Mass Predictions for Pseudoscalar $J^{PC}=0^{-+}$ Charmonium and Bottomonium Hybrids in QCD Sum-Rules

TL;DR

This paper uses QCD sum-rules including the dimension-six gluon condensate to accurately predict the masses of pseudoscalar charmonium and bottomonium hybrids, addressing previous analysis limitations.

Contribution

It introduces a stable sum-rule analysis incorporating the full correlation function and the gluon condensate effects, providing new mass predictions for these hybrids.

Findings

Charmonium hybrid mass ~3.8 GeV

Bottomonium hybrid mass ~10.6 GeV

Full correlation function is essential for accuracy

Abstract

Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeV and the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulation of the sum-rules. The charmonium hybrid mass prediction is discussed within the context of the X Y Z resonances.