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Heavy sterile-like neutrinos may be produced resonantly from the decay ofpseudoscalar mesons and may decay into several different channels in a cascade$\Phi \rightarrow L^\alpha \nu_h;\nu_h\rightarrow \{X\}$. In general these arerare events with displaced vertices. We provide a non-perturbative andmanifestly unitary framework that describes the cascade decay and yields thespace-time evolution of the probabilities for sterile neutrinos, final statesand the total number of events at a far detector. The results are general,valid for Dirac or Majorana neutrinos and only input the total decay rates andbranching ratios for the production and decay channels. We apply the generalresults to two examples of "visible" decay: i) $K^+\rightarrow e^+\nu_h\rightarrow (e^+) e^+ e^- \nu_e$ via a standard model charged currentvertex and ii) the radiative decay $K^+\rightarrow \mu^+ \nu_h \rightarrow(\mu^+) \nu_a \gamma$. For this latter cascade process we find substantialcorrections to previous assessments within the parameter space argued to solvethe anomalous excess of electron-like events at MiniBooNE. These largecorrections may help relieve the tension with recent experimental bounds onradiative decays of heavy sterile neutrinos.

Space-time evolution of heavy sterile neutrinos in cascade decays