Protons: made of quarks, but ruled by gluons

One question that every curious child winds up asking at some point or other is, “what are things made of?” Every ingredient, it seems, is made up of other, more fundamental ingredients at a smaller and smaller scale. Humans are made of up organs, which are made of cells, which are made of organelles, which are made of molecules, which are made of atoms. For some time, we thought that atoms were fundamental — after all, the Greek word that they’re named for, ἄτομος, literally means “uncuttable” — since each species (or element) of atom has its own unique physical and chemical properties.

But experiments taught us that atoms weren’t fundamental, but were made of nuclei and electrons. Moreover, although the electron couldn’t be split apart, those nuclei were further divisible: into protons and neutrons. Finally, the advent of modern experimental high-energy physics taught us that even the proton and neutron have smaller particles inside of them: quarks and gluons. You often hear that each nucleon, like a proton or neutron, has three quarks inside of it, and that the quarks exchange gluons, keeping them bound together. But that isn’t the full picture at all. In fact, if you ask, “what’s more important to the proton: quarks or gluons,” the answer depends on how you ask it. Here’s what really matters when we look inside of a proton.

Newton’s law of universal gravitation (left) and Coulomb’s law for electrostatics (right) have almost identical forms, but the fundamental difference of one type vs. two types of charge open up a world of new possibilities for electromagnetism. In both instances, however, only one force-carrying particle, the graviton or the photon, respectively, is required.

If you take a charged particle and bring it close to an electron, the electron will either attract or repel it with a specific force (the electrostatic force) that’s directly related to only two things:

• the particle’s electric charge
• and the particle’s distance from the electron.

If you then performed the exact same experiment, but used a proton instead of an electron, you’d get a force that was equal-and-opposite to the force the charged particle experienced in the first experiment. The reason? The proton’s charge is equal and opposite to the electron’s charge.

So you might think, then, what would we observe if we measured the magnetic moment of the proton and the electron?

After all, from the first experiment, the only differences that were seen appeared to be based on the charges of the particles. But particles can also have an intrinsic angular momentum to them — known as spin — and an electron, being a fundamental particle with no internal structure, has a magnetic moment that’s directly proportional to four things: its charge, mass, the speed of light, and Planck’s constant. You might think, then, that if you just replace the mass of the electron with the mass of the proton, and flipped the sign (from the opposite electric charge), you’d get the proton’s magnetic moment. Similarly, because the neutron is neutral (with an electric charge of 0), you might expect that its magnetic moment would be zero.

Electrons, like all spin-½ fermions, have two possible spin orientations when placed in a magnetic field. Their charged but point-like nature describes their magnetic moment and explains their behavior, but protons and neutrons do not obey the same relationship, indicating their composite nature.

But that’s not what nature gives us at all! Instead, the proton’s magnetic moment is almost three times as large as that naive expectation, while the neutron’s magnetic moment is about two-thirds of the proton’s value, but with the opposite sign.

What is going on here, and how could that be the case?

Things make a lot more sense if you consider the possibility that the proton and neutron aren’t themselves fundamental, point-like particles, but rather are composite particles made up of multiple charged components. Overall, there are actually two ways that nature can make a magnetic moment. The first is from the inherent angular momentum, or spin, of a particle, like we have for the electron. The second, though, happens whenever we have an electric charge that’s physically moving through space; moving charges make currents, and electric currents induce magnetic fields. Just as an electron orbiting a nucleus makes its own magnetic moment, charged constituent particles inside a single proton (or neutron) will contribute to the proton’s (or neutron’s) magnetic moment, in addition to whatever the intrinsic charges and spins of the individual (fundamental) particles inside contribute.

The interior of a proton is a messy place, with contributions from not only the three quarks that make it up, but from the gluons, the fields inside, and all of the virtual and perturbative particles that arise from the fundamental forces and their interactions with matter.

Those magnetic moment observations served as indirect evidence, before we ever directly probed the internal structure of protons and neutrons, that they must have been composed of smaller, still more fundamental constituent particles.

Another clue came from early experiments that involved colliding low-energy protons (they were considered “high-energy” experiments at the time, but would be considered “low-energy” today) into other particles, and then detecting what came out. In addition to the debris from those collisions — you know, things like other protons, neutrons, and electrons — we were able to detect new kinds of particles that hadn’t been seen before.

