Muon Magnetic Moments Matter say the Penguins

(A 2023 update is at the bottom)

The muon is often referred to as the electron’s cousin with the same charge and spin giving it a magnetic field as well as being about 207x an electrons mass. It was also the first exotic sub-atomic particle discovered.

With quantum mechanics (QM) there is never a “bare” isolated muon. It exists as a cloud of particles and antiparticles popping into existence that then change back into energy and / or other tiny particles. These particles and energy combinations have a subtle effect on the muon’s properties including its magnetic moment. However both the theoretical and experimental values are known with exquisite precision with well-established uncertainty.

Using quantum mechanics particle physicists have perhaps the most precise and elaborate model in science that accounts for basically everything seen with atom smashers with great precision and the same QM underpins much of our electronics-based civilization. You might think that it would be a cause for celebration. However the problem is its been this way for about 40 years and people are desperate for a sign of what is beyond the standard model’s 17 particles. This is because scientists know that it does not account for Dark Matter, Dark Energy nor gravity so it is an incomplete, provisional theory.

Penn State University’s and member of the wonderfully named Budapest Marseille Wuppertal (BMW) Collaboration of physicists Professor Zoltan Fodor echoed Feynman when he said:

“When the results of an experiment don’t match predictions made by the best theory of the day something is off. Fifteen years ago physicists at the Brookhaven National Laboratory (BNL) discovered something perplexing. Muons, a type of sub-atomic particle were moving in unexpected ways that didn’t match their predictions. Was the theory wrong, was the experiment off or, tantalizingly, was this evidence of new physics?... Physicists have been trying to solve this mystery ever since.” (as an aside we used the motor vehicle maker BMW colours in the design).

In April 2021 the experimentalists researching the G-2 experiment revealed results suggesting that they may have measured outcomes significantly different from expected results.

The FermiLab experimentalists updating the BNL results measured the muon’s magnetic field very precisely to show differences from the theoretically predicted number but critically it is also about 4.2x the total uncertainty. Physicists use 5x as a measure of significance for difference so it is pretty near this threshold. However these figures are using only about 6% of the total data they are going to collect so then the uncertainty will shrink by about 75% as more data is included giving greater comfort as to whether we are seeing real signs of ‘new physics’ or not.

Then the BMW Collaboration threw cold water on the reveal - or at least raised further questions - by showing the results of their fiendishly difficult Lattice QCD calculations suggested their updated theoretical values could well agree with the experimental results.

A 2001 paper by Feng (now a Distinguished Professor at the University of California, Irvine) and Matchev suggested an explanation to account for the anomalous muon wobble that might throw light on the nature of dark matter so for this and other reasons the G-2 experiment update attracted lots of attention.

Suffice it to say that we still do not have clarity with regard to new physics from these results but more work is needed and will be done! Another issue is that while the FermiLab experiment is very precise it is not very specific so many scientists may propose different theories to account for any discrepancy. Are we accounting properly for the impact of the rare but impactful particle and energy combinations intermediated by the strong nuclear force?  Is our mathematics up for it? Do our supercomputers have enough power? Will quantum computers help? Do we need more powerful particle colliders to illuminate hypothesized particles?

Some of FermiLab’s Professor Dan Hooper work suggests that a hypothetical gauge boson - the Z’ particle - may be a candidate that would influence the muon’s magnetic moment in a way that might help explain variations between the predicted outcome vs actual observations as well as explain some of the cosmological questions regarding the universes early expansion. Two answers for the price of one! Watch this space!

Interestingly enough but why the penguins?

Feynman diagrams are used to draw permutations of particle evolution through time and space. The simple tree diagrams give the results of the predominant particles but a fuller picture is given by Loop diagrams. Some diagrams have been referred to as penguin diagrams. This was because experimentalist and now Professor Melissa Franklin – who worked on the FermiLab team that found some of the first evidence of the top quark - had a bet with particle theorist John Ellis that if he lost a darts game he would publish a paper using the term penguin. The rest is history. The “penguins” in the picture are pictured cheekily taunting and perturbing the physicists with perturbed muons (from perturbation theory).

The current state of physics is less Q.E D (quod erat demonstrandum – logically prove something) rather more recourse to studying Quantum ElectroDynamics & Quantum Chromo Dynamics with all their attendant complex calculations and experimental implications. Nature is not giving up its secrets easily – we still have many marvellous mysteries of the Universe to uncover!  


In 2021, Fermilab released its first results of the Muon g-2 experiment. Fermilab released an updated value of g in August 2023 which included an additional two years of data from its first results in 2021 to make its results more than twice as accurate,  with a precision of 0.20 parts per million! The collaboration expects its uncertainties to reduce further to just 0.14 parts per million by the time the final results are published in 2025.


Some informative podcasts with people far more qualified to comment than us are given below:

Physics World podcast on Muon Mania

Daniel & Jorge Explain The Universe 15 April 2021 Daniel and Jorge talk about the result of the G-2 experiment at FermiLab and what it means.

Dr Dan Hooper gives a before and after release outline of the critical import of the G-2 experiment on Why this Universe

Physics World Stories April 29 2021 Muon Mania

Space Nuts 15 April 2021 between about 8m 30 sec – 19:30

Science AAAS 16 April 2021 between 1m - 14:15

New Scientist Weekly podcast 9 April 2021


Jorge Cham of PhDComics fame has an explanation of the muon’s magnetic moment here

Some other related Daniel and Jorge Explain The Universe podcasts to expand on the topic

The Marvellous Mystery Of The Muon Magnetic Moment

Is All of Space Magnetized?

What Is The Real Charge of An Electron? (A good explanation of the impossibility of looking at a ‘bare’ particle and its implications)

An interesting book:

Exactly: How Precision Engineers Created The Modern World Simon Winchester


And to close a question weakly interacting with humour:

Why did the muon couple divorce?

There was only a weak interaction