Expanding Einstein-Yang-Mills by Yang-Mills in CHY frame

Abstract

Using the Cachazo-He-Yuan (CHY) formalism, we prove a recursive expansion of tree level single trace Einstein-Yang-Mills (EYM) amplitudes with arbitrary number of gluons and gravitons, which is valid for general spacetime dimensions and any helicity configurations. The recursion is written in terms of fewer-graviton EYM amplitudes and pure Yang-Mills (YM) amplitudes, which can be further carried out until we reach an expansion in terms of pure YM amplitudes in Kleiss-Kuijf (KK) basis. Our expansion then generates naturally a spanning tree structure rooted on gluons whose vertices are gravitons. We further propose a set of graph theoretical rules based on spanning trees that evaluate directly the pure YM expansion coefficients.

36 pages, 3 captioned figures; v2: more details added, revised and published version

References in corpus (15)

• New Relations for Gauge-Theory Amplitudes
• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Symmetry and Action for Flavor-Kinematics Duality
• New Relations for Einstein-Yang-Mills Amplitudes
• Semi-abelian Z-theory: NLSM+phi^3 from the open string
• New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Locality and Unitarity from Singularities and Gauge Invariance
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• Collinear limits beyond the leading order from the scattering equations
• Graviton and gluon scattering from first principles
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism

Cited by in corpus (52)

• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Heterotic and bosonic string amplitudes via field theory
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• Expansion of All Multitrace Tree Level EYM Amplitudes
• The double copy for heavy particles
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Unraveling conformal gravity amplitudes
• One-loop Correlators and BCJ Numerators from Forward Limits
• Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
• Amplitudes, Hopf algebras and the colour-kinematics duality
• String Correlators: Recursive Expansion, Integration-by-Parts and 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
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Scattering of Gravitons and Spinning Massive States from Compact Numerators
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Multiparticle solutions to Einstein's equations
• Kinematic numerators from the worldsheet: cubic trees from labelled trees
• Unified web for expansions of amplitudes
• 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
• Tree level amplitudes from soft theorems
• New relations for graviton-matter amplitudes
• All rational one-loop Einstein-Yang-Mills amplitudes at four points
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• A graphic approach to gauge invariance induced identity
• One-loop Bern-Carrasco-Johansson Numerators on Quadratic Propagators from the Worldsheet
• Chiral Splitting and $\mathcal{N}=4$ Einstein--Yang--Mills Tree Amplitudes in 4d
• Scattering Equations and a new Factorization for Amplitudes I: Gauge Theories
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes
• Expansion of tree amplitudes for EM and other theories
• A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes
• Evaluating EYM amplitudes in four dimensions by refined graphic expansion
• Constructing EYM amplitudes by inverse soft limit
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Off-Shell Yang-Mills Amplitude in the CHY Formalism
• Pfaffian Diagrams for Gluon Tree Amplitudes
• Transmutation operators and expansions for $1$-loop Feynman integrands
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• Non-Abelian gauged supergravities as double copies
• Note on graph-based BCJ relation for Berends-Giele currents
• Permutation in the CHY-Formulation
• Transmuting off-shell CHY integrals in the double-cover framework
• New relations for tree-level form factors and scattering amplitudes
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Tree and $1$-loop fundamental BCJ relations from soft theorems
• A note on multi-trace EYM amplitudes in four dimensions
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• The off-shell expansion relation of the Yang-Mills scalar theory