Cross section and polarization observables for the reaction $e^++e^-\to a_1(1260)+\pi $

TL;DR

This paper develops a model-independent formalism for analyzing the $e^+e^- o a_1(1260)+\pi$ reaction, deriving expressions for cross sections and polarization observables based on electromagnetic form factors.

Contribution

It introduces a formalism that relates observables to electromagnetic form factors without relying on specific models, and fits simple form factor models to experimental data.

Findings

Derived expressions for differential and total cross sections.

Calculated spin-density matrix elements of the $a_1$-meson.

Provided numerical predictions for observables using fitted form factors.

Abstract

A model independent formalism for the electron positron annihilation reaction $e^++e^-\to a_1(1260)+\pi $ has been derived. The differential and total cross sections and the elements of the spin--density matrix of the $a_1$-meson were calculated in terms of the electromagnetic form factors of the corresponding $\gamma^*a_1\pi $ current. Simple models of $a_1$ form factors have been fitted to the available cross section data and they allow to give numerical predictions for the different observables.