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

We determine the phase diagram of completely asymptotically free SU(Nc) gauge theories featuring Ns complex scalars and Nf 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 completely 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 model and summarizing the possible patterns of radiative symmetry breaking. These models are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the standard model.