Decays of $1^{-+}$ Charmoniumlike Hybrid

Abstract

By extracting the transition amplitudes, we give the first lattice QCD prediction of the two-body decay partial widths of the $1^{-+}$ charmoniumlike hybrid ${\eta }_{c1}$. Given the calculated mass value $m_{{\eta }_{c1}}=4.329(36)$ GeV, the ${\eta }_{c1}$ decay is dominated by the open charm modes $D_1\bar{D}$, $D^{\ast }\bar{D}$ and $D^{\ast }{\bar{D}}^{\ast }$ with partial widths of $258(133)$ MeV, $88(18)$ MeV and $150(118)$ MeV, respectively. The coupling of ${\eta }_{c1}$ to ${\chi }_{c1}$ plus a flavor singlet pseudoscalar is not small, but ${\chi }_{c1}\eta$ decay is suppressed by the small $\eta -{\eta }^{\prime }$ mixing angle. The partial width of ${\eta }_{c1}\to {\eta }_c{\eta }^{\prime }$ is estimated to be around 1 MeV. We suggest experiments to search for ${\eta }_{c1}$ in the $P$-wave $D^{\ast }\bar{D}$ and $D^{\ast }{\bar{D}}^{\ast }$ systems. Especially, the polarization of $D^{\ast }{\bar{D}}^{\ast }$ can be used to distinguish the $1^{-+}$ product (total spin $S=1$) from $1^{--}$ products ($S=0$).

17 pages, 7 figures. Revised to article format