Impact of the electroweak Weinberg operator on the electric dipole moment of electron

Abstract

Recent progress in the electric dipole moment (EDM) measurements of the electron using the paramagnetic atom or molecule is 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 this operator inserted induces the electron EDM. We derive the matching condition and find that even if new SU(2)_L particles have masses around the TeV scale, the electron EDM may be larger than the Standard Model (SM) contribution to the paramagnetic atom or molecule EDMs. We also discuss the relation between the Barr-Zee diagram contribution at two-loop level and three-loop one, assuming that the SM Higgs has new Yukawa interactions with the SU(2)_L multiplets.