Modular invariance faces precision neutrino data

Criado, Juan Carlos; Feruglio, Ferruccio

doi:10.21468/SciPostPhys.5.5.042

SciPost Physics

Modular invariance faces precision neutrino data

Juan Carlos Criado, Ferruccio Feruglio

SciPost Phys. 5, 042 (2018) · published 1 November 2018

doi: 10.21468/SciPostPhys.5.5.042
pdf
Submissions/Reports

Abstract

We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or from the seesaw. The constraint provided by modular invariance is so strong that neutrino mass ratios, lepton mixing angles and Dirac/Majorana phases do not depend on any Lagrangian parameter. They only depend on the vacuum of the theory, parametrized in terms of a complex modulus and a real field. Thus eight measurable quantities are described by the three vacuum parameters, whose optimization provides an excellent fit to data for the Weinberg operator and a good fit for the seesaw case. Neutrino masses from the Weinberg operator (seesaw) have inverted (normal) ordering. Several sources of potential corrections, such as higher dimensional operators, renormalization group evolution and supersymmetry breaking effects, are carefully discussed and shown not to affect the predictions under reasonable conditions.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.5.5.042
TI  - Modular invariance faces precision neutrino data
PY  - 2018/11/01
UR  - https://scipost.org/SciPostPhys.5.5.042
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 5
IS  - 5
SP  - 042
A1  - Criado, Juan Carlos
AU  - Feruglio, Ferruccio
AB  - We analyze a modular invariant model of lepton masses, with neutrino masses originating either from the Weinberg operator or from the seesaw. The constraint provided by modular invariance is so strong that neutrino mass ratios, lepton mixing angles and Dirac/Majorana phases do not depend on any Lagrangian parameter. They only depend on the vacuum of the theory, parametrized in terms of a complex modulus and a real field. Thus eight measurable quantities are described by the three vacuum parameters, whose optimization provides an excellent fit to data for the Weinberg operator and a good fit for the seesaw case. Neutrino masses from the Weinberg operator (seesaw) have inverted (normal) ordering. Several sources of potential corrections, such as higher dimensional operators, renormalization group evolution and supersymmetry breaking effects, are carefully discussed and shown not to affect the predictions under reasonable conditions.
ER  -

@Article{10.21468/SciPostPhys.5.5.042,
	title={{Modular invariance faces precision neutrino data}},
	author={Juan Carlos Criado and Ferruccio Feruglio},
	journal={SciPost Phys.},
	volume={5},
	pages={042},
	year={2018},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.5.5.042},
	url={https://scipost.org/10.21468/SciPostPhys.5.5.042},
}

