$B_{(s)}\to V{M}_X$ decays as probes of dark-matter scenarios of Belle II enhancement in $B\to K{M}_X$ decays

Recently, we have shown that the hypothesis of the dark-matter (DM) origin of the Belle II excess events in $B\to K{M}_X$ decays allows for a successful description of the data. The DM parameters (masses and couplings) in two DM scenarios with either scalar (S-scenario) or vector (V-scenario) mediator have been extracted with rather small uncertainty from fits to the $B\to K{M}_X$ data. The same mechanism leads to a similar enhancement of the $B_s\to (\eta ,{\eta }^{\mathrm{\prime }},\phi )M_X$ decay rates. We present a detailed analysis of $B\to K^{\ast }{M}_X$ and $B_s\to \phi M_X$ decays and show that these decays provide a clear probe of the S- and V-scenarios: Compared to the Standard Model, in the S-scenario an enhancement by a factor $\sim 1.6$ is expected, whereas the V-scenario leads to a much larger enhancement by a factor $\sim 3.5$. For the $B\to K^{\ast }{M}_X$ decays, we provide the expected number of events at Belle II for the sample for which a rather large enhancement of $B\to K{M}_X$ decays compared to the Standard Model expectations has been reported.