Modular Invariant Models of Leptons at Level 7

Abstract

We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group ${\Gamma }_7$, which is isomorphic to $PSL(2,Z_7)$, the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as $PS{L}_2(7)$ or $\Sigma (168)$. At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of ${\Gamma }_7$. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on ${\Gamma }_7$ are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.

arXiv comment45 pages, 3 figures

References in corpus (34)

• Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of theta_23, delta_CP, and the mass ordering
• An improved upper limit on the neutrino mass from a direct kinematic method by KATRIN
• Limit on Neutrinoless ββ Decay of Xe-136 from the First Phase of KamLAND-Zen and Comparison with the Positive Claim in Ge-76
• 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 $A_4$ invariance and neutrino mixing
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• CP violation of quarks in $A_4$ modular invariance
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Neutrino Mass and Mixing with $A_5$ Modular Symmetry
• A String Theory of Flavor and CP
• A note on the predictions of models with modular flavor symmetries
• 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
• Modular forms of finite modular subgroups from magnetized D-brane models
• Modular $S_3$ symmetric radiative seesaw model
• New $A_4$ lepton flavor model from $S_4$ modular symmetry
• Modular symmetry origin of texture zeros and quark lepton unification
• Simple Finite Non-Abelian Flavor Groups
• A new family symmetry for SO(10) GUTs
• A Supersymmetric Grand Unified Theory of Flavour with PSL(2,7) x SO(10)
• Theta vocabulary I
• CP violation and modular symmetries
• Classification of discrete modular symmetries in Type IIB flux vacua
• Towards unification of quark and lepton flavors in $A_4$ modular invariance
• Spontaneous breaking of CP symmetry by orbifold moduli
• A two loop induced neutrino mass model with modular $A_4$ symmetry
• Systematic analysis of finite family symmetry groups and their application to the lepton sector

Cited by in corpus (5)

• Double Cover of Modular $S_4$ for Flavour Model Building
• Modular symmetry in the SMEFT
• Quark and lepton flavors with common modulus $\tau$ in $A_4$ modular symmetry
• Flipped SU(5) with modular $A_4$ symmetry
• Modular Origin of Mass Hierarchy: Froggatt-Nielsen like Mechanism