  The $\sigma$ resonance was observed as a conspicuous $\pi^+\pi^-$ peak in
hadronic decays like $J/\psi\to \pi^+\pi^-\omega$ or $D^+\to\pi^+\pi^-\pi^+$.
The phase of the $\sigma\to\pi^+\pi^-$ amplitude, extracted from production
data within the conventional isobar model, is assumed to coincide with that in
$\pi\pi$ elastic scattering. We check the validity of this assumption by using
Lehmann-Symanzik-Zimmermann (LSZ) reduction and unitarity. The rescattering
effects in the final three-particle states are shown to generate a correction
to the phase given by a naive application of Watson theorem. We briefly discuss
the implications of this result for the pole determination from production
data.
