The Muon g-2 (0902.3360v1)

Abstract: The muon anomalous magnetic moment is one of the most precisely measured quantities in particle physics. In a recent experiment at Brookhaven it has been measured with a remarkable 14-fold improvement of the previous CERN experiment reaching a precision of 0.54ppm. Since the first results were published, a persisting "discrepancy" between theory and experiment of about 3 standard deviations is observed. It is the largest "established" deviation from the Standard Model seen in a "clean" electroweak observable and thus could be a hint for New Physics to be around the corner. This deviation triggered numerous speculations about the possible origin of the "missing piece" and the increased experimental precision animated a multitude of new theoretical efforts which lead to a substantial improvement of the prediction of the muon anomaly a_mu=(g_mu-2)/2. The dominating uncertainty of the prediction, caused by strong interaction effects, could be reduced substantially, due to new hadronic cross section measurements in electron-positron annihilation at low energies. Also the recent electron g-2 measurement at Harvard contributes substantially to the progress in this field, as it allows for a much more precise determination of the fine structure constant alpha as well as a cross check of the status of our theoretical understanding.

• The paper integrates precise experimental measurements and advanced QED, hadronic, and electroweak computations to analyze the muon anomalous magnetic moment.
• It details Brookhaven experiments that achieved a 14-fold improvement, exposing a 3.2σ gap between theoretical predictions and empirical data.
• The research suggests that the observed discrepancy may indicate physics beyond the Standard Model, spurring future theoretical and experimental refinements.

Overview of "The Muon g-2"

"The Muon g-2" by Fred Jegerlehner and Andreas Nyfeller provides a comprehensive analysis of the muon anomalous magnetic moment $(g-2)$. This paper consolidates theoretical advancements, experimental measurements, and implications in particle physics. The work aims at understanding discrepancies between the predicted Standard Model (SM) value of $g-2$ for the muon and its experimental observation, which may signal new physics.

Precision Measurement and Theoretical Discrepancy

The muon $g-2$ is one of the most accurately measured quantities in particle physics, due to experiments at Brookhaven that achieved a 14-fold improvement over prior measurements. Despite these efforts, there persists a discrepancy between the experimental results and theoretical predictions (~3.2 standard deviations), arising mainly from ambiguities within the SM. This gap is crucial as it hints at potential physics beyond the SM.

Theoretical Underpinnings

1. QED Contributions: Quantum Electrodynamics (QED) forms the backbone of the theoretical framework, accounting for the electron and muon magnetic moments up to five-loop corrections. The universal nature of these contributions across different leptons is emphasized, with $a_\ell^{\rm QED}$ representing the QED contribution to the anomalous magnetic moment.
2. Hadronic Contributions: The paper explores hadronic vacuum polarization and light-by-light scattering processes. Evaluating these without resorting to perturbative QCD involves using dispersion relations and experimental data, particularly from $e^+e^-$ annihilation into hadrons.
3. Electroweak and New Physics Contributions: These account for a smaller but non-negligible part of the theoretical prediction. The paper suggests that discrepancies might also arise from these sectors, spurring interest in extensions to the SM, including supersymmetry.

Experimental Insights

The experimentation at Brookhaven meticulously measured the deviation in precession frequencies of muon spins in a magnetic storage ring, yielding an accurate value for the muon $g-2$. These measurements have set a benchmark that any theoretical model of particle physics must meet or explain. Recent advancements also suggest potential future experiments that aim to reduce experimental uncertainty further.

Implications and Future Prospects

The persistent discrepancy between theory and experiment provides fertile ground for further investigations. It suggests the possibility of new physics, perhaps involving supersymmetric particles or other beyond-the-SM phenomena. The theoretical community has responded to the experimental challenges by refining techniques for computing contributions from the various sectors of the SM and exploring model-independent approaches for quantifying hadronic effects.

Conclusion

Jegerlehner and Nyfeller's paper elucidates the significant strides made in reducing theoretical and experimental uncertainties in muon $g-2$ studies. The work exemplifies how precision measurements can unveil subtle effects not explained within the current theoretical frameworks, potentially pointing towards new physics. The muon $g-2$ thus remains an active and promising frontier for exploration in particle physics. As theoretical techniques and experimental methods evolve, the field can anticipate deeper insights into the fundamental forces and particles governing the universe.