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

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.