Lattice study onηc2andX(3872)

Abstract

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