Search

In the framework of quark models, hybrid mesons are either seen as two-body $q\bar q$ systems with an excited flux tube connecting the quark to the antiquark or as three-body $q\bar q g$ systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the $q\bar q g$ hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent $q\bar q$ potential. This equivalence between the excited flux tube and the constituent gluon approach is confirmed for heavy hybrid mesons but, for the first time, it is shown to hold in the light sector too, provided the contribution of the quark dynamics is correctly taken into account.

The model for the decay of a meson into two mesons is revisited. In particular, the formalism is extended in order to deal with an arbitrary form for the creation vertex and with the exact meson wave functions. A careful analysis of both effects is performed and discussed. The model is then applied to a large class of transitions known experimentally. Two types of quark-antiquark potentials have been tested and compared.

Solutions of the two‐body Dirac equation with diagonal central potentials are investigated, both for particle–particle and particle–antiparticle cases. A detailed study of the symmetry properties of the solutions is carried out for systems composed of identical or massless particles. The Klein paradox is discussed and several solutions relevant to the study of the quarkonium are presented.

Using the interquark potential due to Bhaduri et al., the energies of all\(L = 0q^2 \bar q^2 \) systems are calculated for any value of the total spinS and for any value of the physical flavors:u, d, s, c, b. A harmonic oscillator basis up to 8 quanta is used to solve the four-body problem within a non-relativistic quark model. The corresponding energies are compared to the meson-meson threshold energies in order to search for stable multiquarks some of them are proposed.

We analyze, within a non-relativistic quark model, the low energy part of the baryonic spectrum in the octet and decuplet flavour representations. The relevance of a strong Coulomb potential is emphasized in order to explain its general features. The addition of a three-body force allows to solve the ‘Roper puzzle’, giving a consistent explanation to its relative position in the spectrum.

The multiphonon method based onβ andγ phonons is tested in a simple model allowing an exact solution for a many body fermion system where pairing and quadrupole forces are acting. The properties exhibiting the anharmonicities of the lowest-lying vibrational states of positive parity are nicely reproduced by this method.

A closed and analytical formula is given for the free Green’s function in a harmonic oscillator basis. It is very useful for solving the Lippman–Schwinger equation for the scattering of two clusters within the resonating group method formula.