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Flip Tanedo | USLHC | USA

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Meet the quarks

One of the most important experiments in the history of physics was the Rutherford experiment where “alpha particles” were shot at a sheet of gold foil. The way that the particles scattered off the foil was a tell-tale signature that atoms contained a dense nucleus of positive charge. This is one of the guiding principles of high-energy experiments:

If you smash things together at high enough energies, you probe the substructure of those particles.

When people say that the LHC is a machine colliding protons at 14 TeV, what they really mean is that it’s a quark/gluon collider since these are the subnuclear particles which make up protons. In this post we’ll begin a discussion about what these subatomic particles are and why they’re so different from any of the other particles we’ve met.

(Regina mentioned QCD in her last post—I think “subtracting the effects of QCD,” loosely phrased, is one of the ‘problems’ that both theorists and experimentalists often struggle with.)

This post is part of a series introducing the Standard Model through Feynman diagrams. An index of these entries can be found on the original post. In this post we’ll just go over the matter particles in QCD. (I’m experimenting with more frequent—but shorter—posts.)

A (partial) periodic table for QCD

The theory that describes quarks and gluons is called Quantum Chromodynamics, or QCD for short. QCD is a part of the Standard Model, but for this post we’ll focus on just QCD by itself. Quarks are the fermions—the matter particles—of the theory. There are six quarks, which come in three “families” (columns in the table below):

The quarks have cute names: the up, down, charm, strange, top, and bottom. Historically the t and b quarks have also been called “truth” and “beauty,” but—for reasons I don’t quite understand—those names have fallen out of use, thus sparing what would have been an endless parade of puns in academic paper titles.

The top row (u,c,t) is composed of particles with +2/3 electric charge while the bottom row is composed of particles of -1/3 charge. These are funny values since we’re used to protons and electrons with charges +1 and -1 respectively. On the one hand this is a historical effect: if we measured the quark charges first we would have said that

  • the down quark has charge -1
  • the up quark has charge +2
  • the electron has charge -3
  • and the proton has charge +3

It’s just a definition of how much is one “unit” of charge. However, the fact that the quark and lepton charges have these particular ratios is a numerical curiosity, since it is suggestive (for reasons we won’t go into here) of something called grand unification. (It’s not really as “grand” as it sounds.)

One quark, two quark, red quark, blue quark?

I drew the above diagram very suggestively: there are actually three quarks for each letter above. We name these quarks according to colors: thus we can have a red up quark, a blue up quark, and a green up quark, and similarly with each of the five quarks. Let me stress that actual quarks are not actually “colored” in the conventional sense! These are just names that physicists use.

The ‘colors’ are really a kind of “chromodynamic” charge. What does this mean? Recall in QED (usual electromagnetism) that the electron’s electric charge means that it can couple to photons. In other words, you can draw Feynman diagrams where photons and electrons interact. This is precisely what we did in my first post on the subject. In QED we just had two kinds of charge: positive and negative. When you bring a positive and negative charge together, they become neutral. In QCD we generalize this notion by having three kinds of charge, and bringing all three charges together gives you something neutral. (Weird!)

The naming of different kinds of quarks according to colors is actually very clever and is based on the way that colored light mixes. In particular, we know that equal parts of red + green + blue = white. We interpret “white” as “color neutral,” meaning having no “color charge.”

There’s a second way to get something color neutral: you can add something of one color with it’s “anti-color.” (You can formalize these in color theory, but this would take us a bit off course.) For example, the “anti-color” of red is cyan. So we could have red + “anti-red” (cyan) = color neutral.

If we don’t see them, are quarks real?

The point of all of these “color mixing” analogies is that [at low energies], QCD is a strongly coupled force. In fact, we often just call it the strong force. It’s responsible for holding together protons and neutrons. In fact, QCD is so strong that it forces all “color-charged” states to find each other and become color neutral. We’ll get into some details about this in follow up posts when we introduce the QCD force particles, the gluons. For now, you should believe (with a hint of scientific skepticism) that there is no such thing as a “free quark.” Nobody has ever picked up a quark and examined it to determine its properties. As far as you, me, the LHC, and everyone else is concerned, quarks are always tied up in bound states.

There are two kinds of bound states:

  • Bound states of 3 quarks: these are called baryons. You already know two: the proton and the neutron. The proton is a combination (uud) while the neutron is a combination (ddu). For homework, check that the electric charges add up to be +1 and 0. Because these have to be color neutral, we know that the quark colors have to sum according to red + green + blue.
  • Bound states of a quark and an anti-quark: these are called mesons. These are color-neutral because you have a color + it’s anti-color. The lightest mesons are called pions and are composed of up and down quarks. For example, the π+ meson looks something like (u anti-d).  (Check to make sure you agree that it has +1 electric charge.)

Collectively these bound states are called hadrons. In the real world (i.e. in our particle detectors) we only see hadrons because any free quarks automatically get paired up with either anti-quarks or two other quarks. (Where do these quarks come from? We’ll discuss that soon!)

This seems to lead to an almost philosophical question: if quarks are always tied up in hadrons, how do we know they really exist?

A neat historical fact: Murray Gell-Mann and Yuval Ne’eman, progenitors of the quark model, originally proposed quarks as a mathematical tool to understand the properties of hadrons; largely because we’d found lots of hadrons, but no isolated quarks. For a period in the 60s people would do calculations with quarks as abstract objects with no physical relevance.

