Scalar-Graviton Amplitudes

TL;DR

Problem: obtain covariant, tree-level amplitudes for two massive scalars interacting with gravitons in $D$-dimensional spacetime, suitable as inputs for unitarity-based classical gravity expansions. Approach: develop CHY-based methods with a double-cover extension to produce covariant currents, turn two gluons into scalar legs via a $D+1$ dimensional embedding, and obtain gravity amplitudes by KLT-squaring (or momentum kernel) of corresponding YM results. Contributions: explicit recursive formulas for two-mass-scalar with an arbitrary number of gluons, a KK/BCJ-based decomposition to streamline higher-point YM amplitudes with masses, and a straightforward gravity construction with checks up to six points. Impact: provides practical, covariant, dimensionally general tools for high-precision classical GR calculations (PN/PM), and suggests new on-shell recursion avenues tied to the CHY double-cover formalism.

Abstract

Using the CHY-formalism and its extension to a double cover we provide covariant expressions for tree-level amplitudes with two massive scalar legs and an arbitrary number of gravitons in D dimensions. Using unitarity methods, such amplitudes are needed inputs for the computation of post-Newtonian and post-Minkowskian expansions in classical general relativity.