Proton Spin Structure from Lattice QCD

A lattice QCD calculation of the proton matrix element of the flavor singlet axial-vector current is reported. Both the connected and disconnected contributions are calculated, for the latter employing the variant method of wall source without gauge fixing. From simulations in quenched QCD with the Wilson quark action on a ${16}^3\times 20$ lattice at $\beta =5.7\mathrm{}$ (the lattice spacing $a\approx 0.14$ fm), we find $\Delta \Sigma =\Delta u+\Delta d+\Delta s=+0.638\mathrm{}\left(54\right)-0.347\mathrm{}\left(46\right)-0.109\mathrm{}\left(30\right)=+0.18\mathrm{}\left(10\right)$ with the disconnected contribution to $\Delta u$ and $\Delta d$ equal to $-0.119\mathrm{}\left(44\right)$, which is reasonably consistent with the experiment.