6-point scattering amplitudes in N=4 SYM at strong coupling
• String-motivated one-loop amplitudes in gauge theories with half-maximal supersymmetry
• Direct reduction of multiloop multiscale scattering amplitudes
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• An all order identity between ABJM and N=4 SYM four-point amplitudes
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• Polarization effects in light-by-light scattering: Euler-Heisenberg versus Born-Infeld
• The analytic structure and the transcendental weight of the BFKL ladder at NLL accuracy
• Global Residues and Two-Loop Hepta-Cuts
• Infrared structure of $e^{+}{e}^{-}\to 3$ jets at NNLO - the $C_F^2$ contribution
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• New ideas for handling of loop and angular integrals in D-dimensions in QCD
• Form factor recursion relations at loop level
• The Unitarity Method using a Canonical Basis Approach
• Augmented Recursion For One-loop Gravity Amplitudes
• Perfecting one-loop BCJ numerators in SYM and supergravity
• R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Triple collinear splitting functions at NLO for scattering processes with photons
• Systematics of One-Loop Scattering Amplitudes in N=4 Super Yang-Mills Theories
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• Constraints on anomalous dimensions from the positivity of the S-matrix
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• NLO QCD Predictions for $Wb\bar{b}$ Production in Association with up to Three Light Jets at the LHC
• Automation of electroweak corrections for LHC processes
• One-Loop Calculations with BlackHat
• Tree-level soft emission of a quark pair in association with a gluon
• Collinear expansion for color singlet cross sections
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• Two-loop Sudakov Form Factor in ABJM
• On n-point Amplitudes in N=4 SYM
• Classical off-shell currents
• On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations
• Polarized triple-collinear splitting functions at NLO for processes with photons
• Null Wilson loops with a self-crossing and the Wilson loop/amplitude conjecture
• Vector Boson + Jets with BlackHat and Sherpa
• Non-planarity through unitarity in ABJM
• One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
• Perturbative correlation functions of null Wilson loops and local operators
• Surface Kinematics and "The" Yang-Mills Integrand
• Perturbative expansion of N<8 Supergravity
• Bootstrapping a Two-Loop Four-Point Form Factor
• Computation of multi-leg amplitudes with NJet
• Binary Dynamics from Worldline QFT for Scalar-QED
• Analytic integration of soft and collinear radiation in factorised QCD cross sections at NNLO
• On the low energy limit of one loop photon-graviton amplitudes
• Prescriptive Unitarity with Elliptic Leading Singularities
• A super MHV vertex expansion for N=4 SYM theory
• Simplifying Algebra in Feynman Graphs, Part III: Massive Vectors
• The four-dimensional helicity scheme and dimensional reconstruction
• AdS super gluon scattering up to two loops: A position space approach
• Color ordering in QCD
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• Two-loop splitting in double parton distributions
• The Noncommutative S-Matrix
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• Null Polygonal Wilson Loops in Full N=4 Superspace
• Worldsheet factorization for twistor-strings
• A general algorithm to build mixed real and virtual antenna functions for higher-order calculations
• QCD gluon vertices from the string-inspired formalism
• Unitarity Method with Spurious Pole
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• Gravity and Form Scattering and Renormalisation of Gravity in Six and Eight Dimensions
• A unitarity compatible approach to one-loop amplitudes with massive fermions
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Cross-Order Integral Relations from Maximal Cuts
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
• Scattering Amplitudes and Toric Geometry
• Manifest colour-kinematics duality and double-copy in the string-based formalism
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• Hidden Simplicity of Gauge Theory Amplitudes
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• A tale of tails through generalized unitarity
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Colourful FKS subtraction
• Frequency-domain approach to self-force in hyperbolic scattering
• An $n$-point QCD two-loop amplitude
• Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse
• Complex Factorisation and Recursion for One-Loop Amplitudes
• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• N=4 SYM NMHV Loop Amplitude in Superspace
• Light fermionic NNLO QCD corrections to top-antitop production in the quark-antiquark channel
• Determination of Boundary Contributions in Recursion Relation
• Gluon induced contributions to WZ and W gamma production at NNLO
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• One-Loop Yang-Mills Integrands from Scattering Equations
• Planar Gravitational Corrections For Supersymmetric Gauge Theories
• Analytic Tadpole Coefficients of One-loop Integrals
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• Quantum corrections to frame-dragging in scattering amplitudes
• On the two-loop hexagon Wilson loop remainder function in N=4 SYM
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• A manifestly MHV Lagrangian for N=4 Yang-Mills
• Multi-spin soft bootstrap and scalar-vector Galileon
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Effective action of dressed mean fields for N = 4 super-Yang-Mills theory
• External leg corrections in the unitarity method
• Integrands for QCD rational terms and N=4 SYM from massive CSW rules
• Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?
