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Sharing disappointing results with a world of researchers working to find what they hope will be the "discovery of the century" isn't an easy task, but that is what Penn State theoretical physicist Zoltan Fodor and his international research group did five years ago with their extensive calculation of the strength of the magnetic field around the muon—a sub-atomic particle similar to, but heavier than, an electron. At the time, their finding was the first to close the gap between theory and experimental measurements, bringing it in line with the Standard Model, the well-tested physics theory that has guided particle physics for decades.

Earlier on the same day, after almost 20 years, a . This was interpreted by most physicists as a sign of new physics, and many physicists shared some skepticism of Fodor's results and hoped that with more research, the other groups' result would ring true.

Why? Twenty-four years ago, in an experiment at Brookhaven National Laboratory, physicists detected what seemed to be a discrepancy between measurements of the muon's "magnetic moment"—the strength of its magnetic field—and theoretical calculations of what that measurement should be, raising the tantalizing possibility of undiscovered physical particles or forces. They reported that the muon was more magnetic than was predicted by the Standard Model.

At the time, this opened up the possibility of a new kind of particle or force—an exciting prospect for physicists, including Fodor, who contributed to researching the mystery in the hopes of making a discovery. Last week, however, the original research group, called the Muon g-2 collaboration, presented its final results at Fermi National Accelerator Laboratory (Fermilab), which .

"Like many other physicists, my original motivation was not to prove that there was agreement between the Standard Model and the muon observation," said Fodor, distinguished professor of physics in the Eberly College of Science and a co-hire of the Institute for Computational and Data Sciences.

"My original goal was to provide a real and controllable calculation and be part of the discovery of the century. That dream was a real motivation for me. But nature has the ultimate say, and we were the first to realize that a new discovery was not the case."

Since their 2020 results, Fodor and his group have also improved on their calculation, with the result showing an even better agreement with the Standard Model.

In the following Q&A, Fodor spoke about his work on the quantum theory surrounding muons, the value of investment in basic research and why even disappointment is a valuable part of scientific discovery.

What is the background of this 24-year-old mystery?

I'd describe the mystery as the tension, or the discrepancy, between a measured quantity, which is the magnetic moment or the magnetism, of the muon and the theoretical calculation. You calculate the particle's magnetism under the Standard Model, and then you measure it directly, and you end up with two different results.

In the Standard Model of particle physics, you can calculate essentially everything. We know only four interactions: gravitation, which we know from our childhood lessons explains apples falling; electromagnetism, which the Greeks realized when they observed that magnets attract iron; and the weak and the strong interactions, which were discovered in the 19th and 20th centuries, respectively.

Finding such a tension, which was the focus of the 24-year-old mystery, could suggest that the physics we know today is not complete, and there might be a new force. It turned many people to think that there could be a new undiscovered physics interaction behind the muon tension. And if you find a new interaction, that would be the discovery of the century.

Our calculation five years ago was the first indication that such tension probably did not exist. What people were observing was somehow a result of a calculation that used data in the form of underestimated experimental uncertainties. It was a complicated issue, in 2020 and have since improved even that precision.

When we first suggested there is nothing here, no new interaction, people didn't want to believe us. Since then, additional evidence has been gathered, and people started to accept our result more and more.

Today, the experimental result is now more precise, matching our 2024 calculated theoretical result. Most theorists are accepting that what we previously suggested explains the earlier tension, and, now, last week's the final experimental result aligns with the Standard Model of particle physics.

How long have you been working on this problem? Can you talk about your group's approach to solving this problem?

Like many other physicists, when I started this work about 10 years ago, my original motivation was to prove that there was a disagreement between the Standard Model and the muon observation. Why?

Faced with the original discrepancy, there were three options: Either the theoretical prediction was incorrect, the experiment was incorrect, or, as most physicists believed, this was a sign of an unknown force of nature.

Originally, we decided to try to find a better way to calculate the prediction. Our team of physicists, called the Budapest-Marseille-Wuppertal collaboration, took the most basic underlying equations of the strong interaction, put the equations on a space-time grid and solved as many of them as possible at once.

So, essentially, instead of relying on experimental data, we simulated every aspect of our calculations from the ground up—a task requiring massive supercomputing power—and we didn't find any disagreement, therefore : The gold-plated, old theory result was off in some way.

The technique we used is kind of like making a weather forecast. As aircraft fly their routes, they measure pressure, temperature and the speed of wind at given points on Earth. Similarly, we placed the strong interaction equation on a space-time grid. The weather data at individual points are then put into a supercomputer that combines all of the data to predict the evolution of the weather.

Our team put the strong interaction forces on a grid and looked for the evolution of these fields. For weather forecasts, the more planes collecting data, the better the prediction. In this metaphor, we used billions of airplanes to calculate the most precise magnetic moment we could using billions of computer processing hours at multiple supercomputer centers in Europe.

Our new approach produced a value of the strength of the muon's magnetic field that closely matches the experimental value measured by the Brookhaven and Fermilab scientists. It essentially closes the gap between theory and experimental measurements and confirms the Standard Model that has guided particle physics for decades.

How does it feel to read about this week's Muon g-2 experiment results five years after publishing your theoretical calculation results?

There were hundreds of people who were involved in these measurements and various calculations within and beyond the Standard Model. At the time, they didn't like our result because they were hoping for a Nobel Prize-worthy discovery. So, we had a very strong headwind against us, and that was a strange feeling.

But that is also where the value of support for basic, theoretical research comes into play. Science is not a democratic institution where you need a consensus. Nature is as it is, and there are not majorities that can define nature without scientific proof. The collective curiosity and contributions of many researchers with many ideas over time is what scientific discovery is all about.

What does last week's latest finding mean for physics? For society?

Our research group's calculations have been checked and recalculated by several groups, and I would say that our research group's result is now so precise that, for me, it is not feasible to make it even more precise.

However, there are other groups who are working in this field from different angles. It's very useful and sensible for these physics research groups to continue to reach for more precision—eventually, they'll be able to say our result should be either confirmed or refuted by other calculations. That's the goal of science—to continue to work through theories and find additional evidence.

For society, of course, whenever you have a new interaction, then you have the hope to solve many problems of mankind, so in a way this finding could be disappointing. For example, electromagnetism solved many questions—that's the reason I can conduct this interview over the phone, using electromagnetic waves.

The weak interaction is responsible for radioactive decay, which is used in medicine, and in many, many other cases. The strong interaction is used in nuclear power plants. So, there are many things you can do once you identify a new interaction, and unfortunately, we don't have the new interaction that we hoped for.

So, it is a consequence for society, but there's also a positive side to emphasize. Our calculation is so precise that it cannot be accidental and provides excellent evidence for the confirmation of quantum field theory. This is the primary theoretical framework for understanding many aspects of the universe and , hopefully including computing, health care and imaging, timing keeping and energy.

And that's a highly meaningful result. Everything established using quantum field theory is justified to an incredible position. So, in other words, this is a huge success!

What do you love most about your work?

I love the Penn State Department of Â鶹ÒùÔºics and my colleagues. My colleagues are conducting an extremely high and impactful level of research, and it's a great honor to be here and working with these scientists. I really like the collaborative nature of Penn State and the huge scope of the research. You don't feel isolated. You have a connection to many, many other fields, and it's just hard to imagine a more interdisciplinary department, college and institution.