Remarks on the lifetime of sterile neutrinos and the effect on detection of rare meson decays M+ →m′-ℓ+ℓ+

We review the detection of the ΔL=2 semileptonic meson decays of the form M+→M′-++ that we studied in a previous work, mediated by a Majorana neutrino with a mass in the range between the masses of the initial and final mesons. For such a range of masses, the Majorana neutrino will go on its mass shell, and the two charged leptons will appear at displaced vertices or, if the lifetime is long enough, most secondary vertices will fall outside the detector. We study the consequences of this effect on the experimental searches and limits that can be extracted.