Renormalization group analysis is made on the relation mH ~ v'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 J-to. With the renormalization group equation at one-loop level, the evolution of the constraint is calculated from J-to down to the low energy region around the observed top quark mass. The result of analysis shows that the Higgs boson mass satisfies mt ;; mH ;; v'2mt for a wide range of the energy scale J-to ~ mt and it approaches 177 Ge V (:::::l mt) for large values of J-to.Confirmation of the existence of the top quark by the Collider Detector Fermilab (CDF and DO) groups 1), 2) has shown that the standard model is a consistent and correct theory of fundamental interactions. To enrich the model further, however, we must solve many basic problems remained concerning its scalar sector. In particular, it is expected to predict the Higgs boson mass for an experiment to observe it in near future.Recently, one of the authors 3), 4) has reformulated the standard model by using the concept of generalized covariant derivatives with gauge and Higgs fields which act on a multi-spinor field consisting of all the chiral fermion fields. In the new model, the bosonic part of the Lagrangian is determined by field strengths of the gauge and Higgs fields which are constructed from the commutators of the generalized covariant derivatives. As one of interesting outcomes of this scheme, the strength of quartic self-interaction in the Higgs potential is fixed exclusively in terms of the Yukawa coupling constants and, as a result, the approximate relation mH :::::i v2mt holds for the masses of the top quark and the Higgs boson at the tree level.Unified description of the gauge and Higgs fields has been pioneered by Connes. 5) Using a noncommutative geometry, he introduced the Higgs field as a connection along the discrete direction in a doublely sheeted Minkowski spacetime. His theory predicts the tree level relation mtop = 2 m wand mHiggs = 3.14 m w . Alvarez et al. 6), 7) investigated the evolution of these relations under the one-loop renormalization group equations. 8), 9) Following their method, we analyze quantum effects on the restriction predicted by the standard model with the generalized covariant derivatives in this article.Collecting three generations of the electroweak doublets o/lj and singlets o/ej of lepton fields (the doublets o/qj, and singlets o/uj and o/dj of quark fields) into a at
We propose a phenomenological formula relating the Kobayashi-Maskawa matrix
$V_{KM}$ and quark masses in a form $(m_d,\ m_s,\ m_b)\propto (m_u,\ m_c,\
m_t)V_{KM}$. The formula agrees with experimental data well and has an
interesting geometric picture. The origin of such a formula is discussed in the
standard model.Comment: 9 pages, LaTeX, no figure
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