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Prog. Theor. Phys. Vol. 114 No. 4 (2005) pp. 873-887

[ Full Text PDF : FREE ACCESS (169K) ]

A Non-Semisimple Hidden Symmetry for Flavor Physics

Ikuo S. Sogami*

Physics Department, Kyoto Sangyo University, Kyoto 603-8555, Japan

(Received July 21, 2005)

Abstract:

With linearly independent elements extracted from unitary 3 ×3 matrix representations Rep(S3) of the permutation group S3, a non-semisimple algebra \breveA and its associated Lie group \breveG(\breveA) are constructed for the purpose of describing flavor physics. While the group \breveG(\breveA) is isomorphic to the SU(2) ×U(1) group, the algebra \breveA has a unique, elaborate structure. A flavor-mixing matrix that is completely different from that of the conventional theory is expressed in terms of four group parameters of the Lie group in an essentially unique way. Adjusting the values of the group parameters of the flavor-mixing matrix for quark sector allows us to account for experimental results to high precision. In order to describe the mass matrices leading to hierarchical mass spectra, a minimal extension of the algebra \breveA is made by adding an additional element.


URL : http://ptp.ipap.jp/link?PTP/114/873/
DOI : 10.1143/PTP.114.873


*E-mail: sogami@cc.kyoto-su.ac.jp

[ Full Text PDF : FREE ACCESS (169K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 115 No. 2 (2006) pp. 461-465 :
    Sum Rules for Elements of Flavor-Mixing Matrices Based on a Non-Semisimple Symmetry
    Ikuo S. Sogami
  2. Progress of Theoretical Physics Vol. 119 No. 2 (2008) pp. 339-344 :
    Notes on Flavor Mixing Matrices Characterized by SU(2) ×U(1) Group Parameters
    Ikuo S. Sogami and Yasufumi Konishi
  3. Progress of Theoretical Physics Vol. 122 No. 4 (2009) pp. 807-829 :
    Gauge Field Theory of Horizontal Symmetry Generated by a Central Extension of the Pauli Algebra
    Ikuo S. Sogami
  4. Progress of Theoretical Physics Vol. 123 No. 2 (2010) pp. 271-283 :
    Dirac Mass Matrices in Gauge Field Theory of Horizontal Symmetry
    Yasufumi Konishi and Ikuo S. Sogami

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