What Is This "Quark-Gluon Plasma" of Which You Speak?

I promised a while ago to talk about quark-gluon plasma, so here's my all-purpose pseudo-expert lecture on the subject.

(About 2500 words!)

I'm going to assume you know at least the basics of particle physics:

That matter is made up of molecules, which come in near-infinite combination;

Which are made up of atoms, of which there are a finite number of types.

Atoms consist of electrons which form a negatively-charged cloud around a nucleus;

Which consists of protons and neutrons, held together by the same powerful force that's responsible for atomic power plants and nuclear weapons.

Protons and neutrons are made up of quarks, which are held together by the strong nuclear force.

OK, here's where the lecture starts:

Quarks come in six different types, but all of the matter you can see or feel or touch is made up of just two types, the up and down quarks, plus electrons. An up quark has a charge of positive 2/3rds; a down quark has a charge of negative 1/3rd. (These are fractions because the unit of charge has been taken to be the charge of the proton.)

The rules of the strong nuclear force are pretty simple: Each quark has a special quantum number called "color" which can take one of three values, red, blue, or green. (These aren't colors you can see, they're just a useful analogy.) Having color is bad: quarks want to get together in gangs so that they have no overall color, which means one red, one blue, and one green quark make a white particle. A proton consists of two up quarks and a down quark, and a neutron consists of two down quarks and an up quark. Protons and neutrons are examples of three-quark objects which are called baryons.

There's no point in talking about the specific color of an individual quark, because the way the strong nuclear force works, quarks change colors rapidly.

In quantum physics, the way you represent the action of a force is by the interchange of a virtual particle.[1] Electromagnetism occurs because two charged particles exchange photons (particles of light). Virtual means that the particle doesn't really exist, or rather, that it takes advantage of a loophole in reality caused by the Uncertainty Principle. Energy and momentum are always exactly conserved, except that the Uncertainty Principle says that you can't quite measure energy or momentum exactly. Under the mathematical formulation of the Uncertainty Principle, energy and time are what's known as conjugate pairs, and the result is that you can just make, out of the vacuum of space, a particle with a little bit of energy, so long as it lasts just a little bit of time, without violating the Uncertainty Principle.

So what happens when two particles feel a force between them is that one of them emits a virtual particle that carries a tiny amount of energy and momentum a tiny distance to the other particle in a tiny bit of time, too little and too short and too quick for the universe to notice you're cheating.

I've already said that the particle that carries the electromagnetic force is the photon. The particle that carries the strong nuclear force--the color force--is the gluon, and there are eight separate types. The description of how all this works is called quantum chromodynamics, or QCD for short. Each gluon carries both color and anti-color, e.g., one of the eight types is red-anti-blue.[2] What happens then is, e.g., a red up quark kicks out a red-anti-blue gluon and becomes a blue up quark; the red-anti- blue gluon then finds another blue quark, maybe a down quark, and gets absorbed, converting the blue down quark into a red down quark, so you can see that the color force is all about changing a quark's color. The gluon also carries a bit of energy and momentum so that the two quarks are strongly attracted towards each other.

Sometimes, a quark can emit a virtual gluon which it itself ends up re- absorbing. The result is called a loop (imagine drawing a diagram of what's happening), and it makes the math of QCD extremely difficult. (Among other things, some of your calculations immediately go to infinity, and you have to use a special kind of mathematical trickery to redefine these infinities as ordinary finite numbers.)

The same phenomenon occurs in electromagnetism, too (where it's called quantum electrodynamics, or QED), except instead of quarks and gluons, it's any charged particle and photons. Imagine a single electron sitting out alone in space. It's constantly emitting virtual photons and re-absorbing them. Sometimes these virtual photons can split into a pair of particles that consist of a virtual electron and a virtual positron (the anti-particle of an electron), which then recombine to form the virtual photon again, which gets re-absorbed by the real electron.

So an electron sitting out in space is covered by this cloud of virtual particles, a bunch of photons and electrons and positrons that exist only in the tiny slice of reality permitted by the Uncertainty Principle. A particle with all these virtual particles around it is said to be "dressed".

Quarks dress themselves, too, in a cloud of virtual gluons and virtual quark-anti-quark pairs. But there's a difference. An electron is dressed for vacation, but a quark is dressed for a White House reception. That's because each vertex--each virtual interaction of particles, such as emitting a virtual photon, or splitting into a virtual quark-anti-quark pair--carries with it a factor that depends on the force. The more vertices in a particular operation, the more factors are applied, and the less likely the operation is to occur. If an electron emits and absorbs a virtual photon, that's two vertices--the emitting and the absorption. If it emits a virtual photon which pair-produces, then collapses the pair, then gets absorbed, that's a four-vertex operation, and it's less likely by the vertex factor squared.

The vertex factor for QED is the "fine structure constant", alpha, which is so-called because it was first recognized as the number behind a tiny split in some of the lines in the hydrogen spectrum. The fine structure constant is 1/137, pretty small, so each time it's applied, the event gets considerably less probable.

The vertex factor for QCD, on the other hand, alpha-s, is twenty or thirty times larger than alpha, so multiple vertices don't become improbable very fast at all. (Vertex factors depend in a complex way on the energy at the vertex. In QED, it doesn't change very fast, but in QCD it does, so it's difficult to say what alpha-s is very precisely.)

The result is that an electron is surrounded by a pretty thin cloud of virtual particles, not very many at all, but a quark is surrounded by a dense cloud of them because the probability of even very complicated virtual interactions is significant.

In fact, because QCD wants colorless objects, what a proton is is a dense cloud of virtual particles, all gluons and up and down quarks, even a few strange quarks, plus anti-up, anti-down, and anti-strange quarks, all changing identity and color very quickly, so that the only thing you can say with any certainty is that, if you average over the whole conglomeration, you end up with a net of two up quarks and one down quark and no strange quarks and no color.

Quarks and gluons evince a quality called "confinement", which works like this. The energy potential of the color force has a 1/r component, like electromagnetism, so that it gets strong when the particles are close, and an r component, so that it also gets strong when the particles are far apart.

Let's take a quark and start pulling it out of a proton. What happens is that the color force starts building up a lot of energy as the quark exchanges more and more gluons with the quarks it's leaving behind. These gluons--which can interact with each other-- form what's called a color tube between the quark and the proton remnants, and it just binds more and more energy as the quark gets further away. You can never put enough energy into the color tube to get the quark free. The same is true of a gluon, as it can interact with other gluons, so it'll also form a color tube as you attempt to extract it from the particle. Eventually, there will be so much energy bound up in the color tube that you can break the color tube by forming a quark-anti-quark pair (real, not virtual) in the middle and immediately make two shorter color tubes. The quark you were pulling on makes a connection with the anti-quark, forming a kind of particle called a meson (quark plus anti-quark equals color plus anti-color equals white), while the anti-quark's counterpart gets sucked back into the proton remnant to make it a colorless hadron again.

Let's imagine that we give Sammy Sosa a bat one quark wide and stand him next to a proton; he takes a mighty swing and pow! connects with one of the quarks in the proton and just sends it flying! What happens? Well, the quark starts out of the proton trailing a color tube behind it. When it gets big enough, it breaks, creating more quarks. But the first quark is still sailing out to the bleachers, dragging the new quarks along with it, making more color tubes. These break, too, creating more quarks. Eventually, enough energy has gone into breaking color tubes that you run out, and what you're left with is a bunch of quarks and anti-quarks which settle down into mesons, all headed the same direction and carrying a bunch of energy with them. That's called a jet. When a particle physicist sees a jet in his detector, he knows that he hasn't just hit the proton, he's actually hit one of the quarks or gluons inside the proton. (This is called "deep inelastic scattering", or DIS, because physicists are poets.)

Now you have enough background that I can start talking about what a quark-gluon plasma is. Hadrons--three-quark objects--are colorless, because they've got a net of three objects with different colors in them, so that all of their virtual particles--which are color-carrying currents--can curve back on the hadron and close themselves off. And the Pauli Exclusion Principle means that it's difficult to bring another hadron close enough to interfere with that hadron's colorful aura of virtual particles. There will be some weak color currents between the two hadrons--that's the force that holds the nucleus together, also called the residual strong force, and it's analogous to the Van der Waals forces that gas molecules experience. But the hadrons will retain their separate identities as colorless objects.

Imagine, though, that you put enough quarks into a small enough space that you lose the idea of colorlessness. A color current doesn't have to curve in on itself because there's always another colored object close enough nearby for it to terminate on, so you don't have individual hadrons and mesons, just an undifferentiated mass of quarks and gluons. That's a quark-gluon plasma.

The way you make a quark-gluon plasma is conceptually pretty easy, and it goes back to the usual way particle physicists think. Particle physics, it is said, is like trying to figure out how a watch works by slamming two watches into each other at the speed of light and looking at the pieces that fall out. To make a QGP, you take a couple of gold atoms, strip off all their electrons, run 'em up to the speed of light (where they look as flat as pancakes because of relativistic contraction), and slam 'em into each other.

A gold atom has about 197 protons and neutrons in it, or about 591 quarks. Slam two of them together, and you've got around 1200 quarks jammed into a disk about 10^-14 meters across and about a thousandth of that thick. That's a lot of quarks and a lot of energy in a small space!

How do you know if you're seeing a QGP and not just a hot chunk of hadronic matter? After all, either way, you're going to be seeing thousands of particles flying off in all directions. There are several possible signatures. One is that it's relatively easier to create the slightly-heavier strange quarks in a QGP than in DIS, so you can look at the types of particles that come out. Another is a QGP is going to expand under its own internal pressure, so you can look at the center of the collision disk to see if it bulges like you'd expect.

Another is a phenomenon called jet quenching, which says that it's harder for a jet to escape from a QGP (because of the color density) than ordinary, so you'd expect to see fewer jets out of a QGP, and it should be proportional to the density of the QGP and the distance the jet has to travel through the QGP, i.e., there should be many fewer jets to the side where they have to travel the width of the collision disk as opposed to the front or back, where they only have to travel the narrow thickness of the disk.

At Brookhaven National Laboratory on Long Island, scientists have built the RHIC--Relativistic Heavy Ion Collider--in an attempt to create QGP, and the various experiments at RHIC are reporting very solid, albeit still preliminary, results that suggest that they've succeeded.

Good work, guys!

[1] All matter particles--electrons, quarks--are a type of particle called fermions, which have a quantum mechanical property of exclusion (the Pauli Exclusion Principle), meaning that they can't to be close to each other if they have the same quantum numbers. All force particles are bosons, which have the opposite property, i.e., they prefer to be right up on each other sharing the same quantum state. (Lasers work because of this.) All particles have a quantum number called spin, which is a tiny amount of intrinsic angular momentum. Fermions have spin in 1/2 or 3/2 unit, while bosons have spin of 0, 1, or 2 units. Fermion wave functions (i.e., the quantum mechanical description of the particle's state) are anti-symmetric under particle interchange; boson wave functions are symmetric under interchange.

[2] Six of the gluons are simple color-anti-other-color combinations, e.g. red-anti-blue. The other two are orthogonal quantum mechanical combinations of color-anti-same-color, i.e., 1/sqrt(2) (g-g-bar - r-r-bar) and 1/sqrt(6) * (g-g-bar + r-r-bar - 2*b-b-bar) (where r,g,b indicates red, green, blue, and bar indicates anti-). There's one more possible combination, i.e., 1/sqrt(3) * (r-r-bar + g-g-bar + b-b-bar), but since it's symmetric, it's white, i.e. colorless, it can't interact with anything, so it doesn't actually exist.

Posted by Greg at January 23, 2004 3:10 PM