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

Abstract

We investigate lepton-number-violating decays $K^{\mp }\to {\pi }^{\pm }{l}^{\mp }{l}^{\mp }$ 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 $\mathcal{O}$(30) TeV.

31 pages, 6 figures

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• Effective portals to heavy neutral leptons
• Long-lived neutral fermions at the DUNE near detector
• Sensitivity prospects for lepton-trijet signals in the $\nu$SMEFT at the LHeC
• RGE solver for the complete dim-7 SMEFT interactions and its application to $0\nu \beta \beta$ decay
• The lepton-number-violating pion decay and the type-I seesaw mechanism in chiral perturbation theory