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Flip Tanedo | USLHC | USA

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QCD and Confinement

Now that we’ve met quarks and gluons, what I should do is describe how they interact with the other sectors of the Standard Model: how do they talk to the leptons and gauge bosons (photon, W, Z) that we met in the rest of this series on Feynman diagrams. I’ll have to put this off a little bit longer, since there’s still quite a lot to be said about the “fundamental problem” of QCD:

The high energy degrees of freedom (quarks and gluons) are not what we see at low energies (hadrons).

Colliders like the LHC smash protons together at high energies so that the point-like interactions are between quarks and gluons. By the time these quarks and gluons scatter into the LHC detectors, however, they have now “dressed” themselves into hadronic bound states. This is the phenomenon of confinement.

As a very rough starting point, we can think about how protons and electrons are bound into the hydrogen atom. Here the electric potential attracts the proton and electron to one another. We can draw the electric field lines something like this:

These are just like the patterns of iron filings near a bar magnet. The field lines are, of course, just a macroscopic effect set up by lots and lots of photons, but we’re in a regime where we’re justified in taking a “semi-classical” approximation. In fact, we could have drawn the same field lines for gravity. They are all a manifestation of the radially symmetric 1/r potential. We can try to extend this analogy to QCD. Instead of a proton and electron attracted by the electric force, let’s draw an up quark and a down quark attracted by the color (chromodynamic) force.

This looks exactly the same as the electric picture above, but instead of photons setting up a classical field, we imagine a macroscopic configuration of gluons. But wait a second! There’s no such thing as a macroscopic configuration of gluons! We never talk about long range classical chromodynamic forces.

Something is wrong with this picture. We could guess that maybe the chromodynamic force law takes a different form than the usual V(r) ~ 1/r potential for electricity and gravity. This is indeed a step in the right direction. In fact, the chomodynamic potential is linear: V(r)~ r. But what does this all mean?

By the way, the form of the potential is often referred to as the phase of the theory. The “usual” 1/r potential that we’re used to in classical physics is known as the Coulomb phase. Here we’ll explain what it means that QCD is in the confining phase. Just for fun, let me mention another type of phase called the Higgs phase, which describes the weak force and is related to the generation of fermion masses.

Okay, so I’ve just alluded to a bunch of physics jargon. We can do better. The main question we want to answer is: how is QCD different from the electric force? Well, thing about electricity is that I can pull an electron off of its proton. Similarly, a satellite orbiting Earth can turn on its thrusters and escape out of the solar system. This is the key difference between electricity (and gravity) and QCD. As we pull the electron far away from the proton, then the field lines near the proton “forget” about the electron altogether. (Eventually, the field lines all reach the electron, but they’re weak.)

QCD is different. The as we pull apart the quarks, the force is that pulls them back together becomes stronger energy stored in the gluon field gets larger. The potential difference gets larger and it takes more energy to keep those quarks separated, something like a spring. So we can imagine pulling the quarks apart further and further. You should imagine the look of anguish on my face as I’m putting all of my strength into trying to pull these two quarks apart—every centimeter I pull they want to spring back towards one another with even more force

… stores more and more energy in the gluon field. (This is the opposite of QED, where the energy decreases as I pull the electron from the proton! Errata: 10/23, this statement is incorrect! See the comments below. Thanks to readers Josh, Leon, Tim, and Heisenberg for pointing this out!) Think of those springy “expander” chest exercise machines. Sometimes we call this long, narrow set of field lines a flux tube. If we continued this way and kept pulling, then classical physics would tell us that we can get generate arbitrarily large energy! Something has to give. Classically cannot pull two quarks apart.

Errata (10/22): Many thanks to Andreas Kronfeld for pointing out an embarrassing error: as I pull the quarks apart the force doesn’t increase—since the potential is linear V(r) ~ r, the force is constant, F(r) ~ -V'(r) ~ constant. Physicists often make this mistake when speaking to the public because in the back of their minds they’re thinking of a quantum mechanical property of QCD called asymptotic freedom in which the coupling “constant” of QCD actually increases as one goes to large distances (so it’s not much of a constant). As Andreas notes, this phenomenon isn’t the relevant physics in the confining phase so we’ll leave it for another time, since a proper explanation would require another post entirely. I’ve corrected my incorrect sentences above. Thanks, Andreas!

What actually happens is that quantum mechanics steps in. At some point, as I’m pulling these quarks apart, the energy in the gluon field becomes larger than the mass energy of a quark anti-quark pair. Thus it is energetically favorable for the gluons to produce a quark–anti-quark pair:

From the sketch above, this pair production reduces the energy in the gluon field. In other words, we turned one long flux tube into two shorter flux tubes. Yet another way to say this is to think of the virtual (quantum mechanical) quark/anti-quark pairs popping in and out of the vacuum, spontaneously appearing and then annihilating. When the energy in the gluon field gets very large, though, the gluons are able to pull apart the quark/anti-quark pair before they can annihilate, thus making the virtual quarks physical.

