Lepton Magnetic Moments: What They Tell Us

TL;DR

The paper presents a comprehensive update on lepton magnetic moments, emphasizing that the FNAL Muon g-2 results, combined with ab initio lattice QCD determinations of hadronic contributions, have substantially tightened the SM test and reduced the prior tension with experiment. It highlights the crucial roles of hadronic vacuum polarization and hadronic light-by-light contributions, the reconciliation between data-driven and lattice results (notably via tau data and rho-gamma mixing corrections), and the ongoing electron $g-2$ precision as a cross-check of QED. The work discusses the remaining challenges in hadronic data interpretation, the potential of MUonE to measure HVP directly, and the need for improved HLbL inputs, while projecting future advancements in alpha determinations and alternative experimental approaches (J-PARC, AION) to further probe BSM scenarios. Overall, the results point to strong SM consistency at the current level of precision, but continued high-precision measurements and cross-checks are essential to either reveal subtle BSM effects or further constrain new physics.

Abstract

Recently, the exciting new Fermilab (FNAL) Muon g-2 measurement impressively confirmed the final Brookhaven (BNL) result from 2004, and with a result four times more precise, has launched a new serious attack on the Standard Model (SM). On the theoretical side, ab initio lattice QCD (LQCD) calculations of hadronic vacuum polarization have made remarkable progress. They are now the new standard for studying the leading non-perturbative contributions, which have previously hindered matching with the precision required for full exploitation of the experimental results. The lattice results affected both leading hadronic contributions the hadronic vacuum polarization (HVP) and the hadronic light-by-light (HLbL) contributions by increasing the previously generally accepted $e^+e^-$ to hadrons based dispersion relation results. The shifts reduced the discrepancy between theory and experiment, leaving nothing missing. One of the most prominent signs of Beyond the Standard Model (BSM) physics has disappeared: the SM appears validated more than ever, in agreement with what other searches at the Large Hadron Collider (LHC) at CERN tell us! A triumph of the SM, even though the SM cannot explain known cosmological puzzles like dark matter or baryogenesis, and why neutrino masses are so tiny, the absence of strong CP violation, for example. I also argue that the discrepancy between the data-driven dispersive result and the lattice QCD results for the hadronic vacuum polarization can be largely explained by correcting the $e^+e^-$ data for 'rho-gamma' mixing effects.

Figures (5)

• Figure 1: Left: At the Magic Energy (muon beam energy $\sim$ 3.1 GeV), the angular frequency $\vec{\omega_a}$ is directly proportional to the magnetic field $\vec{B}$, so that the $a_\mu$ measurement is a frequency counting experiment. Right: The measurements of $a_\mu$ by the Muon g-2 Collaboration at the Fermi National Accelerator Laboratory (FNAL) have significantly improved on the results obtained by Brookhaven National Laboratory (BNL) in 2004.
• Figure 2: Left: A selection of $a_\mu^{{\mathrm{HVP,\ LO}}}$ results obtained using different approaches. WP20 Aoyama:2020ynm is the dispersive result based exclusively on $e^+e^- \to$ hadron data. JS11 refers to an $e^+e^-$-data-based result corrected for $\rho^0-\gamma$ interference, which convincingly explains the puzzle surrounding the $e^+e^-$- versus $\tau$-spectra relation Jegerlehner:2011ti. This correction is necessary to separate the irreducible QCD component from the normally ignored QED-QCD mixing inherent in the experimental $\pi^+ \pi^-$ production data. DHMZ10 Davier:2010fmf and the update DMZ25 Davier:2025jiq have included the isospin breaking (IB)-corrected $\tau$ data in addition to the $e^+e^-$ data. MMR23 is an analysis based exclusively on $\tau$ data Miranda:2020wdgMiranda:2020wdg. BMW, Mainz/CLS, and RBC/UKQCD are the latest lattice QCD results, which currently provide the most reliable hadronic contributions. The last point is the update of WP25 Aliberti:2025beg (wheat-colored band), the result of the consensus theory compared to the experimental result from BNL/FNAL (gray band), represented by the fictitious $a_\mu^{{\mathrm{HVP,\ LO}}}$ term required to close the gap between experiment and the theory prediction when dropping $a_\mu^{{\mathrm{HVP,\ LO}}}$. Right: A selected history of $a_\mu^{{\mathrm{LbL,\ LO}}}$ results. Pioneered by Hayakawa, Kinoshita and Sanda Hayakawa:1995ps, Bijnens, Pallante and Prades Bijnens:1995cc and Knecht and Nyffeler Knecht:2001qfKnecht:2001qg. Data point shown are MV03 Melnikov:2003xd, JN09 Jegerlehner:2009ry, the consensus PdRV Prades:2009tw, my book FJ17 Jegerlehner:2017gek and the result based on the dispersive approach by Colangelo et al. Colangelo:2019uex of the White Paper WP20. The lattice QCD results are BMW-24 Fodor:2024jyn, Mainz/CLS-22 Chao:2020kwqChao:2021tvp and RBC/UKQCD-23 Blum:2017cerBlum:2023vlm. WP25 represents the current consensus of the Mon g-2 theory initiative Aliberti:2025beg.
• Figure 3: Left: The ratio of the isospin $I=1$ pion form factor $|F_\pi(E)|^2$ taking mixing into account, normalized to the case without mixing. Also shown is the same ratio of the $I=1$ part of the $e^+e^-$ data to the $\tau$ data GS fits, mimicked by fictitious parameter shifts in mass and width. Right: Best "proof" for our $\gamma-\rho^0$ mixing profile is the ratio of the ALEPH $\tau$ decay spectrum versus the BaBar $e^+e^-$ spectrum [reproduced as part of Fig. 55 in arXiv:1205.2228 by J. P. Lees et al.] BaBar:2012bdw] (also see Davier:2010fmf).
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