Strong decays of the isovector-scalar D^^ hadronic molecule

We adopt the effective Lagrangian approach to study the strong decays of the 1^- (0^++) D^^ molecular state denoted as T₀ᵃ (4010) according to the LHCb naming convention through triangle diagrams. The decay channels include the open-charm DD, and the hidden-charm c, J/, and ₂₁. The coupling between the T₀ᵃ (4010) and its constituents D^^ is obtained by solving for the residue of the scattering T-matrix at the pole. Our calculation yields a total width of (12. 0-35. 4) MeV for the T₀ᵃ (4010) state, with its main decay channels being c and ₂₁. The X (4100) and X (4050) have similar masses and widths, with both masses being close to the D^^ threshold. Additionally, their decay final states are consistent with those of the T₀ᵃ (4010). Therefore, it is likely that they represent the same state and both potentially correspond to the T₀ᵃ (4010). We suggest that future experiments focus on searching for the T₀ᵃ (4010) signal in the final states c^-, ₂₁^- and D⁰D^- of the B⁰c^-K^+, ₂₁^- K^+ and D⁰D^-K^+ processes, respectively, as well as further investigating its resonance parameters with Flatt\'e-like formula.