How robust are particle physics predictions in asymptotic safety?

TL;DR

This paper critically examines the robustness of particle physics predictions derived from asymptotic safety, analyzing how various common approximations affect the reliability of these predictions in specific Standard Model extensions.

Contribution

It systematically investigates the impact of typical approximations in asymptotic safety calculations on predictions for B-L and leptoquark models, providing uncertainty estimates.

Findings

Dropping approximations significantly affects prediction accuracy.

Uncertainty estimates vary depending on the model and parameters.

Analytical and numerical methods complement each other in assessing robustness.

Abstract

The framework of trans-Planckian asymptotic safety has been shown to generate phenomenological predictions in the Standard Model and in some of its simple new physics extensions. A heuristic approach is often adopted, which bypasses the functional renormalization group by relying on a parametric description of quantum gravity with universal coefficients that are eventually obtained from low-energy observations. Within this approach a few simplifying approximations are typically introduced, including the computation of matter renormalization group equations at 1~loop, an arbitrary definition of the position of the Planck scale at $10^{19}$ GeV, and an instantaneous decoupling of gravitational interactions below the Planck scale. In this work we systematically investigate, both analytically and numerically, the impact of dropping each of those approximations on the predictions for certain particle physics scenarios. In particular we study two extensions of the Standard Model, the gauged $B-L$ model and the leptoquark $S_3$ model, for which we determine a set of irrelevant gauge and Yukawa couplings. In each model, we present numerical and analytical estimates of the uncertainties associated with the predictions from asymptotic safety.