As has been explained in Section~\ref{radret:theo}, the forward-backward asymmetry
\begin{eqnarray}
{\mathcal A}_{FB}(Q^2) =
\frac{N(\theta_{\pi^+}>90^\circ)- N(\theta_{\pi^+}<90^\circ) }
{N(\theta_{\pi^+}>90^\circ)+ N(\theta_{\pi^+}<90^\circ)}\left(Q^2\right)
\label{KLOEasymfb}
\end{eqnarray}
can be used to test the validity of the description of the
various mechanisms of the $\pi^+\pi^-$ final state photon emission, by
confronting the output of the Monte Carlo generator with data. In the
following studies, the Monte Carlo generator PHOKHARA v6.1~\cite{OlgaS} was used.
The parameters for the pion form factor were taken from~\cite{Bruch:2004py}, based
on the parametrisation of K\"uhn and Santamaria~\cite{Kuhn:1990ad}. The
parameters for the description of the direct $\phi$ decay and the double
resonance contribution were taken from the KLOE analysis of the neutral
mode~\cite{Ambrosino:2006hb}.
To suppress higher order effects, for which the interference and thus the
asymmetry is not implemented in the Monte Carlo generator, a rather tight
cut on the track mass variable (see Section~\ref{rr:kloe} and
Fig.~\ref{fig:radret_kloe45}) of $|M_\mathrm{trk} - M_{\pi^\pm}| < 10$ MeV has
been applied in the data, in addition to the {\it large angle} selection cuts
described in Section~\ref{rr:kloe}. This should reduce events with more than one
hard photon emitted and enhance the contribution of the final state radiation
processes under study over the dominant ISR process.
The datasets used in the analysis were taken in two different periods:
\begin{itemize}
\item[$\bullet$]{The data taken in 2002 were collected with DA$\mathrm{\Phi}$NE operating at the $\phi$-peak, at $\sqrt{s}=M_\phi$ (240 pb$^{-1}$).}
\item[$\bullet$]{The data taken in 2006 were collected with DA$\mathrm{\Phi}$NE operating 20 MeV
{\it below} the $\phi$-peak, at $\sqrt{s}=1000$ MeV (230 pb$^{-1}$).}
\end{itemize}
Since the 2006 data were taken more than 4$\Gamma_\phi$ below the resonant peak
($\Gamma_\phi=4.26$ MeV), one expects the contributions from the direct $\phi$
decay and the double resonance contribution to be suppressed compared to the
data taken on-peak in 2002 (see Fig.~\ref{fig3s}).
In fact one observes a very different shape
of the forward-backward asymmetry for the two different datasets, as can be
seen in Figs.~\ref{fig:radret_kloeasy1} and \ref{fig:radret_kloeasy2}.
Especially in the region below 0.4 GeV$^2$ and in the vicinity of the
$f_0(980)$ at 0.96 GeV$^2$, one observes different trends in the asymmetries
for the two datasets.
One can also see that, qualitatively, the theoretical description used to
model the different FSR contributions agrees well with the data, although,
especially at
low $M_{\pi\pi}^2$, the data statistics becomes poor and the data points for the asymmetry have large errors. In particular, the {\it off-peak} data in
Fig.~\ref{fig:radