Challenging Majorana neutrino effects in $B\to K^{(\ast)}\nu\nu$ and $K\to \pi\nu\nu$ decays
We investigate the contributions of Lepton Number Violating (LNV) effective operators to the rare decays $B\to K^{(\ast)}\nu\nu$ and $K\to \pi\nu\nu$. Such operators can modify the kinematic distributions of these processes, providing distinctive probes of physics beyond the Standard Model. Through a renormalization-group analysis, we show that the Standard Model Effective Field Theory (SMEFT) operators responsible for these effects are subject to stringent indirect constraints from neutrino physics. In particular, we find that the mild excess reported by Belle-II in the $B^+\to K^+\nu\nu$ channel cannot be explained by LNV SMEFT operators without introducing significant fine-tuning in neutrino masses. We then show that these constraints can be evaded in the SMEFT minimally extended by a light right-handed neutrino, allowing for sizable effects in rare meson decays. Finally, we explore the implications of this viable scenario for low-energy processes, including neutrinoless double-beta decays.