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

Mixed states for neutral current neutrino oscillation