  The electron positron annihilation reaction into four pion production has
been studied, through the channel $e^++e^-\to \bar \rho+\rho $. The
differential (and total) cross sections and various polarization observables
for this reaction have been calculated in terms of the electromagnetic form
factors of the corresponding $\gamma^*\rho\rho $ current. The elements of the
spin--density matrix of the $\rho -$meson were also calculated. Numerical
estimations have been done, with the help of phenomenological form factors
obtained in the space--like region of the momentum transfer squared and
analytically extended to the time-like region.

High Energy Physics - Phenomenology