Search for lepton-number-violating signals in the charm sector

We explore signals of lepton-number-violation in the charm physics sector. We study the four-body $|\Delta L|= 2$ decays of the $D^0$ meson, $D^0 \to P^- \pi^-\mu^+ \mu^+$ ($P = \pi, K$) as an alternative evidence of the Majorana nature of neutrinos. We carry out an exploratory study on the potential sensitivity that LHCb experiment could achieve for these $|\Delta L|= 2$ processes. We show that for a long term expected integrated luminosity of 300 fb$^{-1}$, a signal significance of branching ratios of the order $\mathcal{O}(10^{-9})$ might be accessible, allowing to improve the experimental bounds obtained by the E791 experiment. Limits on the parameter space of a heavy sterile neutrino that could be obtained from their experimental search are discussed as well.