The Muon g-2 experiment:what it is and why it matters

The Muon g-2 experiment was an experiment conducted by Fermilab whose results were published in April, 2021. Read on to find out what they did in the experiment and the results.
What is Fermilab?
Fermilab, situated in Illinois in the USA, is a particle physics and accelerator laboratory1.

Image 1- Fermilab in the USA
What are muons?
Muons are elementary particles(Particles that are not composed of anything else). Muons and electrons are very alike except that the muon has a mass 207 times that of the electron2.
Mμ = 105.7
Me = 0.511
= 206.843
Masses are in the unit MeV(Mega electron Volt)
Muons have a lifetime of about 2.2 microseconds(2.2× 10-6s), which though is very short, is longer than many subatomic particles. The tau lepton(The tau lepton and muons are part of the same group of particles called leptons) and neutral pion for example, have lifetimes of 2.9×10-13s and 8.4×10-17s respectively4. Pions are mesons( a particle containing one quark,one of the fundamental units of matter, and an antiquark, which is something like the opposite of a quark differing only in a few properties such as electric charge). Muons naturally occur in cosmic rays.(cosmic rays are high energy particles, mostly protons, from space travelling with speeds close to the speed of light5). When protons in cosmic rays strike the nuclei of atoms in the atmosphere, pions are produced.Pions later decay into muons and muon neutrinos.
What is the g factor of a particle?
The magnetic moment of a particle is a way to describe the magnitude of torque(torque is a force that produces or tends to produce rotation6) when it is placed in a magnetic field7.

Image 2- An image depicting the magnetic field around a muon
If you place a magnet with two poles(a dipole magnet) in another magnetic field, it experiences a torque trying to align it with the second magnetic field. This is the magnetic dipole moment. The strength of this phenomenon is determined by the ‘g’ factor. In other words, the g factor relates the magnetic moment of a particle to its spin(the amount of angular momentum linked with a particle8)
The g factor of a muon was predicted to be 2(the g factor is a dimensionless unit/ doesn’t have a unit) by the standard model of particle physics. But a vacuum is full of virtual particles9.

Image 3- A Feynman Diagram showing an electron and a positron annihilating to produce a photon
Space, in terms of the quantum field theory, is filled with quantum fields. Fundamental particles can be thought of as oscillations in these fields with different energies. Quantum fields are not stagnant. They vibrate randomly and sometimes, these vibrations produce energy enough to create a particle. These particles seem to just pop into existence. These are virtual particles. But virtual particles are created along with their antiparticle pair10. Antiparticles and particles have the same mass but opposite charges and a few other differences. For instance, the antiparticle of the electron, the positron has a positive charge unlike the negatively charged electron.The first idea for antiparticles came from a relativistic wave equation provided by Paul Dirac. Dirac,in the 1920s, sought to ‘harmonize’ Einstein’s theory of special relativity with quantum theory. He was successful in his efforts and noticed that his equations for an electron(with a negative charge) could also hold good with respect to electrons with a positive charge. Antiparticles were later discovered by Carl Anderson’s experiments . So, virtual particles and their antiparticles annihilate and disappear11. Scientists thus have to take into account how Muons interact with these virtual particles while calculating their g factor.
Last year, scientists calculated the muon’s g factor to be 2.00233183620.9

