Null-plane formulation of Bethe-Salpeter qqq dynamics: Baryon mass spectra

The Bethe-Salpeter (BS) equation for a qqq system is formulated in the null-plane approximation (NPA) for the BS wave function, as a direct generalization of a corresponding QCD-motivated formalism developed earlier for qq¯ systems. The confinement kernel is assumed vector type (${\gamma }_{\mu }^{\mathrm{}\left(1\right)\mathrm{}}$${\gamma }_{\mu }^{\mathrm{}\left(2\right)\mathrm{}}$) for both qq¯ and qq pairs, with identical harmonic structures, and with the spring constant proportional, among other things, to the running coupling constant ${\alpha }_s$ (for an explicit QCD motivation). The harmonic kernel is given a suitable Lorentz-invariant definition [not ${\square }^2$${\delta }^4$(q)] , which is amenable to NPA reduction in a covariant form. The reduced qqq equation in NPA is solved algebraically in a six-dimensional harmonic-oscillator (HO) basis, using the techniques of SO(2,1) algebra interlinked with $S_3$ symmetry. The results on the nonstrange baryon mass spectra agree well with the data all the way up to N=6, thus confirming the asymptotic prediction M∼$N^{2/3}$ characteristic of vector confinement in HO form. There are no extra parameters beyond the three basic constants (${\omega }_0$,$C_0$,$m_{\mathrm{ud}}$) which were earlier found to provide excellent fits to meson spectra (qq¯).