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 / ε K 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 / ε K . In this talk, we show a solution of the ε ′ K / 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 , while the contribution to εK is suppressed thanks to the Majorana nature of gluinos.