Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

Abstract

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

Comments: 30 pages, 8 figures; references added, version published in JHEP