Cited by 165

Okada et al., Lepton mass matrix from double covering of A 4 modular flavor symmetry*
Chinese Phys. C 46, 123108 (2022) [Crossref]
King et al., Fermion mass hierarchies from modular symmetry
J. High Energ. Phys. 2020, 43 (2020) [Crossref]
Novichkov et al., Modular A5 symmetry for flavour model building
J. High Energ. Phys. 2019, 174 (2019) [Crossref]
Ishiguro et al., Landscape of modular symmetric flavor models
J. High Energ. Phys. 2021, 161 (2021) [Crossref]
Okada et al., Modular invariant flavor model of A4 and hierarchical structures at nearby fixed points
Phys. Rev. D 103, 015005 (2021) [Crossref]
Kobayashi et al., Modular forms of finite modular subgroups from magnetized D-brane models
Phys. Rev. D 99, 046001 (2019) [Crossref]
Kikuchi et al., Remark on modular weights in low-energy effective field theory from type II string theory
J. High Energ. Phys. 2023, 3 (2023) [Crossref]
Kariyazono et al., Modular symmetry anomaly in magnetic flux compactification
Phys. Rev. D 100, 045014 (2019) [Crossref]
Shiba Funai et al., Flavor moonshine
2020, 013B03 (2020) [Crossref]
Ishiguro et al., Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
Nuclear Physics B 973, 115598 115598 (2021) [Crossref]
Abe et al., Quark masses and CKM hierarchies from $$S_4'$$ modular flavor symmetry
Eur. Phys. J. C 83, 1140 (2023) [Crossref]
Gunji et al., Subcritical regime of hybrid inflation with modular A4 symmetry
J. High Energ. Phys. 2022, 2 (2022) [Crossref]
Petcov et al., A4 modular flavour model of quark mass hierarchies close to the fixed point τ = i∞
J. High Energ. Phys. 2023, 86 (2023) [Crossref]
King et al., Spontaneous breaking of SO(3) to finite family symmetries with supersymmetry — an A4 model
J. High Energ. Phys. 2018, 173 (2018) [Crossref]
King et al., Trimaximal TM1 mixing with two modular S4 groups
Phys. Rev. D 101, 015001 (2020) [Crossref]
Belfkir et al., Fermion Masses and Mixing in Pati–Salam Unification with S3 Modular Symmetry
2025, 033B05 (2025) [Crossref]
Abe et al., Loop Fayet-Iliopoulos terms in T2/Z2 models: Instability and moduli stabilization
Phys. Rev. D 102, 045005 (2020) [Crossref]
Kikuchi et al., Quark mass hierarchies and CP violation in A4 × A4 × A4 modular symmetric flavor models
J. High Energ. Phys. 2023, 134 (2023) [Crossref]
Okada et al., Modular S3 symmetric radiative seesaw model
Phys. Rev. D 100, 115037 (2019) [Crossref]
Okada et al., Spontaneous CP violation by modulus τ in A4 model of lepton flavors
J. High Energ. Phys. 2021, 10 (2021) [Crossref]
Wang et al., Explicit perturbations to the stabilizer τ = i of modular $$ {A}_5^{\prime } $$ symmetry and leptonic CP violation
J. High Energ. Phys. 2021, 93 (2021) [Crossref]
Kikuchi et al., Modular symmetry by orbifolding magnetized T2 × T2: realization of double cover of ΓN
J. High Energ. Phys. 2020, 101 (2020) [Crossref]
Nilles et al., Orbifolds from Sp(4,Z) and their modular symmetries
Nuclear Physics B 971, 115534 115534 (2021) [Crossref]
Baur et al., The first string-derived eclectic flavor model with realistic phenomenology
J. High Energ. Phys. 2022, 224 (2022) [Crossref]
Ding et al., Modular binary octahedral symmetry for flavor structure of Standard Model
J. High Energ. Phys. 2023, 83 (2023) [Crossref]
Chen et al., SU(5) GUTs with A4 modular symmetry
J. High Energ. Phys. 2021, 239 (2021) [Crossref]
Almumin et al., Metaplectic flavor symmetries from magnetized tori
J. High Energ. Phys. 2021, 78 (2021) [Crossref]
Liu et al., Half-integral weight modular forms and application to neutrino mass models
