Abstract
We study the lepton flavor violation (LFV), the leptonic magnetic moments (g − 2)μ, e and the electric dipole moment (EDM) of the electron in the Standard-Model Effective Field Theory with the ΓN modular flavor symmetry. We employ the stringy Ansatz on coupling structure that 4-point couplings of matter fields are written by a product of 3-point couplings of matter fields. We take the level 3 finite modular group, Γ3 for the flavor symmetry, and discuss the dipole operators at nearby fixed point τ = i, where observed lepton masses and mixing angles are well reproduced. Suppose the anomaly of the anomalous magnetic moment of the muon to be evidence of the new physics (NP), we have related it with (g − 2)e, LFV decays, and the electron EDM. It is found that the NP contribution to (g − 2)e is proportional to the lepton masses squared likewise the naive scaling. We also discuss the correlations among the LFV processes μ → eγ, τ → μγ and τ → eγ, which are testable in the future. The electron EDM requires the tiny imaginary part of the relevant Wilson coefficient in the basis of real positive charged lepton masses, which is related to the μ → eγ transition in our framework.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Muon g-2 collaboration, Measurement of the positive muon anomalous magnetic moment to 0.46 ppm, Phys. Rev. Lett. 126 (2021) 141801 [arXiv:2104.03281] [INSPIRE].
Muon g-2 collaboration, Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73 (2006) 072003 [hep-ex/0602035] [INSPIRE].
T. Aoyama et al., The anomalous magnetic moment of the muon in the Standard Model, Phys. Rept. 887 (2020) 1 [arXiv:2006.04822] [INSPIRE].
F. Jegerlehner ed., The anomalous magnetic moment of the muon, Springer Tracts Mod. Phys. 274 (2017) 1.
G. Colangelo, M. Hoferichter and P. Stoffer, Two-pion contribution to hadronic vacuum polarization, JHEP 02 (2019) 006 [arXiv:1810.00007] [INSPIRE].
M. Hoferichter, B.-L. Hoid and B. Kubis, Three-pion contribution to hadronic vacuum polarization, JHEP 08 (2019) 137 [arXiv:1907.01556] [INSPIRE].
M. Davier, A. Hoecker, B. Malaescu and Z. Zhang, A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to α(\( {m}_Z^2 \)), Eur. Phys. J. C 80 (2020) 241 [Erratum ibid. 80 (2020) 410] [arXiv:1908.00921] [INSPIRE].
A. Keshavarzi, D. Nomura and T. Teubner, g − 2 of charged leptons, α(\( {M}_Z^2 \)), and the hyperfine splitting of muonium, Phys. Rev. D 101 (2020) 014029 [arXiv:1911.00367] [INSPIRE].
B.-L. Hoid, M. Hoferichter and B. Kubis, Hadronic vacuum polarization and vector-meson resonance parameters from e+e− → π0γ, Eur. Phys. J. C 80 (2020) 988 [arXiv:2007.12696] [INSPIRE].
A. Czarnecki, W.J. Marciano and A. Vainshtein, Refinements in electroweak contributions to the muon anomalous magnetic moment, Phys. Rev. D 67 (2003) 073006 [Erratum ibid. 73 (2006) 119901] [hep-ph/0212229] [INSPIRE].
K. Melnikov and A. Vainshtein, Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited, Phys. Rev. D 70 (2004) 113006 [hep-ph/0312226] [INSPIRE].
T. Aoyama, M. Hayakawa, T. Kinoshita and M. Nio, Complete tenth-order QED contribution to the muon g − 2, Phys. Rev. Lett. 109 (2012) 111808 [arXiv:1205.5370] [INSPIRE].
C. Gnendiger, D. Stöckinger and H. Stöckinger-Kim, The electroweak contributions to (g − 2)μ after the Higgs boson mass measurement, Phys. Rev. D 88 (2013) 053005 [arXiv:1306.5546] [INSPIRE].
S. Borsányi et al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature 593 (2021) 51 [arXiv:2002.12347] [INSPIRE].
G. Panico, A. Pomarol and M. Riembau, EFT approach to the electron electric dipole moment at the two-loop level, JHEP 04 (2019) 090 [arXiv:1810.09413] [INSPIRE].
J. Aebischer, W. Dekens, E.E. Jenkins, A.V. Manohar, D. Sengupta and P. Stoffer, Effective field theory interpretation of lepton magnetic and electric dipole moments, JHEP 07 (2021) 107 [arXiv:2102.08954] [INSPIRE].
L. Allwicher, P. Arnan, D. Barducci and M. Nardecchia, Perturbative unitarity constraints on generic Yukawa interactions, JHEP 10 (2021) 129 [arXiv:2108.00013] [INSPIRE].
