# Are Gluons Massless? Is There a Big Problem With Little Physics?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

Particle physics has made many recent bounds in the last few years. Much of the Standard Model has been confirmed, neutrino interactions are becoming clearer, and the Higgs Boson has been found, possibly hinting at new superparticles. But despite all of these gains, there is a big problem that does not get much attention: gluons. As we will see, scientists don’t know much about them—and finding out anything about them will prove to be more than a challenge to even the most veteran physicist.

## Some Gluon Basic (Questions)

Protons and neutrons are made up of three quarks which are held together by gluons. Now, quarks do come in a wide variety of different flavors, or types, but gluons seem to be just one type of object. And some very simple questions about these quark-gluon interactions require some deep extensions. How do gluons hold quarks together? Why do gluons only work on quarks? How does the spin of the quark-gluon affect the particle it resides in? (Ent 44)

## The Mass Problem

These all may be related to the amazing result of gluons being massless. When the Higgs Boson was discovered, it resolved a major component of the mass problem for particles, for interactions between the Higgs Boson and the Higgs Field can now be our explanation for mass. But a common misconception of the Higgs Boson is that it resolves the missing mass problem of the universe, which it doesn’t! Some places and mechanism are not adding up to the correct mass for reasons unknown. For example, the sum of all the quark masses inside a proton/neutron can only account for 2% of the total mass. Therefore, the other 98% must come from the gluons. Yet experiments have shown again and again that gluons are massless. So what gives? (Ent 44-5, Baggott)

Maybe energy will save us. After all, a result of Einstein’s relativity states that E = mc2, where E is energy in Joules, m is mass in kilograms, and c is the speed of light (about 3*108 meters per second). Energy and mass are just different forms of the same thing, so perhaps that missing mass is the energy the gluon interactions supply to the proton or neutron. But what exactly is that energy? In most basic terms, energy is related to the motion of an object. For free particles, this is relatively easy to measure, but for a dynamic interaction between multiple objects the complexity starts to rise. And in the case of the quark-gluon interactions, there is a very small period of time when they do indeed become free particles. How small? Try about 3*10-24 seconds. Then the interaction resumes. But energy can also arise from a bond in the form of an elastic interaction. Clearly, measuring this presents challenges (Ent 45, Baggott).

## The Binding Problem

So what force governs the quark-gluon interaction that leads to the binding of them? Why, the strong nuclear force. In fact, much like how the photon is the carrier of the electromagnetic force the gluon is the carrier of the strong nuclear force. But through the years of experiments on the strong nuclear force, it yields some surprises that seem incompatible with our understanding of gluons. For example, according to quantum mechanics, the range of the strong nuclear force is inversely proportional to the total mass of the gluons. But the electromagnetic force has infinite range, no matter where you are. The strong nuclear force has a low range outside of the radius of the nucleus, as experiments have shown, but that would then imply based on the proportion that the mass of the gluons is high, which it is certainly not yet should be when looking at the mass problem. And it gets worse. The strong nuclear force actually works harder on quarks the further away they are from each other. This is clearly not like electromagnetic forces at all (Ent 45, 48).

How did they come to this strange conclusion about the distance and how the quarks relate? The SLAC National Accelerator in the 1960s was working on electron collisions with protons in what are known as deeply inelastic scattering experiments. Occasionally, they found that a hit would result in a “rebound speed and direction” which could be measured by the detector. Based on these readings, attributes of quarks were derived. During these trials, no free quarks were seen at a large distance, implying that something was pulling them back (48).

## The Color Problem

The failure to extend behavior of the strong nuclear force with the electromagnetic force was not the only symmetrical failing. When we discuss the state of the electromagnetic force, we refer to the charge it currently processes in an effort to get a mathematical value we can relate to. Similarly, when we discuss the mathematical quantity of the strong nuclear force we discuss the color. We don’t mean in the art sense here of course, which has led to much confusion over the years. The full description of how color is quantifiable and how it changes was developed in the 1970s in a field known as quantum chromodynamics (QCD), which is not only a great read but too lengthy for this article (Ibid).

One of the properties it discusses is a color-blind particle, or simply put something without color. And some particles are indeed color-blind, but most are not and change color by exchanging gluons. Whether it be from quark to quark, gluon to quark, quark to gluon, or gluon to gluon, some net change in color should occur. But gluon to gluon exchanges are a result of a direct interaction. Photons do not work this, exchanging electromagnetic force through direct collisions. So maybe this is another case of the gluons having different behavior than an established norm. Maybe the color change between this exchange could help explain many of the quirky properties of the strong nuclear force (Ibid).

But this color change brings about an interesting fact. You see, gluons typically exist in a singular state, but quantum mechanics have shown that for brief instances one gluon can become a quark-antiquark pair or a gluon-gluon pair before reverting back to a singular object. But as it turns out a quark-antiquark reaction yields a greater color change than a gluon-gluon. Yet gluon-gluon reversions happen more frequently than quark-antiquark, therefore they should be the prevailing behavior of a gluon system. Perhaps this too plays a role in the oddness of the strong nuclear force (Ibid).

