KL -> 0 Formula decay correlating with K in high-scale SUSY

Abstract

We have studied the contribution of high-scale SUSY to the |$K_L \to \pi ^0 \nu {\bar {\nu }}$| and |$K^+ \to \pi ^+ \nu {\bar {\nu }}$| processes by correlating with the CP-violating parameter |$\epsilon _K$|⁠. Taking account of the recent LHC results for Higgs discovery and SUSY searches, we consider high-scale SUSY at the |$10$|–|$50$|TeV scale in the framework of non-minimal squark (slepton) flavor mixing. The Z penguin mediated chargino dominates the SUSY contribution for these decays. At the |$10$|TeV SUSY scale, the chargino contribution can enhance the branching ratio of |$K_L \to \pi ^0 \nu {\bar {\nu }}$| by eight times compared with SM predictions, whereas the predicted branching ratio |${\textit {BR}}(K^+ \to \pi ^+ \nu {\bar {\nu }})$| increases by up to three times that of the SM. The gluino box diagram dominates the SUSY contribution of |$\epsilon _K$| up to |$30{\%}$|⁠. If down-squark mixing is neglected compared with up-squark mixing, the Z penguin mediated chargino dominates both SUSY contributions of |${\textit {BR}}(K_L \to \pi ^0 \nu {\bar {\nu }})$| and |$\epsilon _K$|⁠. Then, a correlation between them is found, but the chargino contribution to |$\epsilon _K$| is at most |$3{\%}$|⁠. Even if the SUSY scale is |$50$|TeV, the chargino process still enhances the branching ratio of |$K_L \to \pi ^0 \nu {\bar {\nu }}$| from the SM prediction by a factor of two, and |$\epsilon _K$| is deviated from the SM prediction by |$\mathcal {O}(10{\%})$|⁠. We also discuss the chargino contribution to the |$K_L \to \pi ^0 e^+e^-$| process.