Predictions for the $\bar B^0 \to \bar K^{*0} X (YZ)$ and $\bar B^0_s \to ϕX (YZ)$ with $X(4160), Y(3940), Z(3930)$

We investigate the decay of $\bar B^0 \to \bar K^{*0} R$ and $\bar B^0_s \to ϕR$ with $R$ being the $X(4160)$, $Y(3940)$, $Z(3930)$ resonances. Under the assumption that these states are dynamically generated from the vector-vector interaction, as has been concluded from several theoretical studies, we use a reaction mechanism of quark production at the elementary level, followed by hadronization of one final $q \bar q$ pair into two vectors and posterior final state interaction of this pair of vector mesons to produce the resonances. With this procedure we are able to predict five ratios for these decays, which are closely linked to the dynamical nature of these states, and also predict the order of magnitude of the branching ratios which we find of the order of $10^{-4}$, well within the present measurable range. In order to further test the dynamical nature of these resonances we study the $\bar B^0_s \to ϕD^* \bar D^*$ and $\bar B^0_s \to ϕD_s^* \bar D_s^*$ decays close to the $D^* \bar D^*$ and $D_s^* \bar D_s^*$ thresholds and make predictions for the ratio of the mass distributions in these decays and the $\bar B^0_s \to ϕR$ decay widths. The measurement of these decays rates can help unravel the nature of these resonances.

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