Among many misconceptions in the description of the proton presented in undergraduate physics lectures is the origin of the proton’s spin. When we tell students about the three quarks in a proton, we usually say that its spin (equal to one half) comes from the arithmetic of three spin-½ quarks that align themselves such that two point “up” and one points “down”. However, as shown in measurements of the spin taken by quarks in deep-inelastic-scattering experiments in which both the lepton beam and the proton target are polarised, this is not the case. Rather, as first revealed in results from the European Muon Collaboration in CERN’s North Area in 1987, the quarks account for less than a third of the total proton spin. This was nicknamed the proton’s “spin crisis”, and attempts to fully resolve it remain the goal of experiments today.
Physicists had to develop cleverer experiments, for example looking at semi-inclusive measurements of fast pions and kaons in the final state, and using polarised proton–proton scattering, to determine where the missing spin comes from. It is now established that about 30% of the proton spin is in the valence quarks. Intriguingly, this is made up of +65% from up-valence and –35% from down-valence quarks. The sea seems to be unpolarised, and about 20% of the proton’s spin is in gluon polarisation, though it is not possible to measure this accurately across a wide kinematic range. Nevertheless, it seems unlikely that all of the missing spin is in gluons, and the puzzle is not yet solved.
What could the origin of the remaining ~50% of the proton’s spin be? The answer may lie in the orbital angular momentum of both the quarks and the gluons, but it is difficult to measure this directly. Orbital angular momentum is certainly connected to the transverse structure of the proton. The partons’ transverse momentum must also be considered, and there is the transverse position of the partons, and the transverse, as opposed to longitudinal, spin. Multi-dimensional measurements of transverse momentum distributions and generalised parton distributions can give access to orbital angular momentum. Such measurements are underway at Jefferson Laboratory, and are also a core part of the future Electron-Ion Collider programme.