Charmonium-like states with the exotic quantum number $J^{PC}=3^{-+}$

Abstract

We apply the method of QCD sum rules to study the $qc\bar{q}\bar{c}$ tetraquark states with the exotic quantum number $J^{PC}=3^{-+}$, and extract the mass of the lowest-lying state to be $4.49_{-0.41}^{+0.45}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematic analysis of these interpolating currents indicates that: a) this state readily decays into the $P$-wave $[\rho J/\psi ]/[\omega J/\psi ]$ channel but not into the $[\rho {\chi }_{c2}]/[\omega {\chi }_{c2}]/[J/\psi f_2(1270)]$ channels, and b) it readily decays into the $[D^{\ast }{\bar{D}}_2^{\ast }]$ channel but not into the $P$-wave $[D^{\ast }{\bar{D}}^{\ast }]$ channel.

Comments: 13 pages, 4 figures, revised version to be published in PRD