Tensions in $e^+e^-\to\pi^+\pi^-(\gamma)$ measurements: the new landscape of data-driven hadronic vacuum polarization predictions for the muon $g-2$
The situation of the experimental data used in the dispersive evaluation of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is assessed in view of two recent measurements: $e^+e^- \to \pi^+\pi^-$ cross sections in the $\rho$ resonance region by CMD-3 and a study of higher-order radiative effects in the initial-state-radiation processes $e^+e^- \to \mu^+\mu^-\gamma$ and $e^+e^- \to \pi^+\pi^-\gamma$ by BABAR. The impact of the latter study on the KLOE and BESIII cross-section measurements is evaluated and found to be indicative of larger systematic effects than uncertainties assigned. The new situation also warrants a reappraisal of the independent information provided by hadronic $\tau$ decays, including state-of-the-art isospin-breaking corrections. The findings cast a new light on the longstanding deviation between the muon $g-2$ measurement and the Standard Model prediction using the data-driven dispersive approach, and the comparison with lattice QCD calculations.