Impact of the Electroweak Weinberg Operator on the Electric Dipole Moment of Electron

Recent progresses in the measurements of the electric dipole moment (EDM) of the electron using the paramagnetic atom or molecule are remarkable. In this paper, we calculate a contribution to the electron EDM at three-loop level, introducing the CP-violating Yukawa couplings of new SU(2)$_L$ multiplets. At two-loop level, the Yukawa interactions generate a CP-violating dimension-six operator, composed of three SU(2)$_L$ field strengths, called the electroweak Weinberg operator. Another one-loop diagram with the operator inserted induces the electron EDM. We find that even if new SU(2)$_L$ particles have masses around TeV-scale, the electron EDM may be larger than the Standard Model contribution to the paramagnetic atom or molecule EDMs. We also discuss the relation between the Barr-Zee diagram contribution at two-loop level and the three-loop one, assuming that the SM Higgs has new Yukawa interactions with the SU(2)$_L$ multiplets.