Renormalization Group Effects on the Mass Relation Predicted by the Standard Model with Generalized Covariant Derivatives

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Renormalization group analysis is made on the relation m H ≃ √2mₜ for masses of the top quark and the Higgs boson, which is predicted by the standard model based on generalized covariant derivatives with gauge and Higgs fields. This relation is a low energy manifestation of a tree level constraint which holds among the quartic Higgs self-coupling constant and the Yukawa coupling constants at a certain high energy scale μ₀. With the renormalization group equation at one-loop level, the evolution of the constraint is calculated from μ₀ down to the low energy region around the observed top quark mass. The result of analysis shows that the Higgs boson mass is in mₜ m H √2mₜ for a wide range of the energy scale μ₀ mₜ and it approaches to 177 GeV (≈ mₜ) for large values of μ₀.