Hidden charmed decays of spin-2 partner of X(3872) within $$D^*\bar{D}^*$$ molecular framework

Abstract The Belle Collaboration recently reported a potential candidate for the spin-2 $$D^*\bar{D}^*$$ D ∗ D ¯ ∗ partner of the X (3872), denoted as $$X_2$$ X 2 , with a mass of $$(4014.3\pm 4.0\pm 1.5)$$ ( 4014.3 ± 4.0 ± 1.5 ) MeV and a width of $$(4\pm 11\pm 6)$$ ( 4 ± 11 ± 6 ) MeV. Assuming the $$X_2$$ X 2 as a $$D^*\bar{D}^*$$ D ∗ D ¯ ∗ molecular state, we calculate its hidden charm decay $$X_2 \rightarrow \pi ^+ \pi ^- \eta _{c}$$ 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: $$\theta =0$$ θ = 0 , $$\pi /6$$ π / 6 , $$\pi /4$$ π / 4 , and $$\pi /2$$ π / 2 . The decay width is found to be sensitive to the mass of the $$X_2$$ X 2 . The decay partial widths are predicted to be on the order of 1 keV. We expect that the present calculations, perfo