Forging a mathematical path to hybrid mesons

Jozef Dudek is pursuing theoretical descriptions of exotic hadrons, a yet-untallied group of short-lived subatomic cousins of the proton and neutron, those more familiar atomic building blocks.

It’s a pursuit that occupied him during a doctoral dissertation at the UK’s University of Oxford and which he brought to the United States in 2004 when he joined the Center for Theoretical and Computational Physics at the U.S. Department of Energy’s Thomas Jefferson National Accelerator Facility as a postdoctoral researcher.

Now, Dudek holds a dual position as a senior scientist at Jefferson Lab, along with a tenured post in William & Mary’s department of physics, where he is the Margaret Hamilton Professor, a position recognizing excellence in research as well as teaching. Dudek also has assembled an impressive slate of publications, citations, awards and discoveries related to both teaching and his research into nuclear physics theory.

For his achievements, Dudek was recently honored by his peers by being named a Fellow of the American Physical Society in October 2024. His citation noted the fellowship is “For contributions to the spectroscopy of hadrons under the strong nuclear force and their impact on experimental programs worldwide.”

From the quark model to lattice QCD

Experiments with beams of high-energy particles, such as those conducted at Jefferson Lab, produce observations of short-lived hadrons. And Dudek says there are a lot of such particles.

“Many of these have been known about for many decades,” he said. “So, there was a ‘phone book,’ if you like, of these hadrons that had been built up experimentally. And people have for a long time tried to understand them.”

Dudek explained that a theory called the quark model was used to understand some of the listings in the growing hadron phone book. Quarks are elementary particles that combine to make up hadrons. For example, protons contain two up quarks and a down quark; neutrons are constructed of two down quarks and an up quark.

It gets more complicated rapidly: the quarks of protons and neutrons are held together by gluons, mediating an interaction known as the strong force. Antiquarks come into play. Oh, and there are six varieties of quarks.

Dudek describes the quark model as a set of quantum mechanical rules outlining all the ways a quark could combine with an antiquark to form a hadron.

“And if you do the quantum mechanics of the allowed ways that they can combine together, that will match the hadrons you see.” Dudek explained, “That worked pretty well.”

Until it didn’t.

He said there were always some observed hadrons that didn’t quite fit the quark model, and these were called ‘exotics.’ Exceptions to the quark model rules continued to grow as more exotic hadrons were observed.

Importantly, physicists found a more fundamental way to describe the interaction of quarks and gluons within the strong force: quantum chromodynamics, or QCD. Dudek said QCD, in addition to being challenging to calculate, contains some theoretical head-scratchers as well.

“Like, why is it that only a quark and an antiquark stick together as in the quark model?” he said. “In particular, why isn't there a situation where the gluon does something non-trivial and produces a state which really has to be thought of as a quark, an antiquark and some glue?”

Dudek said such a gluon-forward exotic particle is called a hybrid meson, searched for by physicists for some time, including in the GlueX experiment at Jefferson Lab. Dudek himself has been probing hybrid mesons for the past 20 years through lattice quantum chromodynamics, a calculational approach to QCD that puts the theory on a four-dimensional space-time grid in order to mathematically model the interactions of quarks and gluons within the strong force using supercomputers.

Like many theoretical physicists, Dudek works in concert with his colleagues who conduct the experiments, his work providing predictions guiding experiment design as well as helping to interpret the results. His work isn’t confined to Jefferson Lab or even the United States. For instance, he is currently working with Mischa Batelaan, a William & Mary postdoc, on a calculation related to results from the BES III experiment in Beijing.

“There’s a candidate state for an exotic hybrid meson that's been observed there,” Dudek said, explaining that the exotic meson candidate shows up in a particular kind of decay in charmonium, the union of a charm quark and a charm antiquark.

“I've been working with this postdoc to try and do some rigorous lattice QCD calculations of this process. And that's moving nicely,” he added.

Toward a world-spanning portfolio of teaching and research

Dudek’s path to the study of exotic hadrons began far from Jefferson Lab. He was born and raised in Derbyshire in the English East Midlands, in a former coal-mining village. His interest in physics was kindled in high school.

“I was pretty strong in mathematics, and I had some really interesting physics teachers, and so I started to be a little bit interested in that,” he said. “And I read a lot of popular physics books that I got out of the library.”

Dudek’s life in Derbyshire did not include much familiarity with the academic world. His parents were not university graduates, and his grandfather was a World War II refugee from Poland, but Dudek was encouraged to try for admission to universities. A science teacher mentor looked over Dudek’s list of mid-tier British schools and looked at him quizzically.

“‘Why are you applying to only these places?’” the teacher asked. “‘You should be applying to Oxbridge,’” using the portmanteau coinage embracing Oxford and Cambridge universities, the twin colossi of higher education.

Dudek explained where British university life differs from the U.S. For starters, a student may apply to Oxford or Cambridge, one or the other, not both.

“I had absolutely no idea whether I had the slightest chance of getting in,” he said. “But I put in a speculative application to Oxford.”

He was accepted, and began to “read physics,” which Dudek explained means that the four-year Oxford curriculum was exclusively devoted to maths and physics, “no gen-ed requirements or anything like that.”

“I really enjoyed the undergraduate degree. I'd done a very interesting research project, and I wanted to do more. I wanted to understand more,” Dudek said. “So again, I applied for Ph.D. positions across the UK. I also put in an application to stay at Oxford.”

He said the Oxford application was, once again, “a bit speculative,” but once again Oxford admitted him, this time to pursue doctoral level study in high-energy physics.

After taking his Oxford doctorate, Dudek joined Jefferson Lab’s Theory Center. The Jefferson Lab/W&M joint appointment began in 2016, following a similar dual role with Old Dominion University. Joint appointments work out quite well for him, Dudek said, and benefits both institutions as well as the holder of the joint position.

“I think I'm a strong researcher, and I want to do research at a place where it is most effective, and in my field, that's Jefferson Lab. That's where I'm in immediate contact with the experimentalists, with colleagues in theory and in high-performance computing. It is the best place, worldwide, to do the research that I do,” he said. “It is the best, but I don't want to just do research. I think I'm a pretty good educator. I want to teach, to educate. The joint appointment is, in principle, the perfect synthesis of these two things.”

By Joe McClain

Contact: Kandice Carter, Jefferson Lab Communications Office, kcarter@JLab.org

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