J. Kley, T. Theil, E. Venturini and A. Weiler, Electric dipole moments at one-loop in the dimension-6 SMEFT, arXiv:2109.15085 [INSPIRE].
G. Isidori, J. Pagès and F. Wilsch, Flavour alignment of new physics in light of the (g − 2)μ anomaly, JHEP 03 (2022) 011 [arXiv:2111.13724] [INSPIRE].
W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators. Part III. Gauge coupling dependence and phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].
D.A. Faroughy, G. Isidori, F. Wilsch and K. Yamamoto, Flavour symmetries in the SMEFT, JHEP 08 (2020) 166 [arXiv:2005.05366] [INSPIRE].
R. Barbieri, G. Isidori, J. Jones-Perez, P. Lodone and D.M. Straub, U(2) and minimal flavour violation in supersymmetry, Eur. Phys. J. C 71 (2011) 1725 [arXiv:1105.2296] [INSPIRE].
R. Barbieri, D. Buttazzo, F. Sala and D.M. Straub, Flavour physics from an approximate U(2)3 symmetry, JHEP 07 (2012) 181 [arXiv:1203.4218] [INSPIRE].
G. Blankenburg, G. Isidori and J. Jones-Perez, Neutrino masses and LFV from minimal breaking of U(3)5 and U(2)5 flavor symmetries, Eur. Phys. J. C 72 (2012) 2126 [arXiv:1204.0688] [INSPIRE].
R.S. Chivukula and H. Georgi, Composite technicolor Standard Model, Phys. Lett. B 188 (1987) 99 [INSPIRE].
G. D’Ambrosio, G.F. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].
T. Kobayashi and H. Otsuka, On stringy origin of minimal flavor violation, Eur. Phys. J. C 82 (2022) 25 [arXiv:2108.02700] [INSPIRE].
T. Kobayashi, H. Otsuka, M. Tanimoto and K. Yamamoto, Modular symmetry in the SMEFT, Phys. Rev. D 105 (2022) 055022 [arXiv:2112.00493] [INSPIRE].
R. de Adelhart Toorop, F. Feruglio and C. Hagedorn, Finite modular groups and lepton mixing, Nucl. Phys. B 858 (2012) 437 [arXiv:1112.1340] [INSPIRE].
F. Feruglio, Are neutrino masses modular forms?, in From my vast repertoire. . . : Guido Altarelli’s legacy, A. Levy, S. Forte and G. Ridolfi eds., World Scientific, Singapore (2019), p. 227 [arXiv:1706.08749] [INSPIRE].
T. Kobayashi, K. Tanaka and T.H. Tatsuishi, Neutrino mixing from finite modular groups, Phys. Rev. D 98 (2018) 016004 [arXiv:1803.10391] [INSPIRE].
J.T. Penedo and S.T. Petcov, Lepton masses and mixing from modular S4 symmetry, Nucl. Phys. B 939 (2019) 292 [arXiv:1806.11040] [INSPIRE].
P.P. Novichkov, J.T. Penedo, S.T. Petcov and A.V. Titov, Modular A5 symmetry for flavour model building, JHEP 04 (2019) 174 [arXiv:1812.02158] [INSPIRE].
G.-J. Ding, S.F. King and X.-G. Liu, Neutrino mass and mixing with A5 modular symmetry, Phys. Rev. D 100 (2019) 115005 [arXiv:1903.12588] [INSPIRE].
T. Kobayashi and S. Tamba, Modular forms of finite modular subgroups from magnetized D-brane models, Phys. Rev. D 99 (2019) 046001 [arXiv:1811.11384] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl. 183 (2010) 1 [arXiv:1003.3552] [INSPIRE].
H. Ishimori, T. Kobayashi, H. Ohki, H. Okada, Y. Shimizu and M. Tanimoto, An introduction to non-Abelian discrete symmetries for particle physicists, Lect. Notes Phys. 858 (2012) 1 [INSPIRE].
T. Kobayashi, H. Ohki, H. Okada, Y. Shimizu and M. Tanimoto, An introduction to non-Abelian discrete symmetries for particle physicists, Lect. Notes Phys. 995 (2022) 1.
D. Hernandez and A.Y. Smirnov, Lepton mixing and discrete symmetries, Phys. Rev. D 86 (2012) 053014 [arXiv:1204.0445] [INSPIRE].
S.F. King and C. Luhn, Neutrino mass and mixing with discrete symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino mass and mixing: from theory to experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
M. Tanimoto, Neutrinos and flavor symmetries, AIP Conf. Proc. 1666 (2015) 120002 [INSPIRE].
S.F. King, Unified models of neutrinos, flavour and CP-violation, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413] [INSPIRE].
