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

TL;DR

This paper investigates the polarization effects and electromagnetic form factors of rho mesons in electron-positron annihilation into rho pairs, providing theoretical calculations and numerical estimations in the time-like momentum transfer region.

Contribution

It introduces a detailed theoretical framework for analyzing polarization and form factors of rho mesons in e+e- reactions, extending phenomenological models to the time-like region.

Findings

Calculated differential and total cross sections for e+e- to rho+ rho-

Derived polarization observables and spin-density matrix elements

Extended phenomenological form factors to 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^*\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.