How QCD Makes The Strong Force Strong (Script) (Patreon)

Quantum mechanics gets weirder as you go to smaller sizes and higher energies. It’s strange enough for atoms, but positively bizarre when we get to the atomic nucleus. And today we’re going nuclear, as we dive into the weird world of quantum chromodynamics.

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As you know, atoms consist of a nucleus of protons and neutrons surrounded by electrons. Those electrons are held in their orbitals by the electromagnetic force - opposite charges attract, so the negatively-charged electrons are attracted by the positively charged protons. But in electromagnetism, like charges repel. So how does that work with heavier elements? Their multiple electrons repel each other, but fortunately are spread out enough to not disturb each other too much. The protons on the other hand are packed together in the nucleus as tightly as any matter in the universe. The repulsive force between them due to electromagnetism is absolutely enormous. So how does the nucleus stay together? Well, it’s due to an even stronger force. Namely, the strong nuclear force. But if the strong force is so strong, why is it confined to the atomic nucleus? The answers to these questions lie in the complex behavior of particles quarks and gluons via the rules of quantum chromodynamics.

Our lead on understanding the strong force came in the 1940s when we switched on our first particle colliders and started to detect a veritable zoo of new particles. As physicists tried to understand the aptly named particle zoo, certain peculiar relationships were observed. In particular, Murray Gell-Mann and others realized that the way these particles were created in particle collisions suggested the existence of a new conserved quantity that they named strangeness.

And strangeness was strange indeed. Gell-Mann and Yuval Ne'eman noticed that if you arrange particles according to their strangeness and their electric charge, they fall into geometric patterns like this hexagon with eight particles or this triangle with ten. This is known as the Eightfold Way and it’s like a periodic table but for  particles.

Before too long it was realized that the particles of the particle zoo were not elementary - they were made of smaller particles still - and those particles are quarks. It turns out that location on these shapes represent the quark content of the particle.  Strangeness just turned out to represent how many strange quarks are present. By the way, these particles of multiple quarks are now called hadrons.

Describing hadrons as groups of quarks explains the eightfold way, but it also introduces a whole new problem. To understand the problem, I want you to imagine you’re at a fancy party and wearing your brand new pretty dress. Or jacket or jumpsuit or whatever, I don’t judge. Anyway, someone shows up wearing the exact same outfit. Mortifying, right?

Well it turns out that nature also has its fashion police. For the class of particles called fermions, no more than one particle can occupy a given quantum state. That includes electrons, quarks, and many of the particles that are composed of quarks.

This restriction is known as the Pauli Exclusion Principle. One consequence of this is that no two electrons can occupy the same energy level in an atom. Well, slight correction: electron orbitals can contain two electrons, but that’s because those electrons can have a different spin state. It’s like, they have the same dress but in different colours. We made an episode about this by the way.

OK, so how does this apply to quarks? Let’s look at the Omega Baryon. It is made of three strange quarks - in reality, 3 valence strange quarks. There must be something different in order for them to comply with the Exclusion Principle. It can’t be spin, because with 3 particles and only two possible spin states two will always have the same spin.

The only solution is that there must be some other property making them different, and that property must have three different values.

With electromagnetism you have one type of charge, which can be positive or negative, with the Strong Force you have three charge types. If our Omega particle’s quarks are going to wear the same dress, they better be different colours. In fact we label these three strong force charges with the colours red, green and blue. And this colourful convention led to the naming of our science of strong force interactions: quantum chromodynamics.

Of course the quarks aren’t literally coloured, but as we’ll see in a bit, there is a very good reason scientists thought about colors when naming this property.

If we have different charges then we have a potential for attractive forces. We need this attraction to hold quarks together in nucleons, and nucleons together in the atomic nucleus. And that attractive force needs to be stronger than the repulsive electromagnetism, while also vanishing outside the atomic nucleus. How can that work?

There’s another weird behavior of the hadrons that will help us answer this question. It turns out that all of these particles are made of three or two quarks. It’s possible to briefly create larger combinations in particle colliders, but not in nature. And most importantly we never see lone quarks except in very particular circumstances.

Let’s lay out what we need from our strong force for all of this to work. The force is similar to electromagnetism in some respects, but it is very different in others. Electrically charged particles interact with each other via the electromagnetic field. We can think of each charged particle as generating a constant buzz of virtual photons around it, forming what we think of as its EM field.

That buzz weakens the further you get from the particle. So an electron bound to an atomic nucleus will feel less force from the nucleus at larger orbitals. The further the electron gets from the nucleus, the more easily it can escape. Assuming the strong force works the same, we need a field to mediate it, and that field should have its own particles. We call those particles gluons. A pair of quarks bound into, say, a pion, are connected by a gluon field, also describable as a constant exchange of virtual gluons. But this field looks very different to the electromagnetic field around a nucleus

For one thing, it does not weaken as the quarks are moved further apart. Instead of forming a fading gradient of field strength, quark pairs are connected by a thread of gluon field called a flux tube. As quarks are separated, the thread doesn’t weaken like the EM field does.  The flux tube has a tension, and just like a stretched elastic band, the more you stretch the flux tube the more energy it holds. At a certain point the tube will snap - but only when exactly enough energy has been built up to create a new pair of quarks. Now each of the original quarks is partnered with one of the new quarks, forming two new pions.

