Kaon Physics with Light Sgoldstinos and Parity Conservation

Superpartners of 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 - 2 m_{\pi}), and the scalar sgoldstino is heavier, m_S > (m_K - m_{\pi}), an interesting place for experimental searches is the poorly explored area of three-body decays of kaons, K^{0}_{S,L} \to \pi^+ \pi^- P, K^{0}_{S,L} \to \pi^0 \pi^0 P and K^{+} \to \pi^+ \pi^0 P, with $P$ subsequently decaying into \gamma\gamma, 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 - K_S mass difference and CP-violation in neutral kaon system, and find that these constraints allow for fairly large Br(K \to \pi \pi P). In the case of maximal CP-violation in sgoldstino-quark interactions, the most sensitive processes are K^{0}_{L} \to \pi^+ \pi^- P, K^{0}_{L} \to \pi^0 \pi^0 P, whose branching ratios are allowed to be as large as 10^{-3}. In the opposite case of no CP-violation in sgoldstino-quark interactions, pseudoscalar sgoldstino may show up in the three-body decays of kaons at or below the levels Br(K^0_S \to \pi \pi P) \sim 10^{-3}, Br(K^+ \to \pi^+ \pi^0 P) \sim 10^{-4}, Br(K_L^0 \to \pi \pi P) \sim 10^{-6}. These searches for light pseudoscalar sgoldstino would be sensitive to the supersymmetry breaking scale \sqrt{F} in the 100 TeV range and above. We also briefly discuss the cases of light scalar sgoldstino and relatively heavy sgoldstinos.