$CP$ violation in modular invariant flavor models

Hikaru Uchida; Kenta Takagi; Morimitsu Tanimoto; Takuya H. Tatsuishi; Tatsuo Kobayashi; Yusuke Shimizu

$CP$ violation in modular invariant flavor models

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arxiv 1910.11553 v2 pith:ZXUX2IUD submitted 2019-10-25 hep-ph hep-th

Tatsuo Kobayashi , Yusuke Shimizu , Kenta Takagi , Morimitsu Tanimoto , Takuya H. Tatsuishi , Hikaru Uchida This is my paper · ORCID

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keywords violationmodularflavorinvariantmodelsspontaneoussymmetryconservation

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abstract

We study the spontaneous $CP$ violation through the stabilization of the modulus $\tau$ in modular invariant flavor models. The $CP$-invaraiant potentential has the minimum only at ${\rm Re}[\tau] = 0$ or 1/2. From this prediction, we study $CP$ violation in modular invariant flavor models. The physical $CP$ phase is vanishing. The important point for the $CP$ conservation is the $T$ transformation in the modular symmetry. One needs the violation of $T$ symmetry to realize the spontaneous $CP$ violation.

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Large and small hierarchies from finite modular symmetries
hep-ph 2024-12 conditional novelty 6.0 of 10

Using finite modular symmetries, radiative stabilization of multiple moduli can simultaneously generate large and small hierarchies, such as Im τ1 ≈ 3 and Im τ2 ≈ 15.

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