Matt Strassler [February 17, 2012]
Final draft form; comments welcome.
You’ve heard the famous statement that “a proton is made from two up quarks and a down quark”. But in this basic article, and this somewhat more advanced one, and in a recent post where I went into some details about what we know about proton structure, I’ve claimed to you that protons are chock full of particles, most of which carry a tiny fraction of the proton’s energy, and most of which are gluons, along with a substantial number of of quarks and antiquarks. [If this sounds unfamiliar, you should read those articles and posts before reading this one, which is a follow-up.] And I claimed that these complications make a big difference at the Large Hadron Collider [LHC].
What I want to do in this article is show you evidence that the statements made about proton structure in this post are true. After all, why should you have to take my word for such things? Let’s look at some LHC data, and see how it confirms these notions (though the current understanding of the proton itself arose three to four decades ago, through numerous past experiments which would form a story of their own.)
In the more advanced article I referenced above, I described the benefits (not all of them obvious) of running the Large Hadron Collider at an energy per collision of 8 TeV in 2012 instead of 7 TeV as in 2011. And at least one of the benefits — more Higgs particles for the same number of collisions — is a consequence of there being so many gluons in the proton. I showed you evidence [reproduced here in Figure 1] that most particles in the proton carry a tiny fraction of its energy. The plot in Figure 1 is made by looking at collisions in which something like what is shown in Figure 2 occurs: a quark or antiquark or gluon from one proton hits a quark or antiquark or gluon from another proton, scatters off of it (or might do something more complicated — for example, two gluons might collide and be converted into a quark and an antiquark), with the result that two particles (again, quarks, antiquarks or gluons) come flying out from the collision point. These two particles turn into jets (sprays of hadrons) for reasons you can learn by clicking this link. And the energies and directions of these jets are observed in whichever of the big particle detectors surrounds the collision point. That information is then used to infer how much energy the collision of the original two quarks/gluons/antiquarks must have had. (Precisely speaking, the invariant mass of the two jets, times c-squared, gives the energy of the collision of the initial quarks/antiquarks/gluons.)
The number of collisions of this type that have a given energy are shown in Figure 1, with energy in GeV running along the horizontal axis. Notice that its a logarithmic plot on the vertical axis: 105 means 1 with 5 zeroes, i.e. 100,000. So there were far, far more collisions observed at lower energy than at higher energy, consistent with the statement that most particles in the proton carry a small fraction of the proton’s energy. But the data shown only go down to 750 GeV, just over 10% of the collision energy.
So let’s look at Figure 3, from the CMS experiment, which was taken in 2010, where they plotted collisions all the way down to 220 GeV. [What is plotted here --- you can ignore this unless you study the plot in detail --- is not the number of events but something slightly more confusing: the number of events per GeV, which means the number of events is divided by the width of the bin. ] You see the same effect continuing down as far as the data is plotted; the number of collisions of the type shown in Figure 2 is much larger at low energy than at high energy. And it continues to grow all the way down in energy until you can’t identify the jets anymore. There are many low-energy particles in a proton, and very few that carry a large fraction of the proton’s energy.
Now how about the claim that there are antiquarks in the proton? Three of the most spectacular processes that don’t look like the collision in Figure 1 and happen occasionally at the LHC (in one in a few million proton-proton collisions, roughly) involve the process: quark + anti-quark –> W+, W- or Z particle. These are shown in Figure 4.
The relevant data from CMS is shown in Figure 5 and Figure 6. Figure 5 shows that the rates for collisions to occur that produce (left) an electron or positron [i.e., anti-electron] and something undetected (presumably a neutrino or anti-neutrino), or (right) produce both a muon and an antimuon, are predicted correctly. The prediction is made by combining the “Standard Model of particle physics” (the equations used to predict the behavior of the known elementary particles) with the structure of the proton that I showed you on Wednesday. The big peaks in the data are due to the W particles and the Z particles produced. You see the agreement between the theory and the data is excellent.
You can see this in even more detail in Figure 6, which shows that the rates for not just these but many related measurements — most of which involve quark collisions with anti-quarks — show excellent agreement of theory and data. [How to read this: Data (red dots) and theory (blue bars) never agree perfectly just due to statistical fluctuations, for the same reason that if you flip a coin ten times you won't necessarily get heads five times and tails five times. The data points are therefore placed within an ``error bar'', a vertical red band. The size of the error bar is such that for about 30% of the measurements the error bar should like outside the theory, but only for 5% of measurements should one expect the theory and the data point to be two error bars apart.] So you see that all the evidence confirms that there are many antiquarks inside a proton. And we do correctly understand how many there are that carry a particular fraction of the proton’s energy.
Now here’s a slightly tricky one. We even understand how many down and up quarks there are as a function of the energy they carry, because we correctly predict — to an accuracy of better than 10% — how many more W+ particles are produced than W- particles (Figure 7). The ratio of up antiquarks to down antiquarks is expected (and measured) to be close to 1, but we do expect more up quarks than down quarks, especially at higher energy. Looking at Figure 2, you can see that the ratio of W+ to W- particles produced should give an estimate of the ratio of up quarks to down quarks that participate in the making of W particles. But notice the ratio of W+ to W- in Figure 7 is measured to be 3-to-2, not 2-to-1. This, too shows that the naive picture of a proton as 2 up quarks and 1 down quark is far too simple. The simplistic 2-to-1 ratio is diluted, because of all the quark-antiquark pairs inside the proton, of which there are roughly equal numbers of up’s and down’s. The amount of dilution is determined by the mass of the W particle being 80 GeV; if you made it lighter, you’d see more dilution, and if you made it heavier you’d see less, because most quark-antiquark pairs in the proton carry low energy.
Finally, let’s confirm that most particles in the proton are gluons. To do this we use the fact that top quarks can be produced in two ways: one is by quark + antiquark –> top quark + top anti-quark, and the other is by gluon + gluon –> top quark + top anti-quark (Figure 8.) Well, we know we have the number of quarks and antiquarks, as a function of the energy they carry, basically right, from all the measurements shown in Figures 5 through 7. And from this we can use the Standard Model’s equations to predict how many top quarks would be produced through quark/antiquark collisions alone. But we also believe, from previous data, that there are many more gluons in the proton, so the process gluon + gluon –> top quark + top anti-quark should be more than 5 times larger. So that makes it easy to check if the gluons are really there; if they are not, then data should lie far below the theoretical prediction.
Well, data matches the theoretical expectation just fine. And so we can confirm that, indeed, most particles in the proton are gluons carrying a small fraction of the proton’s energy.
I could go on from here; if you doubt any of these plots, I can show you dozens more that serve as cross-checks. The point that I hope I have made to you is that particle physicists’ confidence in our understanding of the proton’s structure derives from measurements like these, and from many others, not only at the LHC but also at many past experiments, stretching back decades. We’re not just making this stuff up out of our heads. We got it from the source.