Leptonic dipole operator with Γ2 modular invariance in light of Muon (g-2)μ

We have studied the leptonic EDM and the LFV decays relating with the recent data of anomalous magnetic moment of muon, (g-2)mu in the leptonic dipole operator. We have adopted the successful Gamma 2 modular invariant model by Meloni-Parriciatu as the flavor symmetry of leptons. Suppose the anomaly of (g-2)mu, Delta a mu to be evidence of New Physics (NP), we have related it with the anomalous magnetic moment of the electron Delta ae, the electron EDM de and the mu -> e gamma decay. We found that the NP contributions to Delta ae(mu) are proportional to the lepton masses squared likewise the naive scaling Delta al proportional to ml2. The experimental constraint of |de| is much tight compared with the one from the branching ratio B(mu -> e gamma) in our framework. Supposing the phase of our model parameter delta alpha for the electron to be of order one, we have estimated the upper-bound of B(mu -> e gamma), which is at most 10-21-10-20. If some model parameters are real, leptonic EDMs vanish since the CP phase of the modular form due to modulus tau does not contribute to the EDM. However, we can obtain B(mu -> e gamma)similar or equal to 10-13 with non-vanishing de in a specific case. The imaginary part of a parameter can lead to de in the next-to-leading contribution. The predicted electron EDM is below 10-32e cm, while B(mu -> e gamma) is close to the experimental upper-bound. The branching ratios of tau -> e gamma and tau ->mu gamma are also discussed.