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

TL;DR

This paper calculates radiative corrections for the $e^+ e^- o \pi^+ \pi^- \gamma$ process, incorporating the pion's non-perturbative structure via the GVMD model, to improve precision in experimental measurements.

Contribution

It introduces a model-based approach to compute radiative corrections including the pion form factor, extending previous scalar QED methods for better accuracy.

Findings

Predictions differ from naive scalar QED results for relevant observables.

Quantifies the uncertainty in pion-photon interaction modeling in radiative return experiments.

Provides a framework for more precise measurements of the $e^+ e^- o \pi^+ \\pi^- \\gamma$ process.

Abstract

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.