The $K T_{cc}(3875)$ Interaction: Bound State, Scattering Observables and Correlation Function

We investigate the interaction of a kaon with the $T_{cc}(3875)$ state, evaluating the scattering amplitude and the correlation function of the system within a molecular picture in which the $T_{cc}(3875)$ is regarded as a $D^* D$ bound state. Since the $KD^*$ and $KD$ interactions dynamically generate the $D_{s1}(2460)$ and $D_{s0}^*(2317)$ resonances, respectively, both of which are significantly bound with respect to their corresponding particle thresholds, the $KT_{cc}(3875)$ interaction is found to be strongly attractive, leading to the formation of two bound states with binding energies of about 63 MeV and 51 MeV, respectively, with respect to the $KT_{cc}(3875)$ threshold. We also determine the scattering observables at threshold, including the scattering length and effective range, and calculate the correlation function. The latter exhibits features similar to those found in previous studies of the scattering of an external particle off a dynamically generated resonance of molecular nature.