Searching for femtoscopic signatures of the $D \bar D (I=0) \ [X(3700)]$ bound state

Abstract

The femtoscopic $D \bar D $ correlations correlation functions are investigated to predict the signature of the not-yet-established $X(3700)$ state. Here it is interpreted as a bound state generated by solving the coupled-channel Bethe-Salpeter equations with the local hidden-gauge formalism. We prospect how the relevant properties and observables characterizing this state -- like the pole position, scattering lengths and compositeness -- might be affected by the variation of the parameters of the model. The amplitudes are then used as input into the momentum correlation functions of the $D^0 \bar D^0$ and $D^+ D^- $ pairs. We discuss how their behaviors encode the features of the $X(3700)$ state.