Abstract
We study the textures of SM fermion mass matrices and their mixings in a supersymmetric adjoint SU(5) Grand Unified Theory with modular S4 being the horizontal symmetry. The Yukawa entries of both quarks and leptons are expressed by modular forms with lower weights. Neutrino sector has an adjoint SU(5) representation 24 as matter superfield, which is a triplet of S4. The effective light neutrino masses is generated through Type-III and Type-I seesaw mechanism. The only common complex parameter in both charged fermion and neutrino sectors is modulus τ . Down-type quarks and charged leptons have the same joint effective operators with adjoint scalar in them, and their mass discrepancy in the same generation depends on Clebsch-Gordan factor. Especially for the first two generations the respective Clebsch-Gordan factors made the double Yukawa ratio 𝒴d𝒴μ/𝒴e𝒴s = 12, in excellent agreement with the experimental result. We reproduce proper CKM mixing parameters and all nine Yukawa eigenvalues of quarks and charged leptons. Neutrino masses and MNS parameters are also produced properly with normal ordering is preferred.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
L.J. Hall, H. Murayama and N. Weiner, Neutrino mass anarchy, Phys. Rev. Lett. 84 (2000) 2572 [hep-ph/9911341] [INSPIRE].
K.R. Dienes, E. Dudas and T. Gherghetta, Neutrino oscillations without neutrino masses or heavy mass scales: A Higher dimensional seesaw mechanism, Nucl. Phys. B 557 (1999) 25 [hep-ph/9811428] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali and J. March-Russell, Neutrino masses from large extra dimensions, Phys. Rev. D 65 (2001) 024032 [hep-ph/9811448] [INSPIRE].
R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua: The Seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [INSPIRE].
L.E. Ibáñez and A.M. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [hep-th/0609213] [INSPIRE].
S. Antusch, L.E. Ibáñez and T. Macrì, Neutrino masses and mixings from string theory instantons, JHEP 09 (2007) 087 [arXiv:0706.2132] [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].
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, Models of Neutrino Mass, Mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
S.F. King, Unified Models of Neutrinos, Flavour and CP-violation, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413] [INSPIRE].
D. Meloni, GUT and flavor models for neutrino masses and mixing, Front. in Phys. 5 (2017) 43 [arXiv:1709.02662] [INSPIRE].
P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
P.F. Harrison and W.G. Scott, Symmetries and generalizations of tri - bimaximal neutrino mixing, Phys. Lett. B 535 (2002) 163 [hep-ph/0203209] [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, New York U.S.A. (2019), pg. 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].
H. Okada and Y. Orikasa, Modular S3 symmetric radiative seesaw model, Phys. Rev. D 100 (2019) 115037 [arXiv:1907.04716] [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].
S. Mishra, Neutrino mixing and Leptogenesis with modular S3 symmetry in the framework of type-III seesaw, arXiv:2008.02095 [INSPIRE].
J.C. Criado and F. Feruglio, Modular Invariance Faces Precision Neutrino Data, SciPost Phys. 5 (2018) 042 [arXiv:1807.01125] [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, Quark and lepton flavors with common modulus τ in A4 modular symmetry, arXiv:2005.00775 [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].
T. Nomura and H. Okada, A two loop induced neutrino mass model with modular A4 symmetry, arXiv:1906.03927 [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].
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].
S.J.D. King and S.F. King, Fermion mass hierarchies from modular symmetry, JHEP 09 (2020) 043 [arXiv:2002.00969] [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. Asaka, Y. Heo, T.H. Tatsuishi and T. Yoshida, Modular A4 invariance and leptogenesis, JHEP 01 (2020) 144 [arXiv:1909.06520] [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, arXiv:2007.00545 [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 S4 models of lepton masses and mixing, JHEP 04 (2019) 005 [arXiv:1811.04933] [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].
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].
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].
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].
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].
X. Wang and S. Zhou, The minimal seesaw model with a modular S4 symmetry, JHEP 05 (2020) 017 [arXiv:1910.09473] [INSPIRE].
X. Wang, Dirac neutrino mass models with a modular S4 symmetry, Nucl. Phys. B 962 (2021) 115247 [arXiv:2007.05913] [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].
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].
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].
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, 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, arXiv:2010.10159 [INSPIRE].
C.-Y. Yao, X.-G. Liu and G.-J. Ding, Fermion Masses and Mixing from Double Cover and Metaplectic Cover of A5 Modular Group, arXiv:2011.03501 [INSPIRE].
P. Fileviez Pérez, Supersymmetric Adjoint SU(5), Phys. Rev. D 76 (2007) 071701 [arXiv:0705.3589] [INSPIRE].
P. Minkowski, μ → e𝛾 at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
T. Yanagida, Horizontal symmetry and masses of neutrinos, in Proceedings of the Workshop on Unified Theory and Baryon Number in the Universe, O. Sawada and A. Sugamoto eds., KEK, Tsukuba Japan (1979).
