A consistent description of 0 decays including (500) meson effects

A consistent description of $\sigma(500)$ meson effects in$\rho^0\to\pi^0\pi^0\gamma$ and $\pi^+\pi^-\gamma$ decays is proposed in termsof reasonably simple amplitudes which reproduce the expected chiral-loopbehaviour for large $m_{\sigma}$ values. For the neutral case, in addition tothe well known $\omega$ exchange, there is an important contribution from the$\sigma(500)$ meson that is in agreement with recent experimental data. For thecharged case, where the dominant contribution comes from bremsstrahlung, theeffects of the $\sigma(500)$ meson are relevant only at high values of thephoton energy and compatible with present data. A combined analysis of bothprocesses with moderately improved experimental information should contributedecisively to clarify the status of this controversial $\sigma(500)$ meson.Comment: 11 pages, 3 figures, JHEP style. A comment on the O(p^4) ChPT calculation of the four-pseudoscalar amplitudes is included; a new discussion on the effects of our parametrization on the I=J=0 pi-pi phaseshift is also included. Final version accepted for publicatio