A dedicated measurement of additional radiation in e+e−→μ+μ−γ and e+e−→π+π−γ initial-state-radiation events is presented using the full BABAR data sample. For the first time results are presented at next-to- and next-to-next-to-leading order, with one and two additional photons, respectively, for radiation from the initial and final states. Comparison with predictions from phokhara and afkqed Monte Carlo generators is performed, revealing discrepancies in the one-photon rates and angular distributions for the former. This disagreement has a negligible effect on the BABAR measurement of the e+e−→π+π−(γ) cross section, but could affect other measurements significantly. This study sheds a new light on the longstanding discrepancy in this channel that affects the theoretical prediction of hadronic vacuum polarization contributions to the muon magnetic moment anomaly.