## The QCD Problem

Now, maybe many of these difficulties arise from something missing or wrong in QCD. Even though it is a well-tested theory, revision is certainly possible and likely needed because of some of the other problems in QCD. For example, a proton has three color values residing in it (based on the quarks) but is color-blind when looked at collectively. A pion (a quark-antiquark pair in a hadron) also has this behavior. It would seem at first that this may be analogous to an atom having a net charge of zero, with some components canceling out others. But color doesn’t cancel out the same way, so it is unclear how the protons and pions become color-blind. In fact, OCD also struggles with proton-proton interactions. Specifically, how do the like charges of protons not push the nucleus of an atom apart? You can turn to nuclear physics derived from QCD but the math is crazy hard, especially for large distances (Ibid).

Now, if you can figure out the color-blind mystery, the Clay Mathematics Institute will pay you \$11 million for your troubles. And I will even give you a hint, which is the direction scientists suspect is key: quark-gluon interactions. After all, the number of each varies with the number of protons and so making individual observations becomes harder. In fact, a quantum foam is created where at high velocities the gluons that are in protons and neutrons can split into more, each with less energy than its parent. And, get this, nothing says this has to stop. Under the right conditions it can go on forever. Except that it doesn’t, for a proton would fall apart. So what actually stops it? And how does that help us with the proton problem? (Ibid)

Maybe nature helps out by preventing it, allowing gluons to overlap if a high number of them are present. This would mean that as the overlap increased, more and more low energy gluons would be present, allowing for better conditions for gluon saturation, or when they would begin to recombine because of their low energy state. We would then have constant breaking apart of gluons and recombining balancing each other out. This would hypothetically be a color-glass condensate if it exists and would result in a color-blind particle, just as we expect a proton to be (Ibid).

## The Spin Problem

One of the cornerstones of particle physics is the spin of nucleons aka protons and neutrons, which has been found to be ½ for each. Knowing that each is made of quarks, it made sense at the time to scientists that quarks lead to the spin of the nucleon. Now, what is up with the spin of gluons? When we talk about spin, we are talking about a quantity similar in concept to the rotational energy of a top, but instead of energy impacting the rate and direction it will be the magnetic field. And everything spins. In fact, experiments have shown that the quarks of a proton contribute to 30% of that particle’s spin. This was found in 1987 by firing electrons or muons at nucleons in such a way that the pin axis was parallel to each other. One shot would have the spins pointed to each other while the other would have the pointed away. By comparing the deflections, scientists were able to find the spin that quarks contribute (Ent 49, Cartlidge).

This result is contrary to theory, for it held that 2 of the quarks should be ½ spin up with the remaining 1 having a spin of ½ down. So what is making up the rest? Since gluons are the only object left, it would seem they contribute the remaining 70%. But it has been shown that they only add an additional 20%, based off experiments involving polarized proton collisions. So where is the missing half!? Maybe the orbital motion of the actual quark-gluon interaction. And to get a full picture of that possible spin, we need to make comparisons between different ones, something not readily possible to do (Ent 49, Cartlidge, Moskowitz).

## The Quark-Gluon Plasma Problem

Even after all of these problems, another one rears its head: the quark-gluon plasma. This forms when atomic nuclei are impacted against each other at velocities approaching the speed of light. The possible color-glass condensate would break because of the high speed impact, causing energy to flow freely and releasing gluons. Temperatures climb to about 4 trillion degrees Celsius, similar to the possible conditions of the early universe, and now we have gluons and quarks swimming around (Ent 49, Lajeunesse).

Scientists using the RHIC in New York and the PHENIX detector to examine the powerful plasma, which has a very short lifespan (“less than a billionth of a trillionth of a second”). And naturally, surprises were found. The plasma, which should act like a gas, instead behaves like a liquid. And the formation of the plasma after the collision is way faster than theory predicts it should be. With such a small span of time to examine the plasma, lots of collisions will be needed to unravel these new mysteries (Lajeunesse).

## Future Problems

…who knows? We have clearly seen that when hunting for the solution to one problem, more seem to pop up. With any luck, some solutions will soon pop up that may solve multiple problems at once. Hey, one can dream right?

## Works Cited

Baggott, Jim. "Physics Has Demoted Mass." nautilis.is. NautilusThink Inc., 09 Nov. 2017. Web. 25 Aug. 2020.

Cartlidge, Edwin. “Gluons Get in on Proton Spin.” Physicsworld.com. Institute of Physics, 11 Jul. 2014. Web. 07 Jun. 2016.

Ent, Rolf and Thomas Ulrich, Raju Venugopalan. “The Glue That Binds Us.” Scientific American May 2015: 44-5, 48-9. Print.

Lajeunesse, Sara. “How Physicists Are Unraveling Fundamental Mysteries About the Matter That Makes Up Our World.” Phys.org. Science X Network, 06 May 2014. Web. 07 Jun. 2016.

Moskowitz, Clara. “Proton Spin Mystery Gains a New Clue.” Scientificamerican.com. Nature America, Inc., 21 Jul. 2014. Web. 07 Jun. 2016.