S.T. Petcov, Discrete flavour symmetries, neutrino mixing and leptonic CP-violation, Eur. Phys. J. C 78 (2018) 709 [arXiv:1711.10806] [INSPIRE].
F. Feruglio and A. Romanino, Lepton flavor symmetries, Rev. Mod. Phys. 93 (2021) 015007 [arXiv:1912.06028] [INSPIRE].
J.C. Criado and F. Feruglio, Modular invariance faces precision neutrino data, SciPost Phys. 5 (2018) 042 [arXiv:1807.01125] [INSPIRE].
T. Kobayashi, N. Omoto, Y. Shimizu, K. Takagi, M. Tanimoto and T.H. Tatsuishi, Modular A4 invariance and neutrino mixing, JHEP 11 (2018) 196 [arXiv:1808.03012] [INSPIRE].
G.-J. Ding, S.F. King and X.-G. Liu, Modular A4 symmetry models of neutrinos and charged leptons, JHEP 09 (2019) 074 [arXiv:1907.11714] [INSPIRE].
P.P. Novichkov, J.T. Penedo, S.T. Petcov and A.V. Titov, Modular S4 models of lepton masses and mixing, JHEP 04 (2019) 005 [arXiv:1811.04933] [INSPIRE].
T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto and T.H. Tatsuishi, New A4 lepton flavor model from S4 modular symmetry, JHEP 02 (2020) 097 [arXiv:1907.09141] [INSPIRE].
X. Wang and S. Zhou, The minimal seesaw model with a modular S4 symmetry, JHEP 05 (2020) 017 [arXiv:1910.09473] [INSPIRE].
X.-G. Liu and G.-J. Ding, Neutrino masses and mixing from double covering of finite modular groups, JHEP 08 (2019) 134 [arXiv:1907.01488] [INSPIRE].
P. Chen, G.-J. Ding, J.-N. Lu and J.W.F. Valle, Predictions from warped flavor dynamics based on the T′ family group, Phys. Rev. D 102 (2020) 095014 [arXiv:2003.02734] [INSPIRE].
P.P. Novichkov, J.T. Penedo and S.T. Petcov, Double cover of modular S4 for flavour model building, Nucl. Phys. B 963 (2021) 115301 [arXiv:2006.03058] [INSPIRE].
X.-G. Liu, C.-Y. Yao and G.-J. Ding, Modular invariant quark and lepton models in double covering of S4 modular group, Phys. Rev. D 103 (2021) 056013 [arXiv:2006.10722] [INSPIRE].
X. Wang, B. Yu and S. Zhou, Double covering of the modular A5 group and lepton flavor mixing in the minimal seesaw model, Phys. Rev. D 103 (2021) 076005 [arXiv:2010.10159] [INSPIRE].
C.-Y. Yao, X.-G. Liu and G.-J. Ding, Fermion masses and mixing from the double cover and metaplectic cover of the A5 modular group, Phys. Rev. D 103 (2021) 095013 [arXiv:2011.03501] [INSPIRE].
H. Okada and M. Tanimoto, Spontaneous CP-violation by modulus τ in A4 model of lepton flavors, JHEP 03 (2021) 010 [arXiv:2012.01688] [INSPIRE].
C.-Y. Yao, J.-N. Lu and G.-J. Ding, Modular invariant A4 models for quarks and leptons with generalized CP symmetry, JHEP 05 (2021) 102 [arXiv:2012.13390] [INSPIRE].
H. Okada and M. Tanimoto, CP violation of quarks in A4 modular invariance, Phys. Lett. B 791 (2019) 54 [arXiv:1812.09677] [INSPIRE].
H. Okada and M. Tanimoto, Towards unification of quark and lepton flavors in A4 modular invariance, Eur. Phys. J. C 81 (2021) 52 [arXiv:1905.13421] [INSPIRE].
I. de Medeiros Varzielas, S.F. King and Y.-L. Zhou, Multiple modular symmetries as the origin of flavor, Phys. Rev. D 101 (2020) 055033 [arXiv:1906.02208] [INSPIRE].
T. Asaka, Y. Heo, T.H. Tatsuishi and T. Yoshida, Modular A4 invariance and leptogenesis, JHEP 01 (2020) 144 [arXiv:1909.06520] [INSPIRE].
G.-J. Ding, S.F. King, C.-C. Li and Y.-L. Zhou, Modular invariant models of leptons at level 7, JHEP 08 (2020) 164 [arXiv:2004.12662] [INSPIRE].
T. Asaka, Y. Heo and T. Yoshida, Lepton flavor model with modular A4 symmetry in large volume limit, Phys. Lett. B 811 (2020) 135956 [arXiv:2009.12120] [INSPIRE].
