Asymmetry observables ine+e−→π+π−γin theϕregion within a chiral unitary approach

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We make a theoretical study of the charge and forward-backward pion asymmetries in the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ process on and off the $\ensuremath{\phi}$ resonance energy. These observables are rather sensitive to the inner details of the theoretical models to describe the reaction. In addition to the standard implementation of the initial state radiation and the bremsstrahlung contribution to the final state radiation, we use the techniques of the chiral unitary approach to evaluate the contribution from the mechanisms of $\ensuremath{\phi}$ decay into ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$. This contribution involves the implementation of final state interaction from direct chiral loops, the exchange of vector and axial-vector resonances and the final state interaction through the consideration of the meson-meson unitarized amplitudes, which were found important in a previous work describing the $\ensuremath{\phi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\gamma}$. We find a good reproduction of the experimental data from KLOE for the forward-backward asymmetry, both at the $\ensuremath{\phi}$ peak and away from it. We also make predictions for the angular distributions of the charge asymmetry and show that this observable is very sensitive to the chiral loops involved in $\ensuremath{\phi}$ radiative decay.