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 $g_{ A, Q}^{ (0)}[m_{ \eta '}^{ 2} + m_{ \eta}^{ 2} - 2 m_{ K}^{ 2} ]\simeq - m_{ f_{ 0}^{ '}}^{ 2} - m_{ f_{ 0}}^{ 2} + 2 m_{ K_{ 0}^{ *}}^{ 2}$, where $\eta^{ '}, \eta, K$ 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.
Categories: hep-ph