Abstract
Recent studies have provided evidence for the existence of new asymptotically free trajectories in non-Abelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general mathrm {SU}(N_{mathrm {L}})times mathrm {SU}(N_{mathrm {c}}) Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies. We construct these asymptotically free trajectories within conventional overline{text {MS}} schemes and systematic weak coupling expansions. The existence of these solutions is argued to be a scheme-independent phenomenon, as demonstrated for mass-dependent schemes based on general momentum-space infrared regularizations. A change of scheme induces a map of the theory’s coupling space onto itself, which in the present case also translates into a reparametrization of the space of asymptotically free solutions.
Highlights
Universality in physics characterizes the fact that long-range effective properties of a system can be largely independent of its microscopic details
Recent studies have provided evidence for the existence of new asymptotically free trajectories in nonAbelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general SU(NL) × SU(Nc) Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies
In contrast to standard perturbative investigations, these new solutions become visible beyond the deep Euclidean region, because threshold effects can play an important role on all scales
Summary
Universality in physics characterizes the fact that long-range effective properties of a system can be largely independent of its microscopic details. Since the occurrence of symmetry-breaking-induced thresholds on all scales is an essential ingredient for the corresponding RG flows, the standard reasoning used for the DER and implying one-loop universality is no longer applicable. This raises naturally the question of scheme dependence: is the existence of these new AF UV completions an universal statement? In order to make contact with the most widely used MS scheme of standard perturbation theory, we elucidate the construction of AF trajectories on the basis of one-loop β functions obtained from dimensional regularization. This theory space includes rescaling parameters that distinguish between different AF trajectories
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