Structure-dependent radiative corrections to $e^+ e^- \to \pi^+ \pi^- \gamma$ in the GVMD approach

We compute the radiative corrections to the process of two-pion production in association with a hard photon in $e^+ e^-$ annihilation by taking into account the non-perturbative structure of the pion in the one-loop calculation. For this purpose, we adopt the generalised vector meson dominance model to insert the pion form factor in loop integrals for the treatment of final-state radiation and initial-final state interference at next-to-leading order. We compare our predictions with the results of the naive factorised scalar QED approach for experimentally relevant observables in the measurement of the $e^+ e^- \to \pi^+ \pi^- \gamma$ process. The computation extends previous results obtained for the energy scan process $e^+ e^- \to \pi^+ \pi^-$ and can be used to quantify the uncertainty due to the model describing the pion-photon interaction in radiative return experiments at flavour factories.