• The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
• Generation Function For One-loop Tensor Reduction
• Quantum gravitational corrections for spinning particles
• Quantum corrections to tidal Love number for Schwarzschild black holes
• Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
• Triple-collinear splittings with massive particles
• One-loop Feynman Integral Reduction by Differential Operators
• Massive Quark-Gluon Scattering Amplitudes at Tree Level
• Collinear functions for QCD resummations
• Cutting-Edge Tools for Cutting Edges
• Compact QED Tree-Level Amplitudes From Dressed BCFW Recursion Relations
• The ChPT: top-down and bottom-up
• Constructing multi-loop scattering amplitudes with manifest singularity structure
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• One-loop N=8 Supergravity Amplitudes from MHV Diagrams
• One-loop renormalization and the S-matrix
• Form Factor and Boundary Contribution of Amplitude
• First-quantized N=4 Yang-Mills
• Consistency conditions from generalized-unitarity
• Generalised Unitarity At One-Loop With Massive Fermions
• One-loop SYM-supergravity relation for five-point amplitudes
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• A Combinatoric Shortcut to Evaluate CHY-forms
• The BlackHat Library for One-Loop Amplitudes
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• Coordinate-space singularities of massless gauge theories
• Imaginary parts and discontinuities of Wilson line correlators
• Recent Progress in Perturbative Quantum Field Theory
• Reduction of General One-loop Integrals Using Auxiliary Vector
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• On Perturbative Gravity and Gauge Theory
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Note on Bonus Relations for N=8 Supergravity Tree Amplitudes
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• Relation between Worldline Green Functions for Scalar Two-Loop Diagrams
• A compact representation of the 2 photon 3 gluon amplitude
• Integrability and unitarity
• Feynman Rules for the Rational Part of One-loop QCD Corrections in the MSSM
• On the Classification of Residues of the Grassmannian
• Massive Nonplanar Two-Loop Maximal Unitarity
• On three-point functions in ABJM and the latitude Wilson loop
• Recursion Rules for Scattering Amplitudes in Non-Abelian Gauge Theories
• Reduction with Degenerate Gram matrix for One-loop Integrals
• Color structures and permutations
• Tree-level amplitudes and dual superconformal symmetry
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• Manifest SO(N) invariance and S-matrices of three-dimensional N=2,4,8 SYM
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Tree amplitudes of noncommutative U(N) Yang-Mills Theory
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Strong Field Scattering of Black Holes: Assessing Resummation Strategies
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Hidden Beauty in Multiloop Amplitudes
• Momentum mappings for subtractions at higher orders in QCD
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• BCJ Relations for One-Loop QCD Integral Coefficients
• Scattering amplitudes at strong coupling for 4K gluons
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• On-Shell Unitarity Bootstrap for QCD Amplitudes
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
• Recursion relations, Helicity Amplitudes and Dimensional Regularization
• Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Two-Loop ${\varphi }^4$-Diagrams from String Theory
• A note on on-shell recursion relation of string amplitudes
• Perturbative Quantum Field Theory and Homotopy Algebras
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Color-Kinematics Duality for Sudakov Form Factor in Non-Supersymmetric Pure Yang-Mills Theory
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• Natural Boundaries for Scattering Amplitudes
• Multi-loop Integrand Reduction with Computational Algebraic Geometry
• Non-planar BCFW Grassmannian Geometries
• $W^{+}{W}^{-}$ + 3 Jet Production at the Large Hadron Collider in NLO QCD
• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Syzygies Probing Scattering Amplitudes
• A Surprise in the Amplitude/Wilson Loop Duality
• Position-space cuts for Wilson line correlators
• Loop-level double-copy for massive fermions in the fundamental
• Radiative Corrections to the Azimuthal Asymmetry in Transversely Polarized Moller Scattering
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Testing and improving the numerical accuracy of the NLO predictions
• Poles At Infinity in On-shell Diagrams
• Recursion relations for the general tree-level amplitudes in QCD with massive dirac fields
• Universal Treatment of Reduction for One-Loop Integrals in Projective Space
• Regular Wilson loops and MHV amplitudes at weak and strong coupling
• Decomposition of Triple Collinear Splitting Functions
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
• Selection rules for helicity amplitudes in massive gauge theories
• Emergent unitarity from the amplituhedron
• D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes
• Six-jet production at lepton colliders
• The SAGEX Review on Scattering Amplitudes, Chapter 12: Amplitudes and collider physics
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude
• Off-shell Ward identities for N-gluon amplitudes
• Deviation from Alday-Maldacena Duality For Wavy Circle
• The dimension-shift conjecture for one-loop amplitudes
• Loop Amplitudes in an Extended Gravity Theory
• Nontrivial One-loop Recursive Reduction Relation
• Two-Loop Diagrammatics in a Self-Dual Background
• Supersymmetric Yang-Mills and Supergravity Amplitudes at One Loop
• Gluonic evanescent operators: classification and one-loop renormalization
• Perturbation theory in (2,2) signature
• Antenna subtraction for jet production observables in full colour at NNLO
• Exploring straight infinite Wilson lines in the Self Dual and the MHV Lagrangians
• Applications of Subleading-color Amplitudes in N=4 SYM Theory
