Abstract :
[en] Since the discovery of hadrons in the 1950s, substantial efforts have been made to classify and understand them within quantum chromodynamics (QCD), the theory describing strong interaction. Hadrons are composed of quarks and gluons, bound by the principle of colour confinement, resulting in colour-neutral observable states. The most common hadrons are baryons (three quarks) and mesons (quark-antiquark pairs), but exotic states, such as hybrid states involving excitations of the gluonic field, are also predicted. Hybrid mesons, with distinguishable quantum numbers, have been the focus of extensive theoretical and experimental research. In contrast, hybrid baryons, with no unique quantum number signatures, pose greater challenges in identification. Various theoretical models predict different masses and structures for hybrid baryons, while experimental efforts are ongoing at the Jefferson Lab. This thesis presents a constituent model developed to describe hybrid baryons containing heavy quarks. In our model, the interaction among the three quarks forms a core structure, which subsequently interacts with a gluon. The chosen potential is the funnel one, which combines linear and Coulomb terms. The interaction between the quark core and the gluon is then modelled using a potential derived from the convolution of the funnel potential, accounting for the spatial extension of the quark core. Masses and wavefunctions of hybrid baryons, with specified 𝐽^𝑃 quantum numbers, are computed with the two-body helicity formalism of Jacob and Wick. Another aspect of the thesis focused on the development of the envelope theory (ET), an approximation method for solving the many-body Schrödinger-like equation. The ET finds particular utility in the large-𝑁 approach of QCD, where a baryon is conceived as a bound state of 𝑁 quarks. Extending the ET to accommodate systems with different particles becomes essential for the large-𝑁 treatment of hybrid baryons, where the system comprises 𝑁 quarks and one gluon.
