Kaon physics with light sgoldstinos and parity conservation

Superpartners of the Goldstino—scalar and pseudoscalar sgoldstinos—interact weakly with ordinary particles. One or both of them may be light. We consider a class of supersymmetric extensions of the standard model in which interactions of sgoldstinos with quarks and gluons conserve parity but do not conserve quark flavor. If the pseudoscalar sgoldstino P is light, $m_P<{(m}_K-{2m}_{\pi }),$ and the scalar sgoldstino is heavier, $m_S>{(m}_K-m_{\pi }),$ an interesting place for experimental search is the poorly explored area of the three-body decays of kaons, $K_{S,L}^0\to {\pi }^{+}{\pi }^{-}P,$ $K_{S,L}^0\to {\pi }^0{\pi }^{0}P,$ and $K^{+}\to {\pi }^{+}{\pi }^{0}P,$ with P subsequently decaying into γγ, possibly $e^{+}{e}^{-},$ or flying away from the detector. We evaluate the constraints on the flavor-violating coupling of sgoldstino to quarks which are imposed by $K_L^0-K_S^0$ mass difference and CP violation in neutral kaon system, and find that these constraints allow for fairly large $\mathrm{Br}\left(\overrightarrow{K}\pi \pi P\right).\mathrm{}$ Depending on the phase of sgoldstino-quark coupling, most sensitive to light pseudoscalar sgoldstino are searches either for decays $K_L^0\to \pi \pi P$ or $K^{+}\to {\pi }^{+}{\pi }^{0}P$ and $K_S^0\to \pi \pi P.\mathrm{}$ Generally speaking, there are no bounds on $\mathrm{Br}{(K}_L^0\to \pi \pi P).\mathrm{}$ For most values of the phase, the branching ratio of $K^{+}\to {\pi }^{+}{\pi }^{0}P$ is about 3 orders of magnitude smaller than $\mathrm{Br}{(K}_L^0\to \pi \pi P)$ and the branching ratios of $K_S^0\to \pi \pi P$ are very small. However, for a certain phase the situation is opposite. We find that the most interesting ranges of branching ratios start at $\mathrm{Br}{(K}_L^0\to \pi \pi P)\sim {10}^{-3},$ $\mathrm{Br}{(K}^{+}\to {\pi }^{+}{\pi }^{0}P)\sim {10}^{-4},$ and $\mathrm{Br}{(K}_S^0\to \pi \pi P)\sim {10}^{-3}.$ These searches for a light pseudoscalar sgoldstino would be sensitive to the supersymmetry breaking scale $\sqrt{F}$ in the 100 TeV range and above, provided the minimal supersymmetric standard model flavor violating parameters are close to their experimental bounds. We also briefly discuss the cases of light scalar sgoldstino and relatively heavy sgoldstinos.