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Fermion hierarchies in SU(5) grand unification from \( {\Gamma}_6^{\prime } \) modular flavor symmetry

  • Regular Article - Theoretical Physics
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  • Published: 17 August 2023
  • Volume 2023, article number 97, (2023)
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Fermion hierarchies in SU(5) grand unification from \( {\Gamma}_6^{\prime } \) modular flavor symmetry
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  • Yoshihiko Abe1,
  • Tetsutaro Higaki2,
  • Junichiro Kawamura3 &
  • …
  • Tatsuo Kobayashi4 

  • 214 Accesses

  • 10 Citations

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A preprint version of the article is available at arXiv.

Abstract

We construct an SU(5) grand unified model in which the hierarchies of the quark and lepton masses and mixing are explained by the \( {\Gamma}_6^{\prime } \) modular flavor symmetry. The hierarchies are realized by the Froggatt-Nielsen-like mechanism due to the residual \( {Z}_6^T \) symmetry, approximately unbroken at τ ~ i∞. We argue that the \( {\Gamma}_6^{\left({}^{\prime}\right)} \) symmetry is the minimal possibility to realize the up-type quark mass hierarchies, since the Yukawa matrix is symmetric. We find a combination of the representations and modular weights and then show numerical values of (1) coefficients for the realistic fermion hierarchies.

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Acknowledgments

The work of J.K. is supported in part by the Institute for Basic Science (IBS-R018-D1). This work is supported in part by he Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture (MEXT), Japan No. JP22K03601 (T.H.) and JP23K03375 (T.K.). The work of Y.A. is supported by JSPS Overseas Research Fellowships.

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Authors and Affiliations

  1. Department of Physics, University of Wisconsin, Madison, WI, 53706, USA

    Yoshihiko Abe

  2. Department of Physics, Keio University, Yokohama, 223-8522, Japan

    Tetsutaro Higaki

  3. Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon, 34051, Korea

    Junichiro Kawamura

  4. Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan

    Tatsuo Kobayashi

Authors
  1. Yoshihiko Abe
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  2. Tetsutaro Higaki
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  3. Junichiro Kawamura
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  4. Tatsuo Kobayashi
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Corresponding author

Correspondence to Junichiro Kawamura.

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ArXiv ePrint: 2307.01419

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Cite this article

Abe, Y., Higaki, T., Kawamura, J. et al. Fermion hierarchies in SU(5) grand unification from \( {\Gamma}_6^{\prime } \) modular flavor symmetry. J. High Energ. Phys. 2023, 97 (2023). https://doi.org/10.1007/JHEP08(2023)097

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  • Received: 17 July 2023

  • Revised: 02 August 2023

  • Accepted: 04 August 2023

  • Published: 17 August 2023

  • DOI: https://doi.org/10.1007/JHEP08(2023)097

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Keywords

  • Theories of Flavour
  • Grand Unification
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