  Non-unitarity of the neutrino mixing matrix is expected in many scenarios
with physics beyond the Standard Model. Motivated by the search for deviations
from unitary, we study two neutrino counting observables: the
neutrino-antineutrino gamma process and the invisible $Z$ boson decay into
neutrinos. We report on new constraints for non-unitarity coming from the first
of this observables. We study the potential constraints that future collider
experiments will give from the invisible decay of the Z boson, that will be
measured with improved precision.
