The nucleon spin and momentum decomposition using lattice QCD simulations

TL;DR

Within lattice QCD the nucleon spin carried by valence and sea quarks and gluons is determined using an ensemble of gauge configurations with two degenerate light quarks with mass fixed to approximately reproduce the physical pion mass.

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 $\frac{1}{2}ΔΣ_{u+d+s}{=}0.201(17)_{\rm stat.}(5)_{\rm syst.}$. 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.

Figures (3)

• Figure 1: The disconnected sea quark contribution (denoted by disc.) to the isoscalar axial charge (upper) and momentum fraction (lower) as a function of the sink-source time separation $t_s$ for the plateau method (circles) and as a function of the lower time value of $t_s$ used in the fits for the summation (green triangles) and two-state fit (blue square) methods. The open circle indicates the final value and the band its statistical error, while the open square is the value taken to determine the systematic error due to excited state contamination.
• Figure 2: The up (upper), down (center) and strange (lower) quark intrinsic spin contributions to the nucleon spin versus the pion mass. Open symbols show results with only connected contributions while filled symbols denote both connected and disconnected contributions using the same ensemble as the one for the connected only. Red diamonds are the results of this work. Circles are $N_f{=}2$ results, and squares are $N_f{=}2{+}1{+}1$Alexandrou:2013joaAbdel-Rehim:2013wlzAlexandrou:2013wca by ETMC. We compare with lattice QCD results from other ${\cal O}(a)$-improved actions from Refs.QCDSF:2011aa (filled magenta triangle) by QCDSF, Engelhardt:2012gd (light blue cross) and Chambers:2015bka by CSSM/QCDSF (yellow filled right triangle). We also show results using a hybrid action from PNDME Bhattacharya:2016zcn (open blue triangles). Experiment is denoted by the black asterisks Airapetian:2006vyBlumlein:2010rn.
• Figure 3: Left: Nucleon spin decomposition. Right: Nucleon momentum decomposition. All quantities are given in the $\overline{\rm MS}$-scheme at 2 GeV. The striped segments show valence quark contributions (connected) and the solid segments the sea quark and gluon contributions (disconnected).