SU(3)-flavor breaking in octet baryon masses and axial couplings

The lightest baryon octet is studied within a covariant and confining Nambu–Jona-Lasinio model. By solving the Poincaré covariant Faddeev equations—including scalar and axialvector diquarks—we determine the baryon octet masses and axial charges for strangeness conserving transitions. For the axial charges the degree of violation of SU(3) flavor symmetry, arising because of the strange spectator quark(s), is found to be no more than 10%.

Figure 1

The NJL gap equation in the Hartree-Fock approximation, where the thin line represents the elementary quark propagator, $S_{0q}^{-1}\left(k\right)=\neg k-m_q+i\varepsilon$, and the shaded circle represents the 4-fermion interaction.

Figure 2

Inhomogeneous Bethe-Salpeter equation for quark-quark (diquark) correlations.

Figure 3

Homogeneous Poincaré covariant Faddeev equation whose solution gives the mass and vertex function for each member of the baryon octet.

Figure 4

Feynman diagrams representing the axial current for the octet baryons. The diagram on the left is called the quark diagram and the one on the right the diquark diagram. In the diquark diagram the photon interacts with each quark inside the nonpointlike diquark.

Figure 5

Feynman diagrams that represent the diquark axial current. The shaded circles are the diquark Bethe-Salpeter vertices and the shaded oval is the ${\gamma }^{\mu }{\gamma }_5$ vertex.

Figure 6

Inhomogeneous Bethe-Salpeter equation whose solution gives the quark-axialvector vertex, represented as the large shaded oval. The small dot is the inhomogeneous driving term (${\gamma }^{\mu }{\gamma }_5$), while the shaded circle is the $\overline{q}q$ interaction kernel. Only the $G_{\rho }$ interaction channel of Eq. (1) contributes.