## Chapter 3 

## Heavy Quarkonium Hybrid mass predictions 

## 3.1 Introduction 

The research presented in this chapter involves two closely related publications: 

• D. Harnett, R.T. Kleiv, T.G. Steele, and Hong-Ying Jin, Axial Vector J PC = 1 ++ Char- monium and Bottomonium Hybrid Mass Predictions with QCD Sum-Rules, J. Phys. G39 (2012) 125003. 

• R. Berg, D. Harnett, R.T. Kleiv, and T.G. Steele, Mass Predictions for Pseudoscalar J PC = 0 − + Charmonium and Bottomonium Hybrids in QCD Sum-Rules, Phys. Rev. D86 (2012) 034002. 

The publications above (Refs. [60, 19]) extract mass predictions for heavy quarkonium hybrids with the quantum numbers J PC = 1 ++ and 0 − $^{+}$, respectively. Heavy quarkonium hybrids are widely suspected to exist in the same mass region as charmonia and bottomonia, so it is entirely possible that some of the heavy quarkonium-like states that have been dis- covered so far could be heavy quarkonium hybrids. For instance, the Y (4260) is considered to be a strong candidate for a charmonium hybrid [130]. 

Surprisingly, this possibility has been little explored by QSR practitioners. The original QSR studies of heavy quarkonium hybrids were performed by Govaerts et al. in Refs. [55, 56, 54]. Many different heavy quarkonium hybrid J PC channels were examined, however, only the perturbative and dimension-four gluon condensate 〈 αG $^{2}$〉 were included in the OPE of the correlation functions. Consequently many of the sum rules that were derived were unstable, meaning that the resulting heavy quarkonium hybrid mass predictions are unreliable. How- ever, the authors of Ref. [102] recently updated the sum rule for the vector (1 $^{−−}$) channel, 

