# The Fifth Force of the Universe: what does the muon g-2 experiment show us? - medical - 2023

medical

## Content

- The Four Fundamental Forces and the Standard Model: Are They in Danger?
- Spin, g factor and anomalous magnetic moment: who is who?
- The spin of a subatomic particle: spins and magnetism
- The g factor and electrons
- The anomalous magnetic moment: virtual particles
- The secrets of the muon g-2 experiment
- The fifth fundamental force or new subatomic particles?

The history of Physics is full of moments that marked a revolution within the scientific world. The discovery of gravity, the development of Einstein's theory of relativity, the birth of quantum mechanics. All of these events marked a turning point. But what if we were witnessing such a moment today?

**At the beginning of 2021, the Fermilab laboratory published the results of an experiment that they had been carrying out since 2013: the now famous muon g-2 experiment.**. An experiment that has shaken the foundations of the standard model of particles and that could mean the birth of a new Physics. A new way of understanding the Universe that surrounds us.

Muons, unstable subatomic particles very similar to the electron but more massive, seemed to interact with particles that we still do not know or to be under the influence of a new force other than the four fundamental ones that we believed governed the behavior of the Cosmos.

But what are muons? Why was the Fermilab experiment, is and will be so important? What do your results show us? **Is it true that we have discovered a fifth force in the Universe?** Get ready for your head to explode, because today we will answer these and many other fascinating questions about what may be the beginning of a new chapter in the history of Physics.

- We recommend you read: "What is M Theory? Definition and principles"

## The Four Fundamental Forces and the Standard Model: Are They in Danger?

Today's topic is one of those that force you to squeeze the most of your brain, so before we start talking about muons and the supposed fifth force of the Universe, we must put things in context. And we will do that in this first section. It may seem that it has nothing to do with the topic, but you will see that it does. It has the whole relationship.

**The 30s. The foundations of quantum mechanics begin to settle**. A field within physics that seeks to understand the nature of the subatomic. And it is that physicists saw how, when crossing the border of the atom, this microuniverse was no longer subject to the laws of general relativity that, we believed, governed the entire Universe.

When we move to the subatomic world, the rules of the game change. And we find very strange things: wave-particle duality, quantum superposition (a particle is, simultaneously, in all places in space where it can be and in all possible states), the uncertainty principle, quantum entanglement and many other weird moves.

Even so, what was very clear is that **We had to develop a model that would allow integrating the four fundamental forces of the Universe (electromagnetism, gravity, weak nuclear force and strong nuclear force) within the subatomic world**.

And we did it in a (it seemed) spectacular way: the standard particle model. We developed a theoretical framework where the existence of subatomic particles that explained these fundamental interactions was proposed. The three best known are the electron, the proton and the neutron, since they are the ones that make up the atom.

But then we have many others such as gluons, photons, bosons, quarks (the elementary particles that give rise to neutrons and protons) and the subatomic particles of the family of leptons, where, in addition to electrons, are the tau and, watch out, the muons. But let's not get ahead of ourselves.

Cush, Public domain, via Wikimedia Commons.

The important thing, for now, is that this standard model serves to explain (more or less) the four fundamental forces of the Universe. Electromagnetism? No problem. Photons allow us to explain their quantum existence. The weak nuclear force? The W bosons and Z bosons explain it too. The strong nuclear force? Gluons explain it. Everything is perfect.

But don't get your hopes up. The gravity? Well, gravity cannot be explained on a quantum level. There is talk of a hypothetical graviton, but we have not discovered it and we are not expected to do so. First problem of the standard model.

And second but not least problem: the standard model does not allow to unify quantum mechanics with general relativity. If the subatomic world gives way to the macroscopic, how is it possible that quantum and classical physics are disjointed? **All this should show us how, the reign of the standard model falters, but not because it is wrong, but because, perhaps, there is something hidden in it that we cannot see.**. Luckily the muons may have helped us open our eyes.

- To know more: "The 8 types of subatomic particles (and their characteristics)"

## Spin, g factor and anomalous magnetic moment: who is who?

The time has come to get more technical and talk about three essential concepts to understand the muon g-2 experiment: the spin, the g factor and the anomalous magnetic moment. Yes, it sounds weird. It's just weird. We are in the world of quantum, so it is time to open your mind.

