Note on scalar-graviton and scalar-photon-graviton amplitudes

TL;DR

This paper introduces an algorithm for calculating specific tree-level amplitudes involving scalars, gravitons, and photons, which are essential for post-Newtonian and post-Minkowskian gravitational calculations.

Contribution

It presents a novel algorithm combining amplitude expansions, dimensional reduction, and differential operators for these calculations.

Findings

Provides explicit formulas for scalar-graviton and scalar-photon-graviton amplitudes.

Facilitates more efficient computations in gravitational and electromagnetic interactions.

Supports post-Newtonian and post-Minkowskian expansion calculations.

Abstract

In this short note, we propose an algorithm based on the expansions of amplitudes, the dimensional reduction technic and the differential operators, to calculate the tree level scalar-graviton amplitudes with two massive scalars, as well as the tree level scalar-photon-graviton amplitudes with two massive scalars and one photon. While applying the unitarity method, these amplitudes are necessary inputs for the calculation of post-Newtonian and post-Minkowskian expansions in general relativity for two massive charged objects interact with gravity and electromagnetic field.