Spin Structure of heavy-quark hybrids

Exotic quarkonia are candidates to new types of hadrons including four quarks or gluonic degrees of freedom as constituents, the latter being a unique feature of QCD. We review recent developments in nonrelativistic EFTs to describe exotic quarkonia and in particular recent results on the spectrum of heavy hybrids including spin-dependent contributions up to $1/m_Q^2$-terms in the heavy-quark-mass expansion. We determine the nonperturbative contributions to the matching coefficients of the EFT by fitting our results to lattice-QCD determinations of the charmonium hybrid spectrum and extrapolate the results to the bottomonium hybrid sector where lattice-QCD determinations are still challenging. We also report on a recent new approach to quarkonium hadronic transitions that does not use the twist expansion and uses the hybrid spectrum as the intermediate octet states.