A new family symmetry for SO(10) GUTs

Abstract

We argue that the projective special linear group PSL(2,7), also known as Sigma(168), has unique features which make it the most suitable discrete family symmetry for describing quark and lepton masses and mixing in the framework of SO(10) type unified models. In such models flavon fields in the sextet representation of PSL(2,7) play a crucial role both in obtaining tri-bimaximal neutrino mixing as well as in generating the third family charged fermion Yukawa couplings. In preparation for physical applications, we derive the triplet representation of PSL(2,7) in the basis S,T,U,V where S,T,U are the familiar triplet generators of S(4) in the diagonal charged lepton basis where T is diagonal. We also derive an analogous basis for the real sextet representation and identify the vacuum alignments which lead to tri-bimaximal neutrino mixing and large third family charged fermion Yukawa couplings.

arXiv comment23 pages, 2 figures

References in corpus (68)

• Tri-Bimaximal Mixing and the Neutrino Oscillation Data
• Underlying A_4 Symmetry for the Neutrino Mass Matrix and the Quark Mixing Matrix
• Softly Broken A_4 Symmetry for Nearly Degenerate Neutrino Masses
• Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry
• Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing
• Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions
• Nearly Tri-Bimaximal Neutrino Mixing and CP Violation
• Theory of Neutrinos: A White Paper
• A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4
• Permutation Symmetry, Tri-Bimaximal Neutrino Mixing and the S3 Group Characters
• Neutrino Mass Models
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Tri-bimaximal Neutrino Mixing and Quark Masses from a Discrete Flavour Symmetry
• Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification
• CKM and Tri-bimaximal MNS Matrices in a SU(5) x (d)T Model
• The Unique Horizontal Symmetry of Leptons
• The Horizontal Symmetry for Neutrino Mixing
• A4 family symmetry and quark-lepton unification
• Fermion Masses and Mixing Angles from SU(3) Family Symmetry
• The Flavor Symmetry
• SU(3) family symmetry and neutrino bi-tri-maximal mixing
• Fermion Masses and Mixing Angles from SU(3) Family Symmetry and Unification
• $S_3$ Symmetry and Tri-bimaximal Mixing
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group
• Symmetry of Lepton Mixing
• Fermion Masses and Mixings in a S4 Based Model
• Tribimaximal Neutrino Mixing from a Supersymmetric Model with A_4 Family Symmetry
• S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor
• Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
• The golden ratio prediction for the solar neutrino mixing
• A Simplest A4 Model for Tri-Bimaximal Neutrino Mixing
• A model for fermion masses and lepton mixing in SO(10) x A4
• A predictive A4 model, Charged Lepton Hierarchy and Tri-bimaximal Sum Rule
• The Flavor Group Delta(3n^2)
• Tri-bimaximal mixing, discrete family symmetries, and a conjecture connecting the quark and lepton mixing matrices
• Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups
• Deviation from tri-bimaximal neutrino mixing in A4 flavor symmetry
• Twisted Flavors and Tri/bi-Maximal Neutrino Mixing
• Maximal Neutrino Mixing from a Minimal Flavor Symmetry
• Correlated Hierarchy, Dirac Masses and Large Mixing Angles
• The Flavor Group Delta(6n^2)
• S3 x Z2 model for neutrino mass matrices
• Dihedral Families of Quarks, Leptons and Higgs Bosons
• Predictive flavour symmetries of the neutrino mass matrix
• S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT
• Fermion masses and mixing in models with SO(10) x A_4 symmetry
• Quaternion Family Symmetry of Quarks and Leptons
• Flavor Symmetry for Quarks and Leptons
• Embedding A4 into left-right flavor symmetry: Tribimaximal neutrino mixing and fermion hierarchy
• Lepton Mixing and Cancellation of the Dirac Mass Hierarchy in SO(10) GUTs with Flavor Symmetries T7 and Sigma(81)
• S_4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing
• Towards a Complete Theory of Fermion Masses and Mixings with SO(3) Family Symmetry and 5d SO(10) Unification
• Simple Finite Non-Abelian Flavor Groups
• Neutrino mixing from the double tetrahedral group T^{\prime}
• S_3 Symmetry and Neutrino Masses and Mixings
• A Supersymmetric D4 Model for mu-tau Symmetry
• Neutrino masses and tribimaximal mixing in the minimal renormalizable supersymmetric SU(5) grand unified model with A4 flavor symmetry
• A model realizing the Harrison-Perkins-Scott lepton mixing matrix
• Fermion Mass Hierarchies and Flavour Mixing from a Minimal Discrete Symmetry
• Nonabelian Discrete Family Symmetry to Soften the SUSY Flavor Problem and to Suppress Proton Decay
• $T^{{}^{\prime }}$ Predictions of PMNS and CKM Angles
• The discrete flavor symmetry D5
• Lepton Flavor Model from Delta(54) Symmetry
• theta_C from the Dihedral Flavor Symmetries D_7 and D_14
• Lepton Masses in a Minimal Model with Triplet Higgs Bosons and $S_3$ Flavor Symmetry
• Anomaly Conditions for Non-Abelian Finite Family Symmetries
• Overview of Neutrino Mixing Models and Ways to Differentiate among Them

