Measurement of Initial-State-Final-State Radiation Interference in the Processes e⁺e⁻ → μ⁺μ⁻γ and e⁺e⁻ → π⁺π⁻γ

Charge asymmetry in the processes e⁺e⁻ → μ⁺μ⁻γ and e⁺e⁻ → π⁺π⁻γ is measured using 232 fb⁻¹ of data collected with the BABAR detector at e⁺e⁻ 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 (FSR). The asymmetry is determined as a function 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⁻ → μ⁺μ⁻γ, and from theoretical models for e⁺e⁻ → π⁺π⁻γ. A clear interference pattern is observed in e⁺e⁻ → π⁺π⁻γ, particularly in the vicinity of the f₂(1270) resonance. The inferred rate of lowest-order FSR production is consistent with the QED expectation for e⁺e⁻ → μ⁺μ⁻γ, and is negligibly small for e⁺e⁻ → π⁺π⁻γ.