Low-Energy Pion-Pion Scattering in the Unitarized Strip Approximation

Abstract

We present an improved set of parameters for a successful bootstrap of the $\rho$ and Pomeranchon Regge trajectories in pion-pion scattering. The resulting $\pi -\pi$ amplitudes are compared with the experimental data, with particular reference to the low-energy $S$-wave phase shifts, which agree fairly well with present indications. We obtain for the trajectory intercepts ${\alpha }_P\mathrm{}\left(0\right)=1.0\mathrm{}$ and ${\alpha }_{\rho }\mathrm{}\left(0\right)=0.55\mathrm{}$; for the $\rho$-meson width ${\Gamma }_{\rho }=143\mathrm{}$ MeV; and for the $S$-wave scattering lengths $a_0=(0.15\mathrm{}\pm 0.05){m_{\pi }}^{-1\mathrm{}}$, $a_2=(-0.04\mathrm{}\pm 0.015){m_{\pi }}^{-1\mathrm{}}$.