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

Abstract

Using the recent first lattice results of the RBC-UKQCD collaboration for $K \to ππ$ decays, we perform a phenomenological analysis of $ε_K^{\prime}/ε_K$ and find a discrepancy between SM prediction and experiments by $\sim 3\,σ$. We discuss an explanation by new physics. The well-understood value of $ε_K$, which quantifies indirect $CP$ violation, however, typically prevents large new physics contributions to $ε_K^{\prime}/ε_K$. In this talk, we show a solution of the $ε_K^{\prime}/ε_K$ 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 $ε_K^{\prime}$, while the contribution to $ε_K$ is suppressed thanks to the Majorana nature of gluinos.