$J^PC=1^++$ heavy hybrid masses from QCD sum-rules
QCD Laplace sum-rules are used to calculate axial vector $(J^PC=1^++)$ charmonium and bottomonium hybrid masses. Previous sum-rule studies of axial vector heavy quark hybrids did not include the dimension-six gluon condensate, which has been shown to be important in the $1^--$ and $0^-+$ channels. An updated analysis of axial vector heavy quark hybrids is performed, including the effects of the dimension-six gluon condensate, yielding mass predictions of 5.13 GeV for hybrid charmonium and 11.32 GeV for hybrid bottomonium. The charmonium hybrid mass prediction disfavours a hybrid interpretation of the X(3872), if it has $J^PC=1^++$, in agreement with the findings of other theoretical approaches. It is noted that QCD sum-rule results for the $1^--$, $0^-+$ and $1^++$ channels are in qualitative agreement with the charmonium hybrid multiplet structure observed in recent lattice calculations.