2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/39611We study $e^+e^-\toπ^+π^-$ cross section and phase shift of $I=l=1$ $π-π$ scattering below 1GeV in framework of chiral constituent quark model. The results including all order contribution of the chiral perturbation expansion and all one-loop effects of pseudoscalar mesons, but without any adjust parameters. Width of $ρ$ predicted by the model strongly depends on transition momentum-square $q^2$. We show that the mass pamameter of $ρ$-meson in its propagator is very different from its physical mass due to momentum-dependent width of $ρ$. The mass difference between $ρ^0$ and $ω$ are predicted successfully. The rigorous theoretical prediction on $e^+e^-\toπ^+π^-$ cross section and the phase shift in $I=l=1$ $π-π$ scattering agree with data excellentlly.revtex file, 10 pages, 4 eps figuresHigh Energy Physics - Phenomenologytext