The g-2 Experiment: Why a Fifth Fundamental Force is a Stretch of Reasoning

Figure 1: The 50-foot-wide G-2 detector that was used in Fermilab’s experiment.

Source Credit: Fermilab News (LINK)

What is everything made of? Surely, most people would have learnt in their chemistry classes that we are made up of atoms (originating from the Greek word atomos, meaning “indivisible”)—the so-called “fundamental units of matter.” This to some extent, is true; however, its namesake indivisibility is incorrect. Ever since the advent of quantum mechanics in the early 1900s, scientists have built upon what is now called the standard model of particle physics. This model suggests that a small number of elementary particles not only constitute everything in the universe, but also mediate all the interactions between each particle. Each of these elementary particles are related to its quantum field, in that each particle is merely an excitation in their respective fields. The framework delineating the interactions between elementary particles within these fields is called quantum field theory.

Figure 2: The Standard Model of Particle Physics.

Source Credit: Wikipedia User Cush, Individual Work (LINK)

As can be seen in the diagram above, the elementary particles are mainly divided into the fermions and the bosons. The fermions are generally thought of as the constituents of matter, while the bosons are the mediators of force (the Higgs boson is a bit special, but more on that later).

The fermions are further subdivided into the quarks and leptons. Quarks are the particles that constitute the nucleus of an atom and interact via the strong force, while leptons are those that reside outside the nucleus, and interact via only the electromagnetic and weak forces. The fermions can also be subdivided into different generations. Each subsequent generation is composed of elementary particles with relatively greater mass and shorter lifetimes. For example, the electron, a first generation lepton, has a mass of 0.511 MeV/c^2 and a lifetime of 6.6 × 10^28 years. The tau, a third generation lepton, has a mass of 1776.86 MeV/c^2 and a lifetime of 2.9 × 10^-13 years.

There are five types of bosons— gluons, the mediators of the strong nuclear force; photons, the mediators of the electromagnetic force; and the z0 and w± bosons, which are the mediators of the weak nuclear force. The fourth fundamental force, gravity, is not yet accounted for by the standard model. If there were indeed a fifth fundamental force, it would imply that there is another class of bosons mediating that force. The last boson—the Higgs—is very crucial to the model in that every particle is able to be imbued mass by interacting with the Higgs field. All the elementary particles have an antimatter counterpart (some bosons are antiparticles of themselves), but this discussion is mostly irrelevant to the topic at hand.

What is relevant, though, is the second generation lepton, called the muon, denoted by the greek letter μ (mu). These particles are quite similar to the electron as they have the same charge of -1 and spin of ½. However, it has a greater mass, and much shorter mean lifetime of only 2.2 microseconds. After living its lifetime, a muon decays into an electron, an electron antineutrino, and a muon antineutrino. What the G-2 experiment at Fermilab was to measure the anomalous magnetic dipole moment of the muon. But what is an anomalous magnetic dipole moment?

When an elementary particle displays quantum spin, it generates a dipole magnetic field (a magnetic field with a north and a south pole). When such a particle is thus placed into another magnetic field, it rotates in order to align with that magnetic field. This aligning torque (or rotating force) on the particle is what is known as its magnetic moment.

Now, due to quantum effects, each elementary particle is imbued with a g-factor, which is a kind of constant of proportionality between its magnetic moment and another quantity required for calculation of the magnetic moment (more specifically, the charge of the particle multiplied by angular momentum and divided by 2 times its mass)and this g-factor can be precisely calculated with our theory of the standard model.

The g-factor can be calculated in two ways: by using the Dirac equation (which only accounts for the simplest quantum interactions between a particle and a magnetic field) or by taking into account more diverse quantum interactions the particle may have with the field.

The g-factor of the muon, calculated by the first method, turns out to be 2, and by the second method, 2.001159652181643. The difference between these two numbers is defined as the anomalous magnetic moment.

However, it turns out that the anomalous magnetic moment measured by the recent Fermilab experiment deviates from the estimated anomalous magnetic moment. Furthermore, the results show a confidence level of about 4.1 sigma - that is, there is a “1/40000 chance that the result could be a statistical fluke”, according to BBC.

