U_A(1) symmetry breaking, scalar mesons and the nucleon spin problem in an effective chiral field theory

Abstract

We establish a relationship between the scalar meson spectrum and the $U_A(1)$ symmetry-breaking 't Hooft interaction on one hand and the constituent quark's flavor-singlet axial coupling constant $g_{A,Q}^{(0)}$ on the other, using an effective chiral quark field theory. This analysis leads to the new sum rule $g_{A,Q}^{(0)}[m_{{\eta }^{\prime }}^2+m_{\eta }^2-2m_K^2]\simeq -m_{f_0^{{}^{\prime }}}^2-m_{f_0}^2+2m_{K_0^{\ast }}^2$, where ${\eta }^{{}^{\prime }},\eta ,K$ are the observed pseudoscalar mesons, $K_0^{\ast }$ is the strange scalar meson at 1430 MeV and $f_0,f_0^{{}^{\prime }}$ are "the eighth and the ninth" scalar mesons. We discuss the relationship between the constituent quark flavor-singlet axial coupling constant $g_{A,Q}^{(0)}$ and the nucleon one $g_{A,N}^{(0)}$ (``nucleon's spin content'') in this effective field theory. We also relate $g_{A,Q}^{(0)}$, as well as the flavour-octet constituent quark axial coupling constant $g_{A,Q}^{(1)}$ to vector and axial-vector meson masses in general as well as in the tight-binding limit.

Comments: 16 pages, 3 figures, RevTex, to appear in Nucl.Phys.A