Seeking for a fifth force at the CERN Large Hadron Collider

Elementary particles are known to interact via three fundamental interactions, namely the strong force, the weak force and electromagnetism. The fourth fundamental interaction, gravity, is left apart in the miscroscopic world, as totally negligible.

However, physicists like to consider options for new interactions. And since ‘more than four’ starts with ‘five’, I will discuss in this post how a fifth force is searched for at the Large Hadron Collider, the LHC, at CERN.

Why do we have only four fundamental interactions? We actually do not know, and there could actually be more than four of them. The extra ones would be just hiding.

Physicists therefore try to find some proofs (i.e. facts) about the existence of a new fundamental interaction. For the moment, all searches however indicate that there is not a single sign of such a new force.

The latter is therefore more and more constrained experimentally, but the hunt is not over!

I will explain below how new forces are searched for at the LHC.

But before, I will go back to some basic stuff. If you feel comfortable with that, please go directly to the last section of this post.

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ELEMENTARY PARTICLES - A SHORT DEFINITION

Before starting to discuss the world of the elementary particles, it is good to define what it is.

The fundamental world is comprised of three types of particles. We have the particles that belong to what is generically called the matter sector, the particles connected to the mediation of the fundamental interactions and the Higgs boson.

I will restrain myself from entering into any nasty detail, as this is not the topic of this post. I however recommend this older Steemit article of mine for more information. A summary is provided below.

_{[image credits: homemade (from stuff available everywhere)]}

The particles of the matter sector consist of the particles that are the basic building blocks of matter. We focus of course on the smallest bits of matter, that are the up and down quarks and the electrons.

Up and down quarks (rightmost part of the above picture) are the constituents of the protons and neutrons (middle part of the above picture), and neutrons and protons make what is known as atomic nuclei (for example, the core of the atom on the leftmost part of the above picture). Finally, atoms (leftmost part of the above picture) are made of their nucleus, as well as some orbiting electrons.

On top of this, we need to include neutrinos that play a big role in the weak interactions.

The first generation of fundamental objects is made of the most basic objects introduced above: the up and down quarks, the electron and the associated neutrino.

Nature however likes to have fun of us and decided to multiply all of this by three. Three copies are better than one.

If you know why, this is for you! I personally do not know why.

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THE THREE FUNDAMENTAL INTERACTIONS (THAT WE CARE ABOUT)

So we have 12 basic particles (3 copies of 4 guys), as said above, that interact via three of the fundamental interactions, as also said above.

The way to model those interactions is to use the concept of gauge symmetries. I will once again ignore all details and provide a summary below.

_{[image credits: Particle Zoo]}

What is important to know is that two particles are said to interact when they exchange a gauge boson. The gauge bosons are by definition the particles responsible for the implementation of the interactions in the quantum world.

Having one interaction means that one or more gauge bosons have been exchanged.

We have a bunch of these gauge bosons in the Standard Model, namely the photon (electromagnetism), the W-boson and Z-boson (weak interactions) and the gluons (strong interactions). For instance, an electron and a positron are said to interact electromagnetically if they exchange a photon.

In the case of a fifth force, an extra boson is hence needed.

I will omit from the discussion anything about the Higgs boson. For more information, I refer to here.

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SEARCHING FOR EXTRA INTERACTIONS

After this very long introduction, you now know how extra interactions work in particle physics: they work in the same way as the three other interactions. Particles will interact by exchanging a new boson that is associated with the extra interactions.

Therefore, in order to look for a new force, it is sufficient to look for the corresponding boson. There are thus numerous searches for extra bosons at the LHC, at CERN.

These searches rely on the fact that quarks and leptons (i.e., electrons, muons, taus and neutrinos) interact via the new force. This assumption leads to two important points.

First, we can produce the new boson at the LHC, as the colliding protons are made of quarks. Second, a produced new boson can decay into quarks or leptons.

It is thus sufficient to look for the final-state products to reconstruct the presence of an intermediate extra boson.

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DISCUSSION: A PRACTICAL EXAMPLE

More precisely, let us pick up an example: a pair of muon-antimuon.

In the Standard Model, a muon-antimuon pair can be produced via weak and/or electromagnetic interactions. One of the quarks from one of the colliding protons collides with one of the antiquarks from the other proton. This gives either a photon (electromagnetism), or a Z-boson (weak interactions), that then decays into a muon-antimuon pair.

We can measure the mass of the system made of the muon and the antimuon. In the boring case where nothing new exists, the probability to get a large mass is smaller and smaller with the mass value.

This is illustrated on the figure on the right where the mass of the muon-antimuon pair lies on the x-axis, and the rate to produce a pair of particles with a given mass is shown on the y-axis.

But then, what is this bump in the middle that seems to ruin my explanation? Such a bump is connected to the existence of the Z-boson: it lies exactly at the mass of the Z-boson on the x-axis.

Anywhere else, the intermediate photon or Z-boson is actually virtual. This can be seen as disturbance in the quantum fields that are the real stuff behind all of this. In other words, the intermediate state does not exist but quantum field theory makes the process is possible.

Now, in the case where we would have a fifth force, we just should see another bump.

Here we are! Now you know how extra forces are searched for at the LHC! It is done with electron-positron pairs, muon-antimuon pairs, tau-antitau pairs, jet (objects originating from a quark-antiquark system) pairs, etc.

The absence of any bump for all existing searches means that either there is no fifth force at all, or the boson is heavier so that the LHC cannot probe it. Or, the boson must be stealthy. This will be the topic of another post (this one is already long enough) :)

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