Abstract
The electric dipole moment (EDM) of electron is studied in the supersymmetric A4 modular invariant theory of flavors with CP invariance. The CP symmetry of the lepton sector is broken by fixing the modulus τ. Lepton mass matrices are completely consistent with observed lepton masses and mixing angles in our model. In this framework, a fixed τ also causes the CP violation in the soft SUSY breaking terms. The electron 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 4–6 TeV depending on five cases of the lepton mass matrices. In order to see the effect of CP phase of the modulus τ, we examine the correlation between the electron EDM and the decay rate of the μ → eγ 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 branching ratio is approximately proportional to the square of |de/e|. The SUSY mass scale will be constrained by the future sensitivity of the electron EDM, |de/e| ≃ 10−30 cm. 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 τ in the supersymmetric modular invariant theory of flavors.
Highlights
Models based on flavor symmetries is replaced by the moduli space, and Yukawa couplings are given by modular forms
In order to see the effect of CP phase of the modulus τ, we examine the correlation between the electron electric dipole moment (EDM) and the decay rate of the μ → eγ decay, which is predicted by the soft SUSY breaking terms
In order to see the effect of CP phase in the modulus τ, we examine the correlation between the electron EDM and the decay rate of the μ → eγ decay
Summary
The CP transformation is non-trivial if the non-Abelian discrete flavor symmetry G is set in the Yukawa sector of a Lagrangian [113, 132]. CP symmetry along with a flavor symmetry, is given as follows [133,134,135]: Xrρ∗r(g)X−r 1 = ρr(g ) , g, g ∈ G This is called the consistency condition for Xr. 2.2 Modular symmetry The modular group Γis the group of linear fractional transformations γ acting on the modulus τ , belonging to the upper-half complex plane as: aτ + b τ −→ γτ =. The Kähler potential of chiral matter fields ψi with the modular weight −k is given by. The general Kähler potential consistent with the modular symmetry possibly contains additional terms [137]. These modular forms have been explicitly given [11] in the symmetric base of the A4 generators S and T for the triplet representation (see appendix A) in appendix B
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