• Diagrammar in an Extended Theory of Gravity
• Recovering Infinities in Graviton Scattering Amplitudes using Cutkosky rules
• Permutation Relations of Yangian Invariants, Unitarity Cuts, and Scattering Amplitudes
• Twistor and Polytope Interpretations for Subleading Color One-Loop Amplitudes
• Reduction of one-loop integrals with higher poles by unitarity cut method
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Dijet Invariant Mass Distribution in Top Quark Hadronic Decay with QCD Corrections
• Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
• ALPs, the on-shell way
• Recursive Approach to One-loop QCD Matrix Elements
• Illustrations of Integrand-Basis Building at Two Loops
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Perturbative Gravity and Twistor Space
• Fixing the non-relativistic expansion of the 1PM potential
• Hard QCD at hadron colliders
• A high-precision result for a full-color three-loop three-point form factor in $\mathcal{N}=4$ SYM
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Stable One-Dimensional Integral Representations of One-Loop N-Point Functions in the General Massive Case: I - Three Point Functions
• QCD at high energy
• Top-forms of Leading Singularities in Nonplanar Multi-loop Amplitudes
• Gluonic evanescent operators: two-loop anomalous dimensions
• Nonlinear couplings and tree amplitudes in gauge theories
• Spinor formalism for massive fields with half-integral spin
• UV consistency conditions for CHY integrands
• Jet Physics at Two-Loop Accuracy
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
• One-loop corrections to the celestial chiral algebra from Koszul Duality
• 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
• Generalized unitarity method for unstable particles
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Four photon production at the LHC: an application of 2->4 analytic unitarity
• Renormalising the Field-Space Geometry
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Ultra-Violet Infinities and Counterterms in Higher Dimensional Yang-Mills
• Analytic Computations of Massive One-Loop Amplitudes
• Augmented Recursion For One-loop Amplitudes
• Exploiting Twistor Techniques for One-loop QCD Amplitudes
• Sector-improved residue subtraction: Improvements and Applications
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Pure spinor formulation of the superstring and its applications
• One-Loop Effective Action Approach to Quantum MHV Theory
• Scrambling and Entangling Spinning Particles
• Classical gravitational scattering from a gauge-invariant double copy
• Yangian symmetry of light-like Wilson loops
• All one-loop NMHV gluon amplitudes in N=1 SYM
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• One-loop inelastic amplitudes from tree-level elasticity in 2d
• Locally Finite Observables in sYM
• Minimally helicity violating, maximally simple scalar amplitudes in N=4 SYM
• EERAD3 version 2: QCD corrections in hadronic colour-singlet decays
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Collinear splitting, parton evolution and the strange-quark asymmetry of the nucleon in NNLO QCD
• Numerical evaluation of one-loop QCD amplitudes
• One-loop QCD contributions to differential cross-sections for Higgs production at N${}^3$LO
• Gauge theory one-loop amplitudes and the BCFW recursion relations
• Analytic structure of one-loop coefficients
• On Higgs boson plus gluon amplitudes at one loop
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Note on solutions of scattering equations
• NLO calculations in QCD: a general algorithm
• 1-loop Color structures and sunny diagrams
• Integrated Unitarity for Scattering Amplitudes
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• One-Loop Amplitudes in Supersymmetric QCD from MHV Vertices
• Supersums for all supersymmetric amplitudes
• QCD at hadron colliders
• Recursive relations for a quiver gauge theory
• Evaluation of Multi-Box Diagrams in Six Dimensions
• Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities
• New N=4 SYM Path Integral
• MultivariateResidues - a Mathematica package for computing multivariate residues
• Automated computation of scattering amplitudes
• Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Cross Section Evaluation by Spinor Integration I: The massless case in 4D
• A Recursive Method to Calculate UV-divergent Parts at One-Loop Level in Dimensional Regularization
• The Radial Action from Probe Amplitudes to All Orders
• Considerations Concerning the Little Group
• Non-abelian soft radiation data for a celestial theory
• Universal structure of radiative QED amplitudes at one loop
• Recursive structures in string field theory
• Influence of a Perfectly Conducting Plate on the Uehling Potential of QED
• Two-loop Splitting Amplitudes
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Unitarity Cuts: NLO Six-Gluon Amplitudes in QCD
• Perturbative Unitarity Calls for An Action
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point
• Co-homology of Differential Forms and Feynman diagrams
• Two-loop corrections to $gg\to \gamma \gamma$
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory
• Applications of higher order QCD
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Tropicalized quantum field theory and global tropical sampling
• Forward scattering amplitudes in the imaginary time formalism
• Infrared finite cross sections at NNLO
• Antenna subtraction method for jet calculations at NNLO
• Subtraction method of computing QCD jet cross sections at NNLO accuracy
• Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
• Progress on NNLO subtraction
• Feynman diagrams in terms of on-shell propagators
• Extended DBI and its generalizations from graded soft theorems
• Cross Section Evaluation by Spinor Integration II: The massive case in 4D
• General One-loop Reduction in Generalized Feynman Parametrization Form
• QCD at High Energy
• On the Cuts of Scattering Amplitudes
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity