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

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.Comment: 15 pages, 5 figures, version to appear in J.Phys.