Scheme dependence of asymptotically free solutions

Understand

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.