EM Decay of X(3872) as the $1{}^1{D}_2(2^{-+})$ charmonium

Abstract

The recently BaBar results raise the possibility that X(3872) has negative parity. This makes people reconsider assigning X(3872) to the $1{}^1{D}_2(c\bar{c})$ state. 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 electromagnetic decay widths of the first $2^{-+}$ state which we assume to be the X(3872) particle. The results are $\Gamma (2^{-+}(3872)\to J/\psi \gamma )=1.59_{-0.42}^{+0.53}$ keV, $\Gamma (2^{-+}(3872)\to \psi (2S)\gamma )=2.87_{-0.97}^{+1.46}$ eV and $\Gamma (2^{-+}(3872)\to \psi (3770)\gamma )=0.135_{-0.047}^{+0.066}$ keV. The ratio of branch fractions of the second and first channel is about 0.002, which is inconsistent with the experimental value $3.4\pm 1.4$. So X(3872) is unlikely to be a $2^{-+}$ charmonium state. In addition, we obtain a relatively large decay width for $2^{-+}(3872)\to h_c\gamma$ channel which is $392_{-111}^{+62}$ keV.

Comments: Revised version