Relations for Einstein-Yang-Mills amplitudes from the CHY representation

Abstract

We show that a recently discovered relation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with one graviton and $(n-1)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons, can be derived from the CHY representation. In addition we show that there is a generalisation, which expresses tree-level single trace Einstein-Yang-Mills amplitudes with $r$ gravitons and $(n-r)$ gauge bosons as a linear combination of pure Yang-Mills tree amplitudes with $n$ gauge bosons. We present a general formula for this case.

13 pages, version to be published

References in corpus (42)

• New Relations for Gauge-Theory Amplitudes
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Scattering of Massless Particles in Arbitrary Dimension
• Black holes and the double copy
• Scattering Equations and KLT Orthogonality
• $\pi \pi$ Scattering in Three Flavour ChPT
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Ambitwistor strings in 4-dimensions
• Subleading soft theorem in arbitrary dimension from scattering equations
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Gravity and Yang-Mills Amplitude Relations
• Sub-sub-leading soft-graviton theorem in arbitrary dimension
• Diagrammatic insights into next-to-soft corrections
• Exact solutions for the biadjoint scalar field
• New Relations for Einstein-Yang-Mills Amplitudes
• The Polynomial Form of the Scattering Equations
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• N-Point Tree-Level Scattering Amplitude in the New Berkovits' String
• Soft Graviton Theorem in Arbitrary Dimensions
• Integration Rules for Loop Scattering Equations
• Scattering Equations and String Theory Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Computation of Contour Integrals on ${\mathcal{M}}_{0,n}$
• An Algebraic Approach to the Scattering Equations
• Massless scattering at special kinematics as Jacobi polynomials
• Elliptic scattering equations
• Scattering Equations and Global Duality of Residues
• Subleading Terms in the Collinear Limit of Yang-Mills Amplitudes
• Graviton as a Pair of Collinear Gauge Bosons
• Disk Scattering of Open and Closed Strings (I)
• CHY-Graphs on a Torus
• The Polynomial Form of the Scattering Equations is an H-Basis
• Graviton Amplitudes from Collinear Limits of Gauge Amplitudes
• Permutation Symmetry of the Scattering Equations
• Double copies of fermions as only gravitational interacting matter
• The Scattering Variety
• Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities
• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Infrared behaviour of the one-loop scattering equations and supergravity integrands
• Fermions and the scattering equations

Cited by in corpus (33)

• Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double Copy
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• Heterotic and bosonic string amplitudes via field theory
• Expansion of Einstein-Yang-Mills Amplitude
• Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame
• Extended solutions for the biadjoint scalar field
• Expansion of All Multitrace Tree Level EYM Amplitudes
• The Radiative Double Copy for Einstein-Yang-Mills Theory
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Amplitudes, Hopf algebras and the colour-kinematics duality
• Collinear limits beyond the leading order from the scattering equations
• Note on differential operators, CHY integrands, and unifying relations for amplitudes
• Properties of scattering forms and their relation to associahedra
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory
• One-loop amplitudes in Einstein-Yang-Mills from forward limits
• Unified web for expansions of amplitudes
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• New relations for graviton-matter amplitudes
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• A graphic approach to gauge invariance induced identity
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes
• Expansion of tree amplitudes for EM and other theories
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• New relations for tree-level form factors and scattering amplitudes
• Transmuting off-shell CHY integrals in the double-cover framework
• Note on scalar-graviton and scalar-photon-graviton amplitudes