Cited by in corpus (57)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Neutrino Mass and Mixing with Discrete Symmetry
• Neutrino Mass and Mixing: from Theory to Experiment
• Unified Models of Neutrinos, Flavour and CP Violation
• Modular $S_4$ Models of Lepton Masses and Mixing
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models
• A SUSY GUT of Flavour with S4 x SU(5) to NLO
• Trimaximal TM1 neutrino mixing in S4 with spontaneous CP violation
• Golden Ratio Neutrino Mixing and $A_5$ Flavor Symmetry
• On the origin of neutrino flavour symmetry
• Finite flavour groups of fermions
• $A_4$ Family Symmetry from SU(5) SUSY GUTs in 6d
• Tri-Bimaximal Neutrino Mixing and Discrete Flavour Symmetries
• Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification
• A Supersymmetric Grand Unified Theory of Flavour with PSL(2,7) x SO(10)
• An SO(10) Grand Unified Theory of Flavor
• A4xSU(5) SUSY GUT of Flavour with Trimaximal Neutrino Mixing
• A_4xSU(5) SUSY GUT of Flavour in 8d
• Principal series of finite subgroups of SU(3)
• Discrete family symmetry, Higgs mediators and theta_{13}
• Solving the Flavour Problem in Supersymmetric Standard Models with Three Higgs Families
• On the finite subgroups of U(3) of order smaller than 512
• Measurable Neutrino Mass Scale in A4 x SU(5)
• SUSY SU(5) with singlet plus adjoint matter and A4 family symmetry
• Non-Abelian family symmetries in Pati-Salam unification
• Quark mixing sum rules and the right unitarity triangle
• The Double Cover of the Icosahedral Symmetry Group and Quark Mass Textures
• Neutrino Mixing and Leptonic CP Violation from $S_4$ Flavour and Generalised CP Symmetries
• Toward minimal renormalizable SUSY SU(5) Grand Unified Model with tribimaximal mixing from A4 Flavor symmetry
• Tri-Bimaximal Neutrino Mixing and the $T_{13}$ Flavor Symmetry
• On the Vanishing of the CP Asymmetry in Leptogenesis due to Form Dominance
• Family symmetries and alignment in multi-Higgs doublet models
• Large loop effects of extra SUSY Higgs doublets to CP violation in B^0 mixing
• A natural $S_4\times SO(10)$ model of flavour
• Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO
• Vacuum misalignment corrections to tri-bimaximal mixing and form dominance
• Implications of large CP Violation in B mixing for Supersymmetric Standard Models
• Order and Anarchy hand in hand in 5D SO(10)
• Renormalisation group improved leptogenesis in family symmetry models
• From Flavour to SUSY Flavour Models
• $\mathbf{SO}(10)\times {\mathbf{S}}_4$ Grand Unified Theory of Flavour and Leptogenesis
• Flavor Delta(54) in SU(5) SUSY Model
• A Built-in Horizontal Symmetry of $SO(10)$
• Neutrino Mass and Flavour Models
• Strong coupling, discrete symmetry and flavour
• Modular Invariant Models of Leptons at Level 7
• Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry
• (Z_2)^3 Symmetry of the Tripartite Model
• SUSY SU(5) $\times S_4$ GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large ${\theta }_{13}^{PMNS}$
• Combining Pati-Salam and Flavour Symmetries
• Neutrino Mass Models: Impact of non-zero reactor angle
• SO(10) unification with horizontal symmetry
• Flavor Symmetries in the Yukawa Sector of Non-Supersymmetric SO(10): Numerical Fits Using Renormalization Group Running
• Neutrino mass and grand unification of flavor
• Discrete Flavour Symmetries from the Heisenberg Group
• A realistic pattern of fermion masses from a five-dimensional SO(10) model