Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

In light of a discrepancy of the direct $CP$ violation in $K\to \pi \pi$ decays, ${\epsilon }^{\mathrm{\prime }}\mathrm{/}{\epsilon }_K$, we investigate gluino contributions to the electroweak penguin, where flavor violations are induced by squark trilinear couplings. Top-Yukawa contributions to $\mathrm{\Delta }S=2$ observables are taken into account, and vacuum stability conditions are evaluated in detail. It is found that this scenario can explain the discrepancy of ${\epsilon }^{\mathrm{\prime }}\mathrm{/}{\epsilon }_K$ for the squark mass smaller than 5.6 TeV. We also show that the gluino contributions can amplify $$\mathcal{B}$(K \to \pi \nu \overline{\nu})$,$$\mathcal{B}$(K_S \to \mu^+ \mu^-){\rm eff}$and$\Delta A{\rm CP}(b\to s\gamma)$. Such large effects could be measured in future experiments.