Heavy hybrids in pNRQCD

Abstract: We report on the calculation of the Quarkonium Hybrid masses for the $cg\bar{c}$, $bg\bar{c}$ and $bg\bar{b}$ systems~\cite{hbrpaper}. A QCD analog of the Born-Oppenheimer approximation including the $\Lambda$--doubling terms has been used. The gluonic static energies are obtained combining the short range description from potential non--relativistic QCD (pNRQCD) and lattice QCD calculations. The effect $\Lambda$--doubling terms is to mix the contributions of the static energies to the hybrid states leading to the break of the degeneracy between spin symmetry multiplets with opposite parity. The spin symmetry multiplets with mixed contributions from different static energies have a lower mass with respect to the parity opposite that remains without mixed contributions. We compare with direct lattice calculations and discuss several experimental candidates.