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

Abstract

Using the recent first lattice results of the RBC-UKQCD collaboration for $K\to \pi \pi$ decays, we perform a phenomenological analysis of ${ϵ}_K^{\prime }/{ϵ}_K$ 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 ${ϵ}_K$, 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.

Comments: 6 pages, 4 figures; Contribution to proceedings of KAON 2016 conference, Birmingham, UK, 14-17 September 2016