$σ(600)$ and background in $ππ$ scattering

Abstract

We suggest a simple analytical description of the S-wave isoscalar $ππ$ amplitude, which corresponds to a joint dressing of the bare resonance and background contributions. The amplitude describes well the experimental data on the $δ^0_0$ phase shift in the energy region below 900 MeV and has two poles in the $Re s > 0$ half-plane. Besides the well-known pole of $σ(600)$-meson with $Re s \sim m_π^2$, there exists a more distant pole with $Re s \sim 0.6 GeV^2$. Our analysis indicates for the dynamical origin of the $σ(600)$ pole, while the second pole should be associated with lowest $q\bar{q}$ state.