Why we believe that quarks are real

This seems to lead to an almost philosophical question: if quarks are always tied up in hadrons, how do we know they really exist? Fortunately, we are physicists, not philosophers. Just as Rutherford first probed the structure of the atomic nucleus by smashing high energy alpha particles (which were themselves nuclei), the deep inelastic scattering experiments at the Stanford Linear Accelerator Center (joint with MIT and Caltech) in the 60s collided electrons into liquid hydrogen/deuterium targets and revealed the quark substructure of the proton.

A discussion of deep inelastic scattering could easily span several blog posts by itself. (Indeed, it could span several weeks in a graduate quantum field theory course!) I hope to get back to this in the future, since it was truly one of the important discoveries of the second half of the twentieth century. To whet your appetites, I’ll only draw the Feynman diagram for the process:

This is unlabeled, but by now you should see what’s going on. The particle on top is the electron that interacts with the proton, which is drawn as the three quark lines on the bottom left. The circle (technically called a “blob” in the literature) represents some QCD interactions between the three quarks (holding them together). The electron interacts with a quark through some kind of force particle, the wiggly line. For simplicity you can assume that it is a photon (for homework, think about what is different if it’s a W). We’ve drawn the quark that interacts as the isolated line coming out of the blob.

This quark is somewhat special because it’s the particle that the electron recoils against. This means that it gets a big kick in energy, which can knock it out of the proton. As I mentioned above, this quark is now “free” — but not for long! It has to hadronize into more complicated QCD objects, mesons or baryons. The spectrum of outgoing particles gives clues about what actually happened inside the diagram.

We’ve just glossed over the surface of this diagram: there is a lot of very deep (no pun intended) physics involved here. (These sorts of processes are also a notorious pain in the you-know-where to calculate the first time one meets them in graduate courses.)

(By the way: the typical interactions of interest at the LHC are similar to the diagram above, only with two protons interacting!)

A hint of group theory and unification

I would be negligent not to mention some of the symmetry of the matter content of the Standard Model. Let’s take a look at all of the fermions that we’ve met so far:

There are all sorts of fantastic patterns that one can glean from things that we’ve learned in these blog posts alone!

The top two rows are quarks (each with three different colors), while the bottom two rows are leptons. Each row has a different electric charge. Each column carries the same properties, except that each successive column is heavier than the previous one. We learned that the W boson mediates decays between the columns, and since heavy things decay into lighter things, most of our universe is made up of exclusively the first column.

There are other patterns we can see. For example:

  • When we first met QED, we only needed one type of particle, say the electron. We knew that electrons and anti-electrons (positrons) could interact with a photon.
  • When we met the weak force (the W boson), we needed to introduce another type or particle: the neutrino. An electron and an anti-neutrino could interact with a W boson.
  • Now we’ve met the strong force, QCD. In our next post we’ll meet the force particle, the gluon. What I’ve already told you, though, is that there are three kinds of particles that interact with QCD: red, green, and blue. In order to form something neutral, you need all three color charges to cancel.

There’s a very deep mathematical reason why we get this one-two-three kind of counting: it comes from the underlying “gauge symmetry” of the Standard Model. The mathematical field of group theory is (a rough definition) the study of how symmetries can manifest themselves. Each type of force in the Standard Model is associated with a particular “symmetry group.” Without knowing what these names mean, it should not surprise you if I told you that the symmetry group of the Standard Model is: U(1) SU(2) SU(3). There’s that one-two-three counting!

It turns out that this is also very suggestive of grand unification. The main thrust of the idea is that all three forces actually fit together in a nice way into a single force which is represented by a single “symmetry group,” say, SU(5). In such a scheme, each column in the “periodic table” above can actually be “derived” from the mathematical properties of the GUT (grand unified theory) group. So in the same way that QCD told us we needed three colors, the GUT group would tell us that matter must come in sets composed of quarks with three colors, a charged lepton, and a neutrino; all together!

By the way, while they sound similar, don’t confuse “grand unified theories” with a “theory of everything.” The former are theories of particle physics, while the latter try to unify particle physics with gravity (e.g. string theory). Grand unified theories are actually fairly mundane and I think most physicists suspect that whatever completes the Standard Model should somehow eventually unify (though there has been no direct experimental evidence yet). “Theories of everything” are far more speculative by comparison.

Where we’ll go from here?

I seem to have failed in my attempt to write shorter blog posts, but this has been a quick intro to QCD. Hopefully I can write up a few more posts describing gluons, confinement, and hadrons.

For all of you LHC fans out there: QCD is really important. (For all of you LHC scientists out there, you already know that the correct phrase is, “QCD is really annoying.”) When we say that SLAC/Brookhaven discovered the charm quark or that Fermilab discovered the top quark, nobody actually bottled up a quark and presented it to the Nobel Prize committee. Our detectors see hadrons, and the properties of particular processes like deep inelastic scattering allow us to learn somewhat indirectly about the substructure of these hadrons to learn about the existence of quarks. This, in general, is really, really, really hard—both experimentally and theoretically.

Thanks everyone,
Flip, US LHC Blogs

(By the way, if there are particle physics topics that people want to hear about, feel free to leave suggestions in the comments of the blog. I can’t promise that I’ll be able to discuss all of them, but I do appreciate feedback and suggestions. Don’t worry, I’ll get to the Higgs boson eventually… first I want to discuss the particles that we have discovered!)