B-+ K^?M_X vs. B-+ KM_X as a probe of a scalar mediator dark-matter scenario

Recently, Belle II reported the observation of the decay B -> KMX , where M-X is the missing mass, with the branching ratio much exceeding B(B -> K nu nu ) which is the only Standard Model (SM) process contributing to this reaction. If confirmed, this might be an indication of new non-SM particles produced in this decay. One of the possible explanations of the observed effect could be light dark -matter (DM) particles produced via a scalar mediator field. We give simple arguments, that a combined analysis of the B -> KMX and B -> K*M-X reactions would be a clean probe of the scalar mediator scenario: i) making use of an observed value B(B -> KMX ) similar or equal to 5.4 B(B -> K nu nu )SM and ii) assuming that the effect is due to the light dark -matter coupling to the top quark via a scalar mediator field, one finds an upper limit B(B -> K*M-X ) < 2.8 B(B -> K*nu nu )(SM). Within the discussed scenario, this upper limit does not depend on the mass of the scalar mediator nor on the specific details of the unobserved dark -matter particles in the final state.