A consistent treatment for pion form factors in space-like and time-like regions

Abstract

We write down some relevant matrix elements for the scattering and decay processes of the pion by considering a quark-meson vertex function. The pion charge and transition form factors $F_π$, $F_{πγ}$, and $F_{πγ^*}$ are extracted from these matrix elements using a relativistic quark model on the light-front. We found that, the form factors $F_π$ and $F_{πγ}$ in the space-like region agree well with experiment. Furthermore, the branching ratios of all observed decay modes of the neutral pion, that are related to the form factors $F_{πγ}$ and $F_{πγ^*}$ in the time-like region, are all consistent with the data as well. Additionally, $F_π$ in the time-like region, which deals with the nonvalence contribution, is also discussed.