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

Abstract

We probe the SUSY at the $10\mathrm{TeV}$ 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 ${ϵ}_K$ and ${ϵ}_K^{\prime }/{ϵ}_K$. 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 ${ϵ}_K$ is imposed. It is remarkable that the Z-penguin mediated by the gluino loop can enhance simultaneously ${ϵ}_K^{\prime }/{ϵ}_K$ 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 $K_L\to {\mu }^{+}{\mu }^{-}$, $B^0\to {\mu }^{+}{\mu }^{-}$ and $B_s\to {\mu }^{+}{\mu }^{-}$, which correlate with the $K_L\to {\pi }^0\nu \bar{\nu }$ decay through the Z penguin. It is important to examine the $B^0\to {\mu }^{+}{\mu }^{-}$ process since we expect the enough sensitivity of this decay mode to the SUSY at LHCb.

Comments: 23 pages, 8 figures. Major changes. Discussion for the gluino contributions added