A. Berezhnoy, Wolfgang Lucha, Dmitri Melikhov
Abstract Within the hypothesis of the dark-matter (DM) origin of the excess in $$B\rightarrow K M_X$$ 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 $$\Gamma (B\rightarrow K M_X)$$ Γ ( B → K M X ) and the upper limit on the integrated decay rates $$\Gamma (B\rightarrow K^* M_X)$$ Γ ( B → K ∗ M X ) provides a tight constraint on the vector-mediator mass $$M_V\lesssim 3$$ 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 $$B\rightarrow K M_X$$ 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 $$M_\phi \sim 2.4$$ M ϕ ∼ 2.4 GeV, $$\Gamma _\phi \sim 2.9$$ Γ ϕ ∼ 2.9 GeV, and the DM fermion mass $$m_\chi \sim 0.42$$ m χ ∼ 0.42 GeV. We now extract the parameters for the vector-mediator scenario: $$M_V\sim 3.0$$ M V ∼ 3.0 GeV, $$\Gamma _V\sim 4.0$$ Γ V ∼ 4.0 GeV, and $$m_\chi \sim 0.6$$ 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