Interference effects in semileptonic decays from heavy Majorana neutrinos

Several beyond the Standard Model scenarios introduce new heavy neutrinos, whose Dirac or Majorana nature could be tested by comparing the rates of lepton number violating and lepton number conserving processes: a Dirac fermion induces only the latter, while a Majorana one predicts the same rate for both of them. Nevertheless, in the presence of more than one Majorana fermion, this picture may change drastically due to interference effects. We focus on lepton number violating and lepton flavour violating semileptonic meson decays induced by two heavy Majorana fermions, exploring the necessary conditions to have sizeable interference effects and discussing their implications for current experimental constraints and possible future observations. In particular, we show how the $CP$ violating phases may lead to an enhancement of the lepton number violating modes and suppression of the lepton number conserving ones, and vice-versa.