New Color Decompositions for Gauge Amplitudes at Tree and Loop Level

Abstract

Recently, a color decomposition using structure constants was introduced for purely gluonic tree amplitudes, in a compact form involving only the linearly independent subamplitudes. We give two proofs that this decomposition holds for an arbitrary number of gluons. We also present and prove similar decompositions at one loop, both for pure gluon amplitudes and for amplitudes with an external quark-antiquark pair.

LaTeX, 20 pages

References in corpus (1)

• Multi-Parton Amplitudes in Gauge Theories

Cited by in corpus (274)

• The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations
• MadGraph 5 : Going Beyond
• New Relations for Gauge-Theory Amplitudes
• Comix, a new matrix element generator
• Antenna Subtraction at NNLO
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• General-purpose event generators for LHC physics
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Gravity as the Square of Gauge Theory
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Scattering Forms and the Positive Geometry of Kinematics, Color and the Worldsheet
• One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Open & Closed vs. Pure Open String Disk Amplitudes
• Two-loop QCD corrections to gluon-gluon scattering
• Gluon-Gluon Antenna Functions from Higgs Boson Decay
• Quark-Gluon Antenna Functions from Neutralino Decay
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Color-flow decomposition of QCD amplitudes
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• NLO QCD corrections to top quark pair production in association with one hard jet at hadron colliders
• Color-Kinematics Duality for QCD Amplitudes
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• Color-kinematic Duality for Form Factors
• Improved TMD factorization for forward dijet production in dilute-dense hadronic collisions
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
• Analytic two-loop form factors in N=4 SYM
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Unifying Relations for Scattering Amplitudes
• Symmetry and Action for Flavor-Kinematics Duality
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Two-loop splitting functions in QCD
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Generalized unitarity at work: first NLO QCD results for hadronic W+3jet production
• Color-dressed recursive relations for multi-parton amplitudes
• Antenna Factorization in Strongly-Ordered Limits
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Proof of Gravity and Yang-Mills Amplitude Relations
• Dual Identities inside the Gluon and the Graviton Scattering Amplitudes
• Amplitude Relations in Non-linear Sigma Model
• Berends-Giele recursion for double-color-ordered amplitudes
• Berends-Giele recursions and the BCJ duality in superspace and components
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• One-loop Scattering Equations and Amplitudes from Forward Limit
• Generic multiloop methods and application to N=4 super-Yang-Mills
• BCJ numerators from reduced Pfaffian
• Twistor-Inspired Construction of Electroweak Vector Boson Currents
• Parton showers from the dipole formalism
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Double Copy from Homotopy Algebras
• New Identities among Gauge Theory Amplitudes
• The Non-Abelian Exponentiation theorem for multiple Wilson lines
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• Higgs Boson Production in Association with Three Jets
• One-loop amplitudes for W+3 jet production in hadron collisions
• Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Gluons and gravitons at one loop from ambitwistor strings
• Covariant Color-Kinematics Duality
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Universality in string interactions
• An algebraic approach to BCJ numerators
• BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory
• A Color Dual Form for Gauge-Theory Amplitudes
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• NLO QCD corrections to five-jet production at LEP and the extraction of alpha_s(M_Z)
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Geometric Soft Theorems
• BCJ duality and double copy in the closed string sector
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• The LHC String Hunter's Companion (II): Five-Particle Amplitudes and Universal Properties
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• On-shell recursion relations for all Born QCD amplitudes
• Gauge and Gravity Amplitude Relations
• Iterated amplitudes in the high-energy limit
• Kinematical Limits on Higgs Boson Production via Gluon Fusion in Association with Jets
• Helicity amplitudes for QCD with massive quarks
• Soft evolution of multi-jet final states
• Orthogonal multiplet bases in SU(Nc) color space
• An Introduction to On-shell Recursion Relations
• Tree-level amplitudes from the pure spinor superstring
• The one-loop amplitude for six-gluon scattering
• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Caravel: A C++ Framework for the Computation of Multi-Loop Amplitudes with Numerical Unitarity
• Six Open String Disk Amplitude in Pure Spinor Superspace
• New Relations for Gauge-Theory Amplitudes with Matter
• UV considerations on scattering amplitudes in a web of theories
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• Scattering Amplitudes in Quantum Field Theory
• Super Gluon Five-Point Amplitudes in AdS Space
• Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes
• All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes
• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Multi-Quark Colour Decompositions from Unitarity
• Conformal Gravity from Gauge Theory
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Efficient Color-Dressed Calculation of Virtual Corrections
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• Constraining anomalous gluon self-interactions at the LHC: a reappraisal
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Amplitudes, Hopf algebras and the colour-kinematics duality
• The Infrared Structure of Nambu-Goldstone Bosons
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• Colour Decompositions of Multi-quark One-loop QCD Amplitudes
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Monodromy--like Relations for Finite Loop Amplitudes
• Virtuous Trees at Five and Six Points for Yang-Mills and Gravity
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Automating QCD amplitudes with on-shell methods
• Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
• On Three-Algebra and Bi-Fundamental Matter Amplitudes and Integrability of Supergravity
• Amplitudes at Infinity
• Webs and Posets
• Automated computation of spin- and colour-correlated Born matrix elements
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
