Towards Two-to-Two Scattering of Scalars in Asymptotically Safe Quantum Gravity

TL;DR

This paper calculates scalar particle scattering in asymptotically safe quantum gravity, revealing how the amplitude behaves across energy scales and confirming unitarity in the ultraviolet regime.

Contribution

It provides the first detailed computation of the scalar-graviton scattering amplitude with full momentum dependence in asymptotically safe gravity.

Findings

Cross-section matches General Relativity at low energies

Scattering amplitude respects unitarity at high energies

Full momentum dependence of the vertex is characterized

Abstract

We compute the graviton-mediated two-to-two scattering amplitude and cross section for scalar particles in asymptotically safe quantum gravity. Specifically, we compute the full momentum dependence of the scalar-graviton three-point scattering vertex for spacelike momenta with the functional renormalisation group. We also discuss the analytic continuation to the Minkowski branch, and in particular its angular dependence. Then, the timelike part of the vertex is reconstructed and used to compute the scattering amplitude and cross-section. We show that the cross-section reduces to that in General Relativity at small energies, and it respects unitarity in the UV.