Electric dipole moments of charged leptons in models with pseudo-Dirac sterile fermions

TL;DR

This paper derives a comprehensive two-loop formula for charged lepton EDMs in models with pseudo-Dirac sterile neutrinos, showing predicted EDMs are far below current experimental bounds but could be detectable with additional neutrinos.

Contribution

It provides the first complete analytical two-loop calculation of charged lepton EDMs in minimal pseudo-Dirac neutrino models, including numerical evaluations consistent with experimental constraints.

Findings

Predicted electron EDM is around 10^{-36} e·cm, below current bounds.

Analytical formulas are applicable to any model with pseudo-Dirac heavy neutrinos.

Future experiments might detect EDMs if more pseudo-Dirac neutrinos are included.

Abstract

In this work, we address the impact of a small lepton number violation on charged lepton electric dipole moments - EDMs. Low-scale seesaw models protected by lepton number symmetry and leading to pseudo-Dirac pairs in the neutrino heavy spectrum provide a natural explanation for the smallness of neutrino masses with potentially testable consequences. Among which, it was thought that the small mass gap in each pair of pseudo-Dirac neutrinos may induce important contribution to the charged lepton EDMs. Recently, it has been shown that the contribution from some of the Feynman diagrams to charged lepton EDMs exactly cancel by virtue of the Ward-Takahashi identity in quantum electrodynamics. We thus consider here the Standard Model minimally extended with pairs of pseudo-Dirac sterile fermions and derive the complete analytical formula at two loops for the charged lepton EDMs. In addition, we numerically evaluate the order of the predicted EDMs consistent with the experimental bounds and constraints such as neutrino oscillation data, charged lepton flavour violating processes, sterile neutrino direct searches, meson decays, sterile neutrino decays, and cosmological and astrophysical observations. We find that, in the minimal setup accommodating neutrino data (masses and mixings) with only two pseudo-Dirac pairs, the predicted electron EDM is $\mathcal{O}(10^{-36})~e\hspace{0.05cm}\mathrm{cm}$, at most, which is much smaller than the current experimental bound and even future sensitivity. Hopefully, the electron EDM might reach future sensitivity, once extra pseudo-Dirac neutrinos are taken into account. The analytical formulae we derive are generic to any model involving pseudo-Dirac pairs in the heavy neutrino spectrum.