Rigorous Effective Field Theory Study on Pion Form Factor

Abstract

We study $e^+e^-\to\pi^+\pi^-$ cross section and phase shift of $I=l=1$ $\pi-\pi$ 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 $\rho$ predicted by the model strongly depends on transition momentum-square $q^2$. We show that the mass pamameter of $\rho$-meson in its propagator is very different from its physical mass due to momentum-dependent width of $\rho$. The mass difference between $\rho^0$ and $\omega$ are predicted successfully. The rigorous theoretical prediction on $e^+e^-\to\pi^+\pi^-$ cross section and the phase shift in $I=l=1$ $\pi-\pi$ scattering agree with data excellentlly.