Probing dark-matter scenarios of Belle II excess in $B^+\to K^+M_X$ with $K^+\to π^+ M_X$ decays

The hypothesis of top-philic dark matter as the origin of the Belle II excess events in $B\to K M_X$ decays has direct impact on $K\to πM_X$ decays: Both of these decays proceed via loop diagrams~with a top quark emitting some mediator field $R$ and the subsequent decay of $R$ into a pair of dark-ma