  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.
