Polarization effects in the reaction $e^{+}+e^{-}\to {\rho }^{+}+{\rho }^{-}$ and determination of the $\rho -$ meson form factors in the time--like region

Abstract

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 ${\gamma }^{\ast }\rho \rho$ 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.

Comments: 19 pages, 2 figures, to appear in Phys Rev C