Strange and Charm Quark Spins from Anomalous Ward Identity

TL;DR

This paper calculates the contributions of strange and charm quarks to the nucleon spin using the anomalous Ward identity, employing lattice QCD techniques with overlap fermions to obtain results at physical pion mass.

Contribution

It introduces a novel lattice QCD approach utilizing the anomalous Ward identity with overlap fermions to accurately determine quark spin contributions to the nucleon.

Findings

Charm quark pseudoscalar and topological terms nearly cancel each other.

Strange quark pseudoscalar term is less negative than charm.

Strange quark spin contribution at physical pion mass is approximately -0.0403.

Abstract

We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_{\pi} = 330$ 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 $\Delta s + \Delta {\bar{s}} = -0.0403(44)(78)$.