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disappearance probability is a maximum. The determi- nation of the limit follows the procedure described above, but with the addition of selecting a value of θ$_{24}$ for each test case as well. At 90% confidence level f$_{s}$ < 0 . 52 (0 . 55) for E$_{ν}$ = 1 . 4 GeV in this model. Thus, in either model, approximately 50% of the disappearing ν$_{µ}$ can convert to ν$_{s}$ at 90% confidence level as long as the amount of ν$_{e}$ ap- pearance is less than the limit presented by the CHOOZ collaboration. 

It was noted more than a decade ago that neutrino decay, as an alternative or companion process to neu- trino oscillations, offers some capability for reproducing neutrino disappearance trends [18]. The model investi- gated here [36] includes neutrino oscillations occurring in parallel with neutrino decay. Normal neutrino-mass or- dering is assumed, and the mass eigenstates ν$_{1}$ , ν$_{2}$ are approximately degenerate, so that m$_{3}$ ≫ m$_{2}$ ≈ m$_{1}$ . The heaviest neutrino-mass state ν$_{3}$ is allowed to decay into an invisible final state. With these assumptions, and ne- glecting the small contributions from ν$_{e}$ mixing, only the two neutrino flavor states ν$_{µ}$ and ν$_{τ}$ , and the correspond- ing mass states ν$_{2}$ and ν$_{3}$ , are considered. The evolution of the neutrino flavor states is given by [36]: 

where τ$_{3}$ is the lifetime of the ν$_{3}$ mass state and θ is the mixing angle governing oscillations between ν$_{µ}$ and ν$_{τ}$ . Solving Eq. (16) one obtains probabilities for ν$_{µ}$ survival or decay: 

The limits τ$_{3}$ → ∞ and Δ m 2 32 → 0 correspond to a pure oscillations or a pure decay scenario, respectively. 

In a conventional neutrino oscillations scenario, the ra- tio of the predicted charged-current spectrum in the far- detector with the null-oscillation expectation displays the characteristic “dip” at the assumed Δ m 2 32 value that is 

## IX. OSCILLATIONS WITH DECAY 

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