The proton “spin crisis”

[[note: this is an attempt at an AI language model explain some quite difficult concept. >95% of this was AI generated..]]

The proton spin crisis is a long-standing puzzle in physics that arises from our understanding of the proton’s internal structure and its spin.

What is spin?

Spin is a fundamental property of elementary particles, like electrons and quarks. It’s a form of angular momentum, but it’s intrinsic to the particle and doesn’t come from the particle moving around in space. Think of it like the Earth spinning on its axis, but on a much smaller scale at least for visualization purposes. Spin is also “quantized”, meaning it has a specific energy.

Protons have a spin of 1/2.

The initial expectation

Before the 1980’s, the prevailing idea was that a proton’s spin came from the spins of its constituent quarks. The basic model of a proton involves three quarks: two “up” quarks and one “down” quark (uud). It was expected that the spins of these three quarks would add up to give the total spin of the proton. 

The problem

Protons are made up of quarks and gluons. Initially, physicists thought that the proton’s spin was simply the sum of the spins of its constituent quarks. However, experiments in the 1980s showed that the quarks only contribute a small fraction of the proton’s spin. This unexpected finding led to the “proton spin crisis.”  

Experiments in the 1980s, most notably by the European Muon Collaboration (EMC) at CERN, revealed that the quarks only account for a small fraction of the proton’s spin. The initial EMC measurement suggested that the quarks’ spins contributed very little, possibly even zero, to the proton’s total spin. This unexpected result was called the “proton spin crisis” because it contradicted the simple quark model. The initial results were that quarks accounted for ~0.2 of the proton’s spin, a far cry from 1/2. The measured quark spin was far smaller than the prediction based on the Ellis-Jaffe sum rule.

It became clear that the nucleon spin is more complex than previously thought.

The mystery

The question then becomes: where does the rest of the proton’s spin come from? Several possibilities have been explored:

• Quark spin: The summation of quarks and anti-quarks was the initially expected source of the proton spin but has been shown to only be a small portion of the overall total.
• Quark orbital angular momentum: Quarks move around inside the proton, which is considered to have an orbital motion. Their orbital motion contributes to the overall spin of nuclei like protons.  
• Gluon spin: Gluons, the particles that bind quarks together through the “strong force”, also possess spin, and thus contribute to the spin.
• Gluon orbital angular momentum: Similar to quarks, gluons have orbital motion within the proton.   

The “missing” spin was actually distributed among these other components, mainly orbital angular momentum. The realization that gluons and orbital angular momentum also contribute to the proton’s spin changed the understanding of the nucleon.

How the “crisis” was resolved

The resolution of the spin crisis involved both theoretical advancements and experimental data from different facilities. The modern spin discrepancy can be rather well explained in terms of standard features of the non-perturbative structure of the nucleon, namely relativistic motion of the valence quarks, the pion cloud required by chiral symmetry, and an exchange current contribution associated with the one-gluon-exchange hyperfine interaction.

The experiments measured the spin-dependent structure functions of the nucleon by scattering polarized leptons off polarized protons and neutrons. It was found that the gluon spin contribution seems to be moderate. Theorists, like Myhrer and Thomas, have proposed that relativistic effects, one-gluon exchange, and the pion cloud reduce the naive expectations.

Quantum chromodynamics (QCD)

QCD is the fundamental theory that describes the strong force, one of the four fundamental forces in nature (the others being gravity, electromagnetism, and the weak force). The strong force is responsible for binding quarks together to form protons and neutrons, and for binding protons and neutrons together to form atomic nuclei. QCD describes the interactions of quarks and gluons.

Quarks are elementary particles that make up protons, neutrons, and other composite particles called hadrons. Gluons are the force carriers of the strong force, analogous to photons for the electromagnetic force. Quarks carry a property called “color charge,” which is analogous to electric charge in electromagnetism. However, unlike electric charge, which has only two types (positive and negative), color charge comes in three types (red, green, and blue). Gluons also carry color charge, which makes QCD a much more complex theory than quantum electrodynamics (QED), the theory of electromagnetism.

