Two- and three-gluon glueballs within the helicity formalism

Both positive and negative charge conjugation glueball spectra are computed with a constituent gluon approach. We first compute the spectrum of the Hamiltionian describing two-gluon bound states having <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mo>=</a:mo><a:mo>+</a:mo></a:math>, before tackling the three-gluon bound states having <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mo>=</c:mo><c:mo>−</c:mo></c:math>. We review the construction of two and three particle helicity states in order to build totally symmetric wave functions for our glueball states. In the literature, two different couplings schemes are used to build three particle states. We derive for the first time the relation between these two three-body state definitions. The glueball spectra are compared with those obtained from quantum chromodynamics simulations on a lattice. The two-gluon glueball spectra show a good agreement with the constituent approach and the numerical lattice simulations. The three-gluon spectrum is in overall agreement with the masses observed on the lattice but also predicts additional low-lying states.