Modular Flavor Symmetries and Fermion Mass Hierarchies
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909665710833664 |
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| author | Chen, Mu-Chun Li, Xueqi Liu, Xiang-Gan Ratz, Michael |
| author_facet | Chen, Mu-Chun Li, Xueqi Liu, Xiang-Gan Ratz, Michael |
| contents | We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus $τ$ to be located near one of the critical points, $i$, $i\infty$, or $ω$. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points $i$ and $ω$. We compare the traditional Froggatt--Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular Flavor Symmetries and Fermion Mass Hierarchies Chen, Mu-Chun Li, Xueqi Liu, Xiang-Gan Ratz, Michael High Energy Physics - Phenomenology We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus $τ$ to be located near one of the critical points, $i$, $i\infty$, or $ω$. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points $i$ and $ω$. We compare the traditional Froggatt--Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries. |
| title | Modular Flavor Symmetries and Fermion Mass Hierarchies |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.23343 |