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 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 −2m K 2 ]≃−m f′ 0 2 −m f 0 2 +2m 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 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.