The baryon octet and decuplet masses and Bethe-Salpeter vertex and wave functions are calculated in the ladder approximation to the quark exchange between a scalar or axialvector diquark and a constituent quark. These functions reflecting full Lorentz covariance are given in terms of an expansion in Gegenbauer polynomials. In the rest frame of the baryon, a complete partial wave decomposition of the Bethe-Salpeter wave function is performed. The confinement of quarks and diquarks is implemented via a parametrisation of the corresponding propagators. We also discuss some aspects of the momentum routing in the ladder approximation to the Bethe-Salpeter equation. Numerical results for the octet and decuplet masses with broken flavour SU (3) in the conserved isospin limit are presented.

In a model where constituent quarks and diquarks interact through quark exchange the Bethe-Salpeter equation in ladder approximation for the nucleon is solved. Quark and diquark confinement is effectively parametrized by choosing appropriately modified propagators. The coupling to external currents is implemented via nontrivial vertex functions for quarks and diquarks to ensure gauge invariance at the constituent level. Nucleon matrix elements are evaluated in a generalised impulse approximation, and electromagnetic, pionic and axial form factors are calculated.

In a Nambu-Jona-Lasinio model supplemented with an infrared cutoff in addition to the ultraviolet cutoff we study the issue whether diquarks are confined when the model is extended beyond the rainbow-ladder approximation. The gap equation, obtained in a truncation scheme motivated via a nontrivial quark-gluon vertex function, is solved to determine the constituent quark mass if chiral symmetry is spontaneously broken. In a second step, the Bethe-Salpeter equations for mesons and diquarks beyond ladder approximation are derived, taking care to preserve Goldstone's theorem in the pion channel. While the obtained masses of pseudoscalar and vector mesons are only moderately shifted compared to the values in ladder approximation, we observe that scalar diquarks disappear from the physical spectrum and therefore are confined. For axialvector diquarks we observe indications, that the same mechanism may also work, but the NJL model allows no conclusive answer in this channel.

Nucleon form factors are calculated in a relativistic diquark--quark picture based on the Nambu--Jona-Lasinio model. The nucleon wave function is obtained in a static approximation to the quark exchange interaction between the valence quark and the diquark. We evaluate the valence quark and $0^+$--diquark contribution to the nucleon electromagnetic and weak currents. We find reasonable electric charge radii, magnetic moments as in the additive diquark model, and $g_A \approx 1$. We discuss the dependence on the model parameters.Comment: 10 pages, latex, 1 postscript figure included (uuencoded