The anomalous magnetic moment of the muon in the Standard Model: an update (2505.21476v2)

Abstract: We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_\mu$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\to\pi^+\pi^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_\mu^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_\mu^\text{exp} - a_\mu^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

An Update on the Anomalous Magnetic Moment of the Muon in the Standard Model

This paper provides a comprehensive update on the Standard Model (SM) prediction for the anomalous magnetic moment of the muon, denoted as $a_\mu$. The update includes advancements in theoretical calculations, particularly focusing on refining the hadronic contributions, which are recognized as the dominant sources of uncertainty in the SM prediction. Significant progress has been reported in the evaluation of both the hadronic light-by-light (HLbL) scattering contributions and the leading-order hadronic vacuum polarization (LO HVP) contributions, which have been historically challenging to compute with high precision.

Key Advances in Hadronic Contributions

1. Reduction in Uncertainty for HLbL: The paper details improvements in the calculation of the HLbL scattering contribution, which now benefits from both a data-driven dispersive approach and lattice-QCD calculations. These methodologies have contributed to a notable reduction in the uncertainty of HLbL contributions by nearly half, showcasing an alignment towards more convergent theoretical predictions.
2. Changes in LO HVP Estimates: A critical development is the reassessment of the LO HVP contribution. New measurements, particularly from the CMD-3 experiment involving the $e^+e^-\to\pi^+\pi^-$ cross section, have introduced tensions among existing data-driven evaluations. This situation has made it untenable to combine results meaningfully without addressing these discrepancies. Concurrently, lattice-QCD calculations have matured significantly, now offering a consolidated average of LO HVP contributions with a precision of approximately 0.9%. The adoption of these lattice-based estimates has subsequently prompted a substantial upward shift in the total SM prediction of $a_\mu$.
3. Consolidation of Electroweak and QED Contributions: Besides the hadronic sectors, the QED and electroweak contributions have been further consolidated, contributing to the overall confidence in the auxiliary components of the SM prediction.

Implications for Muon $g-2$ Experiment

The refined SM prediction now reads $a_\mu = 116\ \text{(530 ppb)}$, facilitating a comparison against the current experimental average derived from the combination of historical results from the E821 experiment and recent results from E989 at Fermilab. The reported comparison yields $a_\mu - a_\mu^\text{exp} = 26(66) \times 10^{-11}$, implying that there is presently no significant tension between SM predictions and experimental observations at current precision levels. The expected final precision from E989 is anticipated to be around 140 ppb, which remains a target for future theoretical endeavors.

Future Directions and Theoretical Considerations

The paper suggests that resolving the tensions among data-driven dispersive evaluations of the LO HVP contribution remains a pivotal task for upcoming research. Future theoretical efforts within the community must continue to direct focus on:

• Advancing lattice-QCD techniques to address precision and scalability challenges.
• Refining data-driven methods to reconcile existing discrepancies in hadronic cross-section data.
• Preparing for increased precision levels in experimental measurements, thereby enabling more stringent tests of the SM.

Conclusion

The advances highlighted within this paper illustrate a substantial evolution in the precision of SM predictions for $a_\mu$, predominantly driven by improvements in hadronic computations. The harmonization of results from both traditional data-driven approaches and modern lattice-based methods holds promise in narrowing down the uncertainties currently limiting theoretical predictions. These developments signify pivotal steps toward establishing whether any discrepancies between theory and experiment might suggest physics beyond the Standard Model.