Width of Three-Pion Resonances

A model of three-pion resonances is constructed taking into account only $\pi -\rho$ intermediate states. The $\pi -\rho$ interaction is replaced by a simple pole. The calculated $\omega$-resonance width is approximately 10-20 MeV, depending on the range of the $\pi -\rho$ interaction. These values of the width are consistent with present experimental data.