Image 4- The muon g-2 experiment at Fermilab
What was done in the experiment?
In the muon g minus 2 experiment, muons were put inside a magnetic storage ring and were spun around the tube many times with a speed close to the speed of light. While in the tube, the muon’s precession (the change in the orientation of the rotational axis of a body) was measured using detectors11. A similar experiment had been done by the Brookhaven National Laboratory,also in the USA, in 2001. The fermilab measurement is more precise than the former experiment.
Result
The fermilab experiment measured the muon’s g factor to be equal to 2.00233184080, which though is off by the standard model prediction by a few digits, makes a big difference. Even after accounting for all possible interactions of the muon with known virtual particles, the standard model gives a g factor which does not match the experimental value.As the experimental result doesn’t match with the theoretical value, it may suggest the presence of undiscovered particles or something else beyond the standard model.
This result was announced by observing the second and third observation runs. Fermilab plans to conduct a fifth run sometime in the future. It is just too early to declare it a discovery as there is a one in 40,000 chance that this measurement is a fluke9.
Also, a new study published in the journal Nature showed that using lattice QCD, the muon’s g factor is much higher and is nearer to the experimental value. This technique wasn’t used formerly as it wasn’t ripe yet to produce high precision results. This study still has a considerable chance of being wrong13.
What next?
Scientists at Fermilab will conduct more runs to make sure the results are incredibly precise and not a fluke. According to Chris Polly, a scientist at Fermilab,“So far we have analyzed less than 6% of the data that the experiment will eventually collect. Although these first results are telling us that there is an intriguing difference with the Standard Model, we will learn much more in the next couple of years,”9 So Fermilab still has a lot in store for the future. The future will also see a new experiment on muons by Japan and another experiment Mu2e by Fermilab14.
The results of this experiment have got everyone excited and it may possibly open the doors to a new kind of physics.
References
1. “Fermilab | About Fermilab.” AccessedApril 10, 2021. https://www.fnal.gov/pub/about/index.html.
2.Encyclopedia Britannica. “Muon |Subatomic Particle.” Accessed April 9, 2021.
https://www.britannica.com/science/muon.
3.Particle Data Group. “Particle Data Group.” Accessed July 24, 2021. https://pdg.lbl.gov/2021/listings/contents_listings.html
4.Particle Data Group. “Particle Data Group.” Accessed July 24, 2021. https://pdg.lbl.gov/2021/tables/contents_tables.html.
5.“Cosmic Rays – Introduction.” Accessed April 29, 2021. https://imagine.gsfc.nasa.gov/science/toolbox/cosmic_rays1.html.
6.“Definition of TORQUE.” Accessed July 24, 2021. https://www.merriam-webster.com/dictionary/torque.
7.K&J Magnetics. Magnetic Dipole Moment, 2020. https://www.youtube.com/watch?v=7uicK71lPB4.
8.Encyclopedia Britannica. “Spin |Atomic Physics.” Accessed April 11, 2021.
https://www.britannica.com/science/spin-atomic-physics.
9.“First Results from Fermilab’s Muong-2 Experiment Strengthen Evidence of New Physics.” Accessed April 9, 2021.
https://news.fnal.gov/2021/04/first-results-from-fermilabs-muon-g-2-experiment-strengthen-evidence-of-new-physics/
10.Sorna, Anumeena. “The Nature ofNothingness: Understanding the Vacuum Catastrophe.” Medium, June 22, 2018.
https://medium.com/nakshatra/the-nature-of-nothingness-understanding-the-vacuum-catastrophe-c04033e752f4.
11.Exploratorium: the museum of science, art and human perception. “Origins: CERN: Ideas: Antimatter | Exploratorium.” Accessed July 23, 2021. http://www.exploratorium.edu/origins/cern/ideas/antimatter.html.
12.Fermilab. Muon G-2 Experiment Finds Strong Evidence for NewPhysics, 2021.
https://www.youtube.com/watch?v=ZjnK5exNhZ0.
13.Physics World. “The Muon’sTheory-Defying Magnetism Is Confirmed by New Experiment,” April 7, 2021.
https://physicsworld.com/the-muons-theory-defying-magnetism-is-confirmed-by-new-experiment/.
14.ScienceDaily. “Scientists BolsterEvidence of New Physics in Muon G-2 Experiment.” Accessed April 11, 2021.
https://www.sciencedaily.com/releases/2021/04/210407143806.htm.
Image references
Image 1- Encyclopedia Britannica. “Fermi National Accelerator Laboratory | Laboratory, Batavia, Illinois, United States.” Accessed April 12, 2021. https://www.britannica.com/topic/Fermi-National-Accelerator-Laboratory.
Image 2- University, Penn State. “The Muon’s Magnetic Moment Fits Just Fine: Strength of the Sub-Atomic Particle’s Magnetic Field Aligns.” SciTechDaily (blog), April 7, 2021. https://scitechdaily.com/the-muons-magnetic-moment-fits-just-fine-strength-of-the-sub-atomic-particles-magnetic-field-aligns/.
Image 3- “Feynman Diagram.” In Wikipedia, June 29, 2021. https://en.wikipedia.org/w/index.php?title=Feynman_diagram&oldid=1031038718.
Image 4- Martin, Bruno. “Fermilab’s Muon g-2 Experiment Officially Starts Up.” Accessed April 11, 2021. https://news.fnal.gov/2018/02/fermilabs-muon-g-2-experiment-officially-starts-up/.

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