From The Paul Scherrer Institute [Paul Scherrer Institut](CH) And The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH) : “Making sense of the muon’s misdemeanours” 

From The Paul Scherrer Institute [Paul Scherrer Institut](CH)


The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH)


Dr. Thomas Prokscha
Low Energy Muons Group Head
Paul Scherrer Institut
Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
Telephone: +41 56 310 42 75

Prof. Dr. Paolo Crivelli
Institute for Particle Physics and Astrophysics
Department of Physics
ETH Zurich
HPT E 7.2, Auguste-​Piccard-Hof 1, 8093 Zürich, Switzerland
Telephone: +41 44 633 35 11

Text: Miriam Arrell/Paul Scherrer Institute

By making precise measurements in muonium, Crivelli and Prokscha are aiming to understand puzzling results using muons, which may in turn reveal gaps in the laws of physics as we know them. (Photo: Paul Scherrer Institute / Mahir Dzambegovic)

By studying an exotic atom called muonium, researchers are hoping misbehaving muons will spill the beans 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 Paul Scherrer Institute PSI. The research is published in Nature Communications [below].

The muon is often described as the electron’s heavy cousin. A more appropriate description might be its rogue relation. Since its discovery triggered the words “who ordered that” (Isidor Isaac Rabi, Nobel laureate), the muon has been bamboozling scientists with its law-breaking antics. The muon’s most famous misdemeanour is to wobble slightly too much in a magnetic field: its anomalous magnetic moment hit the headlines with the 2021 muon g-2 experiment at Fermilab.

The muon also notably caused trouble when it was used to measure the radius of the proton – giving rise to a wildly different value to previous measurements and what became known as the proton radius puzzle. Yet rather than being chastized, the muon is cherished for its surprising behavior, which makes it a likely candidate to reveal new physics beyond the Standard Model. 

Aiming to make sense of the muon’s strange behaviour, researchers from PSI and ETH Zürich turned to an exotic atom known as muonium. Formed from a positive muon orbited by an electron, muonium is similar to hydrogen but much simpler. Whereas hydrogen’s proton is made up of quarks, muonium’s positive muon has no substructure. And this means it provides a very clean model system from which to sort these problems out: 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 deviation from the Standard Model. And if we see this, we can then infer which of the theories that go beyond the Standard Model are viable or not,” explains Paolo Crivelli from ETH Zürich, who is leading the study supported by a European Research Council Consolidator grant in the frame of the Mu-MASS project.

Only one place in the world this is possible

A major challenge to making these measurements very precisely is having an intense beam of muonium particles so that statistical errors can be reduced. Making lots of muonium, which incidentally lasts for only two microseconds, is not simple. There is one place in the world where enough positive muons at low energy are available to create this: PSI’s Swiss Muon Source.

“To make muonium efficiently, we need to use slow muons. When they’re first produced they’re going at a quarter of the speed of light. We then need to slow them down by a factor of a thousand without losing them. At PSI, we’ve perfected this art. We have the most intense continuous source of low energy muons in the world. So we’re uniquely positioned to perform these measurements,” says Thomas Prokscha, who heads the Low Energy Muons group at PSI.

At the Low Energy Muons beamline, slow muons pass through a thin foil target where they pick up electrons to form muonium. As they emerge, Crivelli’s team are waiting to probe their properties using microwave and laser spectroscopy.

Tiny change in energy levels could hold the key

The property of muonium that the researchers are able to study in such detail is its energy levels. In the recent publication, the teams were able to measure for the first time a transition between certain very specific energy sublevels in muonium. Isolated from other so-called hyperfine levels, the transition can be modeled extremely cleanly. The ability to now measure it will facilitate other precision measurements: in particular, to obtain an improved value of an important quantity known as the Lamb shift.

The Lamb shift is a miniscule change in certain energy levels in hydrogen relative to where they ‘should’ be as predicted by classical theory. The shift was explained with the advent of Quantum Electrodynamics (the quantum theory of how light and matter interact). Yet, as discussed, in hydrogen, protons – possessing substructure – complicate things. 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 effects relating to the nuclear mass, such as how a particle recoils after absorbing a photon of light, are enhanced. Indetectable in hydrogen, a route to these values at high precision in muonium could enable scientists to test certain theories that would explain the muon g-2 anomaly: for example, the existence of new particles such as scalar or vector gauge bosons.

