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

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.