Sterile neutrinos facing kaon physics experiments

Understand

We discuss weak kaon decays in a scenario in which the Standard Model is extended by massive sterile fermions.

• After revisiting the analytical expressions for leptonic and semileptonic decays we derive the expressions for decay rates with two neutrinos in the final state.
• By using a simple effective model with only one sterile neutrino, compatible with all current experimental bounds and general theoretical constraints, we conduct a thorough numerical analysis which reveals that the impact of the presence of massive sterile neutrinos on kaon weak decays is very small, less than $1\%$ on decay rates.
• The only exception is $\mathcal{B} (K_L\to \nu\nu)$, which can go up to $\mathcal{O}( 10^{-10})$, thus possibly within the reach of the KOTO experiment.