Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries

Abstract

In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus $\tau$ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to $S_3$, $A_4$, $S_4$, and $A_5$, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.

arXiv comment32 pages + appendices, 5 figures, 13 tables; comments and references added; matches version published in JHEP

References in corpus (76)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Non-Abelian Discrete Symmetries in Particle Physics
• Duality Anomaly Cancellation, Minimal String Unification and the Effective Low-Energy Lagrangian of 4-D Strings
• Neutrino Mass and Mixing: from Theory to Experiment
• Global constraints on absolute neutrino masses and their ordering
• Finite Modular Groups and Lepton Mixing
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Neutrino mixing from finite modular groups
• 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
• CP violation of quarks in $A_4$ modular invariance
• Modular $A_5$ Symmetry for Flavour Model Building
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Modular $S_4$ Models of Lepton Masses and Mixing
• 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
• Discrete Flavour Symmetries, Neutrino Mixing and Leptonic CP Violation
• Unification and Fermion Mass Structure
• 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
• Modular symmetry and non-Abelian discrete flavor symmetries in string compactification
• 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
• Modular forms of finite modular subgroups from magnetized D-brane models
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• 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
• Eclectic Flavor Groups
• Lessons from eclectic flavor symmetries
• Modular Flavor Symmetry on Magnetized Torus
• Modular Invariant Quark and Lepton Models in Double Covering of $S_4$ Modular Group
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Modular symmetry origin of texture zeros and quark lepton unification
• Type II seesaw models with modular $A_4$ symmetry
• Modular Invariant Models of Lepton Masses at Levels 4 and 5
• Lepton Flavor Mixing and CP Violation in the Minimal Type-(I+II) Seesaw Model with a Modular $A_4$ Symmetry
• Landscape of Modular Symmetric Flavor Models
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• Pieces of the Flavour Puzzle
• Modular invariant flavor model of ${\mathrm{A}}_4$ and hierarchical structures at nearby fixed points
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• $CP$ violation in modular invariant flavor models
• Lepton flavor model with modular $A_4$ symmetry in large volume limit
• The Minimal Seesaw Model with a Modular $S_4$ Symmetry
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• Automorphic Forms and Fermion Masses
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• A radiative seesaw model with three Higgs doublets in modular $A_4$ symmetry
• Testing Moduli and Flavon Dynamics with Neutrino Oscillations
• The eclectic flavor symmetry of the ${\mathbb{Z}}_2$ orbifold
• SUSY Breaking Constraints on Modular flavor $S_3$ Invariant $SU(5)$ GUT Model
• Modular symmetry anomaly in magnetic flux compactification
• Classification of discrete modular symmetries in Type IIB flux vacua
• Siegel modular flavor group and CP from string theory
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Dirac neutrino mass models with a modular $S_4^{}$ symmetry
• Fermion masses and mixing in modular A4 Symmetry
• Symmetries and stabilisers in modular invariant flavour models
• Adjoint SU(5) GUT model with Modular $S_4$ Symmetry
• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization
• Fitting the Quark and Lepton Masses in String Theories
• Leptonic Sum Rules from Flavour Models with Modular Symmetries
• Stable fermion mass matrices and the charged lepton contribution to neutrino mixing
• Can an unbroken flavour symmetry provide an approximate description of lepton masses and mixing?

Cited by in corpus (38)

• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• The first string-derived eclectic flavor model with realistic phenomenology
• Modular $S_4\times SU(5)$ GUT
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry at level 6 and a new route towards finite modular groups
• Modular symmetry in the SMEFT
• The symmetry approach to quark and lepton masses and mixing
• A minimal modular invariant neutrino model
• Fermion masses, critical behavior and universality
• Quark hierarchical structures in modular symmetric flavor models at level 6
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• A simplest modular $S_3$ model for leptons
• Quark mass hierarchies and CP violation in $A_4\times A_4\times A_4$ modular symmetric flavor models
• More about quark Yukawa textures from selection rules without group actions
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
• Littlest Modular Seesaw
• Minimal seesaw and leptogenesis with the smallest modular finite group
• Texture zeros of quark mass matrices at fixed point $\tau =\omega$ in modular flavor symmetry
• Modular flavor symmetry and vector-valued modular forms
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Finite modular axion and radiative moduli stabilization
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Neutrino Mass Sum Rules from Modular ${\mathcal{A}}_4$ Symmetry
• Moduli trapping mechanism in modular flavor symmetric models
• Linear seesaw model with a modular $S_4$ flavor symmetry
• Modular Invariant Slow Roll Inflation
• Testing Lepton Flavor Universality at the Electron-Ion Collider
• Systematic study of the $SU(3{)}_c\otimes SU(3{)}_L\otimes U(1{)}_X$ local gauge symmetry
• Modular-symmetry-protected seesaw
• Quark-lepton mass relations from modular flavor symmetry
• $SO(10)$ models with $A_4$ modular symmetry
• Fermion masses and mixings and $g-2$ muon anomaly in a $Q_6$ flavored 2HDM
• Quark and lepton flavor model with leptoquarks in a modular $A_4$ symmetry
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• Classification of Modular Symmetries in Type IIB Flux Landscape
• Modular Flavour Symmetries and Modulus Stabilisation