Muon g-2 Theory: the Hadronic Part (1705.00263v1)

Abstract: I present a status report of the hadronic vacuum polarization effects for the muon $g-2$, to be considered as an update of [1]. The update concerns recent new inclusive $R$ measurements from KEDR in the energy range 1.84 to 3.72 GeV. For the leading order contributions I find $a_\mu^{\mathrm{had}(1)}=(688.07\pm 4.14)[688.77\pm3.38]\times 10^{-10}$ based on $e^+e^-$data [incl. $\tau$ data], $a_\mu^{\mathrm{had}(2)}= (-9.93\pm 0.07) \times 10^{-10}$ (NLO) and $a_\mu^{\mathrm{had}(3)}= (1.22\pm 0.01) \times 10^{-10}$ (NNLO). Collecting recent progress in the hadronic light-by-light scattering I adopt $\pi^0,\eta,\eta'$ [$95 \pm 12$] + axial--vector [$8 \pm ~3$] + scalar [$-6\pm ~1$] + $\pi,K$ loops [$-20\pm 5$] + quark loops [$22\pm ~4$] + tensor [$1\pm ~0$] + NLO [$3\pm ~2$] which yields $ a^{(6)}_\mu(\mathrm{lbl},\mathrm{had})=(103 \pm 29) \times 10^{-11}.$ With these updates I find $a_\mu^{\rm exp}-a_\mu^{\rm the}=(31.3\pm 7.7)\times 10^{-10}$ a 4.1 $\sigma$ deviation. Recent lattice QCD results and future prospects to improve hadronic contributions are discussed.

An Analytical Review of "Muon $g-2$ Theory: the Hadronic Part"

The paper authored by Fred Jegerlehner presents an in-depth analysis of the hadronic contributions to the muon anomalous magnetic moment, $g-2$, particularly focusing on hadronic vacuum polarization (HVP) effects. The research builds on prior work by Jegerlehner, involving updates driven by new experimental data from sources like KEDR, aimed at refining the calculation of hadronic contributions to the muon $g-2$.

Key Numerical Findings

The paper provides detailed evaluations of leading-order (LO), next-to-leading-order (NLO), and next-to-next-to-leading-order (NNLO) hadronic contributions to the muon $g-2$. Significant numerical results include:

• The LO hadronic contribution based on $e^+e^-$ data has been determined as $$a_\mu^{\mathrm{had}(1)} = (688.07 \pm 4.14) \times 10^{-10}$$, showing alignment with previous evaluations.
• The NLO and NNLO hadronic vacuum polarization effects are refined as $$a_\mu^{\mathrm{had}(2)} = (-9.93 \pm 0.07) \times 10^{-10}$$ and $$a_\mu^{\mathrm{had}(3)} = (1.22 \pm 0.01) \times 10^{-10}$$, respectively.
• The comprehensive review consolidates contributions to hadronic light-by-light (HLbL) scattering, leading to $$a_\mu^{(6)}(\mathrm{lbl},\mathrm{had}) = (103 \pm 29) \times 10^{-11}$$.

A crucial aspect is the reported discrepancy between experimental and theoretical values for the muon's anomalous magnetic moment, which stands at $(31.3 \pm 7.7) \times 10^{-10}$ or 4.1 standard deviations, inviting further scrutiny into potential new physics beyond the Standard Model.

Theoretical and Practical Implications

This research is pivotal in both theoretical exploration and experimental practice. Correct calculations of hadronic effects are vital to resolve the persistent discrepancies between theoretical predictions and experimental results in the muon $g-2$. The paper leverages contemporary lattice QCD methodologies and emerging data-driven techniques, such as utilizing dispersion relations to incorporate $e^+e^- \rightarrow$ hadron cross-section data. These methods can provide more accurate and high-precision determinations of vacuum polarization.

Moreover, the paper emphasizes the significant role of lower energy experimental data, despite the challenges posed by potential non-perturbative QCD effects in theoretical predictions. Jegerlehner’s analysis paves the way for refining experimental techniques in upcoming studies at facilities like Fermilab and J-PARC, enabling unprecedented precision in muon $g-2$ measurements.

Prospective Developments and Challenges

Future improvements in understanding the muon $g-2$ rely heavily on advancements in both experimental setups and theoretical frameworks. The paper highlights potential adjustments such as improved statistical accuracy in hadronic cross-section measurements below 2 GeV, integral in reducing the theoretical uncertainties in HVP contributions. Furthermore, the interplay between potential new physics interpretations of the $g-2$ discrepancy and the need for strengthened theoretical foundations remains a challenge and an opportunity in particle physics research.

Additionally, the ongoing evolvement of lattice QCD simulations brings optimism for more robust predictions, bridging the gap between experimental evidence and theoretical deductions. The potential reconciliation and fine-tuning of hadronic contributions to HLbL scattering, complemented by cross-validation against future lattice QCD predictions and dispersion relations, represents a critical path forward in elucidating the muon $g-2$ anomaly.

The presented findings and methodologies embodied in Jegerlehner’s paper form an integral component of the broader narrative in particle physics, contributing to a deeper understanding of fundamental interactions and the Standard Model validity. As experiments push the precision frontier, continuous theoretical developments serve as vital companions in deciphering any promising signals of new physics.