Space-like and time-like pion-rho transition form factors in the light-cone formalism

Having calculated the light-cone wave function of the pseudoscalar meson by using two equivalent and fully covariant methods, we generalize such methods to the valence Fock states of the vector meson in the light-cone formalism. We investigate the decay constant of the $\rho$ meson $f_{\rho}$, the $\gamma^{\ast} \pi \to \rho$ and $\gamma^* \rho \to \pi$ transition form factors and especially the transition magnetic moments. By using two groups of constraint parameters, we predict the space-like and time-like form factors $F_{\pi \rho}(Q^2)$ and $F_{\rho \pi}(Q^2)$ at low and moderate energy scale and the electromagnetic radius of these transition processes. In addition, we extend our calculation to $\gamma^* \pi \to \omega$ space-like and time-like form factors by using the same sets of parameters.