$\epsilon_K^\prime/\epsilon_K$: Standard Model and Supersymmetry

Abstract

I give a pedagogical introduction into flavour-changing neutral current interactions of kaons and their role to reveal or constrain physics beyond the Standard Model (SM). Then I discuss the measure $\epsilon_K^\prime$ of direct CP violation in $K\to \pi\pi$ decays, which deviates from the SM prediction by $2.8\sigma$. A supersymmetric scenario with flavour mixing among left-handed squarks can accomodate the measured value of $\epsilon_K^\prime$ even for very heavy sparticles, outside the reach of the LHC. The considered scenario employs mass splittings among the right-handed up and down squarks (to enhance $\epsilon_K^\prime$) and a gluino which is heavier than the left-handed strange-down mixed squarks by at least a factor of 1.5 (to suppress excessive contribution to $\epsilon_K$, the measure of indirect CP violation). The branching ratios of the rare decays $K^+ \to \pi^+ \nu \bar\nu$ and $K_L \to \pi^0 \nu \bar\nu$, to be measured by the NA62 and KOTO-step2 experiments, respectively, are only moderately affected. These measurements have the capability to either falsify the model or to constrain the CP phase associated with strange-down squark mixing accurately.