  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.