Phys. Rev. D 102, 115035 (2020) [Crossref]
Ohki et al., Modular flavor symmetry on a magnetized torus
Phys. Rev. D 102, 085008 (2020) [Crossref]
Kikuchi et al., Yukawa textures in modular symmetric vacuum of magnetized orbifold models
2022, 033B10 (2022) [Crossref]
Asaka et al., Modular A4 invariance and leptogenesis
J. High Energ. Phys. 2020, 144 (2020) [Crossref]
Nomura et al., SU(4)C × SU(2)L × U(1)R models with modular A4 symmetry
2023, 023B04 (2023) [Crossref]
Gerbino et al., Synergy between cosmological and laboratory searches in neutrino physics
Physics of the Dark Universe 42, 101333 101333 (2023) [Crossref]
Kobayashi et al., Radiative correction on moduli stabilization in modular flavor symmetric models
Phys. Rev. D 108, 115038 (2023) [Crossref]
Kikuchi et al., CP phase in modular flavor models and discrete Froggatt-Nielsen models
Phys. Rev. D 109, 115018 (2024) [Crossref]
Abe et al., Fermion hierarchies in SU(5) grand unification from $$ {\Gamma}_6^{\prime } $$ modular flavor symmetry
J. High Energ. Phys. 2023, 97 (2023) [Crossref]
Ganguly et al., Phenomenology of the flavor symmetric scoto-seesaw model with dark matter and TM1 mixing
Phys. Rev. D 110, 035012 (2024) [Crossref]
Ding et al., Non-holomorphic modular S4 lepton flavour models
J. High Energ. Phys. 2025, 191 (2025) [Crossref]
Ding et al., Automorphic forms and fermion masses
J. High Energ. Phys. 2021, 37 (2021) [Crossref]
Novichkov et al., Fermion mass hierarchies, large lepton mixing and residual modular symmetries
J. High Energ. Phys. 2021, 206 (2021) [Crossref]
Hoshiya et al., Classification of three-generation models by orbifolding magnetized T2 × T2
2021, 033B05 (2021) [Crossref]
Liu et al., Modular invariant quark and lepton models in double covering of S4 modular group
Phys. Rev. D 103, 056013 (2021) [Crossref]
Liu et al., Modular flavor symmetry and vector-valued modular forms
J. High Energ. Phys. 2022, 123 (2022) [Crossref]
Meloni et al., A simplest modular S3 model for leptons
J. High Energ. Phys. 2023, 43 (2023) [Crossref]
Kobayashi et al., Modular flavor models with positive modular weights: a new lepton model building
J. High Energ. Phys. 2024, 121 (2024) [Crossref]
Baur et al., A string theory of flavor and CP
Nuclear Physics B 947, 114737 114737 (2019) [Crossref]
Gunji et al., Subcritical hybrid inflation in a generalized superconformal model
Phys. Rev. D 104, 123545 (2021) [Crossref]
Wang et al., The minimal seesaw model with a modular S4 symmetry
J high energy phys 2020, 17 (2020) [Crossref]
Feruglio, Universal Predictions of Modular Invariant Flavor Models near the Self-Dual Point
Phys. Rev. Lett. 130, 101801 (2023) [Crossref]
Nagao et al., Modular A4 symmetry and light dark matter with gauged U(1)B−L
Physics of the Dark Universe 36, 101039 101039 (2022) [Crossref]
Ding et al., SO(10) models with A4 modular symmetry
J. High Energ. Phys. 2021, 7 (2021) [Crossref]
Tang et al., Flavour Symmetry Embedded - GLoBES (FaSE-GLoBES)
Computer Physics Communications 263, 107899 107899 (2021) [Crossref]
Chen et al., Modular invariant holomorphic observables
Physics Letters B 852, 138600 138600 (2024) [Crossref]
Kobayashi et al., A4 lepton flavor model and modulus stabilization from S4 modular symmetry
Phys. Rev. D 100, 115045 (2019) [Crossref]
Chowdhury et al., Moduli portal dark matter
Phys. Rev. D 99, 095028 (2019) [Crossref]
Petcov et al., $$A_4$$ modular flavour model of quark mass hierarchies close to the fixed point $$\tau = \omega $$
Eur. Phys. J. C 83, 579 (2023) [Crossref]
