B̄ₛ⁰ → Dₛ₁(2460)⁺ K⁻, Dₛ₁(2536)⁺ K⁻ and the nature of the two Dₛ₁ resonances

Starting from the molecular picture for the Dₛ₁(2460) D s 1 ( 2460 ) and Dₛ₁(2536) D s 1 ( 2536 ) resonances, which are dynamically generated by the interaction of coupled channels, the most important of which are the D^*K D ∗ K for the Dₛ₁(2460) D s 1 ( 2460 ) and DK^* D K ∗ for the Dₛ₁(2536) D s 1 ( 2536 ) , we evaluate the ratio of decay widths for the B̄ₛ⁰ → Dₛ₁(2460)⁺ K⁻ B ¯ s 0 → D s 1 ( 2460 ) + K - and B̄ₛ⁰ → Dₛ₁(2536)⁺ K⁻ B ¯ s 0 → D s 1 ( 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 Dₛ₁(2460) D s 1 ( 2460 ) resonance to be performed, which would provide valuable information on the nature of these two resonances.