How the proton spin divides among quarks and gluons
In plain words
The proton spin of $1/2$ (in units of $\hbar$) must be the sum of quark spins, gluon spins and the orbital motion of both. Only the quark-spin part is measured well, at about 30 percent.
Precise statement
In a fixed gauge-invariant decomposition (Jaffe-Manohar: $1/2=\Delta \Sigma/2+\Delta G+L_{q}+L_{g}$, or Ji: $1/2=J_{q}+J_{g}$) at $\mu^{2}=10\,\mathrm{GeV}^{2}$ in the MS-bar scheme, determine each term with uncertainty below 0.05. $\Delta \Sigma \sim 0.3$ is known from polarized deep-inelastic scattering; the answer is the complete set of values from data, cross-checked by lattice QCD at the physical pion mass.
What would settle it
Polarized electron-proton collisions at the EIC (Electron-Ion Collider, Brookhaven) covering x down to about 1e-4, combined with lattice QCD calculations of quark and gluon angular momenta at physical quark masses.
Status in the literature
Unverified note
$\Delta \Sigma$ near 0.3 has been fixed since the 1990s and lattice QCD gave full Ji decompositions at the physical pion mass by 2020 (Alexandrou et al.), but the gluon helicity and orbital terms remained experimentally unmeasured at the needed precision as of 2026.
Related problems
- More general than Total gluon spin contribution $\Delta G$ to the proton spin
- More general than Measuring quark and gluon orbital angular momentum in the proton