This interesting result led scientists to believe that maybe our current standard model is incomplete. While some scientists believe that the results of the experiment may have been disturbed due to the chance of muons interacting with other, rarely-occurring virtual particles (a short-lived quantum fluctuation), others believe that the results may hint at the existence of a fifth fundamental force. However, there is currently no solid reason for which we should blame this deviation on a fifth fundamental force. All we know through this experiment is that if its results are correct, then our standard model or our process of deriving a theoretical estimate for the anomalous magnetic moment of an elementary particle must be flawed in some way. In either case, the results of Fermilab’s g-2 experiment calls for more research into the anomalous magnetic moments of diverse elementary particles.

Q&A Section

• Jiwon: Given that you included both the possibility of the existence of a fifth fundamental force and there being an error caused in the experiment, what is your personal take on the situation? More specifically, which of the two sides do you support?

Personally, I think that while it is definitely possible that there exists a fifth force dominating these phenomena, it is too early to suspect so. Logically speaking, an experimental error due to the muons’ interactions with a virtual particle is more plausible, in that the prediction is based on what we already know. If indeed the statistical results were without error, all we know is that our standard model is incomplete, or that our fundamental conception of the universe is flawed in some way - we haven’t yet enough evidence to blame this deviation on a fifth force.

• Sally: If this new discovery can be further researched and possibly confirmed, what kind of changes can we expect? What is the significance?

If this research proceeds, then we would be able to find the missing bits and pieces of our standard model. And the better our theoretical framework of the world, the easier it is to technologically develop. Thus, this research would be the first step in refining our perception of the universe, and a door to a chance to develop.

• Eric: In layman terms, how would the fifth force affect our daily lives, and what is the best way it can be incorporated into the Standard Model?

Even if the fifth force is discovered, our daily lives wouldn’t change that much, given that we have survived without even noticing it. However, in cases in which its effect is significant, we would need to be careful of the dangers the fifth force poses. If the fifth force indeed exists, then hopefully it would be in the form of one or two additional bosons in our standard model; however, we are unsure of that as of now.

• Xavier: What exactly is this fifth fundamental force from a conceptual standpoint?

A fifth fundamental force would be simply a different type of interaction between certain fermions. And this force most likely would be mediated by a boson or two.

• Hannah: Based on your article, it seems possible that a fifth force does exist, as the results of the experiments had high confidence levels. What are some factors that are stopping the scientists from concluding that the force exists?

First, when approving of experimental findings, the confidence levels of the results must reach 5 sigma. 5 sigma indicates that if indeed our null hypothesis is true (that is, if the muon’s anomalous magnetic moment matches that predicted by our theories), there is a 1 in 3.5 million chance that we get such an extreme set of data results from the experiment.

• Wooseok: Considering how the fifth force is a controversial topic, what are some claims made by the opposing side that refutes its existence?

As mentioned before, what the scientists suspect, and hope is that the muons, by chance, interacted with some virtual particles, that may have caused a large deviation in the results. While there is no direct evidence refuting the existence of a fifth force as of now, we need a more reasonable explanation as to why this might be the case.

Works Cited

Ghosh, Pallab. “Muons: 'Strong' Evidence Found for a New Force of Nature.” BBC News, BBC, 7 Apr. 2021, www.bbc.com/news/56643677.

Martin, B. R. Nuclear and Particle Physics an Introduction. John Wiley & Sons, 2009.

Still, Dr Ben. Particle Physics Brick by Brick. Octopus Publishing Group, 2017.

Martin, Bruno. Fermilab's Muon g-2 Experiment Officially Starts Up, news.fnal.gov/2018/02/fermilabs-muon-g-2-experiment-officially-starts-up/.

“File:Standard Model of Elementary Particles Anti.svg.” Wikimedia Commons, commons.wikimedia.org/wiki/File:Standard_Model_of_Elementary_Particles_Anti.svg.