Quark mass hierarchies and CP violation in A × A × A modular symmetric flavor models
Feb 7, 2023
42 pages
Published in:
- JHEP 07 (2023) 134
- Published: Jul 17, 2023
e-Print:
- 2302.03326 [hep-ph]
Report number:
- EPHOU-23-004
View in:
Citations per year
Abstract: (Springer)
We study A× A× A 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, A is broken to Z 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 A× A× A, the residual symmetry is Z× Z× Z which can generate sufficient hierarchies to realize quark mass ratios and absolute values of the CKM matrix |V| 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 J, quark mass ratios and CKM matrix |V| 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
References(100)
Figures(3)
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