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

We investigate lepton-number-violating decays $K^\mp \rightarrow \pi^\pm
l^\mp l^\mp$ 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 $ \mathcal{O}$(300) TeV.