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We study the leptonic CP violation by employing the complete set of dimension-six pure leptonic effective operators. Connection among the observable at different energy scales can be made by the running of the renormalization group equations. Explicitly, we study the charged lepton electric dipole moment, muon Michel decay, and the triple spin-momentum correlations at the Linear Collider. We found the electron electric dipole moment, which starts at 2-loop level, severely constrains the possibilities to detect the CP violating signatures in muon decay and at the linear colliders.

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