nLab proton spin crisis



Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields

Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



In the standard model of particle physics, the hadrons, such as the proton, are supposedly bound states of three constituent quarks, the latter being the fundamental objects in quantum chromodynamics. In fact, quarks are thought to be confined to such colour-charge-neutral bound states. However, at the relevant energy-scale QCD is “strongly coupled” (the coupling constant is large) so that established methods of perturbative quantum field theory do not apply (possibly standard pQFT has to be supplied with an interacting vacuum state, or more general methods of non-perturbative quantum field theory are needed, all of which remains largely open). As a result, the expected confinement of quarks to hadrons is theoretically an open problem, known in mathematical physics essentially as the mass gap problem.

Therefore, together with the very existence of hadrons, also their basic properties, such as mass and spin do not currently have a derivation from first principles in QCD. There exists qualitative understanding and there exists computer simulation in lattice QCD. When experiment showed that also these heuristics drastically failed to provide an understanding of the spin of the proton in terms of the spin of its constitutents quarks and of the gluons binding these quarks together, the situation was called the proton spin crisis or proton spin puzzle.


  • Anthony Thomas, The spin of the proton, Progress in Particle and Nuclear Physics Volume 61, Issue 1, July 2008, Pages 219–228 Quarks in Hadrons and Nuclei — 29th Course International Workshop on Nuclear Physics (arXiv:0805.4437)

  • Anthony Thomas, The resolution of the proton spin crisis, 2008 (pdf)

  • Xiangdong Ji, Feng Yuan, Yong Zhao, Proton spin after 30 years: what we know and what we don’t? (arXiv:2009.01291)

Apparent resolution by lattice QCD-computations:

See also

Last revised on September 6, 2021 at 06:15:04. See the history of this page for a list of all contributions to it.