Direct CP violation in $K\to \pi \pi$ decays and supersymmetry

Abstract

The quantities ${ϵ}_K^{\prime }$ and ${ϵ}_K$ measure the amount of direct and indirect CP violation in $K\to \pi \pi$ decays, respectively. Using the recent lattice results from the RBC and UKQCD Collaborations and a new compact implementation of the $\Delta S=1$ renormalization group evolution we predict $\text{mbox}Re\frac{{ϵ}_K^{\prime }}{{ϵ}_K}=\left(1.06\pm 5.07\right)\times 10^{-4}$ in the Standard Model. This value is $2.8\sigma$ below the experimental value of $\text{mbox}Re\frac{{ϵ}_K^{\prime }}{{ϵ}_K}=\left(16.6\pm 2.3\right)\times 10^{-4}.$ In generic models of new physics the well-understood ${ϵ}_K$ precludes large contributions to ${ϵ}_K^{\prime }$, if the new contributions enter at loop level. However, one can resolve the tension in ${ϵ}_K^{\prime }/{ϵ}_K$ within the Minimal Supersymmetric Standard Model. To this end two features of supersymmetry are crucial: First, one can have large isospin-breaking contributions (involving the strong instead of the weak interaction) which enhance ${ϵ}_K^{\prime }$. Second, the Majorana nature of gluinos permits a suppression of the MSSM contribution to ${ϵ}_K$, because two box diagrams interfere destructively.

Comments: Talk at ICHEP 2016, Chicago