Scattering amplitudes in dimensionless quadratic gravity coupled to QED

TL;DR

This paper derives analytic scattering amplitudes in quadratic gravity coupled to QED, revealing universal ultra-Planckian scaling and interference effects, advancing understanding of high-energy gravitational interactions with matter.

Contribution

It provides the first compact analytic expressions for tree-level scattering amplitudes in quadratic gravity coupled to QED, including photon and matter interactions with interference effects.

Findings

Amplitudes show forward/backward enhancements at small momentum transfer.

Differential cross sections scale as 1/s at ultra-Planckian energies.

Results are independent of gravitational gauge-fixing parameters.

Abstract

We study ultra-Planckian $2\to2$ scattering in an Abelian gauge theory coupled to agravity, the scale-free and renormalizable realization of quadratic quantum gravity. Focusing on charged fermions and scalars interacting with the photon and the higher-derivative graviton, we present compact analytic expressions for the unpolarized squared matrix elements for a broad set of tree-level processes, including photon--photon, fermion--fermion, fermion--photon, scalar--fermion, scalar--photon, scalar--scalar, and annihilation channels. In contrast to purely graviton-mediated analyses, we retain systematically the photon--graviton interference contributions and verify explicitly the independence of the results on the gravitational gauge-fixing parameter. The amplitudes display characteristic forward/backward enhancements associated with small momentum transfer, amplified by the $1/p^{4}$ graviton propagator, while their high-energy scaling reflects the underlying dimensionless gravitational couplings. Moreover, for all channels analyzed the corresponding differential cross sections exhibit the universal ultra-Planckian scaling $d\sigma/d\Omega \propto 1/s$, where $s$ is the Mandelstam invariant (the squared center-of-momentum energy). Our results furnish a unified amplitude-level description of how higher-derivative gravity reshapes familiar QED scattering at ultra-Planckian energies and provide analytic building blocks for further studies of IR definitions and UV consistency in agravity with matter.