π−πscattering in a QCD-based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyze the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom, and quark confinement, allows one to calculate $f_{\pi }$, $m_{\pi }$, $r_{\pi }$, and the partial wave amplitudes in $\pi -\pi$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies $E\simeq 550$ MeV.