by Charlie Wood

June 25, 2025

from QuantaMagazine Website

Muons have mystified physicists since they first revealed themselves in the 1930s.

"Who ever ordered that?" quipped the nuclear physicist I.I. Rabi.

Protons, neutrons and electrons seemed to account for atoms, and therefore all matter.

But when physicists inspected the debris left behind as cosmic rays slammed into air molecules, they discovered evidence of a second type of electron - a particle with precisely the same electric charge, but some 200 times the mass.

This new particle played no role in the atom, since it could hold itself together for just two millionths of a second before disintegrating.

Its entire raison d'être was unclear.

But the muon was the first clue that the known subatomic particles are only the most stable members of much larger families.

Over the following decade, physicists would flesh out three generations of these families, which now form the Standard Model of particle physics.
 

Standard Model of Particle Physics

from Quantum Diaries.

Each matter particle comes in a light, medium and heavy version.

For instance,

there's the electron, the muon and an even beefier (but otherwise identical) particle called the tau...

But why?

To understand if the muon is a true electron clone, researchers investigated its other characteristics, such as whether it feels the same forces as the electron.

In the 1960s, they started measuring the way muons wobble as they move through a magnetic field, a feature known as their "anomalous magnetic moment," referred to as "g–2" for esoteric reasons.

In experiment after experiment, the muon obeyed precisely the same quantum laws as the electron.

Then, in 2001, a more precise measurement spotted a sign of rebellion against those quantum laws.

Researchers at Brookhaven National Laboratory (BNL) in New York noticed that the muon's g–2 value seemed to differ from what the Standard Model predicts by about 0.00036%.
 

DOE's Brookhaven National Laboratory Muon g-2 ring,

since moved to Fermilab and rebuilt.
 

That counts as a sizable discrepancy, since physicists think they understand quantum physics so well.

To see if the difference was a sign of new forces acting on the muon rather than a measurement error, physicists upgraded the experiment.

The heart of the Brookhaven apparatus was a 700-ton ring of superconducting coils generating the experiment's magnetic field.

 

And the country's most productive muon factory sat in Illinois, at the Fermi National Accelerator Laboratory (Fermilab).

 

In 2013, physicists brought the two together.

They loaded the ring onto a barge off the coast of Long Island, then floated it down the East Coast and up the Mississippi river.
 

DOE's Brookhaven National Laboratory

finds a new home in the FNAL Muon g-2 experiment studio.

The move by barge and truck.
 

The Brookhaven ring made it in one piece, and Fermilab physicists started collecting data.

In 2021, they announced that,

the clash between the predicted and measured values of the muon's magnetic moment had intensified - a tantalizing finding.

Physicists are desperate for clues about a more complete theory of the quantum world that goes beyond the particles and forces of the Standard Model.

If the muon g–2 discrepancy got any stronger, it would make history.

"I don't know if it is the last great hope for new physics, but it certainly is a major one," Matthew Buckley, particle physicist at Rutgers University, told Quanta at the time.

What's New and Noteworthy

New findings announced in late May have dashed that hope.
 

DOE's Fermi National Accelerator Laboratory Muon g-2 studio.

As muons race around a ring at the Muon g-2 studio,

their spin axes twirl, reflecting the influence of unseen particles.

Photo: Reidar Hahn, Fermilab.

The Brookhaven and Fermilab measurements of the muon's magnetic moment now exactly align with the predictions of the Standard Model.

Except in this case, it wasn't that the discrepancy disappeared once physicists collected more and better data.

 

Instead, for 25 years, it was the prediction that was off.

The challenge in predicting the outcome of a particle physics experiment is that the experiment can be thought of as playing out an infinite number of ways:

particles may briefly appear and interfere with each other before disappearing again.

So physicists make predictions by focusing on the simplest events (those involving only a few steps) and ignoring the more complicated (and typically rarer) sequences of events.

They organize the comings and goings of particles with visualizations known as Feynman diagrams.

But a complete census of the infinite possibilities - and therefore an exact prediction - is impossible. So every prediction has some uncertainty or error, just like an experiment.

And one type of error in the muon g-2 calculation is especially intractable.

The problem lies with certain rare muon interactions in which particles similar to the proton briefly appear. These particles feel the "strong" nuclear force (as opposed to the weaker electromagnetic force). And when the strong force gets involved, Feynman diagrams fail.

Every possible event meddles with the muon equally.

Because the strong force is so powerful, even complicated events involving many transient particles make a big difference, so no part of the infinite string of possibilities can be safely ignored.

Prediction is futile, so physicists typically resort to painstaking experiments.

In the case of the muon's g-2 value, physicists turned to collisions involving electrons to get a sense of how often protonlike particles might appear:

they then plugged that number into their equations.

In short,

the theoretical prediction secretly hinged on an experiment.

In the new analysis, a team of more than 200 theoretical physicists managed to squeeze the key number out of pure quantum theory, relying on newly improved brute-force computer simulations of the strong force.

They found that the overall prediction closely matched what Fermilab has measured.

 

The muon's magnetism had matched the Standard Model all along...

A major hope of particle physics has died.

This means that the fundamental mystery of the muon lives on.

And that mystery is:

Why has the universe served us three generations of matter particles (such as the electron, the muon and the tau) when just one would do...?