Recent progress on CP violation in $K\to \pi \pi$ decays in the SM and a supersymmetric solution

Using the recent first lattice results of the RBC-UKQCD collaboration for $K \to \pi\pi$ decays, we perform a phenomenological analysis of $\epsilon_K^{\prime}/\epsilon_K$ and find a discrepancy between SM prediction and experiments by $\sim 3\,\sigma$. We discuss an explanation by new physics. The well-understood value of $\epsilon_K$, which quantifies indirect $CP$ violation, however, typically prevents large new physics contributions to $\epsilon_K^{\prime}/\epsilon_K$. In this talk, we show a solution of the $\epsilon_K^{\prime}/\epsilon_K$ discrepancy in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without fine-tuning of $CP$ phases. In this solution, the Trojan penguin diagram gives large isospin-breaking contributions which enhance $\epsilon_K^{\prime}$, while the contribution to $\epsilon_K$ is suppressed thanks to the Majorana nature of gluinos.