Feasibility Study of Lepton Number Violation in Rare $B$ and $K$ Meson Decays

We study lepton-number-violating interactions at dimension seven in the Standard Model effective field theory that contribute to the meson decays $B \to K \nu \nu$ and $K \to \pi \nu \nu$. Such interactions could washout the baryon asymmetry of the Universe and also contribute to the neutrinoless double beta decay, even though the interactions involve a change in down-type quark flavors. We clarify conditions under which excesses in meson decay rates over the Standard Model predictions can be successfully observed. We also show that, although these interactions contribute to neutrino masses at the two-loop level, the Weinberg operator can be introduced consistently without spoiling the scenario.