Inverse problem in femtoscopic correlation functions: the \(T_{cc}(3875)^+\) state

We study the inverse problem of analyzing femtoscopic correlation functions with an efficient tool to extract the maximum information possible about the interaction between the involved coupled-channel hadrons, and derive the existence of possible bound states. The method is flexible enough to accommodate non-molecular components and the effect of missing channels relevant for the interaction. We apply the method to realistic correlation functions for the \(D^{*+}D^0\) and \(D^{*0}D^+\) pairs derived consistently from the properties of the \(T_{cc}(3875)^+\). We can extract the existence of a bound state, its \(D^{*+}D^0\)-\(D^{*0}D^+\) molecular nature, the probabilities of each channel, as well as scattering lengths and effective ranges, together with the size of the source function, all of these quantities with relatively good precision. We analyze (pseudo) data generated with source sizes of \(1\,\text {fm}\) and \(5\,\text {fm}\), and observe that the uncertainties are larger for the second case.