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
G. Lazarides, Q. Shafi and C. Wetterich, Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B 181 (1981) 287 [INSPIRE].
J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation, Phys. Rev. D 23 (1981) 165 [INSPIRE].
R. Foot, H. Lew, X.G. He and G.C. Joshi, Seesaw Neutrino Masses Induced by a Triplet of Leptons, Z. Phys. C 44 (1989) 441 [INSPIRE].
P. Fileviez Perez, Renormalizable adjoint SU(5), Phys. Lett. B 654 (2007) 189 [hep-ph/0702287] [INSPIRE].
D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
D. Binosi, J. Collins, C. Kaufhold and L. Theußl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Commun. 180 (2009) 1709 [arXiv:0811.4113] [INSPIRE].
S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, JHEP 11 (2013) 115 [arXiv:1306.6879] [INSPIRE].
H. Georgi and C. Jarlskog, A new lepton-quark mass relation in a unified theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].
S. Antusch, C. Gross, V. Maurer and C. Sluka, A flavour GUT model with \( {\theta}_{13}^{PMNS}\simeq {\theta}_C/\sqrt{2} \), Nucl. Phys. B 877 (2013) 772 [arXiv:1305.6612] [INSPIRE].
J. Gehrlein, J.P. Oppermann, D. Schäfer and M. Spinrath, An SU(5) × A5 golden ratio flavour model, Nucl. Phys. B 890 (2014) 539 [arXiv:1410.2057] [INSPIRE].
F. Björkeroth, F.J. de Anda, I. de Medeiros Varzielas and S.F. King, Towards a complete A4 × SU(5) SUSY GUT, JHEP 06 (2015) 141 [arXiv:1503.03306] [INSPIRE].
Y. Zhao and P.-F. Zhang, SUSY SU(5) × S4 GUT Flavor Model for Fermion Masses and Mixings with Adjoint, Large \( {\theta}_{13}^{PMNS} \) , JHEP 06 (2016) 032 [arXiv:1402.5834] [INSPIRE].
S. Antusch, S.F. King and M. Spinrath, GUT predictions for quark-lepton Yukawa coupling ratios with messenger masses from non-singlets, Phys. Rev. D 89 (2014) 055027 [arXiv:1311.0877] [INSPIRE].
L.J. Hall, R. Rattazzi and U. Sarid, The Top quark mass in supersymmetric SO(10) unification, Phys. Rev. D 50 (1994) 7048 [hep-ph/9306309] [INSPIRE].
M. Carena, M. Olechowski, S. Pokorski and C.E.M. Wagner, Electroweak symmetry breaking and bottom-top Yukawa unification, Nucl. Phys. B 426 (1994) 269 [hep-ph/9402253] [INSPIRE].
R. Hempfling, Yukawa coupling unification with supersymmetric threshold corrections, Phys. Rev. D 49 (1994) 6168 [INSPIRE].
T. Blazek, S. Raby and S. Pokorski, Finite supersymmetric threshold corrections to CKM matrix elements in the large tan Beta regime, Phys. Rev. D 52 (1995) 4151 [hep-ph/9504364] [INSPIRE].
S. Antusch, C. Hohl, C.K. Khosa and V. Susič, Predicting δPMNS , \( {\theta}_{23}^{PMNS} \) and fermion mass ratios from flavour GUTs with CSD2, JHEP 12 (2018) 025 [arXiv:1808.09364] [INSPIRE].
S. Antusch and M. Spinrath, New GUT predictions for quark and lepton mass ratios confronted with phenomenology, Phys. Rev. D 79 (2009) 095004 [arXiv:0902.4644] [INSPIRE].
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].
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [arXiv:1807.06209] [INSPIRE].
KamLAND-Zen collaboration, Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [Addendum ibid. 117 (2016) 109903] [arXiv:1605.02889] [INSPIRE].
KATRIN collaboration, Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN, Phys. Rev. Lett. 123 (2019) 221802 [arXiv:1909.06048] [INSPIRE].
S. Vagnozzi et al., Unveiling ν secrets with cosmological data: neutrino masses and mass hierarchy, Phys. Rev. D 96 (2017) 123503 [arXiv:1701.08172] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
S. Blanchet and P. Fileviez Pérez, Baryogenesis via Leptogenesis in Adjoint SU(5), JCAP 08 (2008) 037 [arXiv:0807.3740] [INSPIRE].
K. Kannike and D.V. Zhuridov, New Solution for Neutrino Masses and Leptogenesis in Adjoint SU(5), JHEP 07 (2011) 102 [arXiv:1105.4546] [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: 2101.02266
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
Zhao, Y., Zhang, HH. Adjoint SU(5) GUT model with modular S4 symmetry. J. High Energ. Phys. 2021, 2 (2021). https://doi.org/10.1007/JHEP03(2021)002
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)002