Proton spin

Scattering from a proton changes when the spin directions of the probe and proton are aligned differently. Spin is a particle’s intrinsic angular momentum. Inside a proton, quarks and gluons are bound together by the strong interaction. Its total quantum spin is known, but how much comes from these constituents’ spins, and how much from their motion? The measurements reveal parts of this internal budget rather than a simple sum of three quark spins.[1]

Scattering rates change when a proton’s spin and the incoming probe’s spin are aligned differently. Spin is intrinsic angular momentum; the proton’s total is known, but its quarks and gluons form an interacting bound system. How do their spins and orbital motion provide that total at a stated theory scale?

A helicity distribution measures the imbalance between constituent spins along and against motion, as a function of the momentum fraction $x$ they carry. Polarized lepton–proton scattering constrains quark helicity; polarized proton collisions constrain gluon helicity over their measured range. A total contribution integrates over the full range, including poorly measured small $x$.

In a gauge-invariant completion of the canonical decomposition, the budget is $\tfrac12=\tfrac12\Delta\Sigma+\Delta G+L_q+L_g$, in units of reduced Planck’s constant. Here ΔΣ sums quark and antiquark helicity, ΔG is gluon helicity, and each L term is an orbital angular momentum contribution in the canonical definition. Ji’s decomposition instead groups total quark and total gluon angular momentum, using kinetic quark orbital motion. These assignments are not interchangeable, although they describe the same total spin. Their dependence on renormalization scale—the theory scale used to define and compare contributions—must also be kept explicit. Measurements sensitive to orbital structure, such as exclusive scattering in which the proton remains intact, are needed alongside helicity measurements.[1]

Quarks and gluons carrying very little of the proton’s momentum, and orbital motion, remain uncertain. The pieces must be defined at a stated scale.[1] [2]

Small-x helicity and orbital contributions remain difficult to constrain. Analytic evolution solutions exist in restricted limits; they do not provide a complete measured budget or make different orbital definitions identical.[1] [2]

The familiar proton is a bound system of interacting quarks and gluons. Its spin tests how their intrinsic angular momenta and motion combine into one particle’s observed property. Comparing these contributions with scattering measurements tests our description of that internal quantum structure.[1]

The budget connects measured spin asymmetries and orbital-sensitive scattering to the angular momentum of a relativistic bound system. Comparing those observables at consistent definitions and scales tests how quark and gluon interactions build the proton. The unmeasured momentum region matters to that test even though the proton’s total spin is already known.[1]