I spent part of last week at a meeting in the Pyrenees, northern Spain, discussing the internal structure of the proton. The meeting was in the small village of Benasque, hosted by Juan Rojo at the Centro de Ciencias de Benasque Pedro Pascual.

The proton (my favourite particle) is the nucleus of a hydrogren atom, is useful for curing some cancers, and is the particle collided by the Large Hadron Collider as it extends the frontiers of our knowledge of the structure of matter. Protons are made of two up-quarks and a down-quark, but there is quite a lot more than that to discover about their internal structure.

Most what we know about proton structure comes from the scattering of electrons off protons. Electrons and quarks are both electrically charged, so they repel or attract each other, depending whether the quark in question is positively or negatively charged (the electron has negative charge). By measuring how often, and with what energy and angle, electrons scatter off protons, we can work out several things. Firstly, we can tell the proton is not fundamental; it has something inside it. Consider this sketch:



A pointlike proton

This is a rough sketch of what we might see if the proton was fundamental - infinitely small and with no internal strucure. The vertical axis (labelled σ, “sigma”) is proportional to the number of times an electron-proton scattering happens, and the horizontal axis (x) is the fraction of the proton which the electron “saw”. If the proton is fundamental, this is always one, hence the spike at unity.

This is not what happens. We see evidence for three quarks inside the proton. So you might expect this:

Three quarks

... with the spike moved down to x = 1/3, one third, because each quarks carries a third of the momentum of the proton.



(The horizontal axis is a logarithmic scale, for reasons which will become clear, which is why x = 1/3 appears closer to 1 than it would on a linear scale. This also means the label “0” only applies to the vertical axis. The x axis runs from something like 10⁻⁵ to 1).



This is not what we see either, though.

The quarks are not moving independently, each constituting 1/3 of the proton. They are bound together in a small radius - the size of the proton. This means we know something rather precise about their position (it is inside the proton!), and that in turn means that, as described by Heisenberg’s uncertainty principle, their momentum, and so x, must be somewhat uncertain, somewhat spread out. Like this:

Three quarks confined a proton

This is getting closer to what we really see, but there is one more step. Quarks can, and do, radiate gluons all the time. In fact gluons, which carry the strong force, are the reason quarks are bound together inside the proton in the first place. When a quark radiates a gluon, the gluon will carry away some momentum, lowering the momentum of the quark. But gluons have no electrical charge so the electron does not “see” them directly. This means the whole momentum, and thus, x, distribution gets shifted to lower values like this:

Three quarks in a proton, emitting gluons

(The logarithmic scale I mentioned earlier is just chosen to allow us to see the rise at low x more clearly. )



In fact, the more closely you look, the more gluon radiation you see, and the bigger the shift. Here’s is some actual data on proton structure:

Proton structure Photograph: HERA/H1/ZEUS/H1 experiment, DESY



Don’t worry that the vertical axis is labelled “F₂”, it is essentially the same thing we were looking at in the sketches. You can see the strange shoulder and steep slope, which is all that remains of the spike at x = 1/3. The labels in the bottom right corner are just telling you which experiments the data come from. The “Q²” label on each of the three plots is the resolution with which the proton is being studied. As it rises from 0.5 to 7 GeV², you can see the rise at low x getting stronger, and the remains of the spike that started at x= 1/3 getting more and more washed out to lower x, as it becomes possible to resolve the quarks after more and more gluons have been radiated from them.



Using such data to extract precise information about the distribution of quarks and gluons inside the proton - much more precise than my sketches, and with properly evaluated uncertainties - was the topic of the meeting, and lots of the world experts were there.



It was a small, useful and fun gathering in a lovely setting, and there was even a chance to ski. Here’s our group photo, but what you can’t quite see is how much my ribs are twingeing, as indeed they do still, due to a mishap on a strangely-shaped slope not too disimilar to the proton structure distribution above. Not that I deserve, or expect, any sympathy, you understand.



Jon Butterworth has written a book about being involved in the discovery of the Higgs boson, Smashing Physics, available here, and in North America as “Most Wanted Particle”. Some interesting events where you might be able to hear him talk about it etc are listed here. Also, Twitter.

