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Hadronic Corrections to the Muon Anomalous Magnetic Moment

Principal Investigator: Kálmán Szabó, Forschungszentrum Jülich GmbH, Institute for Advanced Simulation (IAS), Jülich Supercomputing Centre, Jülich (Germany)
HPC Platform: JUQUEEN of JSC
Date published: March 2018
Project-ID @ JSC: hfz00

Muon is an elementary particle. It has the same charge and same spin as the electron, but it is about 200 times heavier. It also has a magnetic moment, which means that it is like a tiny magnet: its orientation will change under the influence of a magnetic field. Assuming that it is indeed a tiny magnet the magnetic moment can be calculated very simply. Only the result is simpler:

Hadronic Corrections to the Muon Anomalous Magnetic Moment


where e is the charge and m is the mass of the muon.

This classical result was found incorrect by Paul Dirac. He has taken into account the quantum nature of these particles and got

Hadronic Corrections to the Muon Anomalous Magnetic Moment


with g = 2, ie. twice the classical result. The experimental verification followed soon, so Dirac deservedly got a Nobel Prize in 1933.

Soon after the war the experimental measurement of the magnetic moment got more precise and an anomaly started to take shape: g was deviating from 2 by an order of a per-cent. Just at the same time Julian Schwinger took Dirac’s theory under the loupe and found that Dirac’s result has to be corrected by

Hadronic Corrections to the Muon Anomalous Magnetic Moment


According to Schwinger the reason for the anomaly is the presence of a cloud of particles, which surrounds the muon. The existence of such a cloud is a consequence of Nature being quantum and satisfying the principles of relativity. That this particle cloud is real and the magnetic moment deviates from 2 was soon confirmed by the experiment, so Schwinger also got a Nobel Prize in 1965.

Theoretical and experimental particle physicists continued this hand-in-hand exploration. Experiments got much more precise, theoreticians calculate with more and more complicated forms of the cloud that surrounds the muon. Currently there is an unexplained 4σ tension between experiment (2004) and theory. If it persisted, then this would be a new candidate for a Nobel worthy puzzle.

Huge efforts are undertaken to improve both experimental and theory sides. The new experimental results are expected in 2020. Until then theorists have to reduce the uncertainties in their calculations considerably. Among other theory teams an international collaboration from Wuppertal, Jülich and Marseille is performing computations, the Jülich contribution is coordinated by Kalman Szabo. The equations describing the clouds have very large number of unknowns, order of 10 millions, thus the use of supercomputers is unavoidable. Fortunately massively parallel supercomputers, like JUQUEEN, can be used very efficiently.

Figure 1 (below) shows the current status of the calculations: ”this work” corresponds to Wuppertal-Jülich-Marseille result, which is consistent with both previous theory (with blue) determinations and the experiment (green). In the next years we hope to see a significant reduction in the errors, keeping this long exploration exciting in the near future.

Hadronic Corrections to the Muon Anomalous Magnetic MomentCopyright: Forschungszentrum Jülich

Scientific Contact:

Prof. Dr. Kálmán Szabó
Forschungszentrum Jülich GmbH
Institute for Advanced Simulation (IAS), Jülich Supercomputing Centre (JSC)
Wilhelm-Johnen-Straße, D-52425 Jülich (Germany)
e-mail: szaboka [@] general.elte.hu