Helicity Formalism for two and three gluon glueballs

One of the earliest predictions of Quantum Chromodynamics (QCD) is the existence of color singlet pure-gauge states, known as glueballs. Nevertheless, achieveing consensus on their properties and identifying experimental evidence remain significant challenges. While two-gluon glueball states have been extensively studied both theoretically and experimentally, three-gluon glueballs have received comparatively less attention due to the technical complexities involved. We use the helicity formalism to describe two- and three-gluon systems within constituent models. The formalism for two-body systems is presented and applied to the study of two-gluon glueballs. By incorporating symmetries, selection rules consistent with lattice QCD results are derived. Additionally, the inclusion of dynamical considerations enables the quantitative reproduction of the lattice QCD spectrum. The helicity formalism is further extended to three-body systems to model three-gluon glueballs. The implementation of symmetries involves the use of two distinct definitions of three-body helicity states. By following a procedure analogous to the two-gluon case, the three-gluon glueball spectrum is calculated and compared with lattice QCD data. As a prospect, the odderon trajectory will be investigated using the aforementioned three-gluon glueball calculations within constituent approaches.