In search of a UV completion of the Standard Model - 378.000 models that don't work

TL;DR

This paper investigates the possibility of UV-complete extensions of the Standard Model through asymptotic safety, analyzing numerous models with added fermions and scalar interactions, but finds all candidate fixed points unviable.

Contribution

It provides a detailed perturbative analysis of the renormalization group fixed points in extended Standard Model scenarios, identifying their instability or mismatch with low-energy physics.

Findings

All candidate UV fixed points are unphysical due to instability or mismatch.

Most models do not exhibit viable asymptotically safe fixed points.

The study rules out a broad class of models for UV completion.

Abstract

Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and having Yukawa-like interactions with new scalar fields. Here we study the corresponding renormalization group beta functions to next and next-to-next to leading order in the perturbative expansion, varying the number of extra fermions and the representations they carry. We test the fixed points of the beta functions against various criteria of perturbativity to single out those that are potentially viable. We show that all the candidate ultraviolet fixed points are unphysical for these models: either they are unstable under radiative corrections, or they cannot be matched to the Standard Model at low energies.