Sterile neutrinos facing kaon physics experiments

TL;DR

This paper analyzes how massive sterile neutrinos affect kaon decay rates, finding minimal impact overall but potential observable effects in specific rare decay channels like K_L to neutrinos.

Contribution

It provides a detailed theoretical and numerical analysis of sterile neutrino effects on kaon decays, including new expressions for decay rates with two neutrinos.

Findings

Sterile neutrinos cause less than 1% change in most kaon decay rates.

The branching ratio for K_L to neutrinos can reach 10^{-10}, possibly detectable.

Future measurements consistent with the Standard Model do not exclude sterile neutrinos.

Abstract

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. In other words, if all the future measurements of weak kaon decays turn out to be compatible with the Standard Model predictions, this would not rule out the existence of massive light sterile neutrinos with non-negligible active-sterile mixing. Instead, for a sterile neutrino of mass below $m_K$, one might obtain a huge enhancement of $\mathcal{B} (K_L\to \nu\nu)$, otherwise negligibly small in the Standard Model.