Lepton number violation in D meson decay

The lepton number violation (LNV) process can be induced by introducing a fourth generation heavy Majorana neutrino, which is coupled to the charged leptons of the Standard Model (SM). 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 → Kllπ with the same-sign dilepton final states. We restrict ourselves 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 (NWA), we found that the upper limit for the branching fractions for D⁰ → K^-l⁺l⁺π^- are generally at the order of 10^-12 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 constraints, which is competitive compared to the LNV B decays, on the mixing matrix element |V_eN|² based on the upper limit of D⁰ → K^- e⁺ e⁺ π^- estimated from the Monte-Carlo (MC) study at BESⅢ. Although the constraints are worse than the ones from (0νββ) decay in the literature, the future experiment at the charm factory may yield more stringent constraints.