Large Lepton Flavor Mixing and

There are experimental indications of large flavor mixing between ? ? and ? ?. In the unification models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the ex

hep-ph/9710418 DPNU-97-49 October 1997

Large Lepton Flavor Mixing and E6-type Uni cation ModelsNaoyuki HABA and Takeo MATSUOKA1 1 2

Faculty of Engineering, Mie University Mie, JAPAN 514 2 Department of Physics, Nagoya University Nagoya, JAPAN 464-01

There are experimental indications of large avor mixing between and . In the uni cation models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the extra particles. When large mixings occur, lepton avor mixings can be quite di erent from quark avor mixings. By taking the string inspired SU (6) SU (2)R model with global avor symmetries, we obtain the neutrino avor mixing sin 23 '= sin C around the un cation scale. It can be expected that due to large Yukawa couplings of neutrinos, the renormalization e ect increases sin 2 23 naturally up to 1 at the electroweak scale. Fermion mass spectra and the CKM matrix of quarks obtained in this paper are also phenomenologically viable.

Abstract

There are experimental indications of large flavor mixing between ? ? and ? ?. In the unification models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the ex

1 IntroductionThe hierarchical patterns of quark-lepton masses and avor mixings have been one of the outstanding problems in particle physics. From the viewpoint of quark-lepton uni cation it seems to be plausible that the hierarchical structure of Yukawa couplings for leptons is similar to that for quarks and that lepton avor mixings are also parallel to quark avor mixings. Experimentally, however, the large neutrino avor mixing sin has been suggested by the muon neutrino de cit in the atmospheric neutrino ux 1]. This implies that lepton avor mixings are remarkably di erent from quark avor mixings in their hierarchical pattern. A natural question arises as to whether or not the distinct avor mixings of quarks and leptons are in accord with the quarklepton uni cation. From the viewpoint of uni cation theory, it is reasonable that the hierarchical structure of Yukawa couplings is attributable to some kinds of the avor symmetry at the uni cation scale MU . If there exists the avor symmetry such as ZN or U (1) in the theory, it is natural that Froggatt-Nielsen mechanism is at work for the interactions 2]. For instance, the e ective Yukawa interactions for up-type quarks are of the form23

Mij Qi Ujc Huwith

(1) (2)

where subscripts i and j stand for the generation indices and all of the constants cij are of order O(1) with rank cij= 3. The super eld X, which is singlet under the uni cation gauge group, is an appropriate composite super eld with the canonical normalization. The vaccum expectation value (VEV) of X is supposed to be slightly smaller than MU, where MU is nearly equal to the reduced Planck scale. For simplicity, we introduce global avor U (1) symmetry and Z -symmetry (R-parity) at the uni cation scale. The charge of the super eld X is assumed to be (?1;+) under U (1) Z . Instead of U (1) we may take the ZN -symmetry. In that case the present analysis remains unchanged. Due to the U (1)-symmetry the e

xponents mij in Eq.(2) are determined according as the U (1)-charges of Qi, Ujc and Hu . Here we denote the di erences of U (1)-charges for Q -Q, Q -Q, U c -U c and U c -U c by,, and, respectively. We have 0 1++++++ C;+++ mij= m+ B (3)@ A+ 0 ij2 2 2 1 3 2 2 1 3 2 33

Mij= cij hX i MU

!mij

= cij xmij;

provided that,,, and m are non-negative. The mass matrix of the up-type quarks is described by the matrix M multiplied by vu= hHu i. By taking an ansatz33

There are experimental indications of large flavor mixing between ? ? and ? ?. In the unification models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the ex

that only top-quark has a trilinear coupling, i.e.

m= 0;33

(4)+

we obtain mass eigenvalues

O(vu x

+++

);

O(vu x );

O(vu );

(5)

which correspond to u-, c- and t-quarks, respectively. Thus, naively, the mass hierarchy of quarks and leptons, up to the renormalization e ects, seems to be controlled only by U (1)-charges of the matter elds. However, in a wide class of uni cation models, the situation is not so simple. This is because the massless sector in the uni cation theory includes extra particles beyond the standard model and then there may occur extra-particle mixings such as between quarks(leptons) and colored Higgs elds(doublet Higgs elds). In order to study fermion masses and avor mixings we have to take the e ects of the extra-particle mixings into account. In addition, in the neutrino sector we should incorporate the extra-particle mixings with the see-saw mechanism 3]. In Ref. 4] we explained the observed hierarchical structure of the Cabbibo-Kobayashi-Maskawa(CKM) matrix for quarks in the string inspired SU (6) SU (2)R model. In this paper we explore the CKM matrix for leptons. Several authors have pointed out that large neutrino avor mixing can be obtained as a consequence of the cooperation between Dirac and Majorana mass matrices, provided that the Majorana mass matrix has a speci c structure 5]. In the quark-lepton uni cation, however, the Majorana mass matrix is closely linked to the other mass matrices and then it is di cult to expect such a cooperation between the Dirac and the Majorana mass matrices. In this paper, on the basis of E -type uni cation models we …… 此处隐藏：25475字，全部文档内容请下载后查看。喜欢就下载吧 ……