M.K. Behera, S. Mishra, S. Singirala and R. Mohanta, Implications of A4 modular symmetry on neutrino mass, mixing and leptogenesis with linear seesaw, Phys. Dark Univ. 36 (2022) 101027 [arXiv:2007.00545] [INSPIRE].
S. Mishra, Neutrino mixing and Leptogenesis with modular S3 symmetry in the framework of type-III seesaw, arXiv:2008.02095 [INSPIRE].
F.J. de Anda, S.F. King and E. Perdomo, SU(5) grand unified theory with A4 modular symmetry, Phys. Rev. D 101 (2020) 015028 [arXiv:1812.05620] [INSPIRE].
T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto and T.H. Tatsuishi, Modular S3-invariant flavor model in SU(5) grand unified theory, PTEP 2020 (2020) 053B05 [arXiv:1906.10341] [INSPIRE].
P.P. Novichkov, S.T. Petcov and M. Tanimoto, Trimaximal neutrino mixing from modular A4 invariance with residual symmetries, Phys. Lett. B 793 (2019) 247 [arXiv:1812.11289] [INSPIRE].
T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto, T.H. Tatsuishi and H. Uchida, Finite modular subgroups for fermion mass matrices and baryon/lepton number violation, Phys. Lett. B 794 (2019) 114 [arXiv:1812.11072] [INSPIRE].
T. Nomura and H. Okada, A modular A4 symmetric model of dark matter and neutrino, Phys. Lett. B 797 (2019) 134799 [arXiv:1904.03937] [INSPIRE].
H. Okada and Y. Orikasa, Modular S3 symmetric radiative seesaw model, Phys. Rev. D 100 (2019) 115037 [arXiv:1907.04716] [INSPIRE].
Y. Kariyazono, T. Kobayashi, S. Takada, S. Tamba and H. Uchida, Modular symmetry anomaly in magnetic flux compactification, Phys. Rev. D 100 (2019) 045014 [arXiv:1904.07546] [INSPIRE].
T. Nomura and H. Okada, A two loop induced neutrino mass model with modular A4 symmetry, Nucl. Phys. B 966 (2021) 115372 [arXiv:1906.03927] [INSPIRE].
H. Okada and Y. Orikasa, Neutrino mass model with a modular S4 symmetry, arXiv:1908.08409 [INSPIRE].
T. Nomura, H. Okada and O. Popov, A modular A4 symmetric scotogenic model, Phys. Lett. B 803 (2020) 135294 [arXiv:1908.07457] [INSPIRE].
J.C. Criado, F. Feruglio and S.J.D. King, Modular invariant models of lepton masses at levels 4 and 5, JHEP 02 (2020) 001 [arXiv:1908.11867] [INSPIRE].
S.F. King and Y.-L. Zhou, Trimaximal TM1 mixing with two modular S4 groups, Phys. Rev. D 101 (2020) 015001 [arXiv:1908.02770] [INSPIRE].
G.-J. Ding, S.F. King, X.-G. Liu and J.-N. Lu, Modular S4 and A4 symmetries and their fixed points: new predictive examples of lepton mixing, JHEP 12 (2019) 030 [arXiv:1910.03460] [INSPIRE].
I. de Medeiros Varzielas, M. Levy and Y.-L. Zhou, Symmetries and stabilisers in modular invariant flavour models, JHEP 11 (2020) 085 [arXiv:2008.05329] [INSPIRE].
D. Zhang, A modular A4 symmetry realization of two-zero textures of the Majorana neutrino mass matrix, Nucl. Phys. B 952 (2020) 114935 [arXiv:1910.07869] [INSPIRE].
T. Nomura, H. Okada and S. Patra, An inverse seesaw model with A4-modular symmetry, Nucl. Phys. B 967 (2021) 115395 [arXiv:1912.00379] [INSPIRE].
T. Kobayashi, T. Nomura and T. Shimomura, Type II seesaw models with modular A4 symmetry, Phys. Rev. D 102 (2020) 035019 [arXiv:1912.00637] [INSPIRE].
J.-N. Lu, X.-G. Liu and G.-J. Ding, Modular symmetry origin of texture zeros and quark lepton unification, Phys. Rev. D 101 (2020) 115020 [arXiv:1912.07573] [INSPIRE].
X. Wang, Lepton flavor mixing and CP-violation in the minimal type-(I+II) seesaw model with a modular A4 symmetry, Nucl. Phys. B 957 (2020) 115105 [arXiv:1912.13284] [INSPIRE].
S.J.D. King and S.F. King, Fermion mass hierarchies from modular symmetry, JHEP 09 (2020) 043 [arXiv:2002.00969] [INSPIRE].
