BMW/DMZ calculation of the hadronic vacuum polarisation for the muon magnetic moment

Abstract

For twenty years, a persistent discrepancy between experimental measurements and theoretical calculations of the muon anomalous magnetic moment have provided tantalising hints of new physics. In recent years, improvements to the experimental precision have appeared to make the tension stronger and stronger. However, at the same time, our lattice calculation overturned the theoretical consensus, completely eliminating the tension. I will present the latest results from the Budapest-Marseille-Wuppertal (BMW) and DMZ collaborations, with a hybrid determination of the hadronic vacuum polarisation contribution to a precision of 0.45%

Figures (12)

• Figure 1: Comparison of Standard Model predictions for the muon anomalous magnetic moment with its measured value, taken from Ref. Boccaletti:2024guq. The top panel shows a comparison of the world-average experimental measurement of $a_\mu$Muong-2:2025xyk with the Standard Model prediction obtained by the BMW collaboration Boccaletti:2024guq, denoted by the red band. The middle panel shows a predictions based on the earlier BMW result from Ref. Borsanyi:2020mff as well as results from two other similar calculations, from RBC/UKQCD RBC:2018dosRBC:2023pvnRBC:2024fic and Mainz Djukanovic:2024cmq, along with the consensus combination of the three from Ref. Aliberti:2025beg. The lower panel shows the predictions for $a_{\mu}^\text{LO-HVP}$ obtained in the 2020 approach Aoyama:2020ynm using specific experimental inputs Davier:2023fpl. These correspond to BaBar BaBar:2009wpwBaBar:2012bdw, KLOE KLOE:2008fmqKLOE:2010qeiKLOE:2012anlKLOE-2:2017fda and CMD-3 CMD-3:2023alj, and $\tau$ decays Davier:2009agDavier:2013sfa. Note, all Standard Model predictions include non-HVP contributions from "White paper '25", except for "White paper '20".
• Figure 2: Comparison of lattice values for the leading HVP contribution to the muon magnetic moment. The blue circle is the Standard Model consensus from the 2020 White Paper Aoyama:2020ynm, and the squares are lattice results. The older lattice results Budapest-Marseille-Wuppertal:2017okrRBC:2018dosGiusti:2019hkzShintani:2019waiFermilabLattice:2019uguGerardin:2019ruaLehner:2020crtAubin:2022hgm are consistent with both the Standard Model consensus and the experimental measurement. The four most precise results (from BMW Borsanyi:2020mffBoccaletti:2024guq, Mainz Djukanovic:2024cmq, and RBC/UKQCD RBC:2024fic) agree with the experimental measurement but not the Standard Model consensus.
• Figure 3: Main uncertainties and their reduction in the BMW collaboration's successive lattice calculations of $a_{\mu}^\text{LO-HVP}$. Their sources are labelled (a-e) in the text and are given a short descriptive title below the bars in the plot. Their approximate size relative to the total LO-HVP contribution obtained in the present work is also shown. The orange bars on the left of each group correspond to the 2017 BMW result Borsanyi:2017zdw, the purple ones in the middle to the 2020 findings Borsanyi:2020mff, and the red ones on the right to the latest BMW preprint Boccaletti:2024guq.
• Figure 4: Spread of our ensembles around the physical point, as defined by the masses of the pseudo-scalar mesons $M_{ll}$ and $M_{ss}$. Different colours denote different lattice spacings. The black point denotes the (isospin-symmetric) physical point, with error bars corresponding to the uncertainties from our determination of $M_{ll}$ and $M_{ss}$ in physical units.
• Figure 5: Light-connected window observable $a_{\mu,04-10}^\mathrm{light}$. Top: continuum extrapolations, coloured according to the weight of the fit in our analysis. Lower left: the probability distribution function, which shows a single well-defined peak. The shaded bands correspond to the one- and two-sigma confidence bands. Lower right: we compare our result with others from the literature, both lattice Borsanyi:2020mffLehner:2020crtWang:2022lkqAubin:2022hgmCe:2022kxyExtendedTwistedMass:2022jpwRBC:2023pvnMILC:2024ryz and data-driven Borsanyi:2020mffBenton:2023dci.