Test of FSR in the process $e^+e^-\to\pi^+\pi^-\gamma$ at DA$\Phi$NE

In this paper we consider the possibility to test the FSR model in the reaction $e^+e^-\to\pi^+\pi^-\gamma$ at DA$\Phi$NE. We propose to consider the low $Q^2$ region ($Q^2$ is the invariant mass squared of the di-pion system) to study the different models describing $gamma^*\to\pi^+\pi^-\gamma$ interaction. As illustration we compare the scalar QED and Resonance Perturbation Theory prediction for the $e^+e^-\to\pi^+\pi^-\gamma$ cross section. We also consider the contribution coming from the $\phi$ direct decay ($\phi\to\pi^+\pi^-\gamma$). We find the low $Q^2$ region is sensitive to FSR models.