The dominant uncertainty in the SM prediction of the muon anomalous magnetic moment (a_mu) comes from the hadronic vacuum polarization part and, specifically, from its two-pion contribution. Traditionally, this has been obtained, in the data-driven way, from measurements of the e^+e^- -> pi^+pi^- cross-section using a dispersive integral. However, the recent CMD-3 2pi data is incompatible with KLOE's, which currently prevents updating the White Paper number (basically coming from BaBar and KLOE) obtained this way. Di-pion tau decay data (once isospin-rotated) were very useful in the past to complement the e^+e^- measurements. In the current puzzling situation concerning e^+e^- data, different experiments agree on di-pion tau measurements and isospin-breaking corrections are controlled at the required precision, so as to contribute to the data-driven a_mu^{HVP}, which can in turn be combined with the lattice results to get the updated SM prediction, to be confronted soon to the final FNAL measurement, searching for indirect new physics hints.
Luiz Vale Silva