# Phase structure of complete asymptotically free SU($N_c$) theories with quarks and scalar quarks

## TL;DR

This paper maps the phase diagram of SU(Nc) gauge theories with scalars and quarks, revealing conditions for conformality and symmetry breaking, with implications for extensions of the Standard Model.

## Contribution

It provides a detailed perturbative analysis of the phase structure of complete asymptotically free SU(Nc) theories with scalars and quarks, including quantum corrections and symmetry breaking patterns.

## Key findings

- Infrared dynamics exhibit long-distance conformality under certain conditions.
- The phase diagram reveals a rich structure with various symmetry breaking patterns.
- Theories could serve as UV finite extensions of the Standard Model.

## Abstract

We determine the phase diagram of complete asymptotically free SU($N_c$) gauge theories featuring $N_s$ complex scalars and $N_f$ Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly we discover that the complete asymptotically free conditions guarantee that the infrared dynamics displays long distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the theory and summarising the possible patterns of radiative symmetry breaking. These theories are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the Standard Model.