$CP$ violation in modular invariant flavor models

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 $\mathrm{Re}[\tau ]=0$ 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.

19 pages, 2 figures