$e^+ e^- \to \mu^+ \mu^-$ in the Asymptotically Safe Standard Model

TL;DR

This paper investigates the electron-positron to muon-antimuon scattering in the asymptotically safe Standard Model, incorporating graviton effects, and finds the cross section decreases at high energies, supporting unitarity.

Contribution

It introduces a method to include graviton contributions in scattering amplitudes within the asymptotically safe Standard Model, demonstrating the model's unitarity at high energies.

Findings

Cross section decreases with energy in the ultraviolet regime.

Results are compatible with unitarity bounds.

Provides evidence for the unitarity of the asymptotically safe Standard Model.

Abstract

We study the electron-positron to muon--anti-muon cross-section in the asymptotically safe Standard Model. In particular, we include the graviton contributions to the scattering amplitude, which is computed from momentum-dependent timelike one-particle-irreducible correlation functions. Specifically, we employ reconstruction techniques for the graviton spectral functions. We find that the full asymptotically safe quantum cross section decreases in the ultraviolet with the centre-of-mass energy, and is compatible with unitarity bounds. Importantly, our findings provide non-trivial evidence for the unitarity of the asymptotically safe Standard Model.