Traces of the $X(3960)$ state in the femtoscopic $D_s^+ D_s^- $ correlations
The femtoscopic $ D_s^+D_s^-$ correlations are investigated to predict the signature of the not-yet-established $X(3960)$ state reported by the LHCb Collaboration, in three scenarios: resonant, virtual, or bound. In the last two scenarios, it might also be identified as the state $X(3930)$. The formalism employed to generate this structure dynamically is based on the Bethe-Salpeter equation with a general $S$-wave potential. We investigate how the relevant properties and observables characterizing this state--such as the pole position, scattering length, and effective range--might be affected by variations in the model parameters. The amplitudes encoding the distinct interpretations of the $X(3960)$ state are then used as input to calculate the femtoscopic correlation function of the $D_s^+ D_s^- $ pair, which is analyzed and discussed.