Okada et al., Modulus τ linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model
J. High Energ. Phys. 2021, 184 (2021) [Crossref]
Vien, Renormalizable standard model extension with S4 symmetry for neutrino mass and mixing
Can. J. Phys. 101, 106 (2023) [Crossref]
Penedo et al., Finite modular symmetries and the strong CP problem
J. High Energ. Phys. 2024, 172 (2024) [Crossref]
Zhang, A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix
Nuclear Physics B 952, 114935 114935 (2020) [Crossref]
Abe et al., Quark and lepton hierarchies from S4′ modular flavor symmetry
Physics Letters B 842, 137977 137977 (2023) [Crossref]
Feruglio, Fermion masses, critical behavior and universality
J. High Energ. Phys. 2023, 236 (2023) [Crossref]
Almumin et al., Neutrino Flavor Model Building and the Origins of Flavor and CP Violation
Universe 9, 512 (2023) [Crossref]
Ganguly et al., Common origin of θ13 and dark matter within the flavor symmetric scoto-seesaw framework
J. High Energ. Phys. 2022, 74 (2022) [Crossref]
Wang, Dirac neutrino mass models with a modular S4 symmetry
Nuclear Physics B 962, 115247 115247 (2021) [Crossref]
de Medeiros Varzielas et al., Two A5 modular symmetries for Golden Ratio 2 mixing
Nuclear Physics B 984, 115974 115974 (2022) [Crossref]
Kikuchi et al., Moduli trapping mechanism in modular flavor symmetric models
J. High Energ. Phys. 2023, 81 (2023) [Crossref]
Ding et al., Leptogenesis in SO(10) models with A4 modular symmetry
J. High Energ. Phys. 2022, 71 (2022) [Crossref]
Nomura et al., Texture zeros realization in a three-loop radiative neutrino mass model from modular A4 symmetry
Nuclear Physics B 1004, 116579 116579 (2024) [Crossref]
Novichkov et al., Double cover of modular S4 for flavour model building
Nuclear Physics B 963, 115301 115301 (2021) [Crossref]
Ding et al., Modular S4×SU(5) GUT
Phys. Rev. D 104, 055034 (2021) [Crossref]
Feruglio et al., Modular invariant dynamics and fermion mass hierarchies around τ = i
J. High Energ. Phys. 2021, 242 (2021) [Crossref]
Nilles et al., Lessons from eclectic flavor symmetries
Nuclear Physics B 957, 115098 115098 (2020) [Crossref]
Palavrić, Discrete leptonic flavor symmetries: UV mediators and phenomenology
Phys. Rev. D 110, 115025 (2024) [Crossref]
de Anda et al., SU(5) grand unified theory with A4 modular symmetry
Phys. Rev. D 101, 015028 (2020) [Crossref]
Charalampous et al., FlippedSU(5)with modularA4symmetry
Phys. Rev. D 104, 115015 (2021) [Crossref]
Nomura et al., Zee model in a modular $$A_4$$ symmetry
Eur. Phys. J. C 85, 134 (2025) [Crossref]
Tatsuishi, Modular $S_3$-invariant flavor model in SU(5) grand unified theory
2020, 053B05 (2020) [Crossref]
Kikuchi et al., Quark hierarchical structures in modular symmetric flavor models at level 6
Phys. Rev. D 107, 055014 (2023) [Crossref]
Ding et al., Texture-zero patterns of lepton mass matrices from modular symmetry
J. High Energ. Phys. 2023, 141 (2023) [Crossref]
Du et al., Flavor structures of quarks and leptons from flipped SU(5) GUT with A4 modular flavor symmetry
J. High Energ. Phys. 2023, 36 (2023) [Crossref]
Ding et al., Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing
J. High Energ. Phys. 2019, 30 (2019) [Crossref]
Criado et al., Modular invariant models of lepton masses at levels 4 and 5
J. High Energ. Phys. 2020, 1 (2020) [Crossref]
Kikuchi et al., Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
Phys. Rev. D 104, 065008 (2021) [Crossref]
de Medeiros Varzielas et al., Two A4 modular symmetries for Tri-Maximal 2 mixing
Nuclear Physics B 979, 115793 115793 (2022) [Crossref]
