Modular $S_4\times SU(5)$ GUT

Abstract

Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton field to account for charged fermion mass hierarchies rather than a Froggatt-Nielsen mechanism. Such an approach can be applied to flavoured Grand Unified Theories (GUTs) which can be greatly simplified using modular forms. As an example, we consider a modular version of a previously proposed $S_4\times SU(5)$ GUT, with Gatto-Sartori-Tonin and Georgi-Jarlskog relations, in which all flavons and driving fields are removed, with their effect replaced by modular forms with moduli assumed to be at various fixed points, rendering the theory much simpler. In the neutrino sector there are two right-handed neutrinos constituting a Littlest Seesaw model satisfying Constrained Sequential Dominance (CSD) where the two columns of the Dirac neutrino mass matrix are proportional to $(0,1,-1)$ and $(1,n,2-n)$ respectively, and $n=1+\sqrt{6}\approx 3.45$ is prescribed by the modular symmetry, with predictions subject to charged lepton mixing corrections. We perform a numerical analysis, showing quark and lepton mass and mixing correlations around the best fit points.

arXiv comment31 pages, 3 figures

References in corpus (85)

• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Neutrino Mass and Mixing with Discrete Symmetry
• Cosmological Sign of Neutrino CP Violation
• The Soft Supersymmetry-Breaking Lagrangian: Theory and Applications
• Neutrino Mass and Mixing: from Theory to Experiment
• Large Mixing Angle MSW and Atmospheric Neutrinos from Single Right-Handed Neutrino Dominance and U(1) Family Symmetry
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification
• Unified Models of Neutrinos, Flavour and CP Violation
• Neutrino mixing from finite modular groups
• Running quark and lepton parameters at various scales
• Unification of Flavor, CP, and Modular Symmetries
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular Invariance Faces Precision Neutrino Data
• Modular $A_4$ invariance and neutrino mixing
• Modular $A_5$ Symmetry for Flavour Model Building
• CP violation of quarks in $A_4$ modular invariance
• Modular $S_4$ Models of Lepton Masses and Mixing
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing
• Neutrino Mass and Mixing with $A_5$ Modular Symmetry
• Trimaximal mixing with predicted θ_13 from a new type of constrained sequential dominance
• A String Theory of Flavor and CP
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Double Cover of Modular $S_4$ for Flavour Model Building
• A note on the predictions of models with modular flavor symmetries
• Modular $A_4$ Symmetry Models of Neutrinos and Charged Leptons
• Trimaximal TM${}_1$ mixing with two modular $S_4$ groups
• A modular $A_4$ symmetry realization of two-zero textures of the Majorana neutrino mass matrix
• Multiple modular symmetries as the origin of flavour
• A modular $A_4$ symmetric model of dark matter and neutrino
• Modular $S_3$ symmetric radiative seesaw model
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• A SUSY GUT of Flavour with S4 x SU(5) to NLO
• Modular $A_4$ invariance and leptogenesis
• A modular $A_4$ symmetric scotogenic model
• $A_4$ lepton flavor model and modulus stabilization from $S_4$ modular symmetry
• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Eclectic Flavor Groups
• Lessons from eclectic flavor symmetries
• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
• Modular $S_3$ invariant flavor model in SU(5) GUT
• Modular symmetry origin of texture zeros and quark lepton unification
• Type II seesaw models with modular $A_4$ symmetry
• Lepton Flavor Mixing and CP Violation in the Minimal Type-(I+II) Seesaw Model with a Modular $A_4$ Symmetry
• Modular Invariant Models of Lepton Masses at Levels 4 and 5
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• The Minimal Seesaw Model with a Modular $S_4$ Symmetry
• Lepton flavor model with modular $A_4$ symmetry in large volume limit
• Automorphic Forms and Fermion Masses
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• Minimal see-saw model predicting best fit lepton mixing angles
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• Half-integral weight modular forms and application to neutrino mass models
• Littlest Seesaw
• $SU(5)$ GUTs with $A_4$ modular symmetry
• Twin Modular $S_4$ with $SU(5)$ GUT
• CP Symmetry and Symplectic Modular Invariance
• Testing Moduli and Flavon Dynamics with Neutrino Oscillations
• A model of quark and lepton mixing
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Dirac neutrino mass models with a modular $S_4^{}$ symmetry
• SUSY S4 x SU(5) revisited
• A two loop induced neutrino mass model with modular $A_4$ symmetry
• Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry
• Precision neutrino experiments vs the Littlest Seesaw
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• A radiative seesaw model in modular $A_4$ symmetry
• Fitting high-energy Littlest Seesaw parameters using low-energy neutrino data and leptogenesis
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
• A to Z of Flavour with Pati-Salam
• An Inverse Seesaw model with $A_4$-modular symmetry
• A linear seesaw model with $A_4$-modular flavor and local $U(1{)}_{B-L}$ symmetries
• Littlest Seesaw model from S4 x U(1)
• Phenomenological Implications of an SU(5) x S4 x U(1) SUSY GUT of Flavour
• Lepton Mixing Predictions from $S_4$ in the Tri-Direct CP approach to Two Right-handed Neutrino Models
• Approaching Minimal Flavour Violation from an SU(5) x S4 x U(1) SUSY GUT
• A New Littlest Seesaw Model
• Tri-Direct CP in the Littlest Seesaw Playground

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• The first string-derived eclectic flavor model with realistic phenomenology
• Modular symmetry at level 6 and a new route towards finite modular groups
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• Flipped SU(5) with modular $A_4$ symmetry
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
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• 4D modular flavor symmetric models inspired by higher dimensional theory
• Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT
• Neutrino mixing sum rules and the Littlest Seesaw
• Further study of the maximally symmetry breaking patterns in an $\mathrm{SU}(8)$ theory
• Orbifold Modular GUT of Flavour
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• $SO(10)$ models with $A_4$ modular symmetry