Light sterile neutrinos and lepton-number-violating kaon decays in effective field theory

We investigate lepton-number-violating decays K ∓ → π ± l ∓ l ∓ in the presence of sterile neutrinos. We consider minimal interactions with Standard-Model fields through Yukawa couplings as well as higher-dimensional operators in the framework of the neutrino-extended Standard Model Effective Field Theory. We use SU(3) chiral perturbation theory to match to mesonic interactions and compute the lepton-number-violating decay rate in terms of the neutrino masses and the Wilson coefficients of higher-dimensional operators. For neutrinos that can be produced on-shell, the decay rates are highly enhanced and higher-dimensional interactions can be probed up to very high scales around 𝒪 (30) TeV.