• On Sugawara construction on Celestial Sphere
• Off-shell Currents and Color-Kinematics Duality
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• One-loop monodromy relations on single cuts
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• The role of colour flows in matrix element computations and Monte Carlo simulations
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Scattering Massive String Resonances through Field-Theory Methods
• Loop amplitudes monodromy relations and color-kinematics duality
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
• Hepp's bound for Feynman graphs and matroids
• Relations of loop partial amplitudes in gauge theory by Unitarity cut method
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• Dual-color decompositions at one-loop level in Yang-Mills theory
• A Vertex Operator Algebra Construction of the Colour-Kinematics Dual numerator
• Evolution Kernels from Splitting Amplitudes
• On Primary Relations at Tree-level in String Theory and Field Theory
• Correlation functions of local composite operators from generalized unitarity
• Non-perturbative Double Copy in Flatland
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Perfecting one-loop BCJ numerators in SYM and supergravity
• BCJ Identities and $d$-Dimensional Generalized Unitarity
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Proof of a new colour decomposition for QCD amplitudes
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• The Bottom-Up EFT: Complete UV Resonances of the SMEFT Operators
• One-loop off-shell amplitudes from classical equations of motion
• A Lie bracket for the momentum kernel
• Kinematic Numerators and a Double-Copy Formula for N = 4 Super-Yang-Mills Residues
• The $L_{\infty }$ structure of gauge theories with matter
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• A minimal approach to the scattering of physical massless bosons
• 2-, 3- and 4-Body Decays in the Constructive Standard Model
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• On tree amplitudes with gluons coupled to gravitons
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Local BCJ numerators for ten-dimensional SYM at one loop
• Recursion relations for scattering amplitudes with massive particles
• Unified web for expansions of amplitudes
• TMD gluon distributions for multiparton processes
• Note on symmetric BCJ numerator
• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
• An $n$-point QCD two-loop amplitude
• The Construction of Dual-trace Factor in Yang-Mills Theory
• Explicit BCJ numerators of nonlinear sigma model
• Note on Construction of Dual-trace Factor in Yang-Mills Theory
• All-order celestial OPE from on-shell recursion
• Effective observables for electromagnetic duality from novel amplitude decomposition
• A Portable Parton-Level Event Generator for the High-Luminosity LHC
• New relations for graviton-matter amplitudes
• One-loop SYM-supergravity relation for five-point amplitudes
• BCJ relations from a new symmetry of gauge-theory amplitudes
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• On Positive Geometry and Scattering Forms for Matter Particles
• Color structures and permutations
• Tree amplitudes of noncommutative U(N) Yang-Mills Theory
• Light transformed gluon correlators in CCFT
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• Nonlinear dynamics of soft boson excitations in hot QCD plasma I: plasmon-plasmon scattering
• Recurrence relations of Kummer functions and Regge string scattering amplitudes
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Note on Permutation Sum of Color-ordered Gluon Amplitudes
• Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity
• Perturbative Quantum Field Theory and Homotopy Algebras
• Kleiss-Kuijf Relations from Momentum Amplituhedron Geometry
• Entanglement and the Double Copy
• Loop-level double-copy for massive fermions in the fundamental
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Recursion relations for scattering amplitudes with massive particles II: massive vector bosons
• The chirality-flow formalism
• BCJ, worldsheet quantum algebra and KZ equations
• Expansion of tree amplitudes for EM and other theories
• Forward trijet production in p-p and p-Pb collisions at LHC
• Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• The five-gluon amplitude in the high-energy limit
• Gluonic evanescent operators: classification and one-loop renormalization
• Double copy for tree-level form factors. Part I. Foundations
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Planar radiation zeros in five-parton QCD amplitudes
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Tree amplitudes and color decomposition in broken SU(2)
• Off-shell BCJ Relation in Nonlinear Sigma Model
• The colour matrix at next-to-leading-colour accuracy for tree-level multi-parton processes
• Automated calculations for multi-leg processes
• The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes
• Next-to-MHV Yang-Mills kinematic algebra
• Multiparticle Contributions to the Celestial OPE
• One-loop impact factor for the emission of two gluons
• Introduction to parton-shower event generators
• Transmuting off-shell CHY integrals in the double-cover framework
• Note on graph-based BCJ relation for Berends-Giele currents
• Streamlining resummed QCD calculations using Monte Carlo integration
• Improving Colour Computations in MadGraph5_aMC@NLO and Exploring a 1/Nc Expansion
• Note on off-shell relations in nonlinear sigma model
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• Projectivity of Planar Zeros in Field and String Theory Amplitudes
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• A closed-formula solution to the color-trace decomposition problem
• One-loop triple collinear splitting amplitudes in QCD
• 1-loop Color structures and sunny diagrams
• Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Structure of Massive Gauge/Gravity Scattering Amplitudes, Equivalence Theorems, and Extended Double-Copy with Compactified Warped Space
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• QCD amplitudes with 2 initial spacelike legs via generalised BCFW recursion
• How to calculate colourful cross sections efficiently
• The Unresolved Behaviour of Polarized Scattering Matrix Elements at NNLO in QCD
• The seeds of EFT double copy
• Quantum Off-Shell Recursion Relation
• Factorization Formulas for Tree Amplitudes
• Invariant color calculus and generalized Balitsky-Kovchegov hierarchy
• Color-factor symmetry and BCJ relations for QCD amplitudes
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory
• Color-Kinematics Relation from the Feynman Diagram Perspective
• A Tale Of Two Amplitudes In High Energy Physics
• Recursion in multiplet bases for tree-level MHV gluon amplitudes
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes