Quark spins and anomalous Ward identity
Jian Liang (Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA); Yi-Bo Yang (Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA); Terrence Draper (Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA); Ming Gong (Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China); Keh-Fei Liu (Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA)
We calculate the intrinsic quark spin contribution to the total proton spin using overlap valence quarks on three ensembles of -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 a topological charge derived from the overlap operator, we verify the anomalous Ward identity between nucleon states with momentum transfer. Both the connected and the disconnected insertions of the axial-vector current are calculated. For the disconnected-insertion part, the cluster-decomposition error reduction technique is utilized for the lattice with the largest volume and the error can be reduced by 10%–40%. Nonperturbative renormalization is carried out and the final results are all reported in the scheme at 2 GeV. We determine the total quark spin contribution to the nucleon spin to be , which is consistent with the recent global fitting result of experimental data. The isovector axial coupling we obtain in this study is , which agrees well with the experimental value of 1.2723(23).
