Hidden charmed decays of spin-2 partner of X(3872) within D^*D̄^* molecular framework

The Belle Collaboration recently reported a potential candidate for the spin-2 D^*D̄^* D ∗ D ¯ ∗ partner of the X (3872), denoted as X₂ X 2 , with a mass of (4014.3± 4.0± 1.5) ( 4014.3 ± 4.0 ± 1.5 ) MeV and a width of (4± 11± 6) ( 4 ± 11 ± 6 ) MeV. Assuming the X₂ X 2 as a D^*D̄^* D ∗ D ¯ ∗ molecular state, we calculate its hidden charm decay X₂ → π ⁺ π ⁻ η c X 2 → π + π - η c via box loop diagram using an effective Lagrangian approach. To investigate the dependence of the decay width on the molecular structure, we consider four different phase angles: θ =0 θ = 0 , π /6 π / 6 , π /4 π / 4 , and π /2 π / 2 . The decay width is found to be sensitive to the mass of the X₂ X 2 . The decay partial widths are predicted to be on the order of 1 keV. We expect that the present calculations, perfo