Lattice study on ${\eta }_{c2}$ and X(3872)

Abstract

Properties of $2^{-+}$ charmonium ${\eta }_{c2}$ are investigated in quenched lattice QCD. The mass of ${\eta }_{c2}$ is determined to be 3.80(3) GeV, which is close to the mass of $D$-wave charmonium $\psi (3770)$ and in agreement with quark model predictions. The transition width of ${\eta }_{c2}\to \gamma J/\psi$ is also obtained with a value $\Gamma =3.8(9)$ keV. Since the possible $2^{-+}$ assignment to X(3872) has not been ruled out by experiments, our results help to clarify the nature of X(3872).

Comments: 15 pages, 8 figures. typos, grammatical errors and some references corrected, redundant discussions deleted, conclusion does not change. published version