M. Abbas, Fermion masses and mixing in modular A4 symmetry, Phys. Rev. D 103 (2021) 056016 [arXiv:2002.01929] [INSPIRE].
H. Okada and Y. Shoji, Dirac dark matter in a radiative neutrino model, Phys. Dark Univ. 31 (2021) 100742 [arXiv:2003.11396] [INSPIRE].
H. Okada and Y. Shoji, A radiative seesaw model with three Higgs doublets in modular A4 symmetry, Nucl. Phys. B 961 (2020) 115216 [arXiv:2003.13219] [INSPIRE].
G.-J. Ding and F. Feruglio, Testing moduli and flavon dynamics with neutrino oscillations, JHEP 06 (2020) 134 [arXiv:2003.13448] [INSPIRE].
T. Nomura and H. Okada, A linear seesaw model with A4-modular flavor and local U(1)B−L symmetries, arXiv:2007.04801 [INSPIRE].
T. Nomura and H. Okada, Modular A4 symmetric inverse seesaw model with SU(2)L multiplet fields, arXiv:2007.15459 [INSPIRE].
H. Okada and M. Tanimoto, Quark and lepton flavors with common modulus τ in A4 modular symmetry, arXiv:2005.00775 [INSPIRE].
H. Okada and M. Tanimoto, Modular invariant flavor model of A4 and hierarchical structures at nearby fixed points, Phys. Rev. D 103 (2021) 015005 [arXiv:2009.14242] [INSPIRE].
K.I. Nagao and H. Okada, Neutrino and dark matter in a gauged U(1)R symmetry, JCAP 05 (2021) 063 [arXiv:2008.13686] [INSPIRE].
K.I. Nagao and H. Okada, Lepton sector in modular A4 and gauged U(1)R symmetry, Nucl. Phys. B 980 (2022) 115841 [arXiv:2010.03348] [INSPIRE].
M. Abbas, Modular A4 invariance model for lepton masses and mixing, Phys. Atom. Nucl. 83 (2020) 764 [INSPIRE].
F. Feruglio, V. Gherardi, A. Romanino and A. Titov, Modular invariant dynamics and fermion mass hierarchies around τ = i, JHEP 05 (2021) 242 [arXiv:2101.08718] [INSPIRE].
S.F. King and Y.-L. Zhou, Twin modular S4 with SU(5) GUT, JHEP 04 (2021) 291 [arXiv:2103.02633] [INSPIRE].
P. Chen, G.-J. Ding and S.F. King, SU(5) GUTs with A4 modular symmetry, JHEP 04 (2021) 239 [arXiv:2101.12724] [INSPIRE].
P.P. Novichkov, J.T. Penedo and S.T. Petcov, Fermion mass hierarchies, large lepton mixing and residual modular symmetries, JHEP 04 (2021) 206 [arXiv:2102.07488] [INSPIRE].
X. Du and F. Wang, SUSY breaking constraints on modular flavor S3 invariant SU(5) GUT model, JHEP 02 (2021) 221 [arXiv:2012.01397] [INSPIRE].
T. Kobayashi, T. Shimomura and M. Tanimoto, Soft supersymmetry breaking terms and lepton flavor violations in modular flavor models, Phys. Lett. B 819 (2021) 136452 [arXiv:2102.10425] [INSPIRE].
G.-J. Ding, S.F. King and C.-Y. Yao, Modular S4 × SU(5) GUT, Phys. Rev. D 104 (2021) 055034 [arXiv:2103.16311] [INSPIRE].
H. Kuranaga, H. Ohki and S. Uemura, Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism, JHEP 07 (2021) 068 [arXiv:2105.06237] [INSPIRE].
C.-C. Li, X.-G. Liu and G.-J. Ding, Modular symmetry at level 6 and a new route towards finite modular groups, JHEP 10 (2021) 238 [arXiv:2108.02181] [INSPIRE].
M. Tanimoto and K. Yamamoto, Electron EDM arising from modulus τ in the supersymmetric modular invariant flavor models, JHEP 10 (2021) 183 [arXiv:2106.10919] [INSPIRE].
H. Okada and Y.-H. Qi, Zee-Babu model in modular A4 symmetry, arXiv:2109.13779 [INSPIRE].
T. Kobayashi, H. Okada and Y. Orikasa, Dark matter stability at fixed points in a modular A4 symmetry, arXiv:2111.05674 [INSPIRE].
A. Dasgupta, T. Nomura, H. Okada, O. Popov and M. Tanimoto, Dirac radiative neutrino mass with modular symmetry and leptogenesis, arXiv:2111.06898 [INSPIRE].
