Probing the SUSY with $10$ TeV stop mass in rare decays and CP violation of Kaon

We probe the SUSY at the $10 \ {\rm TeV}$ scale in the rare decays and the CP violation of the kaon. We focus on the processes of $K_L \to \pi^0 \nu{\bar \nu}$ and $K^+ \to \pi^+ \nu{\bar \nu}$ combined with the CP violating parameters $\epsilon_K$ and $\epsilon_K^\prime/\epsilon_K$. The Z-penguin mediated by the chargino loop cannot enhance $K_L \to \pi^0 \nu{\bar \nu}$ and $K^+ \to \pi^+ \nu{\bar \nu}$ because the left-right mixing of the stop is constrained by the $125$ GeV Higgs mass. On the other hand, the Z-penguin mediated by the gluino loop can enhance the branching ratios of both $K_L \to \pi^0 \nu {\bar \nu}$ and $K^+ \to \pi^+ \nu {\bar \nu}$. The former increases up to more than $1.0 \times 10^{-10}$, which is much larger than the SM prediction even if the constraint of $\epsilon_K$ is imposed. It is remarkable that the Z-penguin mediated by the gluino loop can enhance simultaneously $\epsilon^\prime_K/\epsilon_K$ and the branching ratio of $K_L \to \pi^0 \nu {\bar \nu}$, which increases up to $1.0 \times 10^{-10}$. We also study the decay rates of $K_L\rightarrow \mu^+\mu^-$, $B^0\rightarrow \mu^+\mu^-$ and $B_s\rightarrow \mu^+\mu^-$, which correlate with the $K_L \to \pi^0 \nu {\bar \nu}$ decay through the Z penguin. It is important to examine the $B^0\rightarrow \mu^+\mu^-$ process since we expect the enough sensitivity of this decay mode to the SUSY at LHCb.