Asymptotic safety of simple Yukawa systems

TL;DR

This paper investigates whether simple Yukawa systems can be asymptotically safe using the functional RG, finding no non-Gaussian fixed points for realistic fermion flavors but identifying fixed points in a small-flavor model that predict the Higgs and top quark masses.

Contribution

The study demonstrates the absence of UV fixed points in realistic Yukawa systems with multiple fermions and explores fixed points in a small-flavor model, linking UV behavior to Higgs and top quark mass predictions.

Findings

No non-Gaussian fixed point for one or more fermion flavors.

Existence of a fixed point in a small-flavor model with a conformal Higgs.

Predicts Higgs mass and explains heavy top quark mass.

Abstract

We study the triviality and hierarchy problem of a Z_2-invariant Yukawa system with massless fermions and a real scalar field, serving as a toy model for the standard-model Higgs sector. Using the functional RG, we look for UV stable fixed points which could render the system asymptotically safe. Whether a balancing of fermionic and bosonic contributions in the RG flow induces such a fixed point depends on the algebraic structure and the degrees of freedom of the system. Within the region of parameter space which can be controlled by a nonperturbative next-to-leading order derivative expansion of the effective action, we find no non-Gaussian fixed point in the case of one or more fermion flavors. The fermion-boson balancing can still be demonstrated within a model system with a small fractional flavor number in the symmetry-broken regime. The UV behavior of this small-N_f system is controlled by a conformal Higgs expectation value. The system has only two physical parameters, implying that the Higgs mass can be predicted. It also naturally explains the heavy mass of the top quark, since there are no RG trajectories connecting the UV fixed point with light top masses.