Over the last few days, the scientific media has been reporting on a new result in quantum mechanics and particle physics, and promoting it as a major discovery or as the first signs of a fifth force of nature. The actual experimental result is the announcement of a more precise measurement of the magnetic moment of the muon, and further confirmation that it does not agree with the standard predictions of theoretical physics, but unfortunately it may not be as revolutionary as some articles are currently claiming.

(I had previously written an article on the initial experimental results in this topic in April 2021, but since the underlying theory is unchanged, the majority of this article will be an extended clip from that article.)

Most people know about electrons. They are tiny particles that orbit the nuclei of atoms and are responsible for all chemical reactions. The movement of electrons in conductors and semiconductors are responsible for electricity, electronics, and all modern technology. They are one of the most prevalent particles in our Universe.

What most people do not realize is that there exists an exact duplicate of the electron which shares all of the same properties, but which is approximately two hundred times heavier. This particle is called the muon, and it is the subject of today's announcement.

There is something odd about the magnetic moment of the muon.

Every particle has a property called the magnetic moment, which determines the strength of its interaction with a magnetic field. For particles such as the muon, it can be expressed as a multiple of a fundamental magnetic moment, denoted by g, and it was originally believed that the muon had g=2. (which is why this experiment was called the Muon g-2 experiment). 

However further development of quantum field theory changed this prediction slightly. It predicts that all particles are surrounded by a cloud of virtual particles that pop into existence for a brief moment, and then disappear again. All particles that exist in nature will also exist in this cloud, with some lasting for shorter periods of time than others. As these virtual particles will also interact with electric and magnetic fields, they will slightly alter the magnetic moment of the particle. And since the cloud includes exotic particles that have yet to be discovered, precise measurements of this magnetic moment could give us new insights into the laws of physics beyond the Standard Model. 

And that is what this team from Fermilab is claiming to have detected.

Back in 2001 a precision measurement of the muon g value showed a variation from the best predictions of the Standard Model. This was an intriguing result, and was widely reported as being the possible first signs of a new force or particle in nature, but lack of time and funding before the experiment was shut down meant that the preliminary result could be explored no further. 

In the last twenty years though there have been three very important advances in this research. The first was that a group of theoretical physicists focused their efforts on refining the calculation of the g value, and have now produced a much more accurate and precise result. The discrepancy seen twenty years ago cannot be explained away as an error in the theoretical predictions.

The second advance was that Fermilab has built a more intense beam of muons, as well as more sensitive and precise detection methods, and used this to improve the experimental measurements of the muonic magnetic moment. They have been taking measurements for several years using the new muon beam and improved measurement techniques, and today revealed the results of their analysis.

The theoretical prediction and the experimental measurement of the muon's magnetic moment do not match. The difference is not significant enough to definitively declare that there is something new and unknown, but only one in forty thousand experiments would be expected to see such a large discrepancy. (This of course assumes no human error, which is also always a possibility in such large scale experiments)

The leading theory at this point is that the cloud of virtual particles surrounding the muon contains one or more new particles that are not currently known to scientists. There are many such proposals for new particles from the theoretical physics community, but as yet no strong evidence to support any of these theories over the others. However if such particles do exist, then they would be expected to be found in the virtual cloud that surrounds the muon, and when a photon from a magnetic field interacts with these exotic particles it would appear that the muon itself has a slightly odd interaction with the magnetic field. That would explain the observed discrepancy.

However even the discrepancy is slightly controversial. The third advance in this field over the past twenty years has been improvements in a type of particle physics and quantum mechanics simulation called lattice field theory. This method uses a powerful computer to simulate both the muon and its surrounding cloud of virtual particles, and their interactions with photons and other particles. Instead of doing a purely mathematical calculation, as the teams of theoretical physicists were doing, the researchers using lattice field theory were able to let their computers replicate the particle interactions using the basic laws of quantum field theory. And according to their research, the magnetic moment predicted by the Standard Model of particle physics is slightly different from the result produced by the quantum field theory calculations. And this value for g is actually consistent with the experimental result from Fermilab.

The new result in 2023 actually does not do much to clarify the situation. The same team at Fermilab has analysed a few more years of data from the experiments, and they have now confirmed their result up to a five sigma level. At this level most scientists agree that the result is real, and it is the standard for most particle physics discoveries. There is very little doubt now about the experimental value of the muon magnetic moment.

The problem is that the theoretical predictions from the Standard Model have gotten less accurate in that same time. Advances in lattice field theory and other computer simulated models have predicted a value of g much closer to the experimental value from Fermilab.

And further confusing the issue is a series of results from an experiment at the Budker Institute in Russia, in which several of the parameters used in the Standard Model calculations were found to be slightly different from the values that were previously used. It is possible, though not confirmed or universally accepted, that the researchers who had measured these parameters in previous experiments either had an undetected flaw in their detector, or had possibly not calibrated the experiment correctly, or perhaps made a small error in one of the calculations. However when dealing with an anomaly in the muon magnetic moment that is measured in parts per million, and which depends strongly on these parameters, even a tiny error in the original experiments could make a significant change in the theoretical predictions that were derived from them. In fact it has been proven that if these new measurements are used in the theoretical calculations, then there is no statistically significant discrepancy at all in the muon magnetic moment.

So we have more precise measurements and predictions, and yet the original question remains. Have we actually seen the first signs of a new particle or a new fundamental force of nature, or are we still just fooled by errors in the way that we have been making our predictions. Is there a problem with the Standard Model of particle physics, or a more modest human error in how the calculations were made.

In the end it is a stunningly precise result that has once again failed to solve this ongoing mystery.