$J^{PC}=1^{++}$ heavy hybrid masses from QCD sum-rules

TL;DR

This paper uses QCD sum-rules including the dimension-six gluon condensate to predict masses of $J^{PC}=1^{++}$ heavy hybrid mesons, providing insights into their structure and relation to experimental states.

Contribution

It introduces an updated QCD sum-rule analysis that incorporates the dimension-six gluon condensate for axial vector heavy hybrids, refining mass predictions.

Findings

Predicted hybrid charmonium mass: 5.13 GeV

Predicted hybrid bottomonium mass: 11.32 GeV

Disfavors a hybrid interpretation of X(3872) with $J^{PC}=1^{++}$

Abstract

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.