Putting the muon on the scales

However exciting the potential of this may be, the team have a greater goal in their sights: weighing the muon. To do this, they will measure a different transition in muonium to a precision one thousand times greater than ever before.

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

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

Muonium spectroscopy poised to fly with IMPACT project

Given that the main limitation for such experiments is producing enough muonium to reduce statistical errors, the outlook for this research at PSI looks bright. “With the high intensity muon beams proposed for the IMPACT [Isotope and Muon Production using Advanced Cyclotron and Target technologies] project we could potentially go a factor of one hundred higher in precision, and this would be getting very interesting for the Standard Model,” emphasises Prokscha.

Science paper:
Nature Communications
See the science paper for instructive material with images.

See the full article here.

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ETH Zurich campus

The Swiss Federal Institute of Technology in Zürich [ETH Zürich] [Eidgenössische Technische Hochschule Zürich] (CH) is a public research university in the city of Zürich, Switzerland. Founded by the Swiss Federal Government in 1854 with the stated mission to educate engineers and scientists, the school focuses exclusively on science, technology, engineering and mathematics. Like its sister institution The Swiss Federal Institute of Technology in Lausanne [EPFL-École Polytechnique Fédérale de Lausanne](CH) , it is part of The Swiss Federal Institutes of Technology Domain (ETH Domain)) , part of the The Swiss Federal Department of Economic Affairs, Education and Research [EAER][Eidgenössisches Departement für Wirtschaft, Bildung und Forschung] [Département fédéral de l’économie, de la formation et de la recherche] (CH).

The university is an attractive destination for international students thanks to low tuition fees of 809 CHF per semester, PhD and graduate salaries that are amongst the world’s highest, and a world-class reputation in academia and industry. There are currently 22,200 students from over 120 countries, of which 4,180 are pursuing doctoral degrees. In the 2021 edition of the QS World University Rankings ETH Zürich is ranked 6th in the world and 8th by the Times Higher Education World Rankings 2020. In the 2020 QS World University Rankings by subject it is ranked 4th in the world for engineering and technology (2nd in Europe) and 1st for earth & marine science.

As of November 2019, 21 Nobel laureates, 2 Fields Medalists, 2 Pritzker Prize winners, and 1 Turing Award winner have been affiliated with the Institute, including Albert Einstein. Other notable alumni include John von Neumann and Santiago Calatrava. It is a founding member of the IDEA League and the International Alliance of Research Universities (IARU) and a member of the CESAER network.

ETH Zürich was founded on 7 February 1854 by the Swiss Confederation and began giving its first lectures on 16 October 1855 as a polytechnic institute (eidgenössische polytechnische schule) at various sites throughout the city of Zurich. It was initially composed of six faculties: architecture, civil engineering, mechanical engineering, chemistry, forestry, and an integrated department for the fields of mathematics, natural sciences, literature, and social and political sciences.

It is locally still known as Polytechnikum, or simply as Poly, derived from the original name eidgenössische polytechnische schule, which translates to “federal polytechnic school”.

ETH Zürich is a federal institute (i.e., under direct administration by the Swiss government), whereas The University of Zürich [Universität Zürich ] (CH) is a cantonal institution. The decision for a new federal university was heavily disputed at the time; the liberals pressed for a “federal university”, while the conservative forces wanted all universities to remain under cantonal control, worried that the liberals would gain more political power than they already had. In the beginning, both universities were co-located in the buildings of the University of Zürich.

From 1905 to 1908, under the presidency of Jérôme Franel, the course program of ETH Zürich was restructured to that of a real university and ETH Zürich was granted the right to award doctorates. In 1909 the first doctorates were awarded. In 1911, it was given its current name, Eidgenössische Technische Hochschule. In 1924, another reorganization structured the university in 12 departments. However, it now has 16 departments.

ETH Zürich, EPFL (Swiss Federal Institute of Technology in Lausanne) [École polytechnique fédérale de Lausanne](CH), and four associated research institutes form The Domain of the Swiss Federal Institutes of Technology (ETH Domain) [ETH-Bereich; Domaine des Écoles polytechniques fédérales] (CH) with the aim of collaborating on scientific projects.