T. Nomura and H. Okada, Linear seesaw model with a modular S4 flavor symmetry, Chin. Phys. C 46 (2022) 053101 [arXiv:2109.04157] [INSPIRE].
K.I. Nagao and H. Okada, Modular A4 symmetry and light dark matter with gauged U(1)B−L, Phys. Dark Univ. 36 (2022) 101039 [arXiv:2108.09984] [INSPIRE].
T. Nomura, H. Okada and Y. Orikasa, Quark and lepton flavor model with leptoquarks in a modular A4 symmetry, Eur. Phys. J. C 81 (2021) 947 [arXiv:2106.12375] [INSPIRE].
T. Nomura and H. Okada, Radiative neutrino mass model in dark non-Abelian gauge symmetry, Phys. Rev. D 105 (2022) 075010 [arXiv:2106.10451] [INSPIRE].
H. Okada, Y. Shimizu, M. Tanimoto and T. Yoshida, Modulus τ linking leptonic CP-violation to baryon asymmetry in A4 modular invariant flavor model, JHEP 07 (2021) 184 [arXiv:2105.14292] [INSPIRE].
G.-J. Ding, S.F. King and J.-N. Lu, SO(10) models with A4 modular symmetry, JHEP 11 (2021) 007 [arXiv:2108.09655] [INSPIRE].
B.-Y. Qu, X.-G. Liu, P.-T. Chen and G.-J. Ding, Flavor mixing and CP-violation from the interplay of an S4 modular group and a generalized CP symmetry, Phys. Rev. D 104 (2021) 076001 [arXiv:2106.11659] [INSPIRE].
X. Zhang and S. Zhou, Inverse seesaw model with a modular S4 symmetry: lepton flavor mixing and warm dark matter, JCAP 09 (2021) 043 [arXiv:2106.03433] [INSPIRE].
X. Wang and S. Zhou, Explicit perturbations to the stabilizer τ = i of modular \( {A}_5^{\prime } \) symmetry and leptonic CP-violation, JHEP 07 (2021) 093 [arXiv:2102.04358] [INSPIRE].
X. Wang, Dirac neutrino mass models with a modular S4 symmetry, Nucl. Phys. B 962 (2021) 115247 [arXiv:2007.05913] [INSPIRE].
P. Ko, T. Nomura and H. Okada, Muon g − 2, B → K(*)μ+μ− anomalies, and leptophilic dark matter in U(1)μ−τ gauge symmetry, JHEP 05 (2022) 098 [arXiv:2110.10513] [INSPIRE].
T. Nomura, H. Okada and Y.-H. Qi, Zee model in a modular A4 symmetry, arXiv:2111.10944 [INSPIRE].
T. Nomura and H. Okada, A radiative seesaw model in a supersymmetric modular A4 group, arXiv:2201.10244 [INSPIRE].
H. Otsuka and H. Okada, Radiative neutrino masses from modular A4 symmetry and supersymmetry breaking, arXiv:2202.10089 [INSPIRE].
G.-J. Ding, F. Feruglio and X.-G. Liu, CP symmetry and symplectic modular invariance, SciPost Phys. 10 (2021) 133 [arXiv:2102.06716] [INSPIRE].
G. Charalampous, S.F. King, G.K. Leontaris and Y.-L. Zhou, Flipped SU(5) with modular A4 symmetry, Phys. Rev. D 104 (2021) 115015 [arXiv:2109.11379] [INSPIRE].
X.-G. Liu and G.-J. Ding, Modular flavor symmetry and vector-valued modular forms, JHEP 03 (2022) 123 [arXiv:2112.14761] [INSPIRE].
P.P. Novichkov, J.T. Penedo and S.T. Petcov, Modular flavour symmetries and modulus stabilisation, JHEP 03 (2022) 149 [arXiv:2201.02020] [INSPIRE].
S. Kikuchi, T. Kobayashi, H. Otsuka, M. Tanimoto, H. Uchida and K. Yamamoto, 4D modular flavor symmetric models inspired by higher dimensional theory, arXiv:2201.04505 [INSPIRE].
E. Ma and G. Rajasekaran, Softly broken A4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].
K.S. Babu, E. Ma and J.W.F. Valle, Underlying A4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing from discrete symmetry in extra dimensions, Nucl. Phys. B 720 (2005) 64 [hep-ph/0504165] [INSPIRE].
G. Altarelli and F. Feruglio, Tri-bimaximal neutrino mixing, A4 and the modular symmetry, Nucl. Phys. B 741 (2006) 215 [hep-ph/0512103] [INSPIRE].
Y. Shimizu, M. Tanimoto and A. Watanabe, Breaking tri-bimaximal mixing and large θ13, Prog. Theor. Phys. 126 (2011) 81 [arXiv:1105.2929] [INSPIRE].
