Charge asymmetry in processes e+ e- --> mu+ mu- gamma and e+ e- --> pi+ pi- gamma is measured using 232 fb-1 of data collected with the BABAR detector at center-of-mass energies near 10.58 GeV. An observable is introduced and shown to be very robust against detector asymmetries while keeping a large sensitivity to the physical charge asymmetry that results from the interference between initial and final state radiation. The asymmetry is determined as afunction of the invariant mass of the final-state tracks from production threshold to a few GeV/c2. It is compared to the expectation from QED for e+ e- --> mu+ mu- gamma and from theoretical models for e+ e- --> pi+ pi- gamma. A clear interference pattern is observed in e+ e- --> pi+ pi- gamma, particularly in the vicinity of the f_2(1270) resonance. The inferred rate of lowest order FSR production is consistent with the QED expectation for e+ e- --> mu+ mu- gamma, and is negligibly small for e+ e- --> pi+ pi- gamma.
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