Mass spectrum of heavy quarkonium hybrids

Abstract

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.