We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various $J^{ PC}$ quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain $J^{ PC}$, recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify that the negative-parity states with $J^{ PC}=(0, 1, 2)^{ -+}, 1^{ --}$ form the lightest hybrid supermultiplet while the positive-parity states with $J^{ PC}=(0, 1)^{ +-}, (0, 1, 2)^{ ++}$ belong to a heavier hybrid supermultiplet, confirming the supermultiplet structure found in other approaches. The hybrid with $J^{ PC}=0^{ --}$ has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the $J^{ PC}=1^{ ++}$ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.
Categories: hep-ph hep-ex