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What we know and what we don’t know about the proton spin after 30 years

A Publisher Correction to this article was published on 21 December 2020

This article has been updated


More than three decades ago, the European Muon Collaboration published a surprising result on the spin structure of the proton: the spins of its three quark components account for only a small part of the spin of the proton. Ever since, theoretical and experimental progress has been made in understanding the origins of the proton spin. In this Review, we discuss what has been learned so far, what is still missing and what could be learned from the upcoming experiments, including the Jefferson Lab 12 GeV upgrade and the proposed Electron-Ion Collider. In particular, we focus on first-principles calculations and experimental measurements of the total gluon helicity ΔG, and the quark and gluon orbital angular momenta.

Key points

  • There are two established approaches to look at the composition of the proton spin: the frame-independent spin structure (or the Ji sum rule) and the infinite-momentum-frame or parton spin structure (or the Jaffe–Manohar sum rule).

  • In the frame-independent approach, the quark orbital and gluon angular momentum contributions can be extracted from the moments of the generalized parton distributions. Results from the Jefferson Lab 6 GeV and HERMES experiments suggest that there is a substantial quark orbital contribution.

  • In terms of partons, the quark and gluon helicity contributions have a simple physical interpretation, and the result from Relativistic Heavy Ion Collider spin experiments has provided a first important constraint on the total gluon helicity.

  • The development of a large-momentum effective theory along with lattice quantum chromodynamics simulations provide first-principles calculations of the spin structure. The results on the quark and gluon helicity contributions, and the quark orbital and gluon angular momentum contributions have provided the first complete theoretical picture.

  • The Jefferson Lab 12 GeV programme will provide better information on the quark orbital angular momentum and gluon angular momentum. The future Electron-Ion Collider will provide high-precision measurements on the gluon helicity and gluon angular momentum.

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Fig. 1: State-of-the-art lattice quantum chromodynamics studies on the proton spin.
Fig. 2: The Relativistic Heavy Ion Collider at Brookhaven National Laboratory provides strong evidence for the gluon helicity contribution to the proton spin.
Fig. 3: Investigations of a new experimental process called deeply virtual Compton scattering, which has provided a way to study the quark orbital angular momentum in the proton.
Fig. 4: The planned Electron-Ion Collider at Brookhaven National Laboratory and its expected impact on our understanding of nucleon spin.

Change history

  • 21 December 2020

    A Correction to this paper has been published:


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This Review Article is dedicated to late V. Hughes whose drive in polarized DIS experiments lead to the surge and unabated interest in the proton spin structure, and perhaps to the EIC project in the United States. The authors thank C. Aidala, C. Alexandrou, M. Burkardt, Y. Hatta, D. Hertzog, R. Jaffe and K. F. Liu for useful communications relating to this article. This material is supported by the US Department of Energy, Office of Science, Office of Nuclear Physics, under contract numbers DE-AC02-05CH1123, DE-SC0012704 and DE-SC0020682, and within the framework of the TMD Topical Collaboration.

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The authors contributed equally to all aspects of the article.

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Correspondence to Xiangdong Ji, Feng Yuan or Yong Zhao.

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Nature Reviews Physics thanks Volker Burkert and the other, anonymous, reviewers for their contribution to the peer review of this work.

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Pauli–Lubanski spin

A spin four-vector operator generalized for relativistic particles.

Partonic picture

The distribution of physical observables in partons with different momentum fractions x.

Belinfante improvement procedure

A process leading to a symmetric and gauge-invariant energy-momentum tensor in gauge theories.

Boost invariant

A property that does not change under a boost Lorentz transformation.

Dimensional regularization

A process making momentum integrals finite at ultraviolet by changing the space-time dimensions.

(Modified) minimal subtraction

A process subtracting off-ultraviolet divergences in dimensional regularization, often leading to a resolution scale dependence μ.


Physical particles with the correct energy-momentum relation are called on-shell or on-mass-shell; otherwise, they are called off-shell or off-mass-shell. Off-shell particles are virtual and can exist in interaction processes.


The path or separation along a direction of a light cone.


A quantity defined by summing over all quark flavours.

Disconnected diagrams

Contributions in lattice quantum chromodynamics calculations, in which the quark operators do not connect with the external hadron states.

Quenched approximation

A term referring to lattice quantum chromodynamics calculations in which the fermion determinant is neglected to save computational costs.

Exclusive hard scattering

A hard scattering process in which specific final states with a fixed type of particle are produced.

Photon exclusive production

A hard scattering process in which only a photon is produced.

Bethe–Heitler amplitude

An elastic scattering amplitude in which only an extra photon is produced.

Gravitational form factor

The energy-momentum form factor, derived from the fact that energy momentum is the charge for gravitational interaction.

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Ji, X., Yuan, F. & Zhao, Y. What we know and what we don’t know about the proton spin after 30 years. Nat Rev Phys 3, 27–38 (2021).

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