Related papers: Expanding Einstein-Yang-Mills by Yang-Mills in CHY…
In this paper, we investigate the expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes. First, we propose two types of recursive expansions of tree level EYM amplitudes with an arbitrary number of gluons, gravitons and…
In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives. Using the gauge invariance…
In this paper, we have introduced a fundamentally different approach, based on a bottom-up methodology, to expand tree-level Yang-Mills (YM) amplitudes into Yang-Mills-scalar (YMS) amplitudes and Bi-adjoint-scalar (BAS) amplitudes. Our…
Building upon the algebraic consistency construction of one-loop Bern-Carrasco-Johansson (BCJ) numerators for Yang-Mills (YM) and Yang-Mills-scalar (YMS) theories, we explore the expansion formula of one-loop Einstein-Yang-Mills (EYM)…
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,…
Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work \cite{Hou:2018bwm}, we have already proven that the identities…
We demonstrate that the tree level amplitudes and the explicit formulas of soft factors can be uniquely determined by soft theorems and the universality of soft factors. By imposing the soft theorems and the universality, as well as the…
In four dimensions, a tree-level double-trace Einstein-Yang-Mills (EYM) amplitude with two negative-helicity gluons (the $(g^-,g^-)$-configuration) satisfies a symmetric spanning forest formula, which was derived from the graphic expansion…
A proof is given of the formula, recently proposed by Cachazo, He and Yuan (CHY) for gluon tree amplitudes in pure Yang-Mills theory in arbitrary dimension. The approach is to first establish the corresponding result for massless $\phi^3$…
In the maximally-helicity-violating (MHV) configuration, tree-level single-trace Einstein-Yang-Mills (EYM) amplitude with one and two gravitons have been shown to satisfy a formula where each graviton splits into a pair of collinear gluons.…
We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color…
In this work, we prove the new factorization pattern for tree-level Yang-Mills (YM) amplitudes proposed in a companion paper. This pattern reveals a decomposition of amplitudes into a sum of gluings of lower-point amplitudes under specific…
The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph…
In our recent works, a new approach for constructing tree amplitudes, based on exploiting soft behaviors, was proposed. In this paper, we extend this approach to effective theories for gluons which incorporate higher-derivative…
We present a geometric derivation of all-multiplicity (single-trace) tree-level Einstein Yang-Mills (EYM) amplitudes ${\cal A}(n;r)$ involving $n$ gluons and $r$ gravitons by a bilinear of two twisted differential forms on the moduli space…
We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but…
Tree level multi-trace Yang-Mills-scalar (YMS) amplitudes have been shown to satisfy a recursive expansion formula, which expresses any YMS amplitude by those with fewer gluons and/or scalar traces. In an earlier work, the single-trace…
Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary…
Motivated by the problem of expanding single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in the gauge invariant vector space. Starting from…
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…