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Charged lepton electric dipole moment enhancement in the Lorentz violated extension of the standard model

We consider the Lorentz violated extension of the standard model. In this framework, there are terms that explicitly violate CP-symmetry. We examine the CPT-even $d_{μν}$-term to find the electric dipole moment of charged leptons. We show that the form factors besides the momentum transfer, depend on a new Lorentz-scalar, constructing by $d_{μν}$ and the four momenta of the lepton, as well. Such an energy dependence of the electric dipole form factor leads to an enhancement of the lepton electric dipole moment at high energy, even at the zero momentum transfer. We show that at $\frac{|d|p^2}{m^2_l}\sim 1$ the electric dipole moment of the charged lepton can be as large as $10^{-14} e\,\,cm$.