The Large Hadron Collider (LHC) is a big round thing that has protons in it and the protons smash together making smaller things and then we look at the smaller things.
The LHC is arguably the best tool we have currently for discovering new particles. According to the old chestnut of E=mc2, energy can be converted into mass, and vice versa. When protons collide, the energy in the collision can be converted into new particles. The more energy you throw into the collision, the heavier the particle you can make. It’s likely that many of the particles that we haven’t discovered yet are heavier than the ones we know already. That’s why the LHC needed to be mighty big and mighty powerful, so the collisions could create new particles never before seen.
The new particles will only last a fraction of a second before decaying into more familiar ones. But by studying the aftermath of the proton collisions, we can find footprints of these undiscovered particles, therefore peeling back more layers of reality and peering in.
Figure 1: a cross-section of the ATLAS detector at the LHC. Think of the beam of protons to be coming out of the page. All the words will be explained below.
But what’s actually going on when those protons collide? And, more importantly, how can we use said aftermath to learn that juicy new physics? Before jumping into these two questions, we need a little primer about hadrons.
Tell me what a Hadron is
Yes I’ll tell you what a Hadron is. New heavy particles will often decay into hadrons, then it’s the hadrons that we detect. To explain hadrons I must first explain the colour force.
The colour force is the force responsible for holding together the constituents of the proton: quarks and gluons. Quarks are the meat of the proton, and gluons glue the quarks together. The colour force is more often called the strong nuclear force, but this is a bit of a confusing historical hangover.
There are two things I’d like you to know about the colour force:
The strength of the colour force varies depending on the energy of the particles that feel it.
Just after the big bang, the universe was extremely hot, and all the particles contained huge amounts of energy. The colour force was weak at this time. As a result the universe was made of a soup of freely moving quarks and gluons. Over time as the universe cooled, and particles started to mellow out, the colour force became strong and bounded quarks and gluons into tightly bound clumps. We call these clumps hadrons. Protons and neutrons are examples of hadrons, but there are many more kinds.
The behavior of quarks and gluons is well understood, but only at high energies. The theory describing their interactions at high energies is called quantum chromodynamics or QCD. It’s an extremely simple and elegant theory, explaining a veritable smörgåsbord of phenomena with just a tiny number of parameters and a single equation.
At low energies however, it becomes difficult to explain everything in terms of quarks and gluons, we don’t have a good understanding of how they behave in bound states. We can however forget about the quarks and gluons and just treat hadrons as the fundamental particles. The theory that goes with this is, in comparison to QCD, quite messy and unappealing. But hadrons are where the real physics is, since we can only ever do experiments on hadrons. If you want to do an experiment directly on quarks and gluons, the detector you design better be mighty small (smaller than a proton) or be able to withstand mighty high temperatures (like, literally a bajillion degrees).
There is a grey area between high energies and low energies, when it is neither right to explain things in terms of quarks and gluons, or in terms of hadrons. How exactly did the individual quarks and gluons turn into hadrons at the beginning of the universe? That is very poorly understood.
Some particles are completely immune to the colour force, so the above discussion does not apply to them. Particles like the humble electron exist as a concept no matter what energy it has. We refer to these particle that don’t feel the colour force as leptons.
Thing 2 (a consequence of thing 1)
At low energies, it is impossible to see a quark or a gluon by itself.
Say you went back to the big bang, harvested a single quark in a jar, and brought it back to the present day. As it cooled down, it would emit a whole bunch of gluons and other quarks, resulting in not just a single quark but a soup of quarks and gluons. Then, as the soup cools down, and the colour force becomes strong, all the inhabitants of the soup will bind together into hadrons. If you tried to pull one of the hadrons apart into its individual quarks, those individual quarks would just immediately emit more soup and form into hadrons again.
Figure 2: What would happen as a single quark cooled down after being transported to the current day.
You now know all the things about the colour force. At high energies, nature is described by individual quarks and gluons interacting. The colour force is weak so no binding together, no hadrons. At low energies, everything is bounded into hadrons, everything can be described by hadrons alone.
Now we can start to talk about what happens when protons collide at the LHC.
The Proton Collision
There are millions of billions of protons passing each other every second when the LHC is turned on. Most of the time they just shoot past each other, but occasionally (on about every trillionth pass), the protons will collide.
The protons are given lots of energy when they are accelerated around the ring, so when they collide, we need to be thinking about quarks and gluons rather than hadrons. Quarks and gluons from one proton will interact with quarks and gluons from the other, which produces a bunch of other particles. If you’re lucky, one of the new particles will be one that has never been seen before.
Figure 3: A proton collision involving a short-lived Higgs boson.
