Abstract The Coulomb gauge Hamiltonian model is used to calculate masses for selected J
PC states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs),
q ̄ qg hybrid mesons and q ̄ qq ̄ q tetraquark systems. An odderon Regge trajectory is
computed for the J−− glueballs with intercept much smaller than the pomeron, explaining its
nonobservation. The lowest 1−+ hybrid-meson mass is found to be just above 2.2 GeV while
the lightest tetraquark state mass with these exotic quantum numbers is predicted around …

The Coulomb Gauge Hamiltonian (CGH) model, a field theoretical, relativistic, many-body
approach to Quantum Chromodynamics (QCD), is developed, which describes the vacuum
through a Bogoliubov-Valatin transformation. This transformation also dresses the bare
quarks and gluons, producing quasi-particles with constituent masses and quark and gluon
condensates. This framework is then applied, using the variational principle, to the hybrid
meson and tetra-quark problems, where exotic quantum numbers can be generated; light u …