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Universal Texture of Quark and Lepton Mass Matrices with an Extended Flavor $2leftrightarro.pdf

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Universal Texture of Quark and Lepton Mass Matrices with an Extended Flavor $2leftrightarro

a r X i v : h e p - p h / 0 3 1 2 2 0 7 v 2 8 F e b 2 0 0 4 US-03-10 Universal Texture of Quark and Lepton Mass Matrices with an Extended Flavor 2 ? 3 Symmetry Yoshio Koide and Yoshio Koide Department of Physics, University of Shizuoka, 52-1 Yada, Shizuoka, 422-8526 Japan E-mail: koide@u-shizuoka-ken.ac.jp (Dated: February 1, 2008) Against the conventional picture that the mass matrix forms in the quark sectors will take some- what different structures from those in the lepton sectors, on the basis of an idea that all the mass matrices of quarks and leptons have the same texture, a universal texture of quark and lepton mass matrices is proposed by assuming a discrete symmetry Z3 and an extended flavor 2 ? 3 symmetry. The texture is described by three parameters (including phase parameter). According to this ansatz, the neutrino masses and mixings are investigated. PACS numbers: 12.15.Ff, 14.60.Pq, 11.30.Hv I. INTRODUCTION From the point of view of the quark and lepton unification, an idea that their matrix forms are described by a universal texture is very attractive. Especially, against the conventional picture that the mass matrix forms in the quark sectors will take somewhat different structures from those in the lepton sectors, it is interesting to investigate whether or not all the mass matrices of quarks and leptons can be described in terms of the same mass matrix form as in the neutrinos. Recently, a quark and lepton mass matrix model based on a discrete symmetry Z3 and a flavor 2 ? 3 symmetry has been proposed [1]. In the model (we will refer it as Model I hereafter), the quark and lepton mass matrices Mf are given by the texture Mf = PfM?fPf , (1.1) where M?f is a real matrix with a form M?f = af ?? 0 1 11 0 0 1 0 0 ??+ bf ?? 0 0 00 1 xf 0 xf 1 ?? = ?? 0 af afaf bf bfxf af bfxf bf ?? , (1.2) and Pf is a phase matrix defined by Pf = diag(e iδf 1 , eiδ f 2 , eiδ f 3 ) . (1.3) (As seen in the expression in Eq. (1.2), the model is essentially based on a t