Determining $1^{--}$ Heavy Hybrid Masses via QCD Sum Rules

TL;DR

This paper uses QCD sum rules to estimate the masses of $1^{--}$ charmonium and bottomonium hybrids, finding potential experimental implications and suggesting hybrid states may be mixed with other particles.

Contribution

The study provides new mass estimates for heavy hybrid mesons using QCD sum rules, highlighting differences with experimental data and proposing hybrid mixing.

Findings

Charmonium hybrid mass range: 4.12-4.79 GeV.

Bottomonium hybrid mass range: 10.24-11.15 GeV.

Bottomonium hybrid results align with recent BELLE observations.

Abstract

The masses of $1^{--}$ charmonium and bottomonium hybrids are evaluated in terms of QCD sum rules. We find that the ground state hybrid in charm sector lies in $m_{H_c}=4.12\sim 4.79$ GeV, while in bottom sector the hybrid may situated in $m_{H_b} = 10.24\sim 11.15$ GeV. Since the numerical result on charmonium hybrid mass is not compatible with the charmonium spectra, including structures newly observed in experiment, we tempt to conclude that such a hybrid does not purely exist, but rather as an admixture with other states, like glueball and regular quarkonium, in experimental observation. However, our result on bottomonium hybrid coincide with the "exotic structure" recently observed at BELLE.