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.

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

References in corpus (2)

• Mechanism for a next-to-lowest lying scalar meson nonet
• Polarized lepton nucleon scattering - summary of the experimental spin sessions at DIS 99

Cited by in corpus (18)

• Multi-quark interactions with a globally stable vacuum
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• Lowering the critical temperature with eight-quark interactions
• Effective multi-quark interactions with explicit breaking of chiral symmetry
• OZI violating eight-quark interactions as a thermometer for chiral transitions
• Light Quark Masses in Multi-Quark Interactions
• Strange quark matter in the presence of explicit symmetry breaking interactions
• Light Scalar Mesons in the Improved Ladder QCD
• Sum rule analysis of vector and axial-vector spectral functions with excited states in vacuum
• Baryons with U_L(3)*U_R(3) Chiral Symmetry IV: Interactions with Chiral (8,1)+(1,8) Vector and Axial-vector Mesons and Anomalous Magnetic Moments
• On the scalar nonet in the extended Nambu Jona-Lasinio model
• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• Effects of Quark Interactions on Dynamical Chiral Symmetry Breaking by a Magnetic Field
• Evaluating chiral symmetry restoration through the use of sum rules
• Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions
• Sigma meson in QCD sum rules using a two quark current with derivatives
• Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with $U_\A(1)$ Breaking