The Anomalous Anomaly Understanding the Muon’S Magnetic Moment Holds the Key for Unlocking Potential New Physics, As Thomas Teubner Shows

measure for measure The anomalous anomaly Understanding the muon’s magnetic moment holds the key for unlocking potential new physics, as Thomas Teubner shows.

n classical electrodynamics, the magnetic scrutinized and refined. With continued moment of a particle can be understood theoretical and computational efforts, KNT18 Ias arising from a spinning charge its uncertainty has now become smaller distribution. However, even point-like than the experimental error of the BNL particles have a magnetic moment that is BNL measurement. In turn, the discrepancy has µ 3.7σ aligned with their spin s: µ =​ g(q/2m)s with been further consolidated and now stands q and m the charge and mass of the particle, BNL (×4 accuracy) at 3.7 ​(KNT18; ref. 3). The figure shows the 7.0σ σ respectively, and g its so-called g-factor. current discrepancy of 3.7σ​ with a possible From his theory of relativistic quantum future increase to 7σ,​ due to a projected 160 170 180 190 200 210 220 mechanics, Paul Dirac predicted that the four-times improved experimental accuracy (a SM × 1010) − 11,659,000 g-factor of elementary spin-1/2 particles, μ if the mean value stays unchanged. such as the electron, is exactly 2. At first, To decide beyond doubt whether the this seemed to be in agreement with atomic muon is a fundamental particle or has a discrepancy is real, new, more precise

physics experiments, but in 1947 small composite structure. Second, the muon’s measurements of aµ are needed. The next- deviations from the expectations were seen anomaly, aµ, is not only an effect from generation experiment E989 at Fermilab is in the hyperfine structure of hydrogen QED, but also contains significant under way (http://muon-g-2.fnal.gov). It

and deuterium. A small deviation of the contributions from the weak and strong is designed to measure aµ with about four electron’s g-factor from 2 was proposed as forces of the standard model (SM) of times improved accuracy. Also, a second, an explanation. In 1948 Julian Schwinger particle physics. Moreover, any unknown completely different and independent calculated that in quantum electrodynamics particle or force in nature could contribute experiment is currently being built at (QED), fluctuations lead to a tiny in addition to the known ones. For yet J-PARC in Japan, planned to start operation change of g. His famous result, the undiscovered heavy particles, the muon in a few years’ time (http://g-2.kek.jp). so-called anomalous magnetic moment, anomaly would pick up such effects E989 has already recorded first data a =​ (g – 2)/2 =​ α/(2π​), where α ≈ ​1/137 is much more strongly compared to the that the collaboration is now feverishly the fine structure constant, is engraved on electron, typically by a factor of the muon analysing, while at the same time preparing his tombstone and solved the puzzle. mass over the electron mass, squared the experiment to collect data with much Schwinger’s result was just the starting (≈​ 43,000). Therefore, studying the better statistics. The results are eagerly point of a big success story. The further muon with high precision tests our awaited; if a discrepancy is fully confirmed development of QED is very closely quantum understanding of nature, at a higher statistical significance, this connected with ever more accurate including the yet unknown. would be a clear sign for physics beyond

predictions for g – 2 using perturbation Early measurements of aµ at CERN the standard model (BSM). Conversely, theory. Today, the state of the art is the confirmed theoretical predictions, and if after all these efforts there would be inclusion of corrections up to five so-called some influential scientists predicted that agreement between measurements and loops (virtual exchanges with photons and nothing interesting would ever be learned SM theory, then this would exclude many fermions — Schwinger did one loop where from this. Others disagreed and pushed BSM models. Either way, taming the muon’s just one photon is exchanged). In 2012, after for more accurate measurements. At the anomaly is key in driving our physics many years’ work, Toichiro Kinoshita and turn of the millennium, experiment E821 understanding forward. ❐ collaborators finished the calculation of at Brookhaven National Laboratory (BNL) 1 12,672 Feynman diagrams ; their five-loop measured aµ with an accuracy of 0.5 parts Thomas Teubner contribution is proportional to (α/π​)5, per million, much better than before2. Department of Mathematical Sciences, University of which is very small but still relevant when Their result disagreed with the theoretical Liverpool, Liverpool, UK. comparing experiment and theory. The predictions, with a statistical significance e-mail: [email protected] anomalous magnetic moment (also simply of two to three standard deviations. Over

called ‘anomaly’) of the electron, ae, is the past two decades, this discrepancy, Published online: 1 November 2018 measured to an astonishing 0.25 parts despite various small changes and twists, https://doi.org/10.1038/s41567-018-0341-3 per billion and provides a very accurate has never gone away, and has led to a lot References determination of α. of excitement and hundreds of theoretical 1. Aoyama, T., Hayakawa, M., Kinoshita, T. & Nio, M. Phys. Rev. So why were physicists turning to the ideas seeking an explanation in terms of Lett. 109, 111808 (2012). muon, the more than 200 times heavier ‘new physics’. 2. Bennett, G. W. et al.(Muon g-2 Collaboration) Phys. Rev. D 73, 072003 (2006). sibling of the electron? First, a precise In recent years, all aspects of the 3. Keshavarzi, A., Nomura, D. & Teubner, T. Phys. Rev. D 97, measurement of its anomaly tests if the SM theory prediction for aµ have been 114025 (2018).

1148 Nature Physics | VOL 14 | NOVEMBER 2018 | 1148 | www.nature.com/naturephysics