Annihilation rate of 2−+ charmonium and bottomonium

Abstract

The 11 D 2 $ \left( {c\overline{c}} \right) $ state is the ground state of spin-singlet D-wave charmonia. Although it has not been found yet, the experimental data accumulate rapidly. This charmonium attracts more and more attention, especially when the BaBar Collaboration finds that the X(3872) particle has negative parity. In this paper we calculate the double-gamma and double-gluon annihilation processes of 1 D 2 charmonia and bottomonia by using the instantaneous Bethe-Salpeter method. We find the relativistic corrections make the decay widths of 11 D 2 $ \left( {c\overline{c}} \right) $ 2~5 times smaller than the non-relativistic results. If this state is below the D 0 D 0∗ threshold, we can use the sum of annihilation widths and EM transition widths to estimate the total decay width. Our result for 11 D 2 $ \left( {c\overline{c}} \right) $ with m = 3820 GeV is Γ = 432 keV. The dominant decay channel 11 D 2 $ \left( {c\overline{c}} \right) $ → h c γ, whose branching ratio is about 90%, can be used to discover this state.