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 and shrinks at long 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.

Fig. 1: If you tried to pull a quark out of a proton (using a magical pair of tweezers), you would discover the proton would first distort and then break into two hadrons (perhaps a proton and a neutral pion). Thus your attempt to free the quark from its prison would inevitably fail, and the energy that you exerted to do so would instead be converted into the mass-energy of a second hadron.

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.

Fig. 2. Top: An electron, which does not feel the strong nuclear force and easily penetrates the proton, strikes a quark inside the proton and gives it a hard kick. Middle: the quark, rushing out of the proton, leaves a band or “string” of hadronic material behind it, which begins to fragment. Bottom: Numerous fragments, each one a hadron, are formed from the breaking band, and most of those fragments head off in the same direction as the original struck quark, forming a “jet” — a collimated spray of hadrons. (Warning: this is naive; see Figure 3 if you want a less naive picture.)

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.

Fig. 3. Top: as in Figure 2, a quark is struck by an electron and given high motion energy. Top right: the quark radiates a number of gluons which head roughly in the same direction. Middle left: the quark and gluons all emerge from the proton together. Bottom: The emergence from the proton of the quark and the collection of gluons leads, through a process similar to that shown in Figure 2, but more complicated in its details, to a jet of hadrons.

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.

19 responses to “Jets: The Manifestation of Quarks and Gluons

  1. Pingback: Jets: The Manifestation of Quarks and Gluons « physics4me

  2. Dear Prof. Strassler,
    (or may I say hi Matt, not sure if it is appropriate, blushing …)
    as usually I like this article very much. Maybe it could be added that that the observable hadrons constituting have to be color neutral to further explain why the particular hadrons mentioned form?

    The “aside” is nicely explained in this lecture

    http://www.youtube.com/

    from Lenny Susskind :-)

    Cheers

  3. Whoops, what happend?
    I just wanted to give the link and not the video in this huge format, sorry :-/

  4. Prof. Matt Strassler

    Taken from article in 2000

    Is this still a useful analogy here that you are showing in concert with your article??

    http://www.cerncourier.com/objects/2000/cernexotic1_9-00.gif

    “Fig. 1. In quantum chromodynamics, a confining flux tube forms between distant static charges. This leads to quark confinement – the potential energy between (in this case) a quark and an antiquark increases linearly with the distance between them.” http://cerncourier.com/cws/article/cern/28291

    Also current research is helpful.
    Quark Soup: Applied Superstring Theory- http://www.cap.ca/sites/cap.ca/files/article/1413/apr10-offprint-buchel.pdf

    Best,

  5. Hello and thanks for this excellent educational blog!
    You say: “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.”
    What do you have in mind in saying that it still does a terrible job? Thanks!

    • Well, that’s a bit technical, I’m afraid. What I am referring to here as “something surprising” is known as the string-theory/gauge-theory correspondence, also known as the generalized AdS/CFT correspondence, due to Maldacena (and contributed to, before and after his paper, by many other authors.)

      This correspondence works best — the string theory calculations are easiest — for a regime of quantum field theory in which, unfortunately, jets do not form at all; instead a high-energy quark turns into a very broad blob of energy, very different from what we see in experiment. [Essentially, what happens is this: look at the last figure in this article. In this regime, the process by which the quark emits a number of gluons goes into high gear; the quark emits so many gluons in so many directions, which in turn emit so many more gluons, before anything reaches the edge of the proton that the energy ends up going out in all directions, rather than in an organized jet. [By the way, before anyone asks, this is not related to jet quenching in quark gluon plasmas; that's a different effect.]) The first indications of this effect appear, as far as I know, in my work with Polchinski on deep inelastic scattering: http://arxiv.org/PS_cache/hep-th/pdf/0209/0209211v1.pdf

      In the regime of quantum field theory that we see in the real world, for which jets do form, this string/gauge correspondence is not useful, because calculations in the string theory are so difficult as to be currently impossible. And quantum field theory does a pretty good job of describing jets, so it isn’t so clear what string theory could add here anyway.

  6. OK, I see what you are driving at now. Thanks for taking the time to answer!

  7. Thanks for this article and comments. Really appreciated!! Nice balance between easy explanation and technical depth. I am an engineer on the extreme periphery of a CMS group and I always wanted to know what jets were but was afraid to ask!

  8. Here and elsewhere I’ve seen particle physicists refer casually to processes such as a “speeding electron [that] plows into a proton and hits a quark really hard,” as you put it here. I’ve run into similar language when reading about how neutrinos are detected.

    This process of an electron “colliding” with a quark that you mention — am I correct that this is just an electromagnetic interaction whose “strength” (not sure if that’s the right word) depends on the proximity and energy of the particles in question? (Is it the same mechanism that keeps an electron “in orbit” around an atomic nucleus, except that the electron in this case is much closer to the quark and moving directly toward it with great speed, and so the effect of the EM interaction is different?) If this is right, does it matter if the electron “hits” an up or down quark (i.e., will jets appear whether the EM interaction is attractive or repulsive)?

