Lepton Magnetic Moments: What They Tell Us

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, <span class="it">ab-initio</span> 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 to “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 also searches at the Large Hadron Collider (LHC) at CERN tell us! A triumph of the SM, in spite of the fact that the SM cannot explain known cosmological puzzles such as 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 \(\epm \) data for \(\rho ^0\)–\(\gamma \) mixing effects. Abstract Published by the Jagiellonian University 2026 authors