S.T. Petcov and A.V. Titov, Assessing the viability of A4, S4 and A5 flavour symmetries for description of neutrino mixing, Phys. Rev. D 97 (2018) 115045 [arXiv:1804.00182] [INSPIRE].
S.K. Kang, Y. Shimizu, K. Takagi, S. Takahashi and M. Tanimoto, Revisiting A4 model for leptons in light of NuFIT 3.2, PTEP 2018 (2018) 083B01 [arXiv:1804.10468] [INSPIRE].
S. Kikuchi, T. Kobayashi, K. Nasu, H. Otsuka, S. Takada and H. Uchida, Modular symmetry of soft supersymmetry breaking terms, arXiv:2203.14667 [INSPIRE].
L.E. Ibáñez and A.M. Uranga, String theory and particle physics: an introduction to string phenomenology, Cambridge University Press, Cambridge, U.K. (2012).
T. Kobayashi and H. Otsuka, Classification of discrete modular symmetries in type IIB flux vacua, Phys. Rev. D 101 (2020) 106017 [arXiv:2001.07972] [INSPIRE].
S. Ferrara, .D. Lüst and S. Theisen, Target space modular invariance and low-energy couplings in orbifold compactifications, Phys. Lett. B 233 (1989) 147 [INSPIRE].
W. Lerche, D. Lüst and N.P. Warner, Duality symmetries in N = 2 Landau-Ginzburg models, Phys. Lett. B 231 (1989) 417 [INSPIRE].
J. Lauer, J. Mas and H.P. Nilles, Twisted sector representations of discrete background symmetries for two-dimensional orbifolds, Nucl. Phys. B 351 (1991) 353 [INSPIRE].
T. Kobayashi, S. Nagamoto, S. Takada, S. Tamba and T.H. Tatsuishi, Modular symmetry and non-Abelian discrete flavor symmetries in string compactification, Phys. Rev. D 97 (2018) 116002 [arXiv:1804.06644] [INSPIRE].
H. Ohki, S. Uemura and R. Watanabe, Modular flavor symmetry on a magnetized torus, Phys. Rev. D 102 (2020) 085008 [arXiv:2003.04174] [INSPIRE].
S. Kikuchi, T. Kobayashi, S. Takada, T.H. Tatsuishi and H. Uchida, Revisiting modular symmetry in magnetized torus and orbifold compactifications, Phys. Rev. D 102 (2020) 105010 [arXiv:2005.12642] [INSPIRE].
S. Kikuchi, T. Kobayashi, H. Otsuka, S. Takada and H. Uchida, Modular symmetry by orbifolding magnetized T2 × T2: realization of double cover of ΓN, JHEP 11 (2020) 101 [arXiv:2007.06188] [INSPIRE].
S. Kikuchi, T. Kobayashi and H. Uchida, Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds, Phys. Rev. D 104 (2021) 065008 [arXiv:2101.00826] [INSPIRE].
Y. Almumin, M.-C. Chen, V. Knapp-Pérez, S. Ramos-Sánchez, M. Ratz and S. Shukla, Metaplectic flavor symmetries from magnetized tori, JHEP 05 (2021) 078 [arXiv:2102.11286] [INSPIRE].
A. Baur, H.P. Nilles, A. Trautner and P.K.S. Vaudrevange, A string theory of flavor and CP, Nucl. Phys. B 947 (2019) 114737 [arXiv:1908.00805] [INSPIRE].
H.P. Nilles, S. Ramos-Sánchez and P.K.S. Vaudrevange, Lessons from eclectic flavor symmetries, Nucl. Phys. B 957 (2020) 115098 [arXiv:2004.05200] [INSPIRE].
A. Baur, M. Kade, H.P. Nilles, S. Ramos-Sanchez and P.K.S. Vaudrevange, The eclectic flavor symmetry of the Z2 orbifold, JHEP 02 (2021) 018 [arXiv:2008.07534] [INSPIRE].
H.P. Nilles, S. Ramos-Sánchez and P.K.S. Vaudrevange, Eclectic flavor scheme from ten-dimensional string theory — II detailed technical analysis, Nucl. Phys. B 966 (2021) 115367 [arXiv:2010.13798] [INSPIRE].
A. Strominger, Special geometry, Commun. Math. Phys. 133 (1990) 163 [INSPIRE].
P. Candelas and X. de la Ossa, Moduli space of Calabi-Yau manifolds, Nucl. Phys. B 355 (1991) 455 [INSPIRE].
K. Ishiguro, T. Kobayashi and H. Otsuka, Spontaneous CP-violation and symplectic modular symmetry in Calabi-Yau compactifications, Nucl. Phys. B 973 (2021) 115598 [arXiv:2010.10782] [INSPIRE].
