Hybrid mesons and auxiliary fields

Abstract

Hybrid mesons are exotic mesons in which the color field is not in the ground state. Their understanding deserves interest from a theoretical point of view, because it is intimately related to nonperturbative aspects of QCD. Moreover, it seems that some recently detected particles, such as the $π_1(1600)$ and the Y(4260), are serious hybrid candidates. In this work, we investigate the description of such exotic hadrons by applying the auxiliary fields technique to the widely used spinless Salpeter Hamiltonian with appropriate linear confinement. Instead of the usual numerical resolution, this technique allows to find simplified analytical mass spectra and wave functions of the Hamiltonian, which still lead to reliable qualitative predictions. We analyse and compare two different descriptions of hybrid mesons, namely a two-body $q\bar q$ system with an excited flux tube, or a three-body $q\bar q g$ system. We also compute the masses of the $1^{-+}$ hybrids. Our results are shown to be in satisfactory agreement with lattice QCD and other effective models.