Jets: The Manifestation of Quarks and Gluons

Matt Strassler 10/31/11

Quarks, gluons and anti-quarks are the constituents of protons, neutrons and (by definition) other hadrons.  It is a fascinating aspect of the physics of our world that when one of these particles is kicked out of the hadron that contains it, flying out with high motion-energy, it is never observed macroscopically. Instead, a high-energy quark (or gluon or anti-quark) is transformed into a spray of hadrons [particles made from quarks, antiquarks and gluons].  This spray is called a “jet.” [Note this statement applies to the five lighter flavors of quark, and not the top quark, which decays to a W particle and a bottom quark before a jet can form.]

In this article I’ll give you a rough idea of how and why a jet is created from a high-energy quark, anti-quark or gluon.

This feature, which makes quarks behave so differently from charged leptons, neutrinos, photons and the like, is a consequence of the fact that quarks and gluons are affected by the strong nuclear force, while the other known particles are not. Most forces between two particles become weaker with distance; for example, the gravitational force between two planets falls off as the inverse of the square of the distance between them. The same is true of the electrical force between two charged objects, which also falls off like the square of the distance. You see this yourself when you rub a balloon, making it charged with “static electricity” as we call it colloquially; if you bring the balloon close to your head your hair will stand on end as it is attracted to the balloon, but the effect drops off quickly as you move the balloon away.

What happens with the strong nuclear force is that although it too grows at short distances (though a tiny bit slower than electric forces do, which is important in the story of the strong interactions) it stops shrinking at distances of about a millionth of a billionth of a meter (a meter is about three feet), which is just about the radius of a proton, or 100,000 times smaller than the radius of an atom. That’s not an accident; the size of a proton is actually set by this effect. Instead, the force, generated by the gluon field, becomes a constant. And that means that if you could try, for instance, to pull a quark out of a proton, as in Figure 1, you would find that it would not get easier as you tried to pull the quark further and further out. It would be almost like pulling on a rubber band — an elastic string. Except that this rubber band, before you pulled it too far, would always break. Once the energy stored in this elastic band gets large enough, nature would prefer to break the band in two rather than let you keep pulling on it. What happens when it breaks is that instead of one hadron (the proton) you now have two: a proton or neutron, plus (typically) a pion.  (In the breaking, a quark and anti-quark pair form in a particular way— energy in the form of the band’s tension is converted into mass-energy of the quark and anti-quark, along with some motion-energy for some additional gluons.) Energy is conserved: you started with the mass-energy of the proton, you added some energy in stretching the proton, and you end up with the mass-energy of two hadrons (and nothing stretching).  Electric charge is conserved too, so you either end up with a neutral pion and a proton, or a positively-charged pion and a neutron.

 

What happens when a high-energy quark is kicked out of a proton?  For instance, suppose a speeding electron plows into a proton and hits a quark really hard, giving it a motion energy much larger than the mass-energy of the entire proton?!

Roughly — and a warning to experts: a bit of what I’m going to say now is naive and actually misleading, and I’ll correct it later — what happens is the same process shown in Figure 1, but on steroids. So rapidly does the quark move that the band that forms simply can’t break fast enough, and becomes overstretched; see the central panel of Figure 2. As a result, instead of breaking at one point, forming two hadrons, it breaks many times, forming many hadrons (mostly pions and kaons [like pions but with a strange quark or anti-quark] and eta’s, and more rarely protons, neutrons, anti-protons or anti-neutrons.)All of these are heading more or less in the same direction as the band was stretching. And so the end result is a spray of hadrons, most of them heading in the direction of the original quark. That’s a jet.

The initial energy of the high-energy quark is now shared among the hadrons in the jet.   But for a quark with sufficiently high energy (roughly, 10 GeV or more) only a small amount of the quark’s initial energy is used in forming the mass-energy of the new hadrons; most of it is in carried in their motion-energy.  As a result, the total energy and direction of the jet is quite similar to the initial energy and direction of the initial quark.   By measuring the energy and direction of all the hadrons in the jet, and determining the energy and the direction of the jet as a whole, particle physicists obtain a pretty good estimate of the energy, and the direction of motion, of the original quark.

The same story holds for anti-quarks, and, with some largely inessential modification, for high-energy gluons.

I should emphasize that no one can calculate how this process happens in any detail. The reason we know what I’ve just told you is because of a combination of decades of theoretical calculation, theoretical guesswork, and data — detailed data from many sources — which collectively show that the story (with the above-mentioned lies corrected) is true.  And we have good reason to have a lot of confidence in the story. Many of our high-precision tests of the theory of the strong nuclear force would have failed if it weren’t the case.

An aside: this almost-like-a-rubber-band object is called a “QCD string” by high-energy physicists. (“QCD” is the name physicists have given to the equations describing the strong nuclear force.)  Historically, trying to understand the pattern of hadrons that we see in nature (before physicists knew about QCD and gluons, and when quarks were still poorly understood) led theorists in the late 1960s to invent string theory. It was only later that it was understood that the string in this early string theory was actually a real thing, a part of the physics. And even later, it was understood that the QCD string isn’t described well by standard string theory. This was briefly viewed as a failure, until it was pointed out by Scherk and Schwartz that string theory might be better anyway as a theory of quantum gravity (and perhaps of all the fundamental particles.) And off string theorists went in a new direction. More recently, though, it has been understood how to do something surprising with standard string theory so that it does a better job (not a perfect one, but much improved) of describing the QCD string. Unfortunately it still does a terrible job of describing jets.

Clearly there’s much more to the story of the strong nuclear force — to be told later.

Ok, now let me fix the lie that I told in Figure 2.  The problem is that I left out a key step.  A struck quark, like any accelerated particle, will radiate.  A suddenly accelerated electron will radiate photons; a suddenly accelerated quark will radiate many gluons (and photons too, but far fewer.)  This is shown at upper right in Figure 3.  So what actually emerges at the edge of the proton (middle left, Figure 3) is not a fast quark but a collection of fast gluons along with the fast quark.  As a result the process by which the jet of hadrons forms (bottom, Figure 3) is more elaborate than shown in Figure 2, though the end result is similar.  But importantly, the shape of the jet is actually determined mainly by the way that the gluons are radiated before the quark even emerges from the proton.  That process of gluon radiation from the quark can be calculated!  And so, far more properties of jets can be calculated, using the equations of the strong nuclear force, than might be guessed from the more naive picture of Figure 2.  These calculations have been verified in data, thereby testing the equations of the strong nuclear force.