This is remarkably different behavior from QED, where we could just pull off an electron and send it far away. In QCD, you can start with a meson (quark–anti-quark pair) and try to pull apart its constituents. Instead of being able to do this, however, you inadvertently break the meson not into two quarks, but into two mesons. Because of this, at low energies one cannot observe individual quarks, they immediately confine (or hadronize) into hadronic bound states.

Some context

This idea of confinement is what made the quark model so hard to swallow when it was first proposed: what is the use of such a model if one of the predictions is that we can’t observe the constituents? Indeed, for a long time people thought of the quark model as just a mathematical trick to determine relations between hadrons—but that “quarks” themselves were not physical.

On the other hand, imagine how bizarre this confinement phenomenon must have seemed without the quark model. As you try to pull apart a meson, instead of observing “smaller” objects, you end up pulling out two versions of the same type of object! How could it have been that inside one meson is two mesons? This would be like a Russian matryoshka doll where the smaller dolls are the same size as the larger ones—how can they fit? (Part of the failure here is classical intuition.) This sort of confusion led to the Smatrix or “bootstrap” program in the 60s where people thought to replace quantum field theory with something where the distinction “composite” versus “elementary” particles was dropped. The rise of QCD showed that this was the wrong direction for the problem and that the “conservative” approach of keeping quantum theory was able to give a very accurate description of the underlying physics.

In some sense the S-matrix program is a famous “red herring” in the history of particle physics. However, it is a curious historical note—and more and more so a curious scientific note—that this ‘red herring’ ended up planting some of the seeds for the development of string theory, which was originally developed to try to explain hadrons! The “flux tubes” above were associated with the “strings” in this proto-string theory. With the advent of QCD, people realized that string theory doesn’t describe the strong force, but seemed to have some of the ingredients for one of the “holy grails” of theoretical physics, a theory of quantum gravity.

These days string theory as a “theory of everything” is still up in the air, as it turns out that there are some deep and difficult-to-answer questions about string theory’s predictions. On the other hand, the theory has made some very remarkable progress in directions other than the “fundamental theory of everything.” In particular, one idea called the AdS/CFT correspondence has had profound impacts on the structure of quantum field theories independent of whether or not string theory is the “final theory.” (We won’t describe what the AdS/CFT correspondence is in this post, but part of it has to do with the distinction between elementary and composite states.) One of the things we hope to extract from the AdS/CFT idea is a way to describe theories which are strongly coupled, which is a fancy phrase for confining. In this way, some branches of stringy research is finding its way back to its hadronic origins.

Even more remarkable, there has been a return to ideas similar to the S-matrix program in recent research directions involving the calculation of scattering amplitudes. While the original aim of this research was to solve problems within quantum field theory—namely calculations in QCD—some people have started to think about it again as a framework beyond quantum field theory.

High scale, low scale, and something in-between

This is an issue of energy scales. At high energies, we are probing short distance physics so that the actual “hard collisions” at the LHC aren’t between protons, but quarks and gluons. On the other hand, at low energies these “fundamental” particles always confine into “composite” particles like mesons and these are the stable states. Indeed, we can smash quarks and gluons together  at high energies, but the QCD stuff that reaches the outer parts of the experimental detectors are things like mesons.

In fact, there’s an intermediate energy scale that is even more important. What is happening between the picture of the “high energy” quark and the “low energy meson?” The quark barrels through the inner parts of the detector, it can radiate energy by emitting gluons.

… These gluons can produce quark/anti-quark pairs
… which themselves can produce gluons
… etc., etc.

At each step, the energy of the quarks and gluons decrease, but the number of particles increases. Eventually the energy is such that the “free quarks” cannot prevent the inevitable and they must hadronize. Because there are so many, however, there are a lot of mesons barreling through the detector. The detector is essentially a block of dense material which can measure the energy deposited into it, and what it ‘sees’ is a “shower” of energy in a particular direction. This is what we call a jet, and it is the signature of a high energy quark or gluon that shot off in a particular direction and eventually hadronizes. Here’s a picture that I borrowed from a CDF talk:

Read the picture from the bottom up:

  1. First two protons collide… by which we really mean the quarks and gluons inside the proton interact.
  2. High energy quarks and gluons spit off other quark/gluons and increase in number
  3. Doing this reduces their energy so that eventually the quarks and gluons must confine (hadronize) into mesons
  4. … which eventually deposit most of their energy into the detector (calorimeter)

Jets are important signatures at high energy colliders and are a primary handle for understanding the high energy interactions that we seek to better understand at the LHC. In order to measure the energy and momentum of the initial high energy quark, for example, one must be able to measure all of the energy and momentum from the spray of particles in the jet, while taking into account the small cracks between detecting materials as well as any sneaky mesons which may have escaped the detector. (This is the hadronic analog of the electromagnetic calorimeter that Christine recently described.)

Now you can at least heuristically see why this information can be so hard to extract. First the actual particles that are interacting at high energies are different from the particles that exist at low energies. Secondly, even individual high-energy quarks and gluons lead to a big messy experimental signature that require careful analysis to extract even “basic” information about the original particle.