Studying muonium to reveal new physics beyond the Standard Model

By studying an exotic atom called muonium, researchers hope misbehaving muons will spill the wick on the Standard Model of particle physics. To make muonium, they use the most intense continuous beam of low-energy muons in the world at the Paul Scherrer Institute PSI. The research is published in Nature Communication.

The muon is often described as the heavy cousin of the electron. A more apt description might be his rogue relationship. Ever since its discovery sparked the words “who ordered this” (Nobel Laureate Isidor Isaac Rabi), the muon has been confusing scientists with its law-breaking antics.

The muon’s most famous offense is oscillating a little too much in a magnetic field: its anomalous magnetic moment made headlines with the 2021 g-2 muon experiment at Fermilab. The muon also notably caused problems when used to measure the radius of the proton, resulting in a very different value from previous measurements and what has become known as the proton radius puzzle.

Yet, rather than being chided, the muon is cherished for its surprising behavior, making it a likely candidate for revealing new physics beyond the Standard Model.

In an effort to understand the strange behavior of the muon, researchers from PSI and ETH Zurich turned to an exotic atom called muonium. Formed from a positive muon orbited by an electron, muonium is similar to hydrogen but much simpler. While the proton of hydrogen is composed of quarks, the positive muon of muonium has no substructure. And that means it provides a very clean model system from which to sort out these problems: for example, by obtaining extremely precise values ​​of fundamental constants such as the mass of the muon.

“With muonium, because we can measure its properties so precisely, we can try to detect any deviations from the standard model. And if we see that, then we can deduce which of the theories that go beyond the standard model are viable or not,” says Paolo Crivelli of ETH Zurich, who is leading the study supported by a grant from the European Research Council Consolidator as part of the Mu-MASS project.

Only one place in the world is possible

A major challenge to perform these measurements very precisely is to have an intense beam of muonium particles in order to reduce statistical errors. Making a lot of muonium, which incidentally only lasts two microseconds, is not easy. There is one place in the world where enough low-energy positive muons are available to create this: the Swiss muon source at PSI.

“To make muonium efficiently, we need to use slow muons. When they are first produced, they go at a quarter of the speed of light. Then we need to slow them down by a factor of a thousand without losing them. At PSI, we have perfected this art. We have the most intense continuous source of low-energy muons in the world, so we are uniquely placed to make these measurements,” says Thomas Prokscha, who leads the Low Energy Muons group. at PSI.

On the low-energy muon beamline, slow muons pass through a thin sheet target where they pick up electrons to form muonium. As they emerge, Crivelli’s team expects to probe their properties using microwave and laser spectroscopy.

A small shift in energy levels could hold the key

The property of muonium that researchers are able to study in detail is its energy level. In the recent publication, the teams were able to measure for the first time a transition between some very specific energy sublevels in muonium. Isolated from other so-called hyperfine levels, the transition can be modeled in an extremely clean way. Being able to measure it now will make other precision measurements easier: in particular, to get an improved value of an important quantity known as Lamb’s shift.

Lamb’s shift is a tiny shift in certain energy levels in hydrogen from where they “should” be as predicted by classical theory. The change was explained with the advent of quantum electrodynamics (the quantum theory of how light and matter interact). Yet, as discussed, in hydrogen the protons – possessing a substructure – complicate matters. An ultra-precise Lamb shift measured in muonium could put the theory of quantum electrodynamics to the test.

There is more. The muon is nine times lighter than the proton. This means that nuclear mass-related effects, such as the way a particle recoils after absorbing a photon of light, are enhanced. Undetectable in hydrogen, a route to these high-precision values ​​in muonium could allow scientists to test certain theories that would explain the g-2 muon anomaly: for example, the existence of new particles like scalar bosons or gauge icon.

Putting the muon on the scale

As exciting as that potential may be, the team has a bigger goal in sight: to weigh the muon. To do this, they will measure a different transition in muonium with a precision a thousand times greater than ever before.

Ultra-high muon mass accuracy – the goal is 1 part per billion – will support ongoing efforts to further reduce uncertainty for the g-2 muon. “Muon mass is a fundamental parameter that we cannot predict with theory, and so as experimental accuracy improves, we desperately need an improved muon mass value as an input for calculations. “, explains Crivelli.

The measurement could also lead to a new value for the Rydberg constant – an important fundamental constant in atomic physics – which is independent of hydrogen spectroscopy. This could explain the discrepancies between the measurements that gave rise to the proton radius puzzle, and perhaps even solve it once and for all.

Muonium spectroscopy ready to fly with the IMPACT project

Since the main limitation of such experiments is producing enough muonium to reduce statistical errors, the prospects for this research at PSI look promising.

“With the high-intensity muon beams planned for the IMPACT project, we could potentially increase the accuracy by a factor of a hundred, and that would become very interesting for the Standard Model,” says Prokscha.