Some were neutral, some were positively charged, and some were negatively charged. Some lived for a few tens of nanoseconds before decaying, others lived for only fractions of a femtosecond: a factor of a billion less than the longer-lived particles. But all of them were much lighter than either a proton or neutron, while being heavier than an electron or a muon.

Bubble chamber tracks from Fermilab, revealing the charge, mass, energy and momentum of the particles created. Although there are only a few dozen particles whose tracks are shown here, the curvature of the tracks and the displaced vertices allow us to reconstruct what interactions occurred at the collision point.

These newly discovered particles became known as pions (or π mesons), and they came in three varieties: the π+, π-, and π⁰, corresponding to their electric charges that matched the charge of the proton, electron, or neutron, respectively. They were all much lighter than protons and neutrons, but clearly arose from the process of colliding protons with other protons and neutrons.

How could these weird new particles — the pions — exist, particularly if protons and neutrons were fundamental particles?

Before people stumbled upon proton and neutron compositeness, there were other theories that came to the forefront. One brilliant (but, spoiler, incorrect) idea came courtesy of Shoichi Sakata: perhaps the proton and neutron, as well as their antiparticle counterparts, were the only fundamental things in existence. Perhaps you made these pions by leveraging the following combinations:

• a π+ particle is a composite bound state of a proton and an anti-neutron,
• a π- particle is a composite bound state of an anti-proton and a neutron,
• and a π⁰ particle is a mixture of a bound state of a proton-antiproton and neutron-antineutron combination.

The fermions, anti-fermions, and bosons of the Standard Model are shown here. A pion was once thought to be a combination of protons/antiprotons with neutrons/antineutrons, but the quark model, where up/anti-up and down/anti-down quarks compose pions, protons/antiprotons, and neutrons/antineutrons, describes our Universe much more accurately.

The biggest objection to the Sakata Model was that the pions were so much less massive than either the proton or neutron — about 15% of their masses, only — that it was unclear how the negative binding energy could remove that much mass.

The resolution would come later on: when we started building high-energy colliders that enabled us to smash particles into protons with enough energy to truly find out what was inside. These deep inelastic scattering experiments showed, experimentally, that there were indeed individual structures inside the proton, and that individual fundamental particles (like electrons) would scatter off of them in different ways.

On the experimental side, these became known as partons, while the theoretical idea of quarks took hold on the theory side. These ideas attempted to explain the internal structure of matter as well as the compositions of protons, neutrons, pions, and numerous other particles that were subsequently discovered throughout the 1950s and 1960s. We now know that partons and quarks are the same things, and that:

• protons are made of two up quarks and one down quark,
• neutrons are made of one up quark and two down quarks,
• the π+ is made of an up and an anti-down quark,
• the π- is made of an anti-up and a down quark,
• and that the π⁰ particle is a mix of up/anti-up and down/anti-down quarks.

Individual protons and neutrons may be colorless entities, but the quarks within them are colored. Gluons can not only be exchanged between the individual gluons within a proton or neutron, but in combinations between protons and neutrons, leading to nuclear binding. However, every single exchange must obey the full suite of quantum rules.

But those quarks are only an incomplete part of a much richer overall story. In addition to electric charges — up quarks have a charge of +⅔e and down quarks have -⅓e, with the antiquarks having the opposite charge, and where e is the magnitude of the electron’s charge — quarks also have a color charge: a new type of charge that’s responsible for the strong nuclear force. This force has to be strong, and in particular even stronger than the force of electric repulsion between the various quarks, otherwise the proton would simply fly apart.

The way it works is fascinating and a little counterintuitive. The electromagnetic force occurs, in quantum field theory, through the exchange of photons between electrically-charged particles. Similarly, the strong nuclear force occurs through the exchange of gluons between color-charged particles. While the electric force goes to zero at infinite distances but gets stronger the closer two particles get, the strong force goes to zero when particles are very close, but gets stronger — like a stretched spring — when they pull apart. The combination of these factors leads to the proton’s size (about ~0.84 femtometers) and mass (938 MeV/c²), where only about 1-to-2% of its mass, at maximum, comes from the three up-and-down quarks that make it up. All the rest is due to the strong nuclear force: the gluon fields that cause the interactions between particles with a color charge.

As better experiments and theoretical calculations have come about, our understanding of the proton has gotten more sophisticated, with gluons, sea quarks, and orbital interactions coming into play. There are always three valence quarks present, but your chances of interacting with them decrease at higher energies.

