This paper reports a new determination of the leading hadronic vacuum-polarization (HVP) contribution to the muon’s anomalous magnetic moment, a quantity often called the muon g-2. The authors use a continuum approach to quantum chromodynamics (QCD) to compute how quarks and the particles they form influence the muon’s magnetic properties. Their result is close to recent results from lattice QCD, and they find that differences between up and down quarks (isospin breaking) change the HVP value by a small but measurable amount.

To get this number the researchers solved coupled equations for quarks and bound states known as the Dyson–Schwinger and Bethe–Salpeter equations. These are “functional” methods that work directly in continuous spacetime rather than on a discrete grid. The calculation includes several detailed physics ingredients: the effect of pions feeding back into the quark dynamics, a fully dressed quark–photon vertex (meaning the interaction includes the influence of surrounding particles) that develops a ρ (rho) resonance structure in the timelike energy region, and both strong and electromagnetic isospin breaking treated consistently at the quark level.

Their main numerical result for the light and charm quarks (up + down + strange + charm) with isospin breaking is aμ^HVP,LO(u+d+s+c)|_ISB = 709.7 × 10^-10. They quantify the isospin-breaking shift as Δa_μ^HVP,LO = 4.5 × 10^-10, or about 0.6%. Adding the bottom quark contribution and an indicative estimate of systematic uncertainties gives a final value (including u, d, s, c, b quarks) of (710.0 ± 14.5) × 10^-10.

Why this matters: the muon g-2 is a precision test of the Standard Model of particle physics. The HVP piece is the largest source of theoretical uncertainty in the Standard Model prediction. Independent methods that produce consistent HVP numbers help build confidence in the theory value. The finding that isospin breaking shifts the HVP by about 0.6% shows that these effects are small but not negligible when aiming for high precision.