Is neutrino decay really ruled out as a solution to the atmospheric neutrino problem from Super-Kamiokande data?

In this paper we do a detailed $\chi^2$-analysis of the 848 days of Super-Kamiokande(SK) atmospheric neutrino data under the assumptions of $\nu_\mu - \nu_\tau$ oscillation and neutrino decay. For the latter we take the most general case of neutrinos with non-zero mixing and consider the possibilities of the unstable component in $\nu_\mu$ decaying to a state with which it mixes (scenario (a)) and to a sterile state with which it does not mix (scenario (b)). In the first case $\Delta m^2$ (mass squared difference between the two mass states which mix) has to be $>$ 0.1 $eV^2$ from constraints on $K$ decays while for the second case $\Delta m^2$ can be unconstrained. For case (a) $\Delta m^2$ does not enter the $\chi^2$-analysis while in case (b) it enters the $\chi^2$-analysis as an independent parameter. In scenario (a) there is \dm averaged oscillation in addition to decay and this gets ruled out at 100.0% C.L. by the latest SK data. Scenario (b) on the other hand gives a reasonably good fit to the data for \dm $\sim 0.001 ~eV^2$.