Electromagnetic decay ofX(3872) as the 11D2(2−+) charmonium

The recent BaBar results raise the possibility that X (3872) has negative parity; reassigning it to the state should therefore be considered. In this paper we give a general form of the wave function of 2 −+ mesons. By solving the instantaneous Bethe–Salpeter equation, we get the mass spectrum and corresponding wave functions. We calculate the electromagnetic decay widths of the first 2 −+ state which we assume to be the X (3872) particle. The results are Γ(2 −+ (3872) → J /ψγ) = 1.59 +0.53 −0.42 keV, Γ(2 −+ (3872) → ψ(2 S )γ) = 2.87 +1.46 −0.97 eV and Γ(2 −+ (3872) → ψ(3770)γ) = 0.135 +0.066 −0.047 keV. The ratio of the branch fractions of the second and the first channels is about 0.002, which is inconsistent with the experimental value 3.4 ± 1.4. Therefore X (3872) is unlikely to be a 2 −+ charmonium state. In addition, we obtain a relatively large decay width for the 2 −+ (3872) → h c γ channel, 392 +62 −111 keV.