Contributions from SUSY-FCNC couplings to the interpretation of the HyperCP events for the decay Sigma^+ to p μ^+ μ^-

The observation of three events for the decay $\Sigma^+ \to p \mu^+ \mu^-$ with a dimuon invariant mass of $214.3\pm0.5$MeV by the HyperCP collaboration imply that a new particle X may be needed to explain the observed dimuon invariant mass distribution. We show that there are regions in the SUSY-FCNC parameter space where the $A^0_1$ in the NMSSM can be used to explain the HyperCP events without contradicting all the existing constraints from the measurements of the kaon decays, and the constraints from the $K^0-\bar{K}^0$ mixing are automatically satisfied once the constraints from kaon decays are satisfied.