A Built-in Horizontal Symmetry of $SO(10)$

Abstract

In a renormalizable $SO(10)$ theory, all fermion mass matrices are linear combinations of three fundamental types, $M^{10},M^{\overline{126}}$, and $M^{120}$, whose superscripts indicate their $SO(10)$ transformation properties. We point out that each of these fundamental mass matrices possesses a natural symmetry that can be used to generate an unbroken horizontal symmetry $\G$, if the natural symmetry is taken to be the residual symmetry. This built-in symmetry is a Coxeter group. If it is finite, it must be one of five groups, $S_4,\ Z_2\x S_4$,\ $Z_2\x A_5$, plus two `rank-4' groups. These symmetries place constraints on the fundamental mass matrices and reduce the number of parameters in an SO(10) fit. Since they are built-in and can be derived theoretically, it is hoped that they impose better constraints than those without a theoretical basis, but that is to be confirmed because there is no attempt to fit the experimental data in this article, except to count the number of free parameters. To illustrate the similarities and differences of various kinds of constraints, a comparison is made with an existing $S_4$ model, and with models possessing the Fritzsch texture.

Version to be published in Phys.Rev.D. Slight change of wording from previous version

References in corpus (15)

• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• Symmetry of Lepton Mixing
• Fermion Masses in SO(10) Models
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• Lepton Mixing Patterns from a Scan of Finite Discrete Groups
• Mass Independent Textures and Symmetry
• Discrete symmetries and model-independent patterns of lepton mixing
• A new family symmetry for SO(10) GUTs
• Magic Neutrino Mass Matrix and the Bjorken-Harrison-Scott Parameterization
• Group Theory and Dynamics of Neutrino Mixing
• A renormalizable SO(10) GUT scenario with spontaneous CP violation
• Quark and lepton mixing angles with a dodeca-symmetry
• Four Zero Texture Fermion Mass Matrices in SO(10) GUT
• Horizontal Symmetry

Cited by in corpus (3)

• Generalized ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ in Scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis
• Lepton Mixing, Residual Symmetries, and Trigonometric Diophantine Equations
• Flavor Symmetries in the Yukawa Sector of Non-Supersymmetric SO(10): Numerical Fits Using Renormalization Group Running