Charmless decays of the spin-2 partner of X(3872)

Abstract

Abstract The Belle collaboration recently reported a pro-mising candidate for the spin-2 $$D^*\bar{D}^*$$ D ∗ D ¯ ∗ partner of the X(3872), called the $$X_2$$ X 2 for short, having a mass of $$(4014.3 \pm 4.0 \pm 1.5)~\textrm{MeV}$$ ( 4014.3 ± 4.0 ± 1.5 ) MeV and a width of $$(4 \pm 11 \pm 6)~\textrm{MeV} $$ ( 4 ± 11 ± 6 ) MeV . In present work, we assume the $$X_2$$ X 2 as a pure molecule of the $$D^*\bar{D}^*$$ D ∗ D ¯ ∗ under four cases, i.e., pure neutral components ( $$\theta = 0$$ θ = 0 ), isospin singlet ( $$\theta = \pi /4$$ θ = π / 4 ), neutral components dominant ( $$\theta = \pi /6$$ θ = π / 6 ), and purely charged components ( $$\theta = \pi /2$$ θ = π / 2 ), where $$\theta $$ θ is a phase angle describing the proportion of neutral and charged constituents. Using an effective Lagrangian approach, we calculated the partial widths of $$X_2\rightarrow VV$$ X 2 → V V and $$X_2 \rightarrow PP$$ X 2 → P P (V and P stand for light vector and pseudoscalar mesons, respectively). The predicted decay widths of $$X_2 \rightarrow VV$$ X 2 → V V can reach a few hundreds of $$\textrm{keV}$$ keV , while the decay widths of $$X_2 \rightarrow PP$$ X 2 → P P are about several tens of $$\textrm{keV}$$ keV . In addition, the effects from the proportion of neutral and charged constituent on the decay widths of $$X_2\rightarrow VV$$ X 2 → V V and PP are also investigated. We hope that the present calculations will be checked experimentally in the future.