SU(3) breaking in neutral current axial matrix elements and the spin content of the nucleon

We examine the effects of SU(3) breaking in the matrix elements of the flavor-diagonal axial-vector currents between octet baryon states. Our calculations of $K$, $\eta$, and $\pi$ loops indicate that the SU(3) breaking may be substantial for some matrix elements and at the very least indicate large uncertainties. In particular, the strange axial matrix element in the proton determined from the measurements of $g_1\mathrm{}\left(x\right)\mathrm{}$ is found to have large uncertainties and might yet be zero. We estimate the strange axial matrix element in the proton to be $-0.35\lesssim \Delta s\lesssim 0$ and the matrix element of the flavor-singlet current in the proton to be $-0.1\lesssim \Sigma \lesssim +0.3\mathrm{}$ from the E143 measurement of $\int {\mathrm{dxg}}_1\mathrm{}\left(x\right)=0.127\mathrm{}\pm 0.004\pm 0.010$. The up-quark content of the ${\Xi }^{-}$ is discussed and its implications for nonleptonic weak processes discussed. We also estimate the matrix element of the axial-vector current coupling to the $Z^0$ between all octet baryon states. This may be important for neutrino interactions in dense nuclear environments, where hyperons may play an important role.