Electromagnetic decay of X(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(2S)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) → hcγ channel, 392⁺⁶²-111 keV.