Axial Vector $J^{PC}=1^{++}$ Charmonium and Bottomonium Hybrid Mass Predictions with QCD Sum-Rules

Abstract

Axial vector $(J^{PC}=1^{++})$ charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for $1^{--}$ and $0^{-+}$ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result for the charmonium-like XYZ states and the charmonium hybrid multiplet structure observed in recent lattice calculations.