Status on Lattice Calculations of the Proton Spin Decomposition

TL;DR

This paper reviews lattice calculations of the proton spin decomposition, clarifying the roles of quark and glue contributions, and resolving the proton spin crisis with numerical verification and discussion of future experimental comparisons.

Contribution

It provides a comprehensive review of lattice results on proton spin components, clarifies the connection with the anomalous Ward identity, and discusses the implications for future experiments.

Findings

Quark spin from lattice is smaller than constituent quark models.

Negative vacuum polarization from disconnected insertions affects quark spin.

Large glue spin and angular momentum contributions are observed.

Abstract

Lattice calculations of the proton spin components is reviewed. The lattice results of the quark spin from the axial-vector current matrix element at $\sim 0.3- 0.4$ is smaller than those from the constituent quark models. This is largely due to the fact that the vacuum polarization contribution from the disconnected insertion is negative. Its connection with the anomalous Ward identity is clarified and verified numerically. This resolves the contentious issue in the `proton spin crisis'. The glue spin and angular momentum are found to be large and there is notable contribution from the quark orbital angular momentum. Renormalization, mixing and normalization of the quark and glue angular momenta are discussed. With sufficient precision, they can be compared with more precise experimental measurements when the electron-ion collider facility is available.