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 $D_1\bar{ D}$, $D^*\bar{ D}$ and $D^*\bar{ D}^*$ 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 $\eta-\eta'$ mixing angle. The partial width of $\eta_{ c1}\to \eta_c\eta'$ is estimated to be around 1 MeV. We suggest experiments to search for $\eta_{ c1}$ in the $P$-wave $D^*\bar{ D}$ and $D^*\bar{ D}^*$ systems. Especially, the polarization of $D^*\bar{ D}^*$ can be used to distinguish the $1^{ -+}$ product (total spin $S=1$) from $1^{ --}$ products ($S=0$).
Categories: hep-lat hep-ex hep-ph