The Muon G-2 experiment

The Natural Sciences usually work like this; someone uses their current knowledge and observations to come up with a theory. This may consist of explanations, mathematical equations and computational models, but the key is this theory can be used to predict things. An experiment is then designed to test this theory, and uses it to predict the result of the experiment. If they agree, then this theory can continue being used (for now) but if they disagree, then the theory must be incorrect or not encapsulate the full structure of the universe. There is thus a continual process of theory and experiment, and this is what, according to the philosopher Karl Popper separates science from pseudoscience. For something to be a scientific theory, it must be falsifiable. This also tells us that, philosophically speaking, we can never know the whole truth about science and the universe. After Newtonian Mechanics, we thought Physics was complete, but we couldn’t have been more wrong. This article concerns another such example where a new experiment does not seem to match up with theory.

The experiment we discuss today is the Muon G-2 experiment, which shifted paradigms in Particle Physics, and hinted at a new fundamental force.

The Muon is essentially a heavier sibling to the electron, and is the same as an electron in every property other than mass. It’s interesting to study Muons in magnetic fields specifically because their mass makes them sensitive to quantum phenomena and due to spin angular-momentum they seem to have a magnetic moment. For the purpose of this article, we can say that this magnetic moment is analogous to a spinning internal bar magnet that interacts with magnetic fields. The value “g” (not the gravitational constant) is essentially a measure of the gyromagnetic ratio, which is the ratio of a particle’s magnetic moment and its spin.

From our 1935 view of Quantum Mechanics, this ratio can be calculated to be exactly 2, although this was based on a very basic theory of Quantum Mechanics. A similar experiment in 1948 took place which proved that there were some Quantum Phenomena we were not aware of, and this is what led to the rise of Quantum Electrodynamics (QED). QED theorised the existence of virtual particles — pairs of matter and antimatter particles popping into and out of existence that exist everywhere, even in vacuums. Energy can be converted to these matter-antimatter pairs which almost instantly annihilate. These virtual particles can affect the interaction of a muon with its magnetic field, and this is what was said to have caused that excess (this is even more apparent in a muon due to its heft, 207 times the mass of an electron making it much more sensitive to these virtual particles). Now what the latest Muon G-2 experiment says is, even this theoretical value is incorrect! The value of g is quite significantly (in experimental physics terms) greater than the value predicted by our theoretical notions of QED, thus hinting that there is definitely something about the nature of the standard model that we’re missing, and the most popular (but not necessarily true) theory is that this discrepancy between theory and experiment hints at a 5th fundamental force, outside of the strong, weak, electromagnetic and gravitational forces.

Now, another interesting question to ask about this experiment is how exactly it worked, and how we could measure it truly so precisely. It all starts off with a proton beam. 12 times per second, particle accelerators smash a bunch (around 10¹² particles into a target which creates different types of particles. Some of these particles are pions (a part of the meson family, mesons are quark-antiquark pairs and are thus incredibly unstable, decaying very rapidly). Pions quickly decay into muons with completely aligned spins, and powerful superconducting magnets steer these pions and muons into a triangular tunnel called the Muon Delivery Ring. This is a measure to ensure all pions decay into muons creating a nice muon beam, which is then transferred to a storage ring.

The muons now begin their orbit around the storage ring, a ring shaped ultra-powerful electromagnet with a diameter of 50 feet. They travel around the ring at close to the speed of light, and modelling these muons as bar magnets, they will rotate around the magnetic field.

These muons in turn decay into neutrinos and positrons. Neutrinos are virtually undetectable particles (though, of course we do have experiments to detect them, but are useless in this case) but positrons, the antimatter equivalent of electrons travel in the same direction as the muon’s internal bar magnet was pointing at the point of decay. We can study the number of positrons at a particular moment in time to find the gyromagnetic ratio and this gives researchers information about the precession of the muon.

That was essentially the entire Muon G-2 experiment explained at its simplest level, but the engineering and physics intricacies that make this experiment so incredibly precise and make the system tick are incredibly interesting to look into, and Fermilab, the organisation that conducted this experiment, have made a large collection of videos diving into the very fundamentals of each part of the experiment and how it works.

Sources (might harvard reference?)
https://physicstoday.scitation.org/doi/10.1063/1.1688069

https://mriquestions.com/gyromagnetic-ratio-gamma.html

https://muon-g-2.fnal.gov/the-physics-of-g-2.html

https://muon-g-2.fnal.gov/how-does-muon-g-2-work.html

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Aditya Khanna

Aditya Khanna

I'm interested in Physics, Philosophy, Computer Science and Electrical Engineering and this documents some things I've explored for fun or for a competition.