Scheme dependence of asymptotically free solutions

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.

30 pages, 4 figures

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