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

TL;DR

This paper investigates the $ ext{CP}$-violating electron-nucleon interaction mediated by Higgs boson exchange at the quark-gluon level within the Standard Model, revealing it arises at four-loop order and estimating its magnitude.

Contribution

It provides a detailed calculation showing the interaction vanishes at three loops and appears at four loops, with a parametric estimate of the resulting electron EDM.

Findings

Total three-loop contribution vanishes for Higgs exchange.

Nonzero contribution appears at four-loop level with gluon insertion.

Estimated electron EDM magnitude is around 10^{-48} e·cm.

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. $\mathcal{CP}$ 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 $\mathcal{CP}$-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 $ \sim10^{-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.