Enhanced tau neutrino appearance through invisible decay

The decay of neutrino mass eigenstates leads to a change of the conversion and survival probability of neutrino flavor eigenstates. Remarkably, we find that the neutrino decay provides an enhancement of the expected tau appearance signal with respect to the standard oscillation scenario for the long-baseline OPERA experiment. The increase of the $\nu_\mu \rightarrow \nu_\tau$ conversion probability by the decay of one of the mass eigenstates is due to a reduction of the "destructive interference" among the different massive neutrino components. Motivated by the recently released results of the OPERA Collaboration showing a number of observed $\nu_\tau$ events larger than expected, we perform a statistical analysis including the invisible decay hypothesis. We obtain a very mild preference for invisible decays, with a best fit value $\tau_3/m_3 \simeq 2.6\times 10^{-13} $ s/eV, and a constraint at the 90$\%$ confidence level for the neutrino decay lifetime to be $\tau_3/m_3 \gtrsim 1.3\times 10^{-13}$ s/eV.