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SU(5) GUTs with A4 modular symmetry

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  • Published: 26 April 2021
  • Volume 2021, article number 239, (2021)
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SU(5) GUTs with A4 modular symmetry
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  • Peng Chen1,
  • Gui-Jun Ding2,3 &
  • Stephen F. King4 

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  • 41 Citations

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A preprint version of the article is available at arXiv.

Abstract

We combine SU(5) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the representation assignments of the matter fields under A4, we find that there are seven types of SU(5) models with A4 modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models.

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References

  1. S.L. Glashow, Partial Symmetries of Weak Interactions, Nucl. Phys. 22 (1961) 579 [INSPIRE].

    Article  Google Scholar 

  2. Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [arXiv:1807.06209] [INSPIRE].

  3. Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].

  4. 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].

    Article  Google Scholar 

  5. S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].

    Article  Google Scholar 

  6. F. Feruglio, Are neutrino masses modular forms?, in From My Vast Repertoire . . .: Guido Altarelli’s Legacy, A. Levy, S. Forte and G. Ridolfi eds. (2019) [DOI] [arXiv:1706.08749] [INSPIRE].

  7. 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].

    Article  MathSciNet  Google Scholar 

  8. T. Kobayashi, K. Tanaka and T.H. Tatsuishi, Neutrino mixing from finite modular groups, Phys. Rev. D 98 (2018) 016004 [arXiv:1803.10391] [INSPIRE].

    Article  Google Scholar 

  9. 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].

    Article  MathSciNet  Google Scholar 

  10. 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].

  11. H. Okada and Y. Orikasa, Modular S3 symmetric radiative seesaw model, Phys. Rev. D 100 (2019) 115037 [arXiv:1907.04716] [INSPIRE].

    Article  Google Scholar 

  12. J.C. Criado and F. Feruglio, Modular Invariance Faces Precision Neutrino Data, SciPost Phys. 5 (2018) 042 [arXiv:1807.01125] [INSPIRE].

    Article  Google Scholar 

  13. 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].

    Article  Google Scholar 

  14. 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].

    Article  MathSciNet  Google Scholar 

  15. H. Okada and M. Tanimoto, CP violation of quarks in A4 modular invariance, Phys. Lett. B 791 (2019) 54 [arXiv:1812.09677] [INSPIRE].

    Article  MATH  Google Scholar 

  16. 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].

    Article  MathSciNet  MATH  Google Scholar 

  17. 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].

    Article  MATH  Google Scholar 

  18. 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].

    Article  Google Scholar 

  19. 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].

    Article  MathSciNet  Google Scholar 

  20. 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].

    Article  Google Scholar 

  21. H. Okada and Y. Orikasa, A radiative seesaw model in modular A4 symmetry, arXiv:1907.13520 [INSPIRE].

  22. T. Nomura, H. Okada and O. Popov, A modular A4 symmetric scotogenic model, Phys. Lett. B 803 (2020) 135294 [arXiv:1908.07457] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  23. T. Kobayashi, Y. Shimizu, K. Takagi, M. Tanimoto and T.H. Tatsuishi, A4 lepton flavor model and modulus stabilization from S4 modular symmetry, Phys. Rev. D 100 (2019) 115045 [Erratum ibid. 101 (2020) 039904] [arXiv:1909.05139] [INSPIRE].

  24. T. Asaka, Y. Heo, T.H. Tatsuishi and T. Yoshida, Modular A4 invariance and leptogenesis, JHEP 01 (2020) 144 [arXiv:1909.06520] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  25. 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].

    Article  Google Scholar 

  26. 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].

    Article  MathSciNet  Google Scholar 

  27. T. Nomura, H. Okada and S. Patra, An Inverse Seesaw model with A4 -modular symmetry, arXiv:1912.00379 [INSPIRE].

  28. 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].

    Article  MathSciNet  Google Scholar 

  29. 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].

    Article  MathSciNet  Google Scholar 

  30. S.J.D. King and S.F. King, Fermion mass hierarchies from modular symmetry, JHEP 09 (2020) 043 [arXiv:2002.00969] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  31. G.-J. Ding and F. Feruglio, Testing Moduli and Flavon Dynamics with Neutrino Oscillations, JHEP 06 (2020) 134 [arXiv:2003.13448] [INSPIRE].

    Article  Google Scholar 

  32. H. Okada and M. Tanimoto, Quark and lepton flavors with common modulus τ in A4 modular symmetry, arXiv:2005.00775 [INSPIRE].

  33. T. Nomura and H. Okada, A linear seesaw model with A4 -modular flavor and local U(1)B−L symmetries, arXiv:2007.04801 [INSPIRE].

  34. 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].

    Article  MathSciNet  Google Scholar 

  35. 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].

    Article  Google Scholar 

  36. C.-Y. Yao, J.-N. Lu and G.-J. Ding, Modular Invariant A4 Models for Quarks and Leptons with Generalized CP Symmetry, arXiv:2012.13390 [INSPIRE].

  37. F. Feruglio, V. Gherardi, A. Romanino and A. Titov, Modular Invariant Dynamics and Fermion Mass Hierarchies around τ = i, arXiv:2101.08718 [INSPIRE].

