Hidden charmonium decays of spin-2 partner of X(3872)

The Belle Collaboration recently reported a promising candidate for the spin -2 D* over bar 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. Assuming the X2 as a pure molecule of the D* over bar D*, we calculated in detail the hidden charmonium decays of the X2 - J/psi V and X2 - eta cP via the intermediate meson loops, where V = rho 0, omega and P = pi 0, eta, eta 0. The results indicate that the decay widths are strongly dependent on the X2 mass. At present center value of the mass 4014.3 MeV, the width for the X2 - J/psi rho 0 is predicted to be a few tens of keV, while it is on the order of 102-3 keV for the X2 - J/psi omega; the predicted width for the X2 - eta c pi 0 is about a few keV, while the widths for X2 - eta c eta and eta c eta 0 are around a few tens and tenths of keV, respectively. We also investigated the dependence of the ratios between these widths on the X2 mass and on the eta- eta 0 mixing angle, which may be good quantities for experiments. We hope that the present calculations will be checked experimentally in the future.