It has been an interesting summer for particle physics. The first results from the current higher-energy collisions at the Large Hadron Collider (LHC) have seen the light of day. If you have been following the experiment you may know that the energy of the proton beams has been increased from 4000 GeV to 6500 GeV (a GeV is a billion electronVolts), giving a collision energy of 13000 GeV. But also interesting have been some of the refined results which are still being produced using the earlier data, recorded between 2010 and 2012.



Total cross section

As a physicist, one of the first things you might like to know when you fire protons at each other is how likely they are to hit. This is expressed as a “cross section” in physics. By analogy with the fact that large objects present a bigger area to hit than small ones, a larger probability for a collision means a larger cross section. The ATLAS collaboration have produced a first, preliminary measurement of how likely 6500 GeV protons are to hit each other and break up - the inelastic cross section.



The inelastic cross section versus the centre-of-mass energy. The ATLAS measurements based on the Minimum Bias Scintinillator detector are shown after extrapolation to the full inelastic cross section. Measurements from experiments at other colliders, other LHC collaborations and the Pierre Auger collaboration are also shown. Some of the LHC data points have been slightly shifted in the horizontal position for display purposes. The data are compared to various theoretical predictions. The uncertainty on the ATLAS ALFA measurement is smaller than the size of the marker. Photograph: ATLAS/CERN

The horizontal axis is the collision energy in GeV. The units on the vertical axis are millibarns. A barn is a unit of area, supposed to be something big and easy to hit (as in “barn door”) and is roughly the cross-sectional area of a Uranium nucleus - 10-28 square metres, or one ten billion billion billionth of a square metre. Pretty small by everyday standards, and millibarns are 1000 times smaller than that.



It is quite hard to make protons hit each other then, because they are so small. Notice that the cross section increases with energy though. In some sense the area the protons present to each other gets bigger as the energy increases. This makes life marginally easier for the accelerator at high energies (to set against lots of other things which get more difficult).



The rise in the cross section is usually explained in terms of the exchange of a mysterious composite object called a Pomeron, which only exists in such exchanges, and is presumbly an emergent feature of the fundamental strong force, which is what holds the proton together. Connecting this Pomeron business with the fundamental quarks and gluons of the strong force is an outstanding problem in particle physics. To be honest it’s not clear these data will help solve it really, but at least we know now that the rise carries on up to 13 TeV.

Extrapolation



The new ATLAS datapoint at 13 TeV has quite a large uncertainty, shown by the error bars. A lot of that uncertainty is because the LHC luminosity isn’t very well known yet - that is, we don’t know exactly how many protons are in the beams. But another big component of the uncertainty is hinted at by the words “MBTS, extrap.” on the legend of the plot. This means that the measurement is derived from signals in the Minimum Bias Trigger Scintillators, small detectors that fire when they are hit by the debris from a broken-up proton. Unfortunately they only sample a fraction of the debris, so to measure the total inelastic cross section, we have to use some theory to fill in the gaps. That theory has big uncertainties.



You can see that the “ATLAS ALFA” datapoint, and the TOTEM datapoint, have much smaller errors. These measurements use detectors very close to the LHC beam, a few hundred metres downstream from ATLAS and CMS respectively, and because they can directly detect protons which scatter gently and don’t break up, they can use a clever trick to make a measurement which not only does not require extrapolation, but is also independent of the luminosity.



Since the LHC is the highest energy particle collider in the world, you may wonder where the measurement on the far right, at even higher energies, comes from. This is from the Pierre Auger Obervatory, measuring collisions of super-high energy protons bombarding the upper atmosphere. The uncertainities here are even bigger, again in large part because only a fraction of the debris is seen and extrapolations are needed.



This extrapolation issue is very common in particle physics, and is worrying, since it explicitly builds into the experiment a - sometimes substantial - dependence on the theory. We hate that.



Minimising it is a challenge. The best way to do it is to build better detectors, which cover more of the space that the collision debris can fly into. But usually 100% coverage is impossible, so what then?

Top cross sections



A couple of new measurements from ATLAS and CMS, made with the “old” 2012 data, give a good example of progress in that direction. These are measurements involving top quarks. The top quark is the heaviest fundamental particle we know of - about 175 times as massive as the (non-fundamental) proton, and about 40% heavier than the Higgs boson. This makes it an interesting thing to study for various reasons - the top quark plays a special role in many theories which try to extend and improve the “Standard Model” of particle physics.



Both ATLAS and CMS have already measured the probability of producing a top quark and top anti-quark together at the LHC, again expressed as a cross section. The 13 TeV results were released a week or two ago, and the ATLAS one is shown here:

Top pair production cross section at the LHC and at lower energies Photograph: ATLAS/CERN

Note this is in picobarns, a billion times smaller than the millibarns for the total cross section. The chance that a pair of protons will collide to produce a top is a small fraction of the total chance of them colliding in the first place.



The error bar looks much smaller than the uncertainty on the total cross section, but that’s an illusion coming from the fact that the vertical scale is logarithmic. It’s actually about the same, proportionally, as before, and again comes largely from the uncertainty in the luminosity and from the extrapolations needed.



The extrapolations here are less dramatic on the one hand, because top quarks have a lot of mass, so when they decay it is rather likely that the pieces hit the detector. But they are subtly different too, because we can’t actually measure quarks directly. Generally quarks are not free - they are always bound inside hadrons (such as the proton, for instance). In fact the top quark decays to a W boson and a bottom quark even before this happens. The W then also decays, and the bottom quark binds into a hadron. It is the eventual products of all this that we see in the detector¹. Extrapolating backwards, from what we measure to a top quark, brings another set of theoretical uncertainties.



A new hope²



There is hope for better though. ATLAS and CMS have also produced a new style of measurement. When you have enough collision events and a good enough detector, you can define a measurement which minimises these kinds of extrapolations.



First of all you only measure in the regions where your detector is able to see things - we call this a “fiducial”, rather than a total, cross section.



Secondly you define the measurement not in terms of the top quark, which is an object only really defined in the theory, but in terms of the products of the top decay - the hadrons, electrons and muons etc that actually hit your detector. This is often called a “particle level” measurement.



In addition, if you have enough data, you can measure how such cross sections change as a function of the event kinematics - momentum and so on. This is differential cross section. This makes for a really good way of interrogating the theory - which of course has to be good enough to predict these new kinds of measurements - and seeing if there is anything unexpected going on.

This is a new step forward for top quark measurements. This article probably has enough plots in it already, but if you are keen to see them, they are here, here and here³. Already there are some interesting features, with the data showing the cross section falling slightly faster than expected as the transverse momentum of the top increases. And the uncertainties in the fiducial, particle-level measurement are significantly smaller than those in the equivalent measurement extrapolated back to the top quark, because the input from theory is reduced.



I find the principle involved rather exciting (ok, I am a specialist), and reducing the theory that is built into our data is important and satisfying. I think this is the way things will go in the future, now that the high quality of the theory and the detectors make it more feasible than it was previously.

¹ Or don’t see, in those cases when a neutrino is produced.

² Though quite new in top physics, it’s not strictly that new in general. But somehow this seemed like a good title for the fourth sub-heading.



³ The latest of them were shown for the first time by Jean-Francois Arguin and Susan Dittmer at the Boost meeting I went to recently.

Jon Butterworth’s book Smashing Physics is available as “Most Wanted Particle” in Canada & the US and is on the shortlist for the Royal Society Winton Prize for Science Books. He is also on Twitter.



