Abstract
mathbb {Z}_2-Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.
Highlights
Gauged Yukawa models form the backbone of our description of elementary particle physics: they provide mechanisms for mass generation of gauge bosons as well as for chiral fermions via the Brout–Englert–Higgs mechanism
As our methods can address the global behavior of the potential, our work adds new knowledge to the results known from standard perturbation theory: for the asymptotically free Cheng–Eichten–Li solution, we demonstrate that the potential is and remains globally stable when running the renormalization group (RG) towards the UV; an analytic approximation of the potential can be given in terms of hypergeometric functions
Identifying such RG trajectories provides information that can be crucial for our attempt at constructing fundamental models of particle physics
Summary
Gauged Yukawa models form the backbone of our description of elementary particle physics: they provide mechanisms for mass generation of gauge bosons as well as for chiral fermions via the Brout–Englert–Higgs mechanism. The existence of these new trajectories has been confirmed by weak-coupling approximations, effective-fieldtheory approaches, large-N methods, as well as more comprehensively with the functional RG [44] As such dramatic conclusions about the existence of new UV-complete theories requires substantiation and confirmation, the purpose of this work is to study the emergence of these new RG trajectories in a model that exhibits asymptotic freedom already in standard perturbation theory. 6, we construct functional approximations of asymptotically free solutions by inspecting a regime where the scalar fluctuations are dominated by a quartic interaction Another description is obtained from the expansion in powers of the weak Yukawa coupling in Sect.
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