Contribution of the direct decay $\phi\to\pi^+ \pi^- \gamma$ to the process $e^+ e^- \to \pi^+ \pi^- \gamma$ at DA$\Phi$NE

The potential of DAPHNE to explore direct radiative decay $\phi \to \pi^+ \pi^- \gamma$ is studied in detail. Predictions of different theoretical models for this decay are compared. We find that it should be possible to discriminate between these models at DAPHNE in one year, even assuming a relatively low luminosity ${\cal{L}} = 10^{31} {\rm cm}^{-2} {\rm sec^{-1}}$. The influence of the decay $\phi \to \pi^+ \pi^- \gamma$ on the measurement of total cross section $\sigma(e^+e^- \to {\rm hadrons})$ by tagging a photon in the reaction $e^+e^- \to \pi^+\pi^- \gamma$ is also discussed.