  Recently, the KOTO experiment at J-PARC has observed three anomalous events
in the flavor-changing rare decay $K_L \to \pi^0 \nu \bar\nu$, which indicates
that the corresponding branching ratio is almost two orders of magnitude larger
than the Standard Model (SM) prediction. Taking this intriguing result at face
value, we explore model implications of its viable explanation by a long-lived
light 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 parameter
space of such a light scalar in the context of three simple models: (i) a real
singlet scalar extension of the SM; (ii) a $B-L$ extension where neutrino
masses arise via type-I seesaw mechanism from $B-L$ breaking; and (iii) a
TeV-scale left-right symmetric model. The flavor-changing couplings needed to
explain the KOTO excess in models (i) and (ii) originate from tree-level mixing
of 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-precision
searches for flavor-changing charged and neutral kaon decays at NA62, E949,
KOTO and CHARM experiments, as well as the astrophysical and cosmological
constraints on a light scalar, such as those from supernova energy loss, big
bang nucleosynthesis and relativistic degrees of freedom, we find that the
light 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.
