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.

revtex file, 10 pages, 4 eps figures