Lepton number violation in D meson decay

The lepton number violating process can be induced by introducing a fourth generation heavy Majorana neutrino, which is coupled to the charged leptons of Standard Model. There have been many previous studies on the leptonic number violating decay processes with this mechanism, we follow the trend to study the process: $D \to K \ell \ell \pi$ with the same-sign dilepton final states. We restrict ourself to certain neutrino mass regions, in which the heavy neutrino could be on shell and the dominant contribution to the branching fraction comes from the resonance enhanced effect. Applying the Narrow Width Approximation, we found that upper limit for the branching fractions for $D^0 \to K^-\ell^+\ell^+\pi^-$ are generally at the order of $10^{-10}$ to $10^{-9}$, if we take the most stringent upper limit bound currently available in the literature for the mixing matrix elements. We also provide the constrains, which is competitive compared to the LNV B decays, on the mixing matrix element $|V_{eN}|^2$ based on the upper limit of $D^0 \to K^- e^+ e^+ \pi^-$ estimated from Monte-Carlo study at BESIII.