Masses of the Bottom-Charm Hybrid $\bar{b}Gc$ States

QCD sum rules are used to study the mass spectrum of bottom-charm hybrid $\bar{b}Gc$ systems. The correlation functions and the spectral densities are calculated up to dimension six condensates at leading order of ${\alpha }_s$ for several $J^P$ quantum numbers. After performing the QCD sum rule analysis, we predict the masses of the $J^P=0^{-},0^{+},1^{-},1^{+},2^{-},2^{+}$ bottom-charm hybrids. These mass predictions show a similar supermultiplet structure as the bottomonium and charmonium hybrids. Using the QCD sum-rule mass predictions we analyze the possible hadronic decay patterns of the $\bar cGc$,$\bar bGc$and$\bar bGb$ hybrids including the open-flavour and hidden-flavour mechanisms.