Reputation and ranking

ETH Zürich is ranked among the top universities in the world. Typically, popular rankings place the institution as the best university in continental Europe and ETH Zürich is consistently ranked among the top 1-5 universities in Europe, and among the top 3-10 best universities of the world.

Historically, ETH Zürich has achieved its reputation particularly in the fields of chemistry, mathematics and physics. There are 32 Nobel laureates who are associated with ETH Zürich, the most recent of whom is Richard F. Heck, awarded the Nobel Prize in chemistry in 2010. Albert Einstein is perhaps its most famous alumnus.

In 2018, the QS World University Rankings placed ETH Zürich at 7th overall in the world. In 2015, ETH Zürich was ranked 5th in the world in Engineering, Science and Technology, just behind the Massachusetts Institute of Technology, Stanford University and University of Cambridge (UK). In 2015, ETH Zürich also ranked 6th in the world in Natural Sciences, and in 2016 ranked 1st in the world for Earth & Marine Sciences for the second consecutive year.

In 2016, Times Higher Education World University Rankings ranked ETH Zürich 9th overall in the world and 8th in the world in the field of Engineering & Technology, just behind the Massachusetts Institute of Technology, Stanford University, California Institute of Technology, Princeton University, University of Cambridge(UK), Imperial College London(UK) and University of Oxford(UK) .

In a comparison of Swiss universities by swissUP Ranking and in rankings published by CHE comparing the universities of German-speaking countries, ETH Zürich traditionally is ranked first in natural sciences, computer science and engineering sciences.

In the survey CHE Excellence Ranking on the quality of Western European graduate school programs in the fields of biology, chemistry, physics and mathematics, ETH Zürich was assessed as one of the three institutions to have excellent programs in all the considered fields, the other two being Imperial College London (UK) and the University of Cambridge (UK), respectively.

Paul Sherrer Institute SwissFEL Coherent Light Source, Spallation Neutron Source (SINQ), Muon Source (SμS), X-ray free-electron laser (SwissFEL).

The Paul Scherrer Institute [Paul Scherrer Institut] (CH) is the largest research institute for natural and engineering sciences within Switzerland. We perform world-class research in three main subject areas: Matter and Material; Energy and the Environment; and Human Health. By conducting fundamental and applied research, we work on long-term solutions for major challenges facing society, industry and science.

The Paul Scherrer Institute (PSI) is a multi-disciplinary research institute for natural and engineering sciences in Switzerland. It is located in the Canton of Aargau in the municipalities Villigen and Würenlingen on either side of the River Aare, and covers an area over 35 hectares in size. Like ETH Zurich [Swiss Federal Institute of Technology ETH Zürich [Eidgenössische Technische Hochschule Zürich)](CH) and EPFL [Swiss Federal Institute of Technology in Lausanne) [École polytechnique fédérale de Lausanne](CH)], PSI belongs to the Swiss Federal Institutes of Technology Domain of the Swiss Confederation . The PSI employs around 2100 people. It conducts basic and applied research in the fields of matter and materials, human health, and energy and the environment. About 37% of PSI’s research activities focus on material sciences, 24% on life sciences, 19% on general energy, 11% on nuclear energy and safety, and 9% on particle physics.
PSI develops, builds and operates large and complex research facilities and makes them available to the national and international scientific communities. In 2017, for example, more than 2500 researchers from 60 different countries came to PSI to take advantage of the concentration of large-scale research facilities in the same location, which is unique worldwide. About 1900 experiments are conducted each year at the approximately 40 measuring stations in these facilities.

In recent years, the institute has been one of the largest recipients of money from the Swiss lottery fund.

Research and specialist areas

Paul Scherrer Institute develops, builds and operates several accelerator facilities, e. g. a 590 MeV high-current cyclotron, which in normal operation supplies a beam current of about 2.2 mA. PSI also operates four large-scale research facilities: a synchrotron light source (SLS), which is particularly brilliant and stable, a spallation neutron source (SINQ), a muon source (SμS) and an X-ray free-electron laser (SwissFEL).

This makes PSI currently (2020) the only institute in the world to provide the four most important probes for researching the structure and dynamics of condensed matter (neutrons, muons and synchrotron radiation) on a campus for the international user community. In addition, HIPA’s target facilities also produce pions that feed the muon source and the Ultracold Neutron source UCN produces very slow, ultracold neutrons. All these particle types are used for research in particle physics.