Testing decay of astrophysical neutrinos with incomplete information

Neutrinos mix and have mass differences, so decays from one to another must occur. But how fast? The best direct limits on non-radiative decays, based on solar and atmospheric neutrinos, are weak, $τ\gtrsim 10^{-3}$ s ($m$/eV) or much worse. Greatly improved sensitivity, $τ\sim 10^3$ s ($m$/eV), will eventually be obtained using neutrinos from distant astrophysical sources, but large uncertainties — in neutrino properties, source properties, and detection aspects — do not allow this yet. However, there is a way forward now. We show that IceCube diffuse neutrino measurements, supplemented by improvements expected in the near term, can increase sensitivity to $τ\sim 10$ s ($m$/eV) for all neutrino mass eigenstates. We provide a roadmap for the necessary analyses and show how to manage the many uncertainties. If limits are set, this would definitively rule out the long-considered possibility that neutrino decay affects solar, atmospheric, or terrestrial neutrino experiments.