If the heaviest neutrino mass eigenstate is unstable, its decay modes could include lighter neutrino eigenstates. In this case part of the decay products could be visible, as they would interact at neutrino detectors via mixing. At neutrino oscillation experiments, a characteristic signature of such emph{visible neutrino decay} would be an apparent excess of events at low energies. We focus on a simple phenomenological model in which the heaviest neutrino decays as $ u_3 rightarrow u_{1,2} + phi$, where $phi$ is a new light scalar. If neutrinos are Majorana particles the helicity-flipping decays would be observable (i.e., $ u to bar u + phi$), leading to interesting observable consequences on the event rates. We compute the sensitivities of the Deep Underground Neutrino Experiment (DUNE) to the couplings of the new scalar as a function of the lightest neutrino mass. Under the assumption that only the heaviest neutrino is unstable, and for a normal mass ordering, we find that DUNE will be sensitive to values of $tau_3/m_3 > 1.95 - 2.6times 10^{-10}$~s/eV (90% C.L.) (depending on the lightest neutrino mass), where $tau_3$ and $m_3$ are the lifetime and mass of $ u_3$, respectively.
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