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).
Highlights
The decomposition of the proton spin into its quark and glue constituents has long been a puzzle ever since the first deep inelastic scattering (DIS) experiment around three decades ago [1,2] revealed that not all the proton spin originates from the quark intrinsic spin as depicted in the naive quark model, leading to the so-called “proton spin crisis.” we understand that the proton spin, consisting of quark spin, quark orbital angular momentum, glue spin, and glue orbital angular momentum, is the result of complicated QCD dynamics that cannot be described by the quark model
The lowest pion mass of the ensembles is around 171 MeV, which is close to the physical point
The pion mass of 32ID is around 171 MeV, which is close to the physical point
Summary
The decomposition of the proton spin into its quark and glue constituents has long been a puzzle ever since the first deep inelastic scattering (DIS) experiment around three decades ago [1,2] revealed that not all the proton spin originates from the quark intrinsic spin as depicted in the naive quark model, leading to the so-called “proton spin crisis.” we understand that the proton spin, consisting of quark spin, quark orbital angular momentum, glue spin, and glue orbital angular momentum, is the result of complicated QCD dynamics that cannot be described by the quark model. Since for each quark flavor the intrinsic spin is half of the corresponding axial coupling of the nucleon, we need to calculate the axial coupling for the flavor-diagonal case. Both the connected insertions and the disconnected insertions of the correlation functions need to be included. We find that the same normalization constant for the local axial-vector current as used in the isovector case to satisfy the chiral Ward identity satisfies the anomalous Ward identity This is not true in general for nonchiral fermions.
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