paper

Scattering amplitudes in dimensionless quadratic gravity coupled to QED

arXiv:2603.05476 · doi:10.1103/k79x-52gj

Abstract

We study ultra-Planckian 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 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 , where 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.

19 pages, 8 figures. v2 Minor corrections

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