Feruglio et al., Lepton flavor symmetries
Rev. Mod. Phys. 93, 015007 (2021) [Crossref]
Chen et al., A note on the predictions of models with modular flavor symmetries
Physics Letters B 801, 135153 135153 (2020) [Crossref]
King et al., Modulus stabilization in the multiple-modulus framework
Phys. Rev. D 110, 076026 (2024) [Crossref]
Ding et al., Modular A4 symmetry models of neutrinos and charged leptons
J. High Energ. Phys. 2019, 74 (2019) [Crossref]
Ishiguro et al., Flux Landscape with enhanced symmetry not on SL(2, ℤ) elliptic points
J. High Energ. Phys. 2024, 99 (2024) [Crossref]
Ishiguro et al., Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries
J. High Energ. Phys. 2022, 20 (2022) [Crossref]
Nagao et al., Lepton sector in modular A4 and gauged U(1) symmetry
Nuclear Physics B 980, 115841 115841 (2022) [Crossref]
Kobayashi et al., Modular flavor symmetric models
Int. J. Mod. Phys. A 39, 2441012 (2024) [Crossref]
Petcov et al., $$A_4$$ modular invariance and the strong CP problem
Eur. Phys. J. C 84, 914 (2024) [Crossref]
Yao et al., Fermion masses and mixing from the double cover and metaplectic cover of the A5 modular group
Phys. Rev. D 103, 095013 (2021) [Crossref]
Novichkov et al., Modular S4 models of lepton masses and mixing
J. High Energ. Phys. 2019, 5 (2019) [Crossref]
Baur et al., Unification of flavor, CP, and modular symmetries
Physics Letters B 795, 7 (2019) [Crossref]
Tanimoto et al., Electron EDM arising from modulus τ in the supersymmetric modular invariant flavor models
J. High Energ. Phys. 2021, 183 (2021) [Crossref]
Chen et al., Quasi–eclectic modular flavor symmetries
Physics Letters B 824, 136843 136843 (2022) [Crossref]
Kobayashi et al., Classification of discrete modular symmetries in type IIB flux vacua
Phys. Rev. D 101, 106017 (2020) [Crossref]
Petcov, On the normalisation of the modular forms in modular invariant theories of flavour
Physics Letters B 850, 138540 138540 (2024) [Crossref]
King et al., Twin modular S4 with SU(5) GUT
J. High Energ. Phys. 2021, 291 (2021) [Crossref]
Kikuchi et al., 4D modular flavor symmetric models inspired by a higher-dimensional theory
Phys. Rev. D 106, 035001 (2022) [Crossref]
Kobayashi et al., Type II seesaw models with modular A4 symmetry
Phys. Rev. D 102, 035019 (2020) [Crossref]
Wang et al., Double covering of the modular A5 group and lepton flavor mixing in the minimal seesaw model
Phys. Rev. D 103, 076005 (2021) [Crossref]
Kikuchi et al., Mass matrices with CP phase in modular flavor symmetry
2022, 113B07 (2022) [Crossref]
Asaka et al., Lepton flavor model with modular A4 symmetry in large volume limit
Physics Letters B 811, 135956 135956 (2020) [Crossref]
de Medeiros Varzielas et al., Quarks at the modular S4 cusp
J. High Energ. Phys. 2023, 196 (2023) [Crossref]
Ahn et al., Confronting the prediction of leptonic Dirac CP -violating phase with experiments
Phys. Rev. D 106, 095002 (2022) [Crossref]
de Medeiros Varzielas et al., Symmetries and stabilisers in modular invariant flavour models
J. High Energ. Phys. 2020, 85 (2020) [Crossref]
Kikuchi et al., Modular symmetry in magnetized T2g torus and orbifold models
Phys. Rev. D 109, 065011 (2024) [Crossref]
Kobayashi et al., Lepton flavor violation, lepton (g − 2)μ, e and electron EDM in the modular symmetry
J. High Energ. Phys. 2022, 13 (2022) [Crossref]
Tanimoto, Fermion mass hierarchy in modular flavor symmetry
Mod. Phys. Lett. A 39, 2430008 (2024) [Crossref]
Kuranaga et al., Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism
J. High Energ. Phys. 2021, 68 (2021) [Crossref]
