What Happens If an Unbroken Flavor Symmetry Exists?

Abstract

Without assuming any specific flavor symmetry and/or any specific mass matrix forms, it is demonstrated that if a flavor symmetry (a discrete symmetry, a U(1) symmetry, and so on) exists, we cannot obtain the CKM quark mixing matrix $V$ and the MNS lepton mixing matrix $U$ except for those between two families for the case with the completely undegenerated fermion masses, so that we can never give the observed CKM and MNS mixings. Only in the limit of $m_{\nu 1}=m_{\nu 2}$ ($m_d=m_s$), we can obtain three family mixing with an interesting constraint $U_{e3}=0$ ($V_{ub}=0$).

10 pages, no figure, title and presentation changed

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• U(3)-Flavor Nonet Scalar as an Origin of the Flavor Mass Spectra
• Yukawa interactions, flavor symmetry, and non-canonical Kähler potential
• Testing Flavor Symmetries by B-Factory
• Neutrino Mass Hierarchies in a Mass Matrix Form Versus its Inverse Form
• Chasing after flavor symmetries of quarks from bottom up
• Can Massless and Light Yukawaons be Harmless?
• Neutrino Mass Matrix Related to Up-Quark Masses and Nearly Tribimaximal Mixing -- Based on a Yukawaon model --
• A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions
• Partial mass-degeneracy and spontaneous CP violation in the lepton sector
• On a mechanism realizing quark mass hierarchy