Mass Matrix Related to Up - Quark Masses and Nearly Tribimaximal Mixing – Based on a Yukawaon model –

Based on a new approach (the so-called Yukawaon model) to the mass spectra and mixings, a neutrino mass matrix which is described in terms of the up-quark masses and CKM matrix parameters is proposed. The mass matrix successfully leads to a nearly tribimaximal mixing without assuming any discrete symmetry. 1 What is a Yukawaon model? In the standard model of the quarks and leptons, we have many parameters in the theory. Especially, since the Yukawa coupling constants Yf (f = u, d, e, ν) are entirely free, we have no predictions for the mass spectra and mixings. Therefore, usually, we assume a flavor symmetry, and thereby, we discussed relations among the mass spectra and mixings. However, if we want to bring a flavor symmetry into the standard model, we encounter a no-go theorem [1, 2] on the flavor symmetry, so that we cannot impose any flavor symmetry on the standard model. Of course, we can evade[2] the no-go theorem if we consider a multi-Higgs model in which Higgs scalars have flavor quantum numbers. However, such multi-Higgs models will newly bring some troubles, e.g. flavor-changing neutral current problem, rapid evolutions of coupling constants, and so on. There is another idea for the origin of the mass spectra and mixings: In the Yukawa interactions HY = ∑ i,j qL(Yu) j iuRjHu + · · · , (1.1) we regard the Yukawa coupling constants Yf as “effective” coupling constants Y eff f in an effective theory, and we consider that Y eff f originate in vacuum expectation values (VEVs) of new scalars Yf , i.e. Y eff f = yf Λ 〈Yf 〉, (1.2) where Λ is a scale of the effective theory, i.e.