[Paper Review] Theoretical status of the muon g-2

Andreas Nyffeler|ArXiv.org|May 13, 2003

Particle physics theoretical and experimental studies3 citations

TL;DR

This 2003 paper reviews the theoretical status of the muon's anomalous magnetic moment ($g-2$) within the Standard Model, focusing on hadronic contributions from vacuum polarization, light-by-light scattering, and electroweak corrections. It finds that discrepancies between experimental and theoretical values—particularly when based on $e^+e^-$ data—may signal new physics, but current inconsistencies between $e^+e^-$ and $\tau$-based hadronic inputs prevent a definitive conclusion.

ABSTRACT

We review the present status of the theoretical evaluation of the anomalous magnetic moment of the the muon within the Standard Model. We mainly focus on the hadronic contributions in the muon g-2 due to vacuum polarization effects, light-by-light scattering and higher order electroweak corrections. We discuss some recent calculations together with their uncertainties and limitations and point out possible improvements in the future. In view of the inconsistent values for the hadronic vacuum polarization based on e^+ e^- and tau data, no conclusion can be drawn yet, whether the apparent discrepancy between the current experimental and theoretical values for the muon g-2 points to physics beyond the Standard Model.

Motivation & Objective

• To assess the current theoretical prediction of the muon's anomalous magnetic moment ($a_\mu$) within the Standard Model.
• To evaluate the dominant theoretical uncertainties arising from hadronic contributions, particularly vacuum polarization and light-by-light scattering.
• To examine the consistency between theoretical estimates based on $e^+e^-$ and $\tau$-leptons decays, which show conflicting results.
• To determine whether the observed discrepancy between experiment and theory could indicate new physics beyond the Standard Model.
• To identify key uncertainties and limitations in existing calculations and suggest future improvements.

Proposed method

• Uses perturbative QED calculations up to four loops for the electron $g-2$ to benchmark precision and extract $\alpha$.
• Applies short-distance constraints from the operator product expansion (OPE) to improve two-loop hadronic vacuum polarization calculations.
• Performs two-loop electroweak corrections using effective field theory techniques, including resummation of leading logarithms.
• Compares theoretical predictions based on $e^+e^-$ annihilation data and $\tau$-lepton decay data to assess consistency.
• Quantifies uncertainties in hadronic contributions using error propagation and variation of input parameters like $M_H$.
• Averages results from multiple groups to estimate final values with error estimates for $a_\mu^{\text{SM}}$.

Experimental results

Research questions

• RQ1 What is the current theoretical prediction for the muon's anomalous magnetic moment within the Standard Model?
• RQ2 How do hadronic vacuum polarization and light-by-light scattering contribute to the theoretical uncertainty in $a_\mu$?
• RQ3 Why do theoretical estimates of $a_\mu$ differ when based on $e^+e^-$ versus $\tau$-decay data?
• RQ4 Could the discrepancy between experiment and theory point to new physics beyond the Standard Model?
• RQ5 What are the main sources of uncertainty in the hadronic contributions, and how can they be improved?

Key findings

• Theoretical prediction for $a_\mu$ based on $e^+e^-$ data is $11,659,167.5 \pm 7.5 \pm 4.0 \pm 0.35 \times 10^{-10}$, showing a $3.0\sigma$ discrepancy with experiment.
• Theoretical prediction based on $\tau$-decay data is $11,659,192.7 \pm 5.9 \pm 4.0 \pm 0.35 \times 10^{-10}$, showing only a $1.0\sigma$ discrepancy with experiment.
• The electroweak correction is estimated as $15.3(0.2) \times 10^{-10}$, with a two-loop correction of $-4.2(0.2) \times 10^{-10}$.
• The discrepancy between $e^+e^-$ and $\tau$-based evaluations suggests potential inconsistencies in hadronic inputs, undermining a definitive conclusion about new physics.
• An error in the CMD-2 $e^+e^-$ data is expected to reduce the $e^+e^-$-based discrepancy to less than $2\sigma$.
• Hadronic uncertainties remain the largest source of theoretical error, with estimates possibly underestimated, and further work is needed to control them.