16  (deg) 23 30 40 50 60 2 0 1 2 3 =0 13 =12 13  (deg) 34 20 40 60  (deg) 24 2 4 6 8 10 12 68% 90% FIG. 14: Projections of Δ χ 2 as a function of the mixing angles for the m 4 ≫ m 3 model. The solid line is obtained for the case of null ν$_{e}$ appearance whereas the dashed line represents solutions with ν$_{e}$ appearance at the CHOOZ limit. The ranges of values allowed at 68% and 90% confidence levels lie within contours below the horizontal dashed lines. FIG. 15: Contours representing 90% confidence level for the m 4 ≫ m 3 model. The solid line and best-fit point (solid sym- bol) are obtained for the case of null ν$_{e}$ appearance, whereas the dashed line and corresponding best-fit point (open sym- bol) is obtained with ν$_{e}$ appearance included with θ 13 at the CHOOZ limit.  (deg) 23 30 40 50 60 0 5 10 15  (deg) 34 0 20 40 60 (deg) 23 30 40 50 60 (deg) 24 0 5 10 15 =0 13 Best fit point 90% C.L. =12 13 Best fit point 90% C.L. IX. OSCILLATIONS WITH DECAY 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: i d⃗ ν dx = [ Δ m 2 32 4 E ( − cos 2 θ sin 2 θ sin 2 θ cos 2 θ ) − i m$_{3}$ 4 τ$_{3}$E ( 2 sin 2 θ sin 2 θ sin 2 θ 2 cos 2 θ )] ⃗ ν, (16) P$_{µµ}$ = cos 4 θ + sin 4 θe − m$_{3}$L τ$_{3}$E + 2 cos 2 θ sin 2 θe − m$_{3}$L 2 τ$_{3}$E cos ( Δ m 2 $_{32}$L 2 E ) (17) P$_{decay}$ = ( 1 − e − m$_{3}$L τ$_{3}$E ) sin 2 θ. (18) 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. 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