At the beginning of April, the US research laboratory Fermilab published a new result for the magnetic dipole moment of the muon. The result caused a broad media response because it deviates from the theoretical predictions and thus questions the previous understanding of the laws of nature. Researchers from the Albert Einstein Center for Fundamental Physics (AEC) at the University of Bern were involved in the theoretical predictions. Prof. Martin Hoferichter, theoretical physicist at the AEC, explains the background.
Mr Hoferichter, the latest headlines from elementary particle physics concern muons. Muons are the heavy brothers of electrons. While electrons are found in all atoms, muons are unstable, meaning they decay into other particles in fractions of a second. How important are these volatile guys for our world?
Prof. Martin Hoferichter: The matter around us is made up of electrons, protons and neutrons; muons play practically no role there. Nevertheless, we are surrounded by muons: These particles are created when cosmic radiation from the universe hits the Earth's atmosphere. They then hit the Earth's surface like a large shower of particles. Although the muons decay very quickly, many of them make it from their point of origin in the outer atmosphere to the Earth's surface because of relativistic effects. These ‹natural› muons can be detected in laboratory experiments. Muons can also be generated artificially in accelerators, for example in the g-2 experiment (pronounced "g-minus-2 experiment") at Fermilab near Chicago, which has recently made headlines.
Like many other elementary particles, muons have a magnetic dipole moment. Can you give us an example from the macroscopic world to illustrate what this means?
That is difficult, because the magnetic dipole moment is a quantum property of particles. You can think of it as being related to the force that aligns bar magnets in a magnetic field. We describe the magnetic moment indirectly via the constant g (for: gyromagnetic ratio). Roughly speaking, the value for a muon is 2. We physicists want to determine exactly how large the actual value and thus the difference to 2 is. This is where the name of the above experiment ("g-minus-2") comes from.
Can the magnetic dipole moment of muons be used for technical purposes?
Research into this particle property has so far been purely fundamental research. The magnetic dipole moments of elementary particles have long been a key quantity of interest in particle physics. At the time, its measurements on the electron led to the development of quantum field theory, today a cornerstone of the Standard Model of particle physics, which describes the particles and forces known today in the microscopic world. The measurements have become more and more precise over the decades, and our understanding of dipole moments has continuously improved.
You and your colleague and AEC director Gilberto Colangelo are theoretical physicists at the University of Bern. Your goal is to calculate the magnetic dipole moment as accurately as possible. To this purpose, you joined the 'Muon g-2 Theory Initiative' five years ago. What was the goal?
The initiative was launched by Aida El-Khadra (University of Illinois) and Christoph Lehner (University of Regensburg and Brookhaven National Lab/USA). The goal was to calculate the magnetic dipole moment of the muon as accurately as possible, based on the laws of nature as described by the Standard Model of particle physics. Such calculations are very time-consuming and many different aspects have to be taken into account. An important result of the initiative's five years of work was presented last year: At that time, we as theoretical physicists agreed on a single value for prediction of the magnetic dipole moment of the muon after years of expert exchange. That was a great achievement, because previously there were various values in circulation that differed in various respects. Since 2020, however, a single predicted value is available that can be compared with the measurements made at Fermilab and other laboratories. No fewer than 130 authors from 78 institutions in 21 countries were involved in the corresponding publication in the journal 'Physics Reports'.
What makes it so difficult to calculate the magnetic dipole moment of a muon?
All three fundamental forces of the Standard Model must be included in the calculation: the electromagnetic, the weak and the strong interaction. With the perturbation theory, we now have a good handle on the first two of these forces, but it is difficult to quantify the contribution of the strong interaction to the magnetic dipole moment of the muon. There are two ways of doing this: either one calculates their contributions indirectly via results from other experiments, or one goes down the path of lattice simulations, which involves a great deal of numerical effort. The comparison of these two methods has been a core component of the theoretical discussion in recent years - and it will continue to be a topic of discussion in the years to come.
A few days ago, Fermilab published its latest precision measurement for the magnetic dipole moment of the muon. It looks like the measured value does not match the value calculated by the theorists. Have you and your fellow theorists miscalculated?
We assume that we have not made a mistake! This is also because our calculations are also based on other experimental results, as I have explained above. So there are many indications that the predicted value we calculated on the basis of the Standard Model does not correspond to the actual measured value. And that would mean that the Standard Model of particle physics did not describe the laws of nature completely! At high energies, particles and forces that are not described by the Standard Model may play a role! The particle physics community has been waiting for many years for such indications of physics "beyond the Standard Model". This is the reason why the community has reacted very enthusiastically to the latest results.
The fact that the measured value and the theoretical value of the magnetic dipole moment of the muon do not agree is a well-founded assumption so far. When do you think there will be scientific certainty on this?
To achieve this certainty, the experiment at Fermilab wants to present even more precise measurements, and we as theoretical physicists want to improve the prediction value accordingly. If everything goes perfectly, we could reach this certainty in two to three years. We would achieve this if we could establish the deviation to be equal to 5 sigma or larger. This would correspond to a probability for a random fluctuation of less than 0.00003%.
If this succeeds, the Standard Model of particle physics would have to be modified. Do you already have an idea of what the changes might look like?
There are a lot of models in circulation that could explain this deviation - if it is confirmed. These models postulate different types of new elementary particles at different energies. Which of these models best describes reality is not something I want to speculate about today. In order to find good answers here, it will be important to include the results of other experiments that shake up the Standard Model.
In March of this year, new results from the LHCb experiment at CERN have already shaken up the Standard Model. This experiment investigates the decay of so-called bottom quarks in particular. Where do you see the greater potential for "new" physics - in the g-2 experiment or in LHCb?
As far as the significance of the results is concerned, the g-2 experiment is somewhat further ahead, namely the quoted significance of 4.2 is higher than that of the most recent LHCb result with a significance of just over 3. However, in the field of b-physics, which is pursued by the LHCb experiment, there are still other measurements that point in the same direction, and if one includes these, the indications for "new" physics are certainly at least as serious as those from g-2.
The experiment at Fermilab, which you are supporting with theoretical work on the part of the University of Bern, is a comparatively small experiment, in any case smaller than the experiments at the particle accelerator LHC at CERN. Can we learn from this that smaller experiments will pave the way for "new" physics?
I see both experiments - the study of bottom quark decays at LHCb and the muon experiment at Fermilab - as complementary. It is true that the latest results were obtained at lower energies; this is true for Fermilab and, in a sense, also for LHCb, that probes the Standard Model at small energies by CERN standards.
by Benedikt Vogel
Swiss Institute of Particle Physics (CHIPP)
c/o Prof. Dr. Michele Weber
University of Bern
Laboratory for High Energy Physics LHEP