Flavor mixing in quarks and leptons

SUPPLEMENTS Nuclear

ELSEVIER

Physics

B (Proc.

Suppl.)

118 (2003)

474

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Flavor Mixing in Quarks and Leptons Daijiro Suemat& aInstitute

for Theoretical

Physics, Kanazawa University,

Kanazawa 920-1192, JAPAN

In the supersymmetric models with bi-linear Rparity violating terms eaL,H2, it is well-known that neutrino-neutralino mixings can induce a small neutrino mass through the weak scale seeHowever, the light neutrino saw mechanism. mass matrix obtained in this way has only one nonzero mass eigenvalue. It has been suggested that one-loop effects can resolve this mass degeneracy and make both explanations of the solar and atmospheric neutrinos possible. We propose another tree-level solution to this problem by introducing an extra Abelian gauge symmetry to the MSSM, which is assumed to remain unbroken at a TeV region. We assume that this extra U(l)x symmetry has flavor diagonal but generation dependent interactions such as

tion, the proton stability by prohibiting dangerous couplings of extra colored triplets Da, Da to the SM fields, and also the existence of Higgs mixings such as

c = iJzgx(qJxq,v,

This seems to have qualitatively nice features if we take X - 0.22. In the lepton sector we obtain

- fi$ixq&)

+. . . .

(1)

If sneutrinos get nonzero vacuum expectation values, neutrino-gaugino mixing appears through figx qa (fia) which can make us possible to have two nonzero mass eigenvalues of neutrinos at the tree level as far as its charges are generation dependent. We can successfully construct a consistent model for the lepton sector by using this [l]. It is also possible to extend the model to include the quark sector [2]. For this purpose we introduce a new Abelian symmetry U(~)F. We take U(~)F to be an anomalous U(1) symmetry broken near the Planck scale. It plays a role of the flavor symmetry as the Froggatt-Nielsen model to generate the quark and lepton mass hierarchy. The field contents in this extended model consist of quarks/leptons (q,d,d)f, (#,e)f and Higgs fields (D, Hz)~, (D, HI)~ and singlet Higgs fields Si. Suitable U(l)x xU(l)~ charges are assigned for them. We impose several phenomenological conditions, that is, the gauge anomaly cancella0920-5632/03/$ - see front matter doi:l0.1016/S0920-5632(03)01367-7

0 2003 Elsevier

Science

B.V.

(H,1&)

n1(4)

62W2)

Ic4(S4)

K5@5)

(2)

These bring constraints on the U(l)x charges and we study neutrino masses under these constraints. If we introduce a parameter X - ($)/M,I and tanc = ~l(S1)/~2&), the quark mass eigenvalues and the CKM mixing can be written as mu : m, : mt = X6 : X4 : 1 > md:m,:mb=X4sin~:X2cos(‘:cos5,

V us - A,

vu,, N x3,

me : mp : m, = X4sinC:

vcb N x2.

X2cos< : cost.

(3)

(4

The neutrino mass spectrum has a normal hierarchy and the MNS-matrix can be written as

if we take sin< - cost - & and assign the U(l)x charges to the leptons suitably. The solar and atmospheric neutrinos can be explained simultaneously and the LMA solution can be applied to the solar neutrino. REFERENCES 1. D. Suematsu, Phys. Lett. B506 (2001) 131. 2. D. Suematsu, Phys. Rev. D64 (2001) 073013. All rights

reserved.