  The experimental confirmation of neutrino mass and mixing disagrees with the
picture of the Standard Model, and thus provides a good motivation to look for
unknown physics. A seesaw variant in which neutrino masses are radiatively
generated, with neutrinos characterized by Majorana fields and where a set of
three hypothetical neutral heavy leptons are present, has been considered in
the present work. We have calculated, estimated, and analyzed the contributions
from virtual light and heavy neutrinos to the gauge vertex $WWZ$, in the
context of a future electron-positron collider. We have found that
contributions to both $CP$-even and $CP$-odd anomalous couplings are generated.
Our estimations indicate that contributions as large as $~10^{-3}$ can be
achieved in both cases. This is particularly interesting for the $CP$-odd
effects, which are expected to appear in the framework of the Standard Model
since the three-loop order, thus being quite suppressed. By considering the
expected sensitivity of the International Linear Collider to this gauge vertex,
we conclude that these new-physics effects would be within its reach for
$e^+e^-$ collisions taking place at a center-of-mass energy of $800\,{\rm
GeV}$.
