literature

Quark mass hierarchies and CP violation in A4_{4} × A4_{4} × A4_{4} modular symmetric flavor models

Feb 7, 2023
42 pages
Published in:
  • JHEP 07 (2023) 134
  • Published: Jul 17, 2023
e-Print:
Report number:
  • EPHOU-23-004

Citations per year

20222023202401612
Abstract: (Springer)
We study A4_{4}× A4_{4}× A4_{4} modular symmetric flavor models to realize quark mass hierarchies and mixing angles without fine-tuning. Mass matrices are written in terms of modular forms. At modular fixed points τ = i∞ and ω, A4_{4} is broken to Z3_{3} residual symmetry. When the modulus τ is deviated from the fixed points, modular forms show hierarchies depending on their residual charges. Thus, we obtain hierarchical structures in mass matrices. Since we begin with A4_{4}× A4_{4}× A4_{4}, the residual symmetry is Z3_{3}× Z3_{3}× Z3_{3} which can generate sufficient hierarchies to realize quark mass ratios and absolute values of the CKM matrix |VCKM_{CKM}| without fine-tuning. Furthermore, CP violation is studied. We present necessary conditions for CP violation caused by the value of τ. We also show possibilities to realize observed values of the Jarlskog invariant JCP_{CP}, quark mass ratios and CKM matrix |VCKM_{CKM}| simultaneously, if (10) adjustments in coefficients of Yukawa couplings are allowed or moduli values are non-universal.
Note:
  • 42 pages, 3 figures
  • CKM Parameters
  • CP Violation
  • Discrete Symmetries
  • Flavour Symmetries
  • CP: violation
  • quark: mass: hierarchy
  • flavor: model
  • quark: mass ratio
  • mass: hierarchy
  • quark: mass