New physics implications of recent search for $K_L \to \pi^0 \nu\bar{\nu}$ at KOTO

The KOTO experiment recently reported four candidate events in the signal region of $K_L\to \pi^0 \nu\bar\nu$ search, where the standard model only expects $0.10\pm 0.02$ events. If confirmed, this requires physics beyond the standard model to enhance the signal. We examine various new physics interpretations of the result including these: (1) heavy new physics boosting the standard model signal, (2) reinterpretation of "$\nu\bar{\nu}$" as a new light long-lived particle, or (3) reinterpretation of the whole signal as the production of a new light long-lived particle at the fixed target. We study the above explanations in the context of a generalized new physics Grossman-Nir bound coming from the $K^+ \to \pi^+\nu\bar{\nu}$ decay, bounded by data from the E949 and the NA62 experiments.