Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

Abstract

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given by integrals over the positions of $n$ points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein--Yang--Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke--Taylor-like factors of subsets of particle labels.

18 pages. References and a new section on double-trace gluon amplitudes added in v2

References in corpus (24)

• Super-Poincare Covariant Quantization of the Superstring
• Scattering of Massless Particles in Arbitrary Dimension
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Ambitwistor strings and the scattering equations
• The Momentum Kernel of Gauge and Gravity Theories
• Explicit BCJ Numerators from Pure Spinors
• Ambitwistor strings and the scattering equations at one loop
• Ambitwistor strings in 4-dimensions
• On the Coupling of Gravitons to Matter
• Infinite Tension Limit of the Pure Spinor Superstring
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Parity Invariance For Strings In Twistor Space
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• The Polynomial Form of the Scattering Equations
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates
• Graviton as a Pair of Collinear Gauge Bosons
• Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
• The QCD scattering amplitude from area behaved Wilson loops
• On tree amplitudes with gluons coupled to gravitons
• Lightlike contours with fermions
• Observations on Open and Closed String Scattering Amplitudes at High Energies
• Relations Between Closed String Amplitudes at Higher-order Tree Level and Open String Amplitudes
• Disk relations for tree amplitudes in minimal coupling theory of gauge field and gravity

Cited by in corpus (144)

• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
• One-loop amplitudes on the Riemann sphere
• Extensions of Theories from Soft Limits
• On the null origin of the ambitwistor string
• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• BMS Supertranslations and Not So Soft Gravitons
• One-loop Scattering Equations and Amplitudes from Forward Limit
• BCJ numerators from reduced Pfaffian
• Heterotic and bosonic string amplitudes via field theory
• New Double Soft Emission Theorems
• Expansion of Einstein-Yang-Mills Amplitude
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Gluons and gravitons at one loop from ambitwistor strings
• Perturbiner Methods for Effective Field Theories and the Double Copy
• Integration Rules for Scattering Equations
• Factorization of Chiral String Amplitudes
• Expansion of All Multitrace Tree Level EYM Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• On the Double Copy for Spinning Matter
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Subleading Soft Theorem for Multiple Soft Gravitons
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• Unraveling conformal gravity amplitudes
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• Inverse of the String Theory KLT Kernel
• Tree-level amplitudes from the pure spinor superstring
• Celestial double copy from the worldsheet
• An Algebraic Approach to the Scattering Equations
• UV considerations on scattering amplitudes in a web of theories
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Evaluation of the CHY Gauge Amplitude
• Elliptic scattering equations
• Scattering Equations and Global Duality of Residues
• Elimination and recursions in the scattering equations
• String amplitudes from field-theory amplitudes and vice versa
• New Formulas for Amplitudes from Higher-Dimensional Operators
• One-loop Correlators and BCJ Numerators from Forward Limits
• $\Lambda$ Scattering Equations
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Labelled tree graphs, Feynman diagrams and disk integrals
• Scattering equations, generating functions and all massless five point tree amplitudes
• Comments on the evaluation of massless scattering
• Connected formulas for amplitudes in standard model
• CHY Loop Integrands from Holomorphic Forms
• Collinear limits beyond the leading order from the scattering equations
• A String Theory Which Isn't About Strings
• A note on connected formula for form factors
• CHY-Graphs on a Torus
• The Polynomial Form of the Scattering Equations is an H-Basis
• Note on differential operators, CHY integrands, and unifying relations for amplitudes
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Properties of scattering forms and their relation to associahedra
• Kinematic Hopf algebra for amplitudes and form factors
• The momentum amplituhedron of SYM and ABJM from twistor-string maps
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• Soft Gravity by Squaring Soft QED on the Celestial Sphere
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Feynman Rules of Higher-order Poles in CHY Construction
• Positive Geometries for all Scalar Theories from Twisted Intersection Theory
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Chiral Closed strings: Four massless states scattering amplitude
• Algebraic geometry and Bethe ansatz (I) the quotient ring for BAE
• On the New Factorizations of Yang-Mills Amplitudes
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• Unified web for expansions of amplitudes
• The Q-cut Representation of One-loop Integrands and Unitarity Cut Method
• Bosonic sectorized strings and the $(DF{)}^2$ theory
• Tree level amplitudes from soft theorems
• On Chiral Splitting and the Ambitwistor String
• One-Loop Yang-Mills Integrands from Scattering Equations
• Stokes Polytopes and Intersection Theory
• Scattering Amplitudes of Kaluza-Klein Strings and Extended Massive Double-Copy
• The Role of Möbius Constants and Scattering Functions in CHY Scalar Amplitudes
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• New relations for graviton-matter amplitudes
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• A Combinatoric Shortcut to Evaluate CHY-forms
• A Superstring Field Theory for Supergravity
• The CHY representation of tree-level primitive QCD amplitudes
• String-Like Dual Models for Scalar Theories
• CHY formula and MHV amplitudes
• One-loop CHY-Integrand of Bi-adjoint Scalar Theory
• One-loop diagrams with quadratic propagators from the worldsheet
• A differential operator for integrating one-loop scattering equations
• A String Deformation of the Parke-Taylor Factor
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction
• On Polytopes and Generalizations of the KLT Relations
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Recursion and worldsheet formulae for 6d superamplitudes
• Bootstrapping solutions of scattering equations
• Expansion of tree amplitudes for EM and other theories
• Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
• BCJ Numerators from Differential Operator of Multidimensional Residue
• One-loop integrand from generalised scattering equations
• Constructing EYM amplitudes by inverse soft limit
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Ambitwistor String Theory in the Operator Formalism
• On differential operators and unifying relations for $1$-loop Feynman integrands
• CHY formulae in 4d
• Note on recursion relations for the $\mathcal{Q}$-cut representation
• Pfaffian Diagrams for Gluon Tree Amplitudes
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Time-reversal invariant scaling of light propagation in one-dimensional non-Hermitian systems
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Geometric Recursion from Polytope Triangulations and Twisted Homology
• Transmutation operators and expansions for $1$-loop Feynman integrands
• UV consistency conditions for CHY integrands
• Pushforwards via Scattering Equations with Applications to Positive Geometries
• Note on the Labelled tree graphs
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• Note on graph-based BCJ relation for Berends-Giele currents
• Green-Schwarz and Pure Spinor Formulations of Chiral Strings
• New relations for tree-level form factors and scattering amplitudes
• Transmuting off-shell CHY integrals in the double-cover framework
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• Note on solutions of scattering equations
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Characterizing the solutions to scattering equations that support tree-level ${\text{N}}^k\text{MHV}$ gauge/gravity amplitudes
• A note on multi-trace EYM amplitudes in four dimensions
• CHY Theory for Several Fields
• Analytic expressions of amplitudes by the cross-ratio identity method
• Superstring amplitudes meet surfaceology
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Extended DBI and its generalizations from graded soft theorems