Nucleon Spin and Momentum Decomposition Using Lattice QCD Simulations

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)$_{stat}$(48)$_{syst}$ and the gluon contribution is $J_g$ = 0.133(11)$_{stat}$(14)$_{syst}$, giving a total of $J_N$ = 0.54(6)$_{stat}$(5)$_{syst}$ that is consistent with the spin sum. For the quark intrinsic spin contribution, we obtain $\frac 1{2} \Delta \Sigma _{u+d+s}$ 0.201(17)$_{stat}$(5)$_{syst}$. All quantities are given in the modified minimal subtraction scheme at 2 GeV. The quark and gluon momentum fractions are also computed and add up to $\langle x \rangle_{u+d+s} + \langle x \rangle _g = 0.804(121)_{stat}(95)_{syst} + 0.267(12)_{stat}(10)_{syst} = 1.07(12)_{stat}(10)_{syst}$ hxiuþdþs þ hxig ¼ 0.804ð121Þstatð95Þsyst þ 0.267ð12Þstatð10Þsyst ¼ 1.07ð12Þstatð10Þsyst, thussatisfying the momentum sum