Abstract Within the hypothesis of the dark-matter (DM) origin of the excess in B K MX B → K M X decays over the standard-model expectation, observed by Belle II, we report the following results: (i) Combining the available data on the integrated decay rates (B K MX) Γ (B → K M X) and the upper limit on the integrated decay rates (B K^* MX) Γ (B → K ∗ M X) provides a tight constraint on the vector-mediator mass MV 3 M V ≲ 3 GeV, whereas no constraints on the scalar-mediator mass are imposed by these data. (ii) Both scalar- and vector-mediator scenarios allow for a good description of the differential distributions in B K MX B → K M X measured by Belle II and an extraction of dark-model parameters within both scenarios. Previously, for the scalar-mediator scenario, we extracted the scalar-mediator parameters M_ 2. 4 M ϕ ∼ 2. 4 GeV, _ 2. 9 Γ ϕ ∼ 2. 9 GeV, and the DM fermion mass m_ 0. 42 m χ ∼ 0. 42 GeV. We now extract the parameters for the vector-mediator scenario: MV 3. 0 M V ∼ 3. 0 GeV, V 4. 0 Γ V ∼ 4. 0 GeV, and m_ 0. 6 m χ ∼ 0. 6 GeV. (iii) In view of a nice description of the Belle II data in scalar- and vector-mediator scenarios, one faces the problem of discriminating between these scenarios. We propose a novel clear measurable signature to discriminate between two DM scenarios: The ratio of the differential distributions in
Berezhnoy et al. (2026) studied this question.