U(1) Goldberger-Treiman Relation and Its Connection to the Proton Spin

The U(1) Goldberger-Treiman (GT) relation for the axial charge $g_A^0$ is reexamined. It is stressed that the isosinglet GT relation in terms of the $\eta_0$ holds irrespective of the quark masses and the axial anomaly. We pointed out that the identification of the $\eta_0-N$ and $\dk-N$coupling terms with the quark and gluon spin components respectively in a proton is possible but valid only in the chiral-invariant factorization scheme. In general, the two-component U(1) GT relation can be identified in a gauge-invariant way with connected and disconnected insertions. The observation that $(\sqrt{3}f_\pi /2m_N)\getao$ is related to the connected insertion i.e., the total valence quark contribution to the proton spin enables us to determine the physical coupling constants $\getap$ and $\geta$ from the GT relations for $g_A^0$ and $g_A^8$. We found $\getap=3.4$ and $\geta=4.7\,$.