A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\boldsymbolα(m_Z^2)}$ (1908.00921v3)

Abstract: We reevaluate the hadronic vacuum polarisation contributions to the muon magnetic anomaly and to the running of the electromagnetic coupling constant at the $Z$-boson mass. We include newest $e^+e^- \to$ hadrons cross-section data together with a phenomenological fit of the threshold region in the evaluation of the dispersion integrals. The precision in the individual datasets cannot be fully exploited due to discrepancies that lead to additional systematic uncertainty in particular between BABAR and KLOE data in the dominant $\pi^+\pi^-$ channel. For the muon $(g-2)/2$, we find for the lowest-order hadronic contribution $(694.0 \pm 4.0)\cdot10^{-10}$. The full Standard Model prediction differs by $3.3\sigma$ from the experimental value. The five-quark hadronic contribution to $\alpha(m_Z^2)$ is evaluated to be $(276.0\pm1.0)\cdot10^{-4}$.

• The paper refines the evaluation of hadronic corrections, yielding a new a_μ value of (694.0 ± 4.0)×10⁻¹⁰ and highlighting a 3.3σ discrepancy with experimental results.
• The paper integrates the latest e⁺e⁻ → hadrons cross-section data to address systematic uncertainties, notably reconciling differences between BABAR and KLOE measurements in the π⁺π⁻ channel.
• The paper determines the five-quark contribution to α(m_Z²) as (276.0 ± 1.0)×10⁻⁴, enhancing precision electroweak tests within the Standard Model framework.

Evaluation of Hadronic Vacuum Polarization Contributions

The paper presented by Davier, Hoecker, Malaescu, and Zhang provides a refined analysis of the hadronic vacuum polarization contributions to the muon anomalous magnetic moment, denoted as $a_\mu = (g-2)/2$, and the running of the electromagnetic coupling constant at the $Z$-boson mass, $\alpha(m_Z^2)$. This work tackles the ongoing challenge of evaluating these contributions with greater precision by integrating the latest $\ee \to \text{hadrons}$ cross-section data into the calculation of dispersion integrals, a method crucial for accurate theoretical predictions within the Standard Model framework.

Key Contributions and Numerical Findings

1. Muon Anomalous Magnetic Moment: The analysis provides an updated value for the lowest-order hadronic contribution to the muon anomalous magnetic moment, calculated as $(694.0 \pm 4.0) \times 10^{-10}$. This value signifies a deliberate effort to reconcile various datasets despite existing discrepancies which, notably, arise between data from the BABAR and KLOE experiments particularly in the $\pi^+\pi^-$ channel. Such discrepancies are pivotal as they lead to considerable systematic uncertainties that limit the potential precision obtainable from individual datasets. The reported $3.3\sigma$ difference observed between the full Standard Model prediction and the current experimental values for $a_\mu$ accentuates the importance of improving the theoretical precision to elucidate possible physics beyond the Standard Model.
2. Electromagnetic Coupling at $Z$-Boson Mass: The paper presents a precise determination of the five-quark hadronic contribution to $\alpha(m_Z^2)$, yielding a value of $(276.0 \pm 1.0) \times 10^{-4}$. This contributes to an enhanced understanding of the electromagnetic coupling's behavior at higher energies and forms an essential component of precision electroweak tests, which are foundational to verifying the robustness of the Standard Model and probing for potential deviations indicative of novel physics.

Implications and Future Developments

The rigorous methodologies employed in this paper manifest an ongoing advancement in particle physics calculations that are critical for refining theoretical predictions and enhancing the interpretation of experimental data. The precision discrepancies pointed out by this work invite further scrutiny into the systematic uncertainties inherent in current experimental methodologies. Addressing these discrepancies will be pivotal in attaining higher fidelity measurements that could decisively bridge the theoretical predictions with experimental findings.

Looking forward, the results underscore an imperative for continued efforts in both experimental accuracy and theoretical modeling, potentially incorporating additional $\ee \to \text{hadrons}$ data and employing more sophisticated analytic techniques. The insights derived from this research may spark further theoretical explorations into alternative explanations for the observed deviations and stimulate targeted experimental pursuits, enhancing the overall understanding of fundamental interactions.

This paper solidifies the foundational approach to addressing specific aspects of particle physics through meticulous analysis and cross-disciplinary collaboration, enhancing the knowledge base required for exploring new vistas in the field.