Towards a complete $\Delta (27)\times SO(10)$ SUSY GUT

Abstract

We propose a renormalisable model based on $\Delta (27)$ family symmetry with an $SO(10)$ grand unified theory (GUT) leading to a novel form of spontaneous geometrical CP violation. The symmetries, including $\Delta (27)$ and ${\mathbb{Z}}_9\times {\mathbb{Z}}_{12}\times {\mathbb{Z}}_4^R$, are broken close to the GUT breaking scale to yield the minimal supersymmetric standard model (MSSM) with the standard R-parity. $SO(10)$ is broken via $SU(5)$ with doublet-triplet splitting achieved by a version of the Dimopoulos-Wilczek (missing VEV) mechanism. Low-scale Yukawa structure is dictated by the coupling of matter to $\Delta (27)$ antitriplets $\bar{\varphi }$ whose VEVs are aligned in the CSD3 directions by the superpotential. Light physical Majorana neutrinos masses emerge from a specific implementation of the seesaw mechanism within $SO(10)$. The model predicts a normal neutrino mass hierarchy with the best-fit lightest neutrino mass $m_1=0.13$ meV and the PMNS mixing parameters ${\theta }_{13}^l\approx 8.35^{\circ }$, ${\theta }_{12}^l\approx 34^{\circ }$, ${\theta }_{23}^l\approx 43^{\circ }$ and an oscillation phase ${\delta }^l\approx -90^{\circ }$.

32 pages, 22 figures. v3: revised alignment and fit discussion, typos corrected

References in corpus (18)

• Updated fit to three neutrino mixing: status of leptonic CP violation
• Neutrino tri-bi-maximal mixing from a non-Abelian discrete family symmetry
• Discrete R symmetries for the MSSM and its singlet extensions
• Towards a complete $A_4\times SU(5)$ SUSY GUT
• New GUT predictions for quark and lepton mass ratios confronted with phenomenology
• Towards a Complete Theory of Fermion Masses and Mixings with SO(3) Family Symmetry and 5d SO(10) Unification
• An SO(10)XS4 Model of Quark-Lepton Complementarity
• A SUSY SU(5)xT' Unified Model of Flavour with large θ_{13}
• Neutrino masses and tribimaximal mixing in the minimal renormalizable supersymmetric SU(5) grand unified model with A4 flavor symmetry
• Towards predictive flavour models in SUSY SU(5) GUTs with doublet-triplet splitting
• Measurable Neutrino Mass Scale in A4 x SU(5)
• Tri-bi-maximal mixing in viable family symmetry unified model with extended seesaw
• Yukawa Unification Predictions for the LHC
• Symmetries of symmetries and geometrical CP violation
• Geometrical CP violation in the N-Higgs-doublet model
• A to Z of Flavour with Pati-Salam
• Large lepton mixing angles from a 4+1-dimensional SU(5) x A(4) domain-wall braneworld model
• Neutrino tri-bi-maximal mixing through sequential dominance

Cited by in corpus (34)

• Unified Models of Neutrinos, Flavour and CP Violation
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Flavourful Axion Phenomenology
• Littlest Seesaw
• A variant of 3-3-1 model for the generation of the SM fermion mass and mixing pattern
• Accidental Peccei-Quinn Symmetry from Discrete Flavour Symmetry and Pati-Salam
• Fermion Masses and Mixings and Dark Matter Constraints in a Model with Radiative Seesaw Mechanism
• A highly predictive $A_4$ flavour 3-3-1 model with radiative inverse seesaw mechanism
• The first $\Delta (27)$ flavor 3-3-1 model with low scale seesaw mechanism
• A 3-3-1 model with low scale seesaw mechanisms
• Neutrino predictions from a left-right symmetric flavored extension of the standard model
• Radiative Seesaw-type Mechanism of Fermion Masses and Non-trivial Quark Mixing
• CP-odd invariants for multi-Higgs models: applications with discrete symmetry
• Littlest Inverse Seesaw Model
• $\Delta (27)$ framework for cobimaximal neutrino mixing models
• Lepton Mixing Predictions from $S_4$ in the Tri-Direct CP approach to Two Right-handed Neutrino Models
• Flavored Non-Minimal Left-Right Symmetric Model Fermion Masses and Mixings
• $\Delta \left(27\right)$ flavor singlet-triplet Higgs model for fermion masses and mixings
• Controlled flavor violation in the MSSM from a unified $\Delta (27)$ flavor symmetry
• Golden Littlest Seesaw
• Muon anomalies and the $SU(5)$ Yukawa relations
• Controlled fermion mixing and FCNCs in a $\Delta (27)$ 3+1 Higgs Doublet Model
• Effective alignments as building blocks of flavour models
• Effective alignments and the landscape of $S_4$ flavour models
• Exceptional Unification of Families and Forces
• SO(10) models with flavour symmetries: Classification and examples
• Leptogenesis in $\Delta (27)$ with a Universal Texture Zero
• 3HDM with $\Delta (27)$ symmetry and its phenomenological consequences
• Implications of the Muon g-2 result on the flavour structure of the lepton mass matrix
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• Sculpting the Standard Model from low-scale Gauge-Higgs-Matter $E_8$ Grand Unification in ten dimensions
• Revisiting the Universal Texture Zero of Flavour: a Markov Chain Monte Carlo Analysis
• Predictive linear seesaw model with $\Delta \left(27\right)$ family symmetry
• Flavon alignments from orbifolding: $SU(5)\times SU(3)$ model with ${\mathbb{T}}^6/\Delta (54)$