A new mysterious particle won’t last very long, it’ll be around for a tiny fraction of a second before it decays into something else. This is true almost by definition, a particle we haven’t seen before can’t be something that hangs around after it is produced – otherwise there would be loads of them just lying around and getting in the way.
The new particle will inevitably decay into particles we already know. These familiar particles will shoot off away from the event, and smash into one of the detectors (which we’ll get onto later). In order to work out what happened at the proton collision, we need to be able to work out what particles emerged, and their initial trajectories. More on this later.
So what will come out of the collision? Sometimes it will create leptons, the particles resistant to the colour force. These will likely travel undisturbed until they reach the detector. Since the reaction is bursting with energy, it can also create individual quarks and gluons. In this case, it can’t be as simple as a quark shooting off and hitting a detector. An individual quark could never reach the detector, as by that time it would have cooled down to low energies, and at low energies quarks are no longer a thing. Somewhere along the way, that lonely little quark must somehow become part of a hadron.
We have a single energetic quark, and before it gets anywhere near the detectors, it’s going to turn into a bunch of hadrons. As I said, the grey area between quarks/gluons and hadrons is not very well understood. We want to be able to deduce the presence of that quark from the hadrons that hit the detectors, but the presence of this grey area may give you the impression that it’s an impossible task.
Luckily, there is a something about quarks and gluons that will make this problem easy. Easyish. Consider the very first thing the quark emits: it’ll probably be a gluon. The theory of QCD can tell us the probability of the emission:
Pemission ≃ 1 / Eθ
where E is the energy inside the gluon, and θ is the angle between the two particle’s trajectories. Look at this equation a little bit and you’ll see that the most likely angle θ of an emitted gluon is very small. In other words, the gluon most of the time ends up traveling in basically the same direction as the quark. It’s also apparent that it’s most likely for the gluon to have a small energy. The importance of this I’ll get onto in a minute.
Figure 4: a quark emitting a gluon.
This won’t just apply to the first emission. Either the quark or gluon could go on to have another emission, of a new quark or a new gluon. In that case, our equation above can be used again. This will lead you to the conclusion that the vast majority of new particles will travel in the same direction as its mother, and will have a low energy.
Figure 5: A jet.
This results in some broad statements that can be made about the end products of our original quark. To start off with, all the quark/gluon soup resulting from the quark will be concentrated in a narrow beam. Since new particles in general have smaller energies, the soup quickly approaches the low energy regime where it will clump up into hadrons, and these resulting hadrons will also be moving in that one specific direction. The result is what is called a jet, a narrow beam of hadrons. The detector will eventually be hit with a bunch of hadrons all clustered in a small area.
So what about these detectors then. There are a number of locations around the LHC where detectors are placed. Each is designed slightly differently and tuned to spot different things. The largest and most famous of them is called the ATLAS experiment, so we’ll focus on that as an example and well you know, fuck the rest of them.
ATLAS is a veritable onion of detectors. It’s basically a cylinder that encloses the beam of protons with a number of layers of detectors. Each layer is a different kind of detector, specialized to detecting certain types of particle.
The only things that survive long enough to get to the detectors are hadrons and leptons. The first layer samples the energy of leptons as they interact with the electrically charged particles in the detector. Successive detectors measure the energy of hadrons as they interact with the nuclei of atoms in the detector.
It’s not just the energy of the particles we can measure, we can also work out exactly where the particle hit the detector. ATLAS can be thought of as a rather expensive 100 megapixel camera.
There are some types of particle, for example the neutrino, that are well sneaky and will shoot straight through all the detectors unnoticed. The presence of these particles can however be deduced, using a little thing called conservation of energy. We know how much energy is in the initial protons (since we gave them that energy), and we can measure the energy in all of the gunk that hits our detectors. If a neutrino escapes detection, then there will be energy missing between the initial protons and the energy measured by the detectors, from that we can deduce the presence and energy of the neutrino.
From Hadrons in the detector to Quarks at the collision
So, imagine we have measured the energy and location on the detector of a bunch of hadrons and leptons that came from the proton collision. We need to deduce exactly what happened just as the protons collided, to see if anything new and exciting happened; the production of a shiny new particle perhaps.
For leptons, it’s pretty easy to trace things back. An electron doesn’t tend to do much as it flies through space, so if we know where it hit the detector and how fast it was moving, we can just extrapolate backwards to work out how it emerged from the collision.
Hadrons are, as you now know, a different story. The detectors can receive hundreds of hadrons from a single jet. We use things called jet finding algorithms, these are an attempt to deduce what quarks flew out the collision given the hadrons hitting the detector. It is a highly not-so-easy problem, since we don’t really understand that grey area between quarks/gluons and hadrons. The original attempts amounted to just adding up all the energy picked up from some region of the detector. The most popular algorithms of recent days involve attempting to trace back the process step by step, emission by emission.
