Deriving the Muon g-Factor from Fundamental Constants and M o

2018

Two next generation muon g − 2 experiments at Fermilab in the USA and at J-PARC in Japan have been designed to reach a four times better precision from 0.54 ppm to 0.14 ppm and the challenge for the theory side is to keep up in precision as far as possible. This has triggered a lot of new research activities. The main motivation is the persisting 3 to 4σ deviation between standard theory and experiment. As the Standard Model predictions almost without exception match perfectly all other experimental information, the deviation in one of the most precisely measured quantities in particle physics remains a mystery and inspires the imagination of model builders. Plenty of speculations are aiming to explain what beyond the Standard Model effects could fill what seems to be missing. Here, very high precision experiments are competing with searches for new physics at the high-energy frontier lead by the Large Hadron Collider at CERN. Actually, the tension is increasing steadily as no new s...

Journal of High Energy Physics, 2021

The Fermilab Muon g −2 experiment recently reported its first measurement of the anomalous magnetic moment $$ {a}_{\mu}^{\mathrm{FNAL}} $$ a μ FNAL , which is in full agreement with the previous BNL measurement and pushes the world average deviation $$ \Delta {a}_{\mu}^{2021} $$ ∆ a μ 2021 from the Standard Model to a significance of 4.2σ. Here we provide an extensive survey of its impact on beyond the Standard Model physics. We use state-of-the-art calculations and a sophisticated set of tools to make predictions for aμ, dark matter and LHC searches in a wide range of simple models with up to three new fields, that represent some of the few ways that large ∆aμ can be explained. In addition for the particularly well motivated Minimal Supersymmetric Standard Model, we exhaustively cover the scenarios where large ∆aμ can be explained while simultaneously satisfying all relevant data from other experiments. Generally, the aμ result can only be explained by rather small masses and/or la...

Physics Reports, 2020

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant α and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including O(α 5) with negligible numerical uncertainty. The electroweak contribution is suppressed by (m µ /M W) 2 and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at O(α 2) and is due to hadronic vacuum polarization, whereas at O(α 3) the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads a SM µ = 116 591 810(43) × 10 −11 and is smaller than the Brookhaven measurement by 3.7σ. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

Nuclear Physics B - Proceedings Supplements, 2005

Recent developments in the theory of the muon anomalous magnetic moment are reviewed. The Standard Model contributions, including QED, electroweak, and hadronic parts, are summarized.

2004

Modifications of the gyromagnetic moment of electrons and muons due to a minimal length scale combined with a modified fundamental scale M f are explored. Deviations from the theoretical Standard Model value for g − 2 are derived. Constraints for the fundamental scale M f are given.

Nuclear Physics B - Proceedings Supplements, 2003

We calculate (g − 2)/2 of the muon, by improving the determination of the hadronic vacuum polarisation contribution, a had,LO µ , and its uncertainties. The different e + e − data sets for each exclusive (and the inclusive) channel are combined in order to obtain the optimum estimate of the cross sections and their uncertainties. QCD sum rules are evaluated in order to resolve an apparent discrepancy between the inclusive data and the sum of the exclusive channels. We conclude a had,LO µ = (683.1 ± 5.9 exp ± 2.0 rad) × 10 −10 which, when combined with the other contributions to (g − 2)/2, is about 3σ below the present world average measurement.

Electromagnetic mass of the elementary particle is well-studied for the electron. Here the electromagnetic mass of the muon is calculated by invoking the relation of the masses of the elementary particles with the fine structure constant. Our result relates to the magnetic self-energy of the two leptons (electron and muon) using relativistic spinning sphere model. Finally, the relation between electron and muon radii is derived in this paper.

2003

The Muon g - 2 collaboration has measured the anomalous magnetic g value, a = (g - 2)/2, of the positive muon with an unprecedented uncertainty of 0.7 parts per million. The result amu+(expt) = 11659204(7)(5) × 10-10, based on data collected in the year 2000 at Brookhaven National Laboratory, is in good agreement with the preceeding data on amu+

Journal of Physics G: Nuclear and Particle Physics, 2015

Using the momentum dependence of the dressed quark mass and the well-known formulae for the mass dependent quark loop contribution to the light-by-light scattering insertions, we compute the hadronic light-by-light contribution to the the muon anomalous magnetic moment. We ascribe for the first time a systematic error on the calculation.

We present a model based on the implication of an exceptional E 6-GUT symmetry for the anomalous magnetic moment of the muon. We follow a particular chain of breakings with Higgses in the 78 and 351 representations. We analyze the radiative correction contributions to the muon mass and the effects of the breaking of the so-called Weinberg symmetry. We also estimate the range of values of the parameters of our model.