Quark spins and Anomalous Ward Identity

TL;DR

This study calculates the quark spin contribution to the proton spin using lattice QCD with overlap fermions, verifying the anomalous Ward identity and providing results consistent with experimental data.

Contribution

First lattice QCD calculation of quark spin contribution using overlap fermions on near-physical ensembles with verification of the anomalous Ward identity.

Findings

Total quark spin contribution: ΔΣ=0.401(25)(37)

Isovector axial coupling: g_A^3=1.256(16)(30)

Error reduction achieved with CDER technique

Abstract

We calculate the intrinsic quark spin contribution to the total proton spin using overlap valence quarks on three ensembles of $2+1$-flavor RBC/UKQCD domain-wall configurations with different lattice spacings. The lowest pion mass of the ensembles is around 171 MeV which is close to the physical point. With overlap fermions and topological charge derived from the overlap operator, we verify the anomalous Ward identity between nucleon states with momentum transfer. Both the connected and disconnected insertions of the axial-vector current are calculated. For the disconnected-insertion part, the cluster-decomposition error reduction (CDER) technique is utilized for the lattice with the largest volume and the error can be reduced by $10\%\sim40\%$. Nonperturbative renormalization is carried out and the final results are all reported in the $\overline{{\rm MS}}$ scheme at 2 GeV. We determine the total quark spin contribution to the nucleon spin to be $\Delta\Sigma=0.401(25)(37)$, which is consistent with the recent global fitting result of experimental data. The isovector axial coupling we obtain in this study is $g_A^3=1.256(16)(30)$, which agrees well with the experimental value of 1.2723(23).