Lu et al., Modular symmetry origin of texture zeros and quark-lepton unification
Phys. Rev. D 101, 115020 (2020) [Crossref]
Knapp-Pérez et al., Matter matters in moduli fixing and modular flavor symmetries
Physics Letters B 844, 138106 138106 (2023) [Crossref]
Kobayashi et al., Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
Phys. Rev. D 102, 026004 (2020) [Crossref]
Argüelles et al., Measuring Oscillations with a Million Atmospheric Neutrinos
Phys. Rev. X 13, 041055 (2023) [Crossref]
Hutauruk et al., Muon g−2, dark matter, and neutrino mass explanations in a modular A4 symmetry
Physics of the Dark Universe 44, 101440 101440 (2024) [Crossref]
Hoshiya et al., Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models
2022, 013B04 (2022) [Crossref]
Kikuchi et al., Revisiting modular symmetry in magnetized torus and orbifold compactifications
Phys. Rev. D 102, 105010 (2020) [Crossref]
Nomura et al., A linear seesaw model with A 4-modular flavor and local U(1) B-L symmetries
J. Cosmol. Astropart. Phys. 2022, 049 (2022) [Crossref]
Kikuchi et al., Modular symmetry of soft supersymmetry breaking terms
2022, 123B02 (2022) [Crossref]
Okada et al., Towards unification of quark and lepton flavors in $$A_4$$ modular invariance
Eur. Phys. J. C 81, 52 (2021) [Crossref]
Novichkov et al., Modular flavour symmetries and modulus stabilisation
J. High Energ. Phys. 2022, 149 (2022) [Crossref]
Kobayashi et al., CP violation in modular invariant flavor models
Phys. Rev. D 101, 055046 (2020) [Crossref]
Nilles et al., Eclectic flavor groups
J. High Energ. Phys. 2020, 45 (2020) [Crossref]
Yao et al., Modular invariant A4 models for quarks and leptons with generalized CP symmetry
J. High Energ. Phys. 2021, 102 (2021) [Crossref]
de Medeiros Varzielas et al., Multiple modular symmetries as the origin of flavor
Phys. Rev. D 101, 055033 (2020) [Crossref]
Kikuchi et al., Modular symmetry anomaly and nonperturbative neutrino mass terms in magnetized orbifold models
Phys. Rev. D 105, 116002 (2022) [Crossref]
Kikuchi et al., Texture zeros of quark mass matrices at fixed point $$\tau =\omega $$ in modular flavor symmetry
Eur. Phys. J. C 83, 591 (2023) [Crossref]
Nomura et al., Leptonic dipole operator with $$\Gamma _2$$ modular invariance in light of Muon $$(g-2)_\mu $$
Eur. Phys. J. C 84, 1329 (2024) [Crossref]
Kashav et al., Residual flavor symmetries at the modular self-dual point and constraints on neutrino masses and mixing
Phys. Rev. D 111, 015010 (2025) [Crossref]
Ding et al., Universal predictions of Siegel modular invariant theories near the fixed points
J. High Energ. Phys. 2024, 52 (2024) [Crossref]
Novichkov et al., S 4 modular symmetry, seesaw mechanism and lepton masses and mixing
J. Phys.: Conf. Ser. 1586, 012020 (2020) [Crossref]
Tanimoto,
292, 99 (2023) [Crossref]
Du et al., SUSY breaking constraints on modular flavor S3 invariant SU(5) GUT model
J. High Energ. Phys. 2021, 221 (2021) [Crossref]
Zhao et al., Adjoint SU(5) GUT model with modular S4 symmetry
J. High Energ. Phys. 2021, 2 (2021) [Crossref]
Nomura et al., Linear seesaw model with a modular S 4 flavor symmetry *
Chinese Phys. C 46, 053101 (2022) [Crossref]
Kobayashi et al., New A4 lepton flavor model from S4 modular symmetry
J. High Energ. Phys. 2020, 97 (2020) [Crossref]
Ding et al., A minimal modular invariant neutrino model
J. High Energ. Phys. 2023, 125 (2023) [Crossref]
Kobayashi et al., Modular A4 invariance and neutrino mixing
J. High Energ. Phys. 2018, 196 (2018) [Crossref]
