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Renormalization group analysis is made on the relation $m_{\rm H} \simeq\sqrt{2}m_t$ for masses of the top quark and the Higgs boson, which ispredicted by the standard model based on generalized covariant derivatives withgauge and Higgs fields. This relation is a low energy manifestation of a treelevel constraint which holds among the quartic Higgs self-coupling constant andthe Yukawa coupling constants at a certain high energy scale $\mu_0$. With therenormalization group equation at one-loop level, the evolution of theconstraint is calculated from $\mu_0$ down to the low energy region around theobserved top quark mass. The result of analysis shows that the Higgs boson massis in $m_t \lesssim m_{\rm H} \lesssim \sqrt{2}m_t$ for a wide range of theenergy scale $\mu_0 \gtrsim m_t$ and it approaches to 177 GeV ($\approx m_t$)for large values of $\mu_0$.Comment: 13 pages, LaTeX, no figure

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