Asymptotically Safe Standard Model Extensions?

TL;DR

This paper investigates whether extensions of the Standard Model with many charged fermions can achieve asymptotic safety in gauge interactions, finding that non-Abelian sectors can, but the Abelian U(1) cannot.

Contribution

It provides a leading-order 1/N_F resummation of RG equations for Standard Model extensions, demonstrating asymptotic safety in non-Abelian sectors.

Findings

SU(2) and SU(3) can be asymptotically safe

U(1) cannot be made asymptotically safe while remaining perturbative

Higgs quartic coupling remains non-asymptotically safe in U(1) extensions

Abstract

We consider theories with a large number $N_F$ of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in $1/N_F$. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.