These more recent algorithms are designed according to the equation we had for probability of emission, Pemission ≃ 1 / Eθ. Hence, the algorithm decides that two particles came from the same mother particle if they are traveling in a similar direction, and at least one of them has a low energy.
Now that we’re talking about the practicalities of applying this equation, there’s something about it I didn’t bring up before that we now have to pay attention to. You may feel slightly unnerved by the possibility of a gluon coming off a quark that has zero energy (E=0). Or a tad unhinged by a gluon moving in exactly the same direction as the quark (θ=0). In either of these cases, Pemission is infinite. It doesn’t make any sense for a probability to be infinite, probabilities must be between 0 (definitely won’t happen) and 1 (definitely will happen).
If we don’t pay attention to these infinities, they will mess up our jet finding algorithms. We need to understand what is going on. There must be some deep physics reason this is happening, right?
Let’s deal with the θ=0 problem first. The situation it describes is a quark emitting a gluon moving in exactly the same direction. Due to conservation of energy, the energy contained in the final quark/gluon pair is the same as the energy that was in the mother quark. Think about this in terms of where the energy is: a little point of energy (the quark) changes into a point containing the same energy (the quark and gluon). As far as we’re concerned, this is indistinguishable from the outcome of the quark emitting nothing, since the outcome will be the appearance of a hadron in exactly the same place containing exactly the same energy. So actually, this kind of event in a sense “doesn’t exist”, we don’t need to include the possibility of this happening in our jet algorithm.
It’s a similar story for the E=0 problem. If a gluon with no energy is emitted in the woods and no one is around to hear it, does it make a sound? In this case no, that gluon can never be seen by the detectors, and it won’t ever contribute to the creation of any hadron. So that event is just the same as no emission at all.
The algorithm must be designed so that it does not take these θ=0 and E=0 possibilities into account. It’s safe for an algorithm to completely ignore these possibilities, since they don’t exist.
The deep physics shit going on here is this – some things about quarks and gluons are unknowable. As a result, thinking too hard about the quarks and gluons inside the jets themselves leads you to nonsense. Asking something like “how many gluons are inside the jet?” is a nonsense question, there exists no answer. It’s a question we can never answer with any experiment (since we can never measure a gluon by itself), and it can never be predicted theoretically. Quarks and gluons are very much mathematical concepts, while it’s only really the hadrons that have a solid physical interpretation.
How to Find the Higgs Boson
Plugging the energy and location of detected hadrons into jet algorithms, we can deduce how many quarks initially emerged from the collision, their direction of travel, and their energy. By tracing back the trajectory of the leptons that hit the detector, we can also deduce the number of leptons produced by the collision, direction of travel and energy. Our task now is to translate this knowledge into information about the collision itself.
To do this we need to ask: what possible events at the proton collision could have produced these outgoing quarks and leptons? I’ll refer to a specific combination of quarks and leptons, with some given directions and energies, as the collision’s final state. Usually there are not one, but a number of possibilities that could have resulted in our deduced final state. Some of those possible events will only include boring old familiar particles. These possibilities are referred to as background. A possibility that includes the production of an undiscovered particle is called the signal.
We can predict how often a background event will lead to our given final state, since we already understand how all the particles in a background event work. Therefore, if our final state occurs more often than we expect, this is evidence of a new particle – the signal is shining through. The final state is appearing more often than expected because there is a “new unexpected way” that the colliding protons can produce that given final state.
The probability of a given final state varies with the total energy of the final state, i.e., the energy of each outgoing particle added up. This can be seen from fig. 6. We can predict the frequency of our background events at each energy, defining the dotted curve on the plot. Most of the time the observed curve from the LHC agrees with the background curve. But if there’s a bump that cannot be explained by the background, this would be evidence of a new particle.
Moreover, the energy at which the bump appears is important. To see this, consider that the probability of the final state occuring will be roughly proportional to the number of different ways the final state can be created. The creation and destruction of a new particle represents a new way that the final state could be created, so, when the right amount of energy is involved to make the new particle, the probability of the final state increases.
From fig. 6, it looks like there’s an “extra way” to create a final state of energy 125GeV, this extra way is a new particle being created and destroyed. Via E=mc2, we can work out what mass the new particle would need to have to create a final state of that energy. By dividing 125GeV by c2, one can find the mass of this new particle. The numbers I’ve chosen here lead us to the Higgs mass, since this is how its mass was deduced.
Figure 6 is essentially a cartoonist impression of one of the plots used to discover the Higgs. You can have a look at the real plot in the original discovery paper, on page 10, figure 4.
The discovery of the Higgs was a huge success, but the search for new particles at the LHC is far from over. Physicists are still squinting away at plots like the above, hoping to find the next bump.