Towers of hybrid mesons

2 figuresA hybrid meson is a quark-antiquark pair in which, contrary to ordinary meson, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An approximate, but accurate, analytical solution of the Schr\"{o}dinger equation with such a potential is presented. Applied to the case of heavy hybrid mesons, towers of states are predicted in which the masses are a linear function of a harmonic oscillator band number for the quark-antiquark pair. Such a formula could be a reliable guide for the experimental detection of heavy hybrid mesons