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arXiv · 2607.12918

Hadronic vacuum polarization contribution to $a_\mu$ from functional methods with strong and electromagnetic isospin breaking

Angel S. Miramontes·Adnan Bashir·Christian S. Fischer·Pablo Roig
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Abstract

We present a continuum-QCD determination of the leading-order hadronic vacuum-polarization contribution to the anomalous magnetic moment of the muon within the Dyson-Schwinger and Bethe-Salpeter equation framework. The calculation incorporates pion back-reaction, a fully dressed quark-photon vertex with a dynamically generated $\rho$-resonance structure in the timelike region, and both strong and electromagnetic isospin breaking treated self-consistently at the quark level. We obtain $a_\mu^{\mathrm{HVP,LO}}(u+d+s+c)|_{\mathrm{ISB}} = 709.7 \times 10^{-10}$, in good agreement with recent lattice-QCD determinations, and find an isospin-breaking shift of $\Delta a_\mu^{\mathrm{HVP,LO}} = 4.5 \times 10^{-10}$ ($0.6\%$), demonstrating that isospin-breaking effects, while quantitatively modest, are not negligible. Including the bottom-quark contribution and an indicative estimate of the systematic uncertainties, we obtain our final result, $a_\mu^{\mathrm{HVP,LO}}(u+d+s+c+b)|_{\mathrm{ISB}} = (710.0 \pm 14.5) \times 10^{-10}$.

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Angel S. Miramontes, Adnan Bashir, Christian S. Fischer, Pablo Roig. 2026-07-14. Hadronic vacuum polarization contribution to $a_\mu$ from functional methods with strong and electromagnetic isospin breaking. https://arxiv.org/abs/2607.12918

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