Titre de la dissertation: The quantum three-body problem: baryons and glueballs as pivotal examples

Promoteurs de thèse: Monsieur Claude Semay et Monsieur Vincent Mathieu (Université de Barcelone)

Résumé de la dissertation: The primary aim of the thesis is to study two- and three-gluon glueballs within the framework of constituent approaches. These states, theoretically predicted in 1972, remain experimentally elusive to this day. In this context, gaining theoretical insight into glueball properties may help to guide experimental efforts, such as those underway at BESIII or GlueX.The approach adopted in the thesis involves an adaptation of the constituent-quark model to glueballs. In this model, constituent gluons are treated as massless particles with negative parity. The spin degrees of freedom for massless particles are handled using the helicity formalism developed by Jacob and Wick. Two- or three-gluon states are decomposed into the helicity basis to construct trial states with the good symmetries and the good quantum numbers. Matrix elements of a phenomenological QCD-inspired Hamiltonian are then evaluated, and the corresponding eigenvalues are minimised with respect to variational parameters. This procedure yields accurate approximations for glueball masses and wave functions. The results are in agreement with previous studies of two-gluon systems, and the formalism has been explicitly extended to study three-gluon glueballs, yielding original results.Beyond this specific application, the thesis contributes more broadly to the study of three-body problems in quantum mechanics. In particular, a numerical code based on expansions in harmonic oscillator bases has been developed. This tool has been extensively used in the research unit for studies on hybrid baryons, the quark-diquark approximation for baryons, and for assessing the accuracy of the envelope theory, a distinct approximation method. The latter application necessitated extending harmonic oscillator basis expansions techniques to incorporate three-body forces. By exploiting the symmetries of the harmonic oscillator Hamiltonian in hyperspherical coordinates, an efficient method for computing a specific kind of three-body matrix elements has been devised. In the future, this code is expected to support further applications in the study of various hadronic systems.