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Recently, the KOTO experiment at J-PARC has observed three anomalous eventsin the flavor-changing rare decay $K_L \to \pi^0 \nu \bar\nu$, which indicatesthat the corresponding branching ratio is almost two orders of magnitude largerthan the Standard Model (SM) prediction. Taking this intriguing result at facevalue, we explore model implications of its viable explanation by a long-livedlight SM-singlet scalar ($S$) emission, i.e. $K_L \to \pi^0 S$, with $S$decaying outside the KOTO detector. We derive constraints on the parameterspace of such a light scalar in the context of three simple models: (i) a realsinglet scalar extension of the SM; (ii) a $B-L$ extension where neutrinomasses arise via type-I seesaw mechanism from $B-L$ breaking; and (iii) aTeV-scale left-right symmetric model. The flavor-changing couplings needed toexplain the KOTO excess in models (i) and (ii) originate from tree-level mixingof the scalar with SM Higgs field ($h$), and in model (iii), from the mixing of$S$ and $h$ with the neutral component of the heavy bidoublet Higgs field.After taking into account the stringent constraints from high-precisionsearches for flavor-changing charged and neutral kaon decays at NA62, E949,KOTO and CHARM experiments, as well as the astrophysical and cosmologicalconstraints on a light scalar, such as those from supernova energy loss, bigbang nucleosynthesis and relativistic degrees of freedom, we find that thelight scalar interpretation of the KOTO excess is allowed in all these models.Parts of the parameter range can be tested in future NA62 and DUNE experiments.

Constraints on long-lived light scalars with flavor-changing couplings and the KOTO anomaly