Model independent analysis of femtoscopic correlation functions: An application to the D∗s0(2317)

We face the inverse problem of obtaining the interaction between coupled channels from the correlation functions of these channels. We apply the method to the interaction of the (DK+)-K-0, (D+K0), and D-s(+)eta channels, from where the D-s0(& lowast;)(2317) state emerges. We use synthetic data extracted from an interaction model based on the local hidden gauge approach and find that the inverse problem can determine the existence of a bound state of the system with a precision of about 20 MeV. At the same time, we can determine the isospin nature of the bound state and its compositeness in terms of the channels. Furthermore, we evaluate the scattering length and effective range of all three channels, as well as the couplings of the bound state found to all the components. Lastly, the size parameter of the source function, R, which in principle should be a magnitude provided by the experimental teams, can be obtained from a fit to the data with relatively high accuracy. These findings show the value of the correlation function to learn about the meson-meson interaction for systems which are difficult to access in other present facilities.

Automated summary

This study uses the correlation function method to investigate the interaction between coupled channels. By analyzing synthetic data, we successfully determine the interaction of the (DK+)-K-0, (D+K0), and D-s(+)eta channels as well as the existence of a bound state. The study also evaluates the scattering characteristics of the three channels and the coupling of the bound state to its components.