Two key features of QCD are “confinement” and “asymptotic freedom”. Quarks are never observed in isolation; they are always confined within hadrons. This is because the strong force becomes stronger as quarks are pulled apart. At very high energies or short distances, the strong force becomes weaker, and quarks behave almost like free particles.

It was also realized that the initial analysis of the data made a wrong assumption about the flux of polarized virtual photons. The true flux is smaller than assumed and so quark polarization is actually larger.

Lattice QCD – nuclear physics simulations

Lattice QCD calculations, which numerically simulate QCD, have played a significant role in solving the “spin crisis”. Lattice QCD is a formulation of QCD on a discrete space-time lattice. This allows physicists to perform numerical simulations of QCD using powerful supercomputers. Lattice QCD calculations involve generating a large number of possible configurations of the gluon fields on the lattice and then averaging over these configurations to calculate physical observables, such as the masses of hadrons or the forces between them. Lattice QCD calculations involve generating a large number of possible configurations of the gluon fields on the lattice and then averaging over these configurations to calculate physical observables, such as the masses of hadrons or the forces between them. Lattice QCD calculations are computationally very demanding, and they are limited by the finite size of the lattice and the finite spacing between lattice points. However, as computer technology advances, lattice QCD is becoming an increasingly powerful tool for studying the strong force.

Lattice QCD calculations have confirmed that quark spin does not account for the majority of the proton’s spin and the contributions from the gluon spin and orbital angular momenta are significant. Lattice QCD calculations reveal that the vacuum polarization contribution from disconnected insertions is negative and resolves the contentious issue of the “proton spin crisis”.

Additional concepts

The proton spin crisis is a complex puzzle that has led to a deeper understanding of the strong force and the structure of matter. One aspect of this puzzle is the axial anomaly. This quantum effect can influence the way quarks and gluons contribute to the proton’s spin. However, while it was initially thought to be a major factor, it turns out to have a smaller impact than originally believed.

To help piece together the puzzle, physicists use sum rules. These are mathematical relationships that connect different aspects of the proton’s spin. For example, the nucleon spin sum rule states that the total spin of the proton must equal the sum of the spins of its constituent quarks, gluons, and their orbital angular momentum.

Quarks inside the proton are not stationary; they move at relativistic speeds – that is, they are moving near the speed of light. Relativistic effects significantly influence the proton’s spin by reducing the contribution from quark spins and by generating a significant amount of orbital angular momentum, which is crucial for understanding the observed proton spin. Relativism means their motion must be described by the Dirac equation, a relativistic quantum mechanical equation. In a non-relativistic model, the lower spin components are negligible. However, when quarks move at relativistic speeds, the lower component becomes significant. Relativistic effects arise from the fast motion of the quarks inside the proton, the presence of a pion cloud, and one-gluon exchange interactions. A challenge in understanding proton spin is the non-perturbative nature of the strong force. This means that traditional methods of calculation break down at the relativistic speeds or energy scales relevant to the proton. To overcome this, scientists rely on models and other non-perturbative techniques.

To delve deeper into the inner workings of the proton, scientists turn to Generalized Parton Distributions (GPDs). These provide a more sophisticated way to describe how quarks and gluons move within the proton, allowing us to access information about their orbital angular momentum.

Finally, light-front quantization offers a framework for understanding the internal structure of hadrons, such as protons. This approach provides a way to derive spin sum rules and analyze the contributions of different components to the proton’s spin.

The current status

Current experimental and theoretical efforts are focused on measuring the orbital angular momentum of quarks and gluons, as well as understanding how these components evolve as the energy scale changes. The precise values of each contribution depend on the energy scale at which measurements are made and the specific definitions used.

While significant progress has been made, the proton spin crisis remains an active area of research. Experiments at facilities like the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are continuing to investigate the contributions of quarks, gluons, and their orbital motion to the proton’s spin. It showed the importance of effects like relativistic motion, pion clouds, and gluon contributions in the understanding of the proton’s spin.