  38. 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].

    Article  MATH  Google Scholar 

  39. 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].

    Article  MathSciNet  Google Scholar 

  40. 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].

    Article  MathSciNet  Google Scholar 

  41. 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].

    Article  Google Scholar 

  42. 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].

    Article  Google Scholar 

  43. 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].

    Article  MathSciNet  Google Scholar 

  44. X. Wang and S. Zhou, The minimal seesaw model with a modular S4 symmetry, JHEP 05 (2020) 017 [arXiv:1910.09473] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  45. X. Wang, Dirac neutrino mass models with a modular S4 symmetry, Nucl. Phys. B 962 (2021) 115247 [arXiv:2007.05913] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  46. 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].

    Article  MathSciNet  Google Scholar 

  47. 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].

    Article  Google Scholar 

  48. 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].

    Article  MathSciNet  Google Scholar 

  49. 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].

    Article  Google Scholar 

  50. 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].

    Article  MathSciNet  Google Scholar 

  51. 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].

    Article  MathSciNet  Google Scholar 

  52. 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].

    Article  MathSciNet  Google Scholar 

  53. X.-G. Liu, C.-Y. Yao, B.-Y. Qu and G.-J. Ding, Half-integral weight modular forms and application to neutrino mass models, Phys. Rev. D 102 (2020) 115035 [arXiv:2007.13706] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  54. 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].

  55. P.P. Novichkov, J.T. Penedo, S.T. Petcov and A.V. Titov, Generalised CP Symmetry in Modular-Invariant Models of Flavour, JHEP 07 (2019) 165 [arXiv:1905.11970] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  56. A. Baur, H.P. Nilles, A. Trautner and P.K.S. Vaudrevange, Unification of Flavor, CP, and Modular Symmetries, Phys. Lett. B 795 (2019) 7 [arXiv:1901.03251] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  57. A. Baur, H.P. Nilles, A. Trautner and P.K.S. Vaudrevange, A String Theory of Flavor and \( \mathcal{CP} \) , Nucl. Phys. B 947 (2019) 114737 [arXiv:1908.00805] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  58. G.-J. Ding, F. Feruglio and X.-G. Liu, Automorphic Forms and Fermion Masses, JHEP 01 (2021) 037 [arXiv:2010.07952] [INSPIRE].

    Article  Google Scholar 

  59. H. Georgi and S.L. Glashow, Unity of All Elementary Particle Forces, Phys. Rev. Lett. 32 (1974) 438 [INSPIRE].

    Article  Google Scholar 

  60. S.F. King, Unified Models of Neutrinos, Flavour and CP-violation, Prog. Part. Nucl. Phys. 94 (2017) 217 [arXiv:1701.04413] [INSPIRE].

    Article  Google Scholar 

  61. E. Ma and G. Rajasekaran, Softly broken A4 symmetry for nearly degenerate neutrino masses, Phys. Rev. D 64 (2001) 113012 [hep-ph/0106291] [INSPIRE].

  62. 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].

    Article  Google Scholar 

  63. 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].

    Article  Google Scholar 

  64. Y. Zhao and H.-H. Zhang, Adjoint SU(5) GUT model with modular S4 symmetry, JHEP 03 (2021) 002 [arXiv:2101.02266] [INSPIRE].

    Article  Google Scholar 

  65. H. Georgi and C. Jarlskog, A New Lepton-Quark Mass Relation in a Unified Theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].

    Article  Google Scholar 

  66. P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].

  67. T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].

  68. M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].

  69. R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].

    Article  MATH  Google Scholar 

  70. J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].

    Article  Google Scholar 

  71. S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].

  72. P.H. Frampton, S.L. Glashow and T. Yanagida, Cosmological sign of neutrino CP-violation, Phys. Lett. B 548 (2002) 119 [hep-ph/0208157] [INSPIRE].

  73. S. Antusch and V. Maurer, Running quark and lepton parameters at various scales, JHEP 11 (2013) 115 [arXiv:1306.6879] [INSPIRE].

    Article  Google Scholar 

  74. https://root.cern.ch/doc/master/classTMinuit.html.

  75. 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].

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Authors and Affiliations

  1. College of Information Science and Engineering, Ocean University of China, Qingdao, 266100, China

    Peng Chen

  2. Peng Huanwu Center for Fundamental Theory, Hefei, 230026, Anhui, China

    Gui-Jun Ding

  3. Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Gui-Jun Ding

  4. Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, U.K.

    Stephen F. King

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  1. Peng Chen
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Correspondence to Gui-Jun Ding.

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Chen, P., Ding, GJ. & King, S.F. SU(5) GUTs with A4 modular symmetry. J. High Energ. Phys. 2021, 239 (2021). https://doi.org/10.1007/JHEP04(2021)239

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  • Received: 09 February 2021

  • Revised: 30 March 2021

  • Accepted: 30 March 2021

  • Published: 26 April 2021

  • DOI: https://doi.org/10.1007/JHEP04(2021)239

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Keywords

  • Discrete Symmetries
  • GUT
  • Neutrino Physics
  • Quark Masses and SM Parameters
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