## The spin of a subatomic particle: spins and magnetism

All electrically charged subatomic particles of the standard model (such as electrons) have their own spin associated with them. But what is spin? Let's say (wrongly but to understand it) that it is **a twist attributed to magnetic properties**. It is much more complex than this, but to understand it, it is enough to keep in mind that it is a value that determines how a subatomic particle with an electric charge rotates.

Be that as it may, the important thing is that this intrinsic spin to the particle causes it to have what is known as a magnetic moment, which gives rise to macroscopic magnetism effects. This magnetic moment of spin is, therefore, an intrinsic property of particles. Each has its own magnetic moment.

## The g factor and electrons

**And this value of magnetic moment depends on a constant: the factor g**. Do you see how everything is taking shape (more or less)? Again, in order not to complicate it, it is enough to understand that it is a specific constant for a type of subatomic particle linked to its magnetic moment and, therefore, to its specific spin.

And let's talk about electrons. The Dirac equation, a relativistic wave equation formulated in 1928 by Paul Dirac, a British electrical engineer, mathematician, and theoretical physicist, predicts a value of g for the electron of g = 2. Exactly 2. 2.000000. Important that you stay with this. 2 means that an electron responds to a magnetic field twice as strong as you would expect for a classical rotating charge.

And until 1947, physicists stuck with this idea. But what happened? Well, Henry Foley and Polykarp Kusch made a new measurement, seeing that, for the electron, the g factor was 2.00232. A slight (but important) difference from that predicted by Dirac's theory. Something strange was happening, but we did not know what.

Fortunately, Julian Schwinger, an American theoretical physicist, explained, through a simple (for physicists, of course) formula, **the rationale for the difference between the measure obtained by Foley and Kusch and the one predicted by Dirac**.

And it is now that we will dive into the darker side of quantum. Do you remember that we said that a subatomic particle is, at the same time, in all possible places and in all the states in which it can be? Good. Because now your head is going to explode.

Julian Schwinger.

## The anomalous magnetic moment: virtual particles

If this simultaneity of states is possible (and it is) and we know that subatomic particles disintegrate into other particles, this means that, simultaneously, a particle is disintegrating into as many particles as it can. **It is, therefore, surrounded by a mass of particles**.

These particles are known as virtual particles. Therefore, the quantum vacuum is full of particles that appear and disappear constantly and simultaneously around our particle. And these virtual particles, however ephemeral they may be, influence the particle at a magnetic level, even in a very small way.

Subatomic particles do not always follow the most obvious path, they follow each and every possible path that they may follow. But what does this have to do with the g-value and the discrepancy? Well, basically everything.

In the most obvious way (the simplest Feynman diagram), an electron is deflected by a photon. And period. **When this happens, here the g-value is just 2.Because there is not a mass of virtual particles around it**. But we have to contemplate all possible states.

And it is here, when we add the magnetic moments of all the states that we arrive at the deviation in the g value of the electron. And this deviation caused by the influence of the multitude of virtual particles is what is known as anomalous magnetic moment. And here we finally define the third and last concept.

Therefore, knowing and measuring the different conformations, can we arrive at a value of g for the electron taking into account the anomalous magnetic moment and the influence of the sum of all possible virtual particles? Of course.

Schwinger predicted a G = 2.0011614. And, later, more and more layers of complexity were added until reaching a value G = 2.001159652181643 which, in fact, **it is considered, literally, the most accurate calculation in the history of physics**. A probability of error of 1 in 1 billion. Not bad.

We were doing very well, so the physicists set out to do the same with subatomic particles very similar to electrons: muons. And it was here that the countdown began to one of the most shaky discoveries in physics in recent history.

- We recommend you read: "The 4 fundamental forces of the Universe (and their characteristics)"

## The secrets of the muon g-2 experiment

The 1950s. Physicists are very happy with their calculation of the g factor in electrons, so, as we have said, they venture to do the same with muons. **And in doing so, they found something strange: the theoretical values did not coincide with the experimental ones.**. What did so well with electrons did not fit with their older brothers, muons.

Like older brothers? But what are muons? You are right. Let's talk about muons. Muons are considered the older siblings of electrons because not only are they from the same family as leptons (along with tau), but they are exactly the same in all their properties except for mass.

Muons have the same electrical charge as electrons, the same spin and the same interaction forces, they only differ in that they are 200 times more massive than them. **Muons are particles more massive than electrons that are produced by radioactive decay and have a life of only 2.2 microseconds**. This is all you need to know.

The important thing is that when, in the 1950s, they went to calculate the g-value of muons, they saw that there were discrepancies between theory and experimentation. The difference was very slight, but enough to suspect that something was happening with the muons in the quantum vacuum that was not contemplated in the standard model.