K. Ishiguro, T. Kobayashi and H. Otsuka, Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries, JHEP 01 (2022) 020 [arXiv:2107.00487] [INSPIRE].
G.F. Giudice, P. Paradisi and M. Passera, Testing new physics with the electron g − 2, JHEP 11 (2012) 113 [arXiv:1208.6583] [INSPIRE].
D. Hanneke, S. Fogwell and G. Gabrielse, New measurement of the electron magnetic moment and the fine structure constant, Phys. Rev. Lett. 100 (2008) 120801 [arXiv:0801.1134] [INSPIRE].
R.H. Parker, C. Yu, W. Zhong, B. Estey and H. Müller, Measurement of the fine-structure constant as a test of the Standard Model, Science 360 (2018) 191 [arXiv:1812.04130] [INSPIRE].
L. Morel, Z. Yao, P. Cladé and S. Guellati-Khélifa, Determination of the fine-structure constant with an accuracy of 81 parts per trillion, Nature 588 (2020) 61 [INSPIRE].
MEG collaboration, Search for the lepton flavour violating decay μ+ → e+γ with the full dataset of the MEG experiment, Eur. Phys. J. C 76 (2016) 434 [arXiv:1605.05081] [INSPIRE].
Y. Okada, K.-I. Okumura and Y. Shimizu, μ → eγ and μ → 3e processes with polarized muons and supersymmetric grand unified theories, Phys. Rev. D 61 (2000) 094001 [hep-ph/9906446] [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2020 (2020) 083C01 [INSPIRE].
G. Blankenburg, J. Ellis and G. Isidori, Flavour-changing decays of a 125 GeV Higgs-like particle, Phys. Lett. B 712 (2012) 386 [arXiv:1202.5704] [INSPIRE].
R. Harnik, J. Kopp and J. Zupan, Flavor violating Higgs decays, JHEP 03 (2013) 026 [arXiv:1209.1397] [INSPIRE].
ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature 562 (2018) 355 [INSPIRE].
D.M. Kara, I.J. Smallman, J.J. Hudson, B.E. Sauer, M.R. Tarbutt and E.A. Hinds, Measurement of the electron’s electric dipole moment using YbF molecules: methods and data analysis, New J. Phys. 14 (2012) 103051 [arXiv:1208.4507] [INSPIRE].
J. Doyle, Search for the electric dipole moment of the electron with thorium monoxide — the ACME experiment, talk at the KITP, https://online.kitp.ucsb.edu/online/nuclear_c16/doyle/, University of California, Santa Barbara, CA, U.S.A., 21 September 2016.
A. Crivellin, M. Hoferichter and P. Schmidt-Wellenburg, Combined explanations of (g − 2)μ,e and implications for a large muon EDM, Phys. Rev. D 98 (2018) 113002 [arXiv:1807.11484] [INSPIRE].
Y. Ema, T. Gao and M. Pospelov, Improved indirect limits on muon electric dipole moment, Phys. Rev. Lett. 128 (2022) 131803 [arXiv:2108.05398] [INSPIRE].
D. Buttazzo and P. Paradisi, Probing the muon g − 2 anomaly with the Higgs boson at a muon collider, Phys. Rev. D 104 (2021) 075021 [arXiv:2012.02769] [INSPIRE].
S. Ferrara, D. Lüst, A.D. Shapere and S. Theisen, Modular invariance in supersymmetric field theories, Phys. Lett. B 225 (1989) 363 [INSPIRE].
M.-C. Chen, S. Ramos-Sánchez and M. Ratz, A note on the predictions of models with modular flavor symmetries, Phys. Lett. B 801 (2020) 135153 [arXiv:1909.06910] [INSPIRE].
R.C. Gunning, Lectures on modular forms, Princeton University Press, Princeton, NJ, U.S.A. (1962).
B. Schoeneberg, Elliptic modular functions, Springer, Berlin, Heidelberg, Germany (1974).
N. Koblitz, Introduction to elliptic curves and modular forms, Springer, New York, NY, U.S.A. (1984).
I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, T. Schwetz and A. Zhou, The fate of hints: updated global analysis of three-flavor neutrino oscillations, JHEP 09 (2020) 178 [arXiv:2007.14792] [INSPIRE]
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2204.12325
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kobayashi, T., Otsuka, H., Tanimoto, M. et al. Lepton flavor violation, lepton (g − 2)μ, e and electron EDM in the modular symmetry. J. High Energ. Phys. 2022, 13 (2022). https://doi.org/10.1007/JHEP08(2022)013
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)013