Completely asymptotically free chiral theories with scalars

TL;DR

This paper establishes conditions under which chiral gauge theories with scalars remain completely asymptotically free, extending models like Georgi-Glashow and Bars-Yankielowicz with multiple fermion families.

Contribution

It systematically analyzes the interplay of gauge, Yukawa, and quartic couplings to identify new asymptotically free chiral theories with scalars and multiple fermion families.

Findings

Complete asymptotic freedom achieved for specific color and family numbers.

Both fundamental and adjoint scalar representations can support asymptotically free models.

Conditions derived for the coexistence of gauge, Yukawa, and quartic couplings to remain asymptotically free.

Abstract

We provide the conditions for complete asymptotic freedom for chiral gauge theories including scalars, as motivated by grand unified models. These are generalised Georgi-Glashow and Bars-Yankielowicz theories that feature a scalar field transforming either in the fundamental or in the adjoint of the gauge group. In both scenarios, we consider the addition of multiple chiral fermion families. We systematically analyse the interplay between gauge, Yukawa, and quartic couplings required for all interactions to remain asymptotically free at short distances. We find that for both scalar representations, complete asymptotic free models can be obtained for a specific number of colours and multiplicity of vector-like and chiral families.