And the same would happen with any other particle made of quarks. If you want to break them apart you just end up forming new particles, so they never end up alone except in the most extreme energies. With enough energy, like in the very early universe or at impact point in a large particle collider, space gets sort of saturated so that new quarks can’t be formed. This allows quarks to move freely in a state of matter known as Quark Gluon Plasma.

This behavior of the gluon field explains why we only see quarks in groups, but we need one more puzzle piece to explain why the strong force is never seen outside the nucleus. The answer is something called  "color confinement". It ensures that colour charge is mostly only felt inside the hadrons. There are two parts to this: the first one is that quarks always get together in groups that are color neutral, and the second is that there are no neutral gluons. To understand the first one we have to see how the Strong Force is similar to electromagnetism.

Let's say we have a proton and an electron, their electric charges attract and they form a neutral hydrogen atom. This is what electrical charges do, they attract each other until their electric fields cancel out, that's why everything around you is electrically neutral. You would have to get really close to an atom to feel the positive electric field of the nucleus, or the negative electric field of the electrons. Something similar happens with color charges. They also attract each other until they form groups that have neutral color.

This makes sense when we have two quarks, they have opposite color charges so they cancel out. For example, the quarks of a pion could be red and anti-red. But what happens when we have three quarks? How do they cancel out? Maybe they didn’t teach you this equation in school, but it turns out that red + blue + green = 0. And that same formula tells us that for example blue = -red-green. In fact each color charge is equal to having the opposite of the other two. This may sound crazy, but it may not if you are a photographer or a graphic designer, because this is exactly how the RGB system works.

Your screen can’t make this color, or this one, or even this pure white. All it can do is combinations of red, green and blue. White is what you get when you combine the three in equal quantities - that’s your red + green + blue = 0. Yellow is just red + green, which also means that yellow is … minus blue. Or anti-blue if we’re using the language of chromodynamics.

The mathematics used to describe this system just happen to be the same as the mathematics that describe the behavior of the charges of the strong force. It has 3 primary colors like the 3 charges of the strong force, each of which can be positive or negative, and transform into each other additively in the same way, or cancel out to neutrality. This apparent coincidence is why physicists called them color charges in the first place. But it’s not as weird a coincidence as you might think - and I’ll tell you why shortly.

First let's get to the other requirement for color confinement: no neutral gluons. And for this we need to compare the Strong Force electromagnetism once again. Electrically neutral objects cannot feel electrical attraction, but they can certainly feel magnetism. You see it all the time when a piece of neutral metal is attracted to a magnet which is itself also neutral.

This is possible because the mediating particle of electromagnetism, the photon, is itself electrically neutral. That means photons can interact with objects without affecting their electric charge, and thus neutral objects can interact with magnetic fields.

There is a strong interaction similar to magnetism called Chromomagnetism, but that's where the similarities end, because gluons are not neutral like photons. Gluons carry color charge, in fact they carry two charges at the same time - a positive and a negative of different colours - or more accurately, a superposition of multiple positive-negative colours, and they can’t be colour-neutral. This means gluons are unable to interact with neutral particles like the combinations of quarks that form the hadrons. If they could, hadrons would be able to feel chromomagnetism which could make the strong force a long-range force. That would probably be very bad - or at least very different from the universe that we know.

Gluons can carry many different combinations of colors, and are always in a superposition of multiple combos. For example a gluon could be a combination of green-antiblue and blue-antigreen, which we write like this. Such a gluon might turn a blue quark green or a green quark blue. Sometimes we even have to consider three possibilities like red-antired + blue-antiblue - 2 times green-antigreen. This last one looks color neutral because each of those three combos appears to cancel out, but it's not really neutral because the probability of the green interaction is double the other ones.

It turns out that we can express the state of any gluon as a combination of only eight gluons. Six of them have color charge, and two of them are neutral but unbalanced. Doesn't this look familiar? It's the eightfold way from before, and in fact, we can also use it for the eight colors of the RBG, red, blue and green plus anti-red, anti-blue, anti-green - or as we know them better, cyan, yellow and magenta, and then black and white at the center. The position of each object in the hexagon tells you how much they have of a certain kind of quark, a certain color charge, or actual color.

The reason this pattern arises in so many different places is a question of symmetry. Whenever you have combinations of three degrees of freedom in groups of three, and two of those combinations are neutral, like black and white for example, you get this mathematical structure. It's name is the Special Unitary group of order three, but we are all friends here, so we can call it SU(3).

This symmetry is baked into the laws of physics and it manifests as the Strong Force, but SU(3) is free to appear in many other contexts, like the behavior of the colour receptors in our eyes. We have 3 colour receptors, and our brains use the SU(3) symmetry group to combine the input from those receptors into our subjective sense of colour. When we build a screen to display only red, blue and green pixels, we’re manipulating the way our brain interprets combinations of these colours. But this isn’t the only way biology does this. Birds have four color receptors, dogs have two and the mantis shrimp has sixteen. By chance we have the same number as their are degrees of freedom in the strong force colour charge.

Ok, this was a brief introduction to chromodynamics and the strong force. As you can imagine, there’s a lot more to it - and in future episodes we’ll dive deeper into the strongest force in all of space time.