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Review of hadronic vacuum polarization calculations via $e^+e^-$ measurements

The discrepancy on the muon anomalous magnetic moment values obtained via a direct measurement and via a data-driven theory determination that uses the experimentally measured hadronic cross section, is among the long standing and most significant deviations from the Standard Model predictions. The recently presented final result of the direct measurement performed at the experiment at Fermilab, with an impressive accuracy of 127 parts-per-billion, further stresses the need for a theory estimate of comparable accuracy. The $e^+e^-$ hadronic cross section is the experimental input to the dispersive integral for the calculation of the hadronic contribution to the $g-2$, which is largely dominated by the $e^+e^-\to π^+π^-$ channel. Precise measurements of the $e^+e^-\to π^+π^-$ cross section with a sub-percent accuracy, in the energy region of the $ρ$-resonance peak, have been performed by several experiments, but the results differ way more than the published accuracies limiting the comparison with the Fermilab direct measurement. New results are expected to become available in the near future from KLOE, CMD-3, SND and BESIII experiments, while a new measurement from the BABAR collaboration is presented today and its impact on the present situation is discussed. This measurement makes use of the entire BABAR data set and adopts a different analysis strategy, with results (still preliminary) largely independent of the results published in the 2009 BABAR publication.