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 $g_{A, Q}^{(0)}[m_{η'}^{2} + m_η^{2} - 2 m_{K}^{2} ]\simeq - m_{f_{0}^{'}}^{2} - m_{f_{0}}^{2} + 2 m_{K_{0}^{*}}^{2}$, where $η^{'}, η, K$ are the observed pseudoscalar mesons, $K_{0}^{*}$ is the strange scalar meson at 1430 MeV and $f_{0}, f_{0}^{'}$ 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.