The proton radius puzzle

25 January 2018

His results have made headlines beyond the academic world of physics. In May 2016, Randolf Pohl was appointed to a professorship at the PRISMA Cluster of Excellence of Johannes Gutenberg University Mainz (JGU). Using a new technique, he succeeded in measuring the size of the proton, one of the fundamental building blocks of the atomic nucleus. According to his results, the radius of the proton is four percent smaller than the previous value accepted by science. This result is puzzling and could have serious consequences for the Standard Model of particle physics.

From the window of his office on the fifth floor of the Institute of Physics, Prof. Randolf Pohl looks out over a complex of buildings under which, deep below ground, JGU’s particle accelerator, the Mainz Microtron MAMI, is hidden. MAMI was where a good friend and colleague of Pohl’s, the nuclear physicist Jan C. Bernauer, once worked on the size of the proton. To determine its radius, Bernauer bombarded hydrogen atoms with electrons. In his doctoral project, which he began in 2005, he arrived at a value of around 0.877 femtometers. One femtometer is equivalent to quadrillionth of a meter (10−15 m). His results agreed with the results of previous experiments and with the predictions of the physics world.

Eight years earlier than this, Pohl and his team at the Paul Scherrer Institute (PSI) in Switzerland had already started developing an alternative method of measuring the size of the proton. In this technique, laser beams were used to survey the inside of hydrogen atoms. In and of itself this was not new. What was new was that they replaced the electron that normally orbits the nucleus of the hydrogen atom with a particle known as a muon. This hugely increased the accuracy of their measurements, and in 2010 they finally published the value they had obtained and this came as a real surprise as it was four percent less than the value Bernauer and his team had calculated.

Muons in protons

“We push the muon from one state to another,” says Pohl, describing the scientific process in layman’s language. “Electrons – or muons in our experiment – orbit the atomic nucleus at different levels, called orbitals. We use a laser to boost the muon from a 2S to a 2P orbital.”

What is important to realize is that particles don’t behave simply, like the Moon orbiting the Earth. The orbitals are more complex: “The negatively-charged muon actually spends some time in the proton.” And this time is the critical factor. Pohl measures the energy difference between the 2S state, in which the muon can be located inside the proton, and the 2P state, in which it can’t. This measurement allows him to calculate how long the muon resides in the proton. And from this, in turn, he can deduce the radius of the proton. “A muon is 207 times heavier than an electron. This means that it spends ten million times longer inside the proton. This allows us to determine the size of the nucleus much more accurately.”

Pohl jumps up from his chair in the office when he talks about his research. Standing in front of a large chalkboard on the wall of his office, he tries explaining. He draws a diagram of the Moon and the Earth, and, next to this, the muon and electron states, in which – at least in his version – an S orbital resembles a circle and a P orbital is more like an egg timer.

It’s clear that Pohl is used to presenting the complexities of his work in a comprehensible way. “I have given public lectures on my research several times and have also taken part in science slams,” he says. Pohl points to an issue of Spektrum der Wissenschaft, the German sister journal of Scientific American, lying on his desk. In 2014, together with Bernauer, he wrote an article for the popular science magazine. “We simplified our description of the physics until it hurt,” he says with a smile. Even so, it was their paper that made to the front cover. The eye-catching headline drew attention to the ‘paradox of the proton’. And below in smaller letters it was pointed out that the conflicting results for the measurement of proton size could well be indicative of the need for a ‘new physics’.

Not in line with the Standard Model

Pohl is not sure he’d go that far. There are various factors that could explain the discrepancy in the measured values. “Maybe some kind of systematic effect that we, as well as other groups, have overlooked is playing a role,” he suggests. There is a lot to consider in such experiments. Background effects need to be factored out. Pohl talks of ‘smear effects’ that leave unwanted traces in their wake. “Of all the conceivable explanations, that would be the most boring.” Another possibility would be that the theories on which the measurements are based are flawed.

Pohl leaves the most exciting of the three possibilities for last. “Maybe there’s something genuinely wrong with the Standard Model of particle physics as we know it. It’s possible the discrepancy is telling us we need a new particle. And such a solution might also explain other problems that, current research suggests, clash with the Standard Model.” It’s clear in any case that: “The discrepancy has made the area we work in rather intriguing. Even after seven years, we still don’t have a clear answer.”

Pohl joined the PRISMA cluster of excellence at JGU to with the aim of furthering research in his field. “If our group doesn’t undertake measurements using muons, nobody will,” he says. The structure of hydrogen’s atomic nucleus is relatively simple. It consists of only one proton, making it a good starting point. Next, Pohl and his working group took on deuterium. Its nucleus consists of a neutron and a proton. “Once again, our results revealed the same discrepancy and this was clearly attributable to the proton.” Then they moved on to helium-3 and helium-4.

“We’re hoping to take measurements using tritium. Its nucleus has two protons and two neutrons.” A few floors below Pohl’s office, his group is beginning to set up the experiment. “We’re just starting to feel our way,” explains Pohl. “Experiments like this demand a lot of persistence. From our first attempts to take measurements using muonic hydrogen, it took us twelve years to achieve our first results. We expect we’ll need at least another five years.” As with all their previous experiments, the team will be performing the actual experiment at the Paul Scherrer Institute in Villingen, Switzerland.

A cluster of excellence with international kudos

The flying visits to Switzerland are indispensable for Pohl’s research; the institute there produces the most powerful muon beams in the world. But, that aside, as a physicist he feels very much at home in his new post of Chair of Experimental Atomic Physics at the PRISMA cluster of excellence. “I was very fortunate; Mainz came knocking on my door. JGU is the ideal place to do my kind of physics. So many of my colleagues here work in intersecting fields. There’s so much expertise important for my research just a stone’s throw away. Next door at the Helmholtz Institute, for example, is Sonia Bacca.” In the summer of 2017, she came to Mainz from Vancouver, Canada, as Professor of Theoretical Physics. “She’s the world’s foremost expert on how muons interact with light nuclei.”

PRISMA has an appeal that is far-reaching, Pohl emphasizes. “Its portfolio is diverse, and, at the same time, the cluster of excellence attracts precisely the right people to team up and achieve results. We’re all mutually interdependent, and it’s an environment like this that allows us to really shine.”

Pohl looks around his office. The chalkboard is now covered with diagrams, and the surrounding furniture still looks quite new. “For most professors, it is a once in a lifetime opportunity to furnish an office like this,” he muses. And his is on the Gutenberg Campus, with a view over MAMI and the new Helmholtz Institute – and just around the corner from all the scientists that will support him in his research.