Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models

TL;DR

This paper investigates how the electron electric dipole moment (EDM) in a supersymmetric modular invariant flavor model constrains the SUSY mass scale and CP violation originating from the modulus , with implications for future experiments.

Contribution

It demonstrates that the electron EDM constrains the SUSY mass scale and CP violation from the modulus  in a supersymmetric  modular invariant flavor model, linking EDM measurements to flavor physics.

Findings

Electron EDM excludes SUSY masses below 2-6 TeV.

Future EDM sensitivity could probe SUSY masses up to 10-20 TeV.

Correlations between electron EDM and  decay rate are predicted.

Abstract

The electric dipole moment (EDM) of electron is studied in the supersymmetric $\rm A_4$ modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus $\tau$. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed $\tau$ also causes the CP violation in the soft SUSY breaking terms. The elecrton EDM arises from the CP non-conserved soft SUSY breaking terms. The experimental upper bound of the electron EDM excludes the SUSY mass scale below $2-6$ TeV for five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus $\tau$, we examine the correlation between the electron EDM and the decay rate of the $\mu \rightarrow e \gamma$ decay, which is also predicted by the soft SUSY breaking terms. The correlations are clearly predicted in contrast to models of the conventional flavor symmetry. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, $|d_e/e| \simeq 10^{-30}$. Indeed, it could probe the SUSY mass range of $10-20$ TeV in our model. Thus, the electron EDM provides a severe test of the CP violation via the modulus $\tau$ in the supersymmetric modular invariant theory of flavors.