  The theory of neutrino oscillation predicts that if both neutrino and
antineutrino coming from $Z_0$ decay are detected, one can observe an
oscillation pattern between the corresponding detectors. This prediction is
based on two properties; the neutrino-antineutrino pairs are produced
coherently and they are detected with definite flavor in detectors. In this
paper, we reanalyze this problem by considering some massive neutrinos which
are mixed with light neutrinos but they either participate incoherently or are
decoupled in the production and detection processes. In fact, neutrinos whose
masses are larger than the upper bound on the mass uncertainty to be compatible
with the coherence conditions (we will see it is about 1 keV) must be treated
incoherently. Very heavy neutrinos whose masses are much larger than the
neutrino energy in the neutrino production process are decoupled. Under these
conditions, the created neutrino-antineutrino state as well as the states of
detected neutrino and antineutrino is mixed. We see that the oscillation
pattern cannot be observed for incoherent neutrinos and the standard
oscillation pattern is recovered if the light neutrino masses are ignored in
the production and detection processes. Moreover, since the $Z_0$ decay process
is performed blindly with respect to flavors, the oscillating contributions in
the event rates are independent of the $Z_0$ decay width.

High Energy Physics - Phenomenology;Quantum Physics