    I know that neutrinos interact weakly but not electromagnetically. Is it the same thing here, then, except with the weak nuclear force? In other words, when particle physicists say that a neutrino was detected because it “collided” with another particle in a detector, are they really saying that the neutrino got close enough to the other particle to interact with it weakly?

    Finally, I know that leptons and quarks feel the weak force, too. When an electron “hits” a quark, can the electron cause weak decay of the hadron in addition to (or instead of?) electromagnetically “kicking” the quark/gluons outward and forming a jet? I’d imagine that the answer to this question might have something to do with the proximity and energy required for the particles to interact weakly vs. that required for the electron to impart enough “kick” to the quark to overcome the strong force holding the hadron together, but obviously I’m just speculating.

    Really informative article — thanks, Doc!

    • In an atom, electrons are coasting around and not banging into each other. But if you throw two electrons almost straight at each other at high energy, they will scatter off each other through the electromagnetic interaction — in much the same way, and for much the same reason, that two electrically charged ping pong balls will be repelled from one another and will scatter due to electromagnetic repulsion, even without physically touching each other. [Similarly an electron and a positron heading nearly straight at each other will scatter -- they will be attracted rather than repelled, but this will still cause scattering, because both of them will change direction, and they won't stick to each other if their motion energy was high enough to start with... similarly to the near-collision of two stars.]

      Quarks are electrically charged, and electrons scatter off quarks in exactly the same way for exactly the same reason. And it doesn’t matter, except in minor detail, whether the electron hits an up or down quark; it just matters what direction the two head out after the collision.

      Collisions of neutrinos with quarks or electrons are also the same, but the force involved is very short range, so neutrinos have to by chance come about 100 times closer to a quark or electron than the distance across a proton, the scattering will be too tiny to have any effect. Instead of the force law being 1/r^2 as it is for electric forces, it is something like F = exp[- r/L_W] (1/[r L_W] + 1/r^2) where L_W = 10^-18 meters is inversely proportional to the W particle’s mass. This is 1/r^2 at short distance and exponentially suppressed for r > L_W.

      Weak interactions of electrons with quarks are much less likely than electromagnetic ones, because indeed the electron must come much closer to the quark for the weak interaction to happen — but such interactions do occur. The process electron + proton –> neutron + neutrino is an important example of a weak interaction process; in fact, it is the dominant process that occurs during the formation of a neutron star in the middle of a star going supernova, when the densities are so high that the electrons are jammed into the protons, making the weak interaction much more likely.

  9. Pingback: The Constancy of the Heavens — Verified Anew | Of Particular Significance

  10. If the strong nuclear force stops shrinking (above a small distance) then this would initially imply that it could affect particles a very large distance away – an effect we don’t see in the macro world. I assume therefore that the strong force not only can cancel out, but must always cancel out by having a matched number of particles in any composite particle.
    I’m aware the simple model is the u-d-d of a neutron is electric charge wise matched with the u-u-d of the proton, does this mean there is some other constraint on the number of quarks in a hadron such that the strong force must be cancelled out, and any missing numbers cause an imbalance in the strong force field which would almost suck extra quark pairs into existence – yes I imagine this is a terrible way to phrase it but it’s what I’m picturing in my head at the moment.

  11. Pingback: At a CMS/Theory Workshop in Princeton | Of Particular Significance

  12. Im not sure if comments for older articles get read but here goes.

    The elastic band effect between quarks; would pulling on it become more and more difficult as with a literal elastic band? Or would it remain constant? (I notice you said that the force of the gluon field becomes constant but I wanted to make sure of what that means because of the elastic band analogy and from what Ive read elsewhere.)

    Or cant we be sure because of how fast it breaks down?

    • The force does go a constant; we can see that, in a way I don’t have time to explain just now, in data on the masses of classes of hadrons as a function of their spin: for instance http://inspirehep.net/record/1233875/files/f3mes.png .

      We can also do numerical simulations of theories with no light quarks, in which case the “elastic bands” don’t break. And we can see then that the force goes to a constant.

      There are other deep theoretical reasons to expect the force goes to a constant.

      All in all there is little doubt.

  13. Pingback: Quantum Field Theory, String Theory and Predictions (Part 9) | Of Particular Significance

  14. I usually doo not create a lot of comments, but i did a
    few searching and wound upp here Jets: Thhe Manifestation of
    Quarks and Gluons | Of Particular Significance. And
    I ddo have a couple of questions for you if you do not mind.

    Is it simply mee or does it give the impression like some of these remarks
    look like left by brain deaad visitors? :-P And, if you are writing oon additional online sites,
    I’d like to keep up with everything new you have to post.
    Could you mzke a list of alll of all your social pages like your Facebook
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