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In this work, we study the long-standing experimental anomaly in muon $(g-2)$and also recent anomalous excess in $K_L\to \pi^0+\nu\bar\nu$ at the J-PARCKOTO experiment with sgoldstino. After supersymmetry breaking, the interactionsbetween quarks and sgoldstino ($s$) make the decays $K\to \pi+s$ sizablethrough loop diagrams, which affects the measurements of decays $K\to\pi+\mathrm{invisible}$. Furthermore, the couplings between photons andsgoldstino contribute to $\Delta a_\mu$ as well as the bino-sleptoncontribution. With satisfying all known experimental constraints such as fromNA62, E949, E137, Orsay, KTEV and CHARM experiments, these two anomalies can beexplained simultaneously. The mass of CP-even sgoldstino is close to theneutral pion mass which does not violate the Grossman-Nir bound. The parameterspace can be further tested in future NA62, DUNE experiments, as well asexperiments in the LHC.

The Light Sgoldstino Phenomenology: Explanations for the Muon $(g-2)$ Deviation and KOTO Anomaly