# Scheme dependence of asymptotically free solutions

## TL;DR

This paper investigates the scheme dependence of asymptotically free solutions in non-Abelian Higgs-Yukawa models, confirming their existence across various regularization schemes and demonstrating their scheme independence.

## Contribution

It extends previous findings to a general SU(N_L) x SU(N_c) model, showing that asymptotically free trajectories are scheme-independent and persist under different regularizations.

## Key findings

- Asymptotically free solutions exist in a broad class of regularizations.
- Scheme changes correspond to reparametrizations of the coupling space.
- Solutions are confirmed within conventional MS-bar and momentum-space IR schemes.

## 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 ${\rm SU}(N_{\rm L})\times {\rm SU}(N_{\rm c})$ 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.