# Compton-like scattering of a scalar particle with N photons and one graviton

## TL;DR

This paper calculates tree-level scattering amplitudes involving a scalar particle, multiple photons, and a graviton using the worldline formalism, providing a systematic method to construct and verify these complex interactions.

## Contribution

It introduces a novel approach to compute scalar particle scattering amplitudes with multiple photons and a graviton, including a tree replacement rule for reducible parts.

## Key findings

- Derived explicit amplitude expressions for arbitrary N photons and one graviton.
- Verified gauge and diffeomorphism Ward identities at all N.
- Established a systematic method for constructing complex scattering amplitudes.

## Abstract

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.