CP violation with Majorana neutrinos in K meson decays

We study the possibility of having CP asymmetries in the decay K± → π
∓`
±`
±
(` = e, µ). This decay violates Lepton Number by two units and occurs only if there are
Majorana particles that mediate the transition. Even though the absolute rate is highly
suppressed by current bounds, we search for Majorana neutrino scenarios where the CP
asymmetry arising from the lepton sector could be sizeable. This is indeed the case if there
are two or more Majorana neutrinos with similar masses in the range around 102 MeV. In
particular, the asymmetry is potentially near unity if two neutrinos are nearly degenerate,
in the sense ∆mN ∼ ΓN . The full decay, however, may be difficult to detect not only
because of the suppression caused by the heavy-to-light lepton mixing, but also because of
the long lifetime of the heavy neutrino, which would induce large space separation between
the two vertices where the charge leptons are produced. This particular problem should be
less serious in heavier meson decays, as they involve heavier neutrinos with shorter lifetimes.