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

TL;DR

This paper investigates the potential effects of supersymmetry at a 10 TeV scale on rare kaon decays and CP violation, highlighting gluino loop contributions that could significantly enhance certain decay rates beyond Standard Model predictions.

Contribution

It demonstrates that gluino-mediated Z-penguin diagrams can simultaneously enhance rare kaon decay branching ratios and CP violation parameters, providing new insights into SUSY effects at high energy scales.

Findings

Gluino loops can increase $K_L o \pi^0 u ar{ u}$ branching ratio beyond $1.0 imes 10^{-10}$.

Enhanced $ ext{ extbackslash}epsilon_K^ ext{ extbackslash}prime/ ext{ extbackslash}epsilon_K$ correlates with increased rare decay rates.

Potential observable effects in $B^0 o \mu^+\mu^-$ decay at LHCb.

Abstract

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.