Strange and charm quark spins from the anomalous Ward identity

Abstract

We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). This is performed with overlap valence quarks on $2+1$-flavor domain-wall fermion gauge configurations on a $2{4}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice with lattice spacing ${a}^{\ensuremath{-}1}=1.73\text{ }\text{ }\mathrm{GeV}$ and the light sea mass at ${m}_{\ensuremath{\pi}}=330\text{ }\text{ }\mathrm{MeV}$. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite ${q}^{2}$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange ${g}_{A}({q}^{2})$ at ${q}^{2}=0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with ${g}_{A}({q}^{2})$ and the induced pseudoscalar form factor ${h}_{A}({q}^{2})$ at finite ${q}^{2}$. The chiral extrapolation to the physical pion mass gives $\mathrm{\ensuremath{\Delta}}s+\mathrm{\ensuremath{\Delta}}\overline{s}=\ensuremath{-}0.0403(44)(78)$.