$\mathcal{T}$, $\mathcal{P}$-odd electron-nucleon interaction via a Higgs-boson exchange at the quark-gluon level

Abstract

The electron pseudoscalar -- nucleon scalar $\mathcal{T}$,~$\mathcal{P}$-odd interaction within the framework of the Standard Model is considered as an exchange mediated by the Higgs boson at the quark-gluon level. $\mathcal{C}\mathcal{P}$ 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 $\mathcal{C}\mathcal{P}$-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 $\sim 10^{-28}$. The final result, expressed in terms of the equivalent electron electric dipole moment ($e$EDM), is $10^{-48}e\text{cm}$, and its order of magnitude coincides with that of the GIM estimate of the $e$EDM at the quark-gluon level. Our parametric estimate of the $e$EDM differs from previous studies by a factor that depends on the mass of the $b$ quark.