# The nucleon spin and momentum decomposition using lattice QCD simulations

## TL;DR

This study uses lattice QCD simulations to decompose the nucleon spin and momentum into contributions from valence and sea quarks and gluons, providing quantitative insights consistent with the spin sum rule.

## Contribution

It presents a first-principles lattice QCD calculation of the nucleon spin and momentum decomposition, including both quark and gluon contributions, at near-physical pion mass.

## Key findings

- Total quark angular momentum: 0.408(61)(48)
- Gluon angular momentum: 0.133(11)(14)
- Quark spin contribution: 0.201(17)(5)

## Abstract

We determine within lattice QCD, the nucleon spin carried by valence and sea quarks, and gluons. The calculation is performed using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass. We find that the total angular momentum carried by the quarks in the nucleon is $J_{u+d+s}{=}0.408(61)_{\rm stat.}(48)_{\rm syst.}$ and the gluon contribution is $J_g {=}0.133(11)_{\rm stat.}(14)_{\rm syst.}$ giving a total of $J_N{=}0.54(6)_{\rm stat.}(5)_{\rm syst.}$ consistent with the spin sum. For the quark intrinsic spin contribution we obtain $\frac{1}{2}\Delta \Sigma_{u+d+s}{=}0.201(17)_{\rm stat.}(5)_{\rm syst.}$. All quantities are given in the $\overline{\textrm{MS}}$ scheme at 2~GeV. The quark and gluon momentum fractions are also computed and add up to $\langle x\rangle_{u+d+s}+\langle x\rangle_g{=}0.804(121)_{\rm stat.}(95)_{\rm syst.}+0.267(12)_{\rm stat.}(10)_{\rm syst.}{=}1.07(12)_{\rm stat.}(10)_{\rm syst.}$ satisfying the momentum sum.