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${Z}_2$-Yukawa-QCD models are a minimalistic model class with a Yukawa and aQCD-like gauge sector that exhibits a regime with asymptotic freedom in all itsmarginal couplings in standard perturbation theory. We discover the existenceof further asymptotically free trajectories for these models by exploitinggeneralized boundary conditions. We construct such trajectories as quasi-fixedpoints for the Higgs potential within different approximation schemes. Wesubstantiate our findings first in an effective-field-theory approach, andobtain a comprehensive picture using the functional renormalization group. Weinfer the existence of scaling solutions also by means of aweak-Yukawa-coupling expansion in the ultraviolet. In the same regime, wediscuss the stability of the quasi-fixed point solutions for large fieldamplitudes. We provide further evidence for such asymptotically free theoriesby numerical studies using pseudo-spectral and shooting methods.

Asymptotic freedom in ${Z}_2$-Yukawa-QCD models