Recent progress on CP violation in K→ππ decays in the SM and a supersymmetric solution

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