Lepton electric dipole moment and strong CP violation

Contribution of the strong CP angle, θ¯, to the Wilson Coefficients of electron and muon electric dipole moment (EDM) operators are discussed. Previously, θ¯ contribution to the electron EDM operator was calculated by Choi and Hong [1]. However, the effect of CP-violating three meson coupling was missing in [1]. We include this missing contribution for the first time in the literature, and reevaluate the Wilson coefficients of the lepton EDM operator. We obtain de=−(2.2–8.6)×10−28θ¯e-cm which is 15–70% of the result obtained in [1]. We also estimated the muon EDM as dμ=−(0.5–1.8)×10−25θ¯e-cm. Using |θ¯|≲10−10 suggested by the neutron EDM measurements, we obtain |de|≲8.6×10−38e-cm and |dμ|≲1.8×10−35e-cm. The θ¯ contribution to the muon EDM is much below the sensitivities of the current and near future experiments. Our result shows that the θ¯ contribution to de,μ can be larger than the CKM contributions by many orders of magnitude