Excited string and constituent gluon descriptions of hybrid mesons

We analyze and compare two different descriptions of hybrid mesons, namely a two-body quark-antiquark system with an excited string linking both particles, or a three-body quark-antiquark-constituent gluon system. In particular, we prove that the constituent gluon approach is equivalent to an effective excited string in the heavy hybrid sector. The quantum numbers of the gluon are then replaced by the string excitation number. In the light hybrid sector, the equivalence between the excited string and the constituent gluon models remains valid provided the quark dynamics is properly taken into account as a dynamical contribution to the string energy.