Marciano et al., Minimal seesaw and leptogenesis with the smallest modular finite group
J. High Energ. Phys. 2024, 20 (2024) [Crossref]
Wang, Lepton flavor mixing and CP violation in the minimal type-(I+II) seesaw model with a modular A4 symmetry
Nuclear Physics B 957, 115105 115105 (2020) [Crossref]
Ding et al., Modular invariant models of leptons at level 7
J. High Energ. Phys. 2020, 164 (2020) [Crossref]
Dev et al., Neutrino non-standard interactions: A status report
SciPost Phys. Proc., 001 (2019) [Crossref]
Baur et al., Top-down anatomy of flavor symmetry breakdown
Phys. Rev. D 105, 055018 (2022) [Crossref]
Qu et al., Flavor mixing and CP violation from the interplay of an S4 modular group and a generalized CP symmetry
Phys. Rev. D 104, 076001 (2021) [Crossref]
Zhang et al., Revisiting Trimaximal TM2 mixing in two A4 modular symmetries
Int. J. Mod. Phys. A 39, 2450027 (2024) [Crossref]
Liu et al., Neutrino masses and mixing from double covering of finite modular groups
J. High Energ. Phys. 2019, 134 (2019) [Crossref]
Higaki et al., Spontaneous CP violation and partially broken modular flavor symmetries
J. High Energ. Phys. 2024, 24 (2024) [Crossref]
Athar et al., Status and perspectives of neutrino physics
Progress in Particle and Nuclear Physics 124, 103947 103947 (2022) [Crossref]
Kobayashi et al.,
995, 251 (2022) [Crossref]
Kobayashi et al., Dark matter stability at fixed points in a modular A4 symmetry
Physics of the Dark Universe 37, 101080 101080 (2022) [Crossref]
Kobayashi et al., Modular symmetry in the SMEFT
Phys. Rev. D 105, 055022 (2022) [Crossref]
Kang et al., Natural mass hierarchy among three heavy Majorana neutrinos for resonant leptogenesis under modular A4 symmetry
J. High Energ. Phys. 2022, 50 (2022) [Crossref]
Hoshiya et al., Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points
Phys. Rev. D 106, 115003 (2022) [Crossref]
Baur et al., Modular flavored dark matter
J. High Energ. Phys. 2024, 91 (2024) [Crossref]
Li et al., Modular symmetry at level 6 and a new route towards finite modular groups
J. High Energ. Phys. 2021, 238 (2021) [Crossref]
Baur et al., Completing the eclectic flavor scheme of the ℤ2 orbifold
J. High Energ. Phys. 2021, 110 (2021) [Crossref]
Nomura et al., Quark and lepton flavor model with leptoquarks in a modular $$A_4$$ symmetry
Eur. Phys. J. C 81, 947 (2021) [Crossref]
Orikasa et al., Dark Matter Stability at Fixed Points in a Modular A4 Symmetry
SSRN Journal, (2022) [Crossref]
Ding et al., Neutrino mass and mixing with A5 modular symmetry
Phys. Rev. D 100, 115005 (2019) [Crossref]
Novichkov et al., Generalised CP symmetry in modular-invariant models of flavour
J. High Energ. Phys. 2019, 165 (2019) [Crossref]
Okada et al., Quark and lepton flavors with common modulus τ in A4 modular symmetry
Physics of the Dark Universe 40, 101204 101204 (2023) [Crossref]

Ontology / Topics

See full Ontology or Topics database.

Modular invariance Weinberg operator

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ Juan Carlos Criado,
² ³ Ferruccio Feruglio

Funders for the research work leading to this publication

Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía (through Organization: Consejería de Economía Innovación Ciencia y Empleo)
Horizon 2020 (through Organization: European Commission [EC])
Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])
Ministerio de Educación y Cultura - Spain (MEC) (through Organization: Ministerio de Educación y Cultura - España / Ministry of Education and Culture - Spain [MEC Spain])
Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])