Dark-sector physics in the search for the rare decays $K^+\rightarrow \pi^+ \bar \nu \nu$ and $K_L\rightarrow \pi^0 \bar \nu \nu$

TL;DR

This paper investigates how dark-sector particles could contribute to rare kaon decays, providing new bounds and potential signals for experiments like NA62 and KOTO, and analyzing how experimental cuts affect these bounds.

Contribution

It calculates the dark-sector contributions to rare kaon decay widths and discusses how experimental cuts influence the bounds on dark-sector parameters.

Findings

NA62 sets strict bounds on dark-sector parameters.

KOTO could observe $K_L ightarrow ext{invisible}$ decays within its sensitivity.

The Grossman-Nir bound is weakened due to experimental kinematic cuts.

Abstract

We compute the contribution of the decays $K_L \rightarrow \pi^0 Q \bar Q$ and $K^+ \rightarrow \pi^+ Q \bar Q$, where $Q$ is a dark fermion of the dark sector, to the measured widths for the rare decays $K^+\rightarrow \pi^+ \nu \bar \nu$ and $K_L\rightarrow \pi^0 \nu \bar \nu$. The recent experimental limit for $\Gamma (K^+ \rightarrow \pi^+ \nu \bar \nu)$ from NA62 sets a new and very strict bound on the dark-sector parameters. A branching ratio for $K_L \rightarrow \pi^0 Q \bar Q$ within the reach of the KOTO sensitivity is possible. The Grossman-Nir bound is weakened by the asymmetric effect of the different kinematic cuts enforced by the NA62 and KOTO experiments. This last feature holds true for all models where the decay into invisible states takes place through a light or massless intermediate state.