And in the 1990s, at the Brookhaven National Laboratory, New York, work continued with muons in a particle accelerator. We expect them to disintegrate almost always into neutrinos (practically undetectable subatomic particles) and into an electron, which "goes out" almost always in the direction of the "magnet" which is the muon (remember about the spin and the magnetic field), so that we can detect them and reconstruct their trajectory in order to know the precession of the muon.

Accuracy refers to the rotational movement that particles undergo when they are subjected to an external magnetic field. But be that as it may, the important thing is that if the g value of the muon were 2, the precession would be perfectly synchronized with the rotation of the muon on the throttle. Do we see this? No. We already knew, considering the electron and the anomalous magnetic moment and that in the 1950s we saw this discrepancy, that we would not see this.

But what we did not expect (it is actually what physicists wanted) is that **statistically, the discrepancy became larger**. In 2001 their results are published, giving a G = 2.0023318404. The value was still not statistically certain, since we had a sigma of 3.7 (an error probability of 1 in 10,000, something not powerful enough) and we would need, to confirm the deviation, a sigma of 5 (an error probability of 1 between 3,500,000).

We were pretty sure that the muons behaved in a way that broke the standard model, but we couldn't launch rockets yet. So in 2013, he started a project at Fermilab, a high-energy physics laboratory near Chicago, in which muons were studied again, now with state-of-the-art facilities. The muon g-2 experiment.

**And it was not until 2021 that the results were published, which showed, more robustly, that the magnetic behavior of the muons did not fit the standard model.**. With a difference of 4.2 sigmas (a probability of error of 1 in 40,000), the results were statistically stronger than those of 2001 in Brookhaven, where they obtained a sigma of 3.7.

The results of the muon g-2 experiment, far from saying that the deviation was an experimental error, confirm this deviation and improve the precision to announce the discovery of signs of rupture within the principles of the standard model. It is not 100% statistically reliable, but it is much more than before.

But why has this deviation in muon g factor been such a big announcement? Because its g-value does not coincide with the expected one with an error probability of only 1 in 40,000 makes **we're pretty close to changing the standard model pillars**.

- You may be interested: "What is a particle accelerator?"

The Fermilab facility where the muon g-2 experiment was carried out.

## The fifth fundamental force or new subatomic particles?

**We cannot be 100% sure, but it is quite likely that Fermilab's g-2 muon experiment has discovered that, in the quantum vacuum, these muons are interacting with forces or subatomic particles unknown to physics.**. Only in this way could it be explained that its g-value was not the one expected by the standard model.

It is true that for now we have an error probability of 1 in 40,000 and that to be sure of the deviation we would need an error probability of 1 in 3.5 million, but it is enough to strongly suspect that in the quantum vacuum there is something strange that it is hidden from our eyes.

As we have already discussed, muons are practically the same as electrons. They are "just" 200 times more massive. But this difference in mass could be the difference between being blind (with electrons) and seeing the light of what is hidden in the quantum vacuum (with muons).

We explain ourselves. The probability of a particle to interact with other virtual particles is proportional to the square of its mass. This means that muons, being 200 times more massive than electrons, **are 40,000 times more likely to be disturbed** by known virtual particles (such as protons or hadrons), but also with other unknown particles.

So if these muons, through this discrepancy in their g-value, they could be screaming that there is something that we have not contemplated in the standard model. Mysterious particles that we cannot see directly but that do interact with muons, altering their expected g-factor and allowing us to perceive them indirectly, as they form part of the mass of virtual particles that modify their magnetic moment.

And this opens up an incredible range of possibilities. **From new subatomic particles within the standard model to a new fundamental force** (the fifth force of the Universe) that would be similar to electromagnetism and that would be mediated by the hypothetical dark photons.

Confirming the discrepancy results in the g value of the muons may seem somewhat anecdotal, but the truth is that it could represent a paradigm shift in the world of physics, by helping us understand something as mysterious as dark matter, by modifying the standard model that we considered unshakable, by adding a new force to the four that we believed alone governed the Universe and by adding new subatomic particles to the model.

Without a doubt, an experiment that can change the history of Physics forever. **We will need much more time and more experiments to get to the point of being able to confirm the results with the highest possible reliability.**. But what is clear is that in muons we have the way to go to change, forever, our conception of the Universe.

- We recommend you read: "What is dark matter?"