Supersymmetric Explanation of CP Violation in $K\to ππ$ Decays

Recent progress in the determination of hadronic matrix elements has revealed a tension between the measured value of $ε_K^{\prime}/ε_K$, which quantifies direct $CP$ violation in $K \to ππ$ decays, and the Standard-Model prediction. The well-understood indirect $CP$ violation encoded in the quantity $ε_K$ typically precludes large new-physics contributions to $ε_K^{\prime}/ε_K$ and challenges such an explanation of the discrepancy. We show that it is possible to cure the $ε_K^{\prime}/ε_K$ anomaly in the Minimal Supersymmetric Standard Model with squark masses above 3 TeV without overshooting $ε_K$. This solution exploits two features of supersymmetry: the possibility of large isospin-breaking contributions (enhancing $ε_K^{\prime}$) and the Majorana nature of gluinos (permitting a suppression of $ε_K$). Our solution involves no fine-tuning of $CP$ phases or other parameters.

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