Combined analysis on nature of X (3960), χ _c0(3930) , and X_0(4140)

In this work, a study of the D_sD̅_s interaction and its couplings to the channels DD̅ and J/ψϕ is performed in a quasipotential Bethe–Salpeter equation approach. The D_s^+D_s^- and D^+D^- invariant mass spectra in three-body B decays are investigated in order to understand the origin of X (3960), χ _c0(3930) , and X_0(4140) structures reported at LHCb. With the help of effective Lagrangians, the potential kernel can be constructed with meson exchanges, from which the scattering amplitudes can be obtained. By inserting it into the three-body decay processes, the invariant mass spectra can be calculated with an additional Breit–Wigner resonance introduced. The D_s^+D_s^- invariant mass spectrum in the decay process B^+→ D^+_sD^-_sK^+ is well reproduced, and the X (3960) structure can be explained as a molecular state from the D_sD̅_s interaction. The state also exhibits as a peak in the D^+D^- invariant mass spectrum in the decay B^+→ D^+D^-K^+ , however, it is too narrow to reproduce the experimental structure around 3930 MeV. The dip around 4140 MeV in the D_s^+D_s^- invariant mass spectrum can be reproduced by the additional resonance with interference effect. However, a small bump instead of a dip is produced from the D_sD̅_s-J/ψϕ coupled-channel effect, which suggests that the X_0(4140) cannot be interpreted as the D_sD̅_s-J/ψϕ coupling in the current model.