Lattice study on $η_{c2}$ and X(3872)

Properties of $2^{-+}$ charmonium $η_{c2}$ are investigated in quenched lattice QCD. The mass of $η_{c2}$ is determined to be 3.80(3) GeV, which is close to the mass of $D$-wave charmonium $ψ(3770)$ and in agreement with quark model predictions. The transition width of $η_{c2}\to γJ/ψ$ is also obtained with a value $Γ=3.8(9)$ 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).

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