At today’s modern high-energy colliders, we smash protons into other protons at exceedingly high energies: energies that correspond to them moving at up to 99.999999% the speed of light. Based on what comes out, we can tell what it is that’s interacting.

• Is it a quark from one proton interacting with a quark from another proton?
• Is it a quark from one proton interacting with a gluon from another proton?
• Or is it a gluon from one proton interacting with a gluon from another proton?

Although all three can (and do) occur, they don’t occur in equal ratios. The interesting thing that we find is that whether quark-quark, quark-gluon, or gluon-gluon interactions dominate depends on the energy of the collision itself!

Lower energy collisions are dominated by quark-quark interactions, and practically all of the quarks are the ones you’d expect: up and down quarks.

Higher energy collisions start to see greater percentages of quark-gluon interactions in addition to quark-quark interactions, and some of the quarks may turn out to be strange or even charm quarks in nature: heavier, unstable, second-generation cousins of the lighter first-generation up and down quarks.

And at still higher energies, you become dominated by gluon-gluon interactions. At the LHC, for example, over 90% of all of the collisions recorded are reconstructed to be gluon-gluon interactions, with collisions involving quark-gluon interactions making up most of the rest, as quark-quark interactions become the rarest of all at these high energies.

This reconstruction of particle tracks shows a candidate Higgs event in the ATLAS detector at the Large Hadron Collider at CERN. Despite clear signatures and transverse tracks, there is a shower of other particles, due to the fact that protons are composite particles, where dozens of proton-proton collisions occur with every bunch crossing. Based on the outgoing signatures, we can reconstruct whether a quark-quark, quark-gluon, or gluon-gluon collision occurred inside the protons, initially.

What this teaches us is that our picture of the proton, like pretty much everything else in the quantum Universe, changes depending on the method we use for looking at it.

• At the lowest energies — energies significantly below the rest mass of a proton — it purely behaves as a point-like particle, and we cannot detect its internal structure directly.
• As we go to higher energies, we see that protons go from being point-like to having an internal structure.
• At a few times the proton’s rest mass energy, we see that internal structure as being composed of three (valence) quarks: up-and-down quarks only.
• At higher energies (many times the proton’s rest mass), that simplified picture gives way to a more complex picture inside: where a sea of gluons and quark-antiquark pairs begin to appear.
• At as we go to even higher energies, we become much more likely to detect aspects of those internal structures (the gluon see and quark-antiquark pairs) as opposed to the valence quarks, and as those energies increase, we become more likely to see particles with higher rest masses (like the heavier quarks).
• And at the highest energies we’ve reached, the fraction of collisions that are gluon-gluon collisions completely dominates over collision involving quarks at all.

The more energetically you look, the denser the sea of internal particles gets, and this trend continues up to and including the highest energies we’ve ever used to probe matter. At low energies, a proton is more “quarky” in nature, but at higher energies, it’s rather a “gluey” situation.

A proton isn’t just three quarks and gluons, but a sea of dense particles and antiparticles inside. The more precisely we look at a proton and the greater the energies that we perform deep inelastic scattering experiments at, the more substructure we find inside the proton itself. There appears to be no limit to the density of particles inside; it increases without bound as the collision energy rises.

I like to make intuitive sense of this by thinking of the three valence quarks inside the proton as being points, and the particle that comes to collide with it as a wave. At higher energies, the incoming (colliding) particle has a shorter wavelength, and so it starts to get small compared to the size of a proton. At lower energies, the wavelength is large compared to the overall size of the proton, and it’s very difficult to avoid all of those quarks: like sliding a pizza stone down a shuffleboard course with lots of “pucks” (or weights, or shuckles) populating it.

But at higher energies, you’re shrinking your wavelength; instead of a pizza stone, now you’re sliding a dime down the same course. There’s a chance you’ll still hit those quarks (the other “pucks” along the course), but overwhelmingly, you’re much more likely to hit something in the “sea” between the quarks, which is overwhelmingly composed of gluons.

Many physicists wonder just how deep this trend continues. At higher and higher energies, will we just keep encountering an ever-denser sea gluons, with the occasional quark-antiquarks pair showing up as well? Or will we reach a point where something novel and exciting appears, and if so, what will it be and where? The only way we’ll find out is by looking farther: with more collisions and — if humanity has the will to make it happen — at higher energies. At the energies we’ve been able to reach, we’ve learned that the interior of a proton is more “gluey” than “quarky” inside, but at higher energies still, there could be new physics just awaiting discovery.