${\overline{B}}_s^0$ → D${}_{s1}$(2460)${}^{+}$K${}^{-}$, D${}_{s1}$(2536)${}^{+}$K${}^{-}$ and the nature of the two D${}_{s1}$ resonances

Starting from the molecular picture for the D${}_{s1}$(2460) and D${}_{s1}$(2536) resonances, which are dynamically generated by the interaction of coupled channels, the most important of which are the D*K for the D${}_{s1}$(2460) and DK* for the D${}_{s1}$(2536), we evaluate the ratio of decay widths for the ${\overline{B}}_s^0$ → D${}_{s1}$(2460)${}^{+}$K${}^{-}$ and ${\overline{B}}_s^0$ → D${}_{s1}$(2536)${}^{+}$K${}^{-}$ decays, the latter of which has been recently investigated by the LHCb collaboration, and we obtain a ratio of the order of unity. The present results should provide an incentive for the related decay into the D${}_{s1}$(2460) resonance to be performed, which would provide valuable information on the nature of these two resonances.