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

The Belle collaboration recently reported a promising candidate for the spin-2 D^*D^* partner of the X (3872), called the X₂ for short, having a mass of (4014. 3 4. 0 1. 5) ~MeV and a width of (4 11 6) ~MeV. In present work, we assume the X₂ as a pure molecule of the D^*D^* under three cases, i. e. , pure neutral components (= 0), isospin singlet (= /4) and neutral components dominant (= /6), where is a phase angle describing the proportion of neutral and charged constituents. Using an effective Lagrangian approach, we calculated the partial widths of X₂ VV and X₂ PP (V and P stand for light vector and pseudoscalar mesons, respectively). The predicted decay widths of X₂ VV can reach a few hundreds of keV, while the decay widths of X₂ PP are about several tens of keV. In addition, the effects from the proportion of neutral and charged constituent on the decay widths of X₂ VV and PP are also investigated. We hope that the present calculations will be checked experimentally in the future.