<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math> violation in modular invariant flavor models

Abstract

We study the spontaneous $CP$ violation through the stabilization of the modulus $\ensuremath{\tau}$ in modular invariant flavor models. The $CP$-invariant potential has the minimum only at $\mathrm{Re}[\ensuremath{\tau}]=0$ or $1/2(\mathrm{mod}\text{ }1)$. From this result, 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 $CP$ violation.

Topics & Concepts