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A dedicated measurement of additional radiation in$e^+e^-\to\mu^+\mu^-\gamma$ and $e^+e^-\to\pi^+\pi^-\gamma$initial-state-radiation events is presented using the full BABAR data sample.For the first time results are presented at next-to- andnext-to-next-to-leading order, with one and two additional photons,respectively, for radiation from the initial and final states. Comparison withpredictions from Phokhara and AfkQed Monte Carlo generators is performed,revealing discrepancies in the one-photon rates and angular distributions forthe former. This disagreement has a negligible effect on the BABAR measurementof the $e^+e^-\to\pi^+\pi^-(\gamma)$ cross section, but could affect othermeasurements significantly. This study sheds a new light on the longstandingdiscrepancy in this channel that affects the theoretical prediction of hadronicvacuum polarization contributions to the muon magnetic moment anomaly.

Measurement of additional radiation in the initial-state-radiation processes $e^+e^-\to \mu^+\mu^-\gamma$ and $e^+e^-\to \pi^+\pi^-\gamma$ at BABAR