T, P-odd electron-nucleon interaction via a Higgs-boson exchange at the quark-gluon level

The electron pseudoscalar -- nucleon scalar T,~P-odd interaction within the framework of the Standard Model is considered as an exchange mediated by the Higgs boson at the quark-gluon level. CP violation is introduced through a phase factor in the Cabibbo-Kobayashi-Maskawa matrix, which characterizes the flavor structure of the quark loop. We explicitly demonstrate that the total three-loop contribution vanishes for the Higgs boson exchange mechanism. A nonzero contribution appears at the four-loop quark-gluon level only with the insertion of an additional gluon line between the quarks. The estimate of the CP-odd electron-nucleon interaction coupling constant after reduction of divergencies of the quark loop integral using the Glashow-Iliopoulos-Maiani (GIM) mechanism yields a value ~10⁻²⁸. The final result, expressed in terms of the equivalent electron electric dipole moment (eEDM), is 10⁻⁴⁸ \,\, ecm, and its order of magnitude coincides with that of the GIM estimate of the eEDM at the quark-gluon level. Our parametric estimate of the eEDM differs from previous studies by a factor that depends on the mass of the b quark.