Scalar resonance contributions in the $D_{s1}(2460)^{+} \rightarrow D_{s}^{+}\pi^{+}\pi^{-}$ reaction

Inspired by the newly observed $T_{c\bar{s}}$ state in the $D_{s1}(2460)^{+} \rightarrow D_{s}^{+}\pi^{+}\pi^{-}$ reaction by the LHCb Collaboration, we investigate the amplitude of this decay to explore the origins and properties of the open-charm tetraquark state based on the final state interaction. The invariant mass distributions of $D_{s}^{+}\pi^{+}$ and $\pi^{+}\pi^{-}$ are well reproduced by the $S$-wave scattering amplitudes of the coupled channel systems $D_{s}\pi$ and $\pi\pi$. However, neither the tree-level nor both the tree-level and $\pi\pi$ coupled channel scattering contributions can describe the experimental data well, which indicates that the $D_{s}\pi$ coupled channel scattering is required. We find that the $T_{c\bar{s}}$ and $f_{0}(500)$ resonances are dynamically generated from the pseudoscalar-pseudoscalar meson interaction within the chiral unitary approach. In addition, we find the corresponding poles and also calculate the $S$-wave scattering length for the $DK$ channel, which is on the same scale as the result extracted from the experiment. We propose that the $T_{c\bar{s}}$ and $f_{0}(500)$ resonances in the $D_{s1}(2460)^{+} \rightarrow D_{s}^{+}\pi^{+}\pi^{-}$ reaction are hadronic molecular type particles.