ALICE has just submitted its fourth paper, on the anti-proton to proton ratio in p+p collisions, to Physical Review Letters. This is a really cool measurement because it is one way of quantifying how many of the particles we create in our collisions – as opposed to how many of the particles we see are remnants of the beam.
A proton has three valence quarks, two up quarks and one down quark. The proton’s electric charge is +1. An anti-proton has three valence anti-quarks, two anti-up quarks and one anti-down quark. The anti-proton’s electric charge is -1. The anti-proton is the proton’s anti-particle. When a proton and an anti-proton come together, they annihilate.
A baryon has three valence quarks – examples are protons (two up quarks and a down quark) and neutrons (two down quarks and an up quark). There are many more exotic baryons – my favorites are the Λ (an up quark, a down quark, and a strange quark) and the Ω (three strange quarks) . A proton is a baryon, while an anti-proton is an anti-baryon. Baryon number is the net number of baryons in a system and it is conserved in all processes we have observed in the laboratory. In our p+p collisions, the baryon number is 2 because there are two incoming baryons. Because the anti-proton is an anti-baryon, it had to be created in the collision. Moreover, because there were no (net) anti-quarks in our incoming protons, all three anti-quarks in any anti-proton we see had to be created in the collision. If we just look at protons, we can’t tell if they were created in the collision or if they are remnants of the beam.
Since anti-protons don’t exist prior to collision, one way of quantifying how many particles were created in the collisions, as opposed to how many are beam remnants, is their ratio. If this is near zero, most of the particles we observe are remnants of the beam. If this is near one, most of the particles we see were created in the collision. At low energies, the anti-proton to proton ratio is closer to zero, but we expect it to be almost one at LHC energies. Here you can see the collision energy dependence of the anti-proton to proton ratio (Figure 4 of the new paper):
The y-axis is the anti-proton to proton ratio. The upper x-axis is the center-of-mass energy of the collision. The different data points are measurements from different experiments. The line shows a fit to the data. The lower y-axis is a little more complicated – I’ve put an explanation below, but you can skip it and just look at the top x-axis. You can see that the anti-proton to proton ratio is very close to one at LHC energies. But of course, we have to quantify how close the anti-proton to proton ratio is to one. Specifically, we measured it to be 0.957 ± 0.006(statistical) ± 0.014(systematic) at 0.9 TeV and 0.991 ± 0.005(statistical) ± 0.014(systematic) at 7 TeV. Most of the work went into determining the uncertainty. We could reduce the statistical uncertainty by just taking more data, but the systematic uncertainty is limited by the method and the experiment.
What do we learn from this measurement? It helps us test and refine our understanding of baryon production in proton-proton collisions. We can compare to models for proton and anti-proton production and this lets us constrain some models and exclude others.
To give a feel for how complicated it can be to do the measurement, I’ll explain one of the details that has to be considered to do this measurement right. If we see an anti-proton, we’re pretty sure it was really created in the collision. But we have billions and billions of protons in our detector. A very fast particle created in the collision could knock a proton out of our detector. If we measure a proton, how can we be sure that it didn’t come from our detector? We have accurate enough charged particle tracking to see where the proton came from. This figure (Figure 2 from the paper)
shows the distribution of the distance of closest approach (dca) of protons and anti-protons to the collision vertex. Real protons and anti-protons created in the collision will mostly be close to the collision point (near a dca of 0), so this shows up as a peak around a dca of 0. Our largest background is from protons knocked out of the beam pipe by a fast particle created in the collision. These protons don’t get close to the collision vertex – their dca is larger. This is why the proton peak on the left sits on top of a plateau. But we can’t knock anti-protons out of the beam pipe – so we don’t see the same plateau under the anti-proton peak. Protons knocked out of the beam pipe will also be slower on average than protons created in the collision. This is why we see the plateau from protons knocked out of the beam pipe on the left (for protons with momentum p≈0.5 GeV/c) but we don’t see it on the right (for protons with roughly twice the momentum, p≈1.0 GeV/c). To get an accurate anti-proton to proton ratio, we have to subtract off the protons knocked out of the beam pipe. We can tell where particles travelling practically at the speed of light went to within a few mm – and we need to in order to do our measurements.
Isn’t that cool? ALICE is a wonderful detector!
Explanation of the lower x-axis of the anti-proton to proton ratio plot:
This is the difference between the beam rapidity, y, and the rapidity where the measurement is done (|y|<0.5). You can calculate the beam rapidity using
y = 1/2 ln((E+pz)/(E-pz))
where pz is the momentum along the beam axis and E=√(E2+m2) is the total energy. If you plug in the numbers, you’ll see that the beam rapidity is about 7.6 for 900 GeV and about 9.6 for 7 TeV. I have fudged over a detail, which is that it matters where we do the measurement. If we look closer to the beam axis, we’ll see a lower anti-proton to proton ratio and we’ll get the highest anti-proton to proton ratio at rapidities close to zero (roughly perpendicular to the beam axis).
The Bohr model isn’t exactly right – but it’s close enough to get some feel for what’s going on. In a more precise quantum mechanical picture, the electron isn’t actually orbiting the nucleus – it’s smeared out in what we call a 
