$D_{s0}^{\ast\pm}(2317)$ and $KD$ scattering from $B^0_s$ decay

We study the $\bar{B}_s^0\to D_s^-(DK)^+$ weak decay, and look at the $DK$ invariant mass distribution with the aim of obtaining relevant information on the nature of the $D_{s0}^{\ast+}(2317)$ resonance. We make a simulation of the experiment using the actual mass of the $D_{s0}^{\ast+}(2317)$ resonance and recent lattice QCD relevant parameters of the $KD$ scattering amplitude. We then solve the inverse problem of obtaining the $KD$ amplitude from these synthetic data, to which we have added a 5\% or 10\% error. We prove that one can obtain from these "data" the existence of a bound $KD$ state, the $KD$ scattering length and effective range, and most importantly, the $KD$ probability in the wave function of the bound state obtained, which was found to be largely dominant from the lattice QCD results. This means that one can obtain information on the nature of the $D_{s0}^{\ast+}(2317)$ resonance from the implementation of this experiment, in the line of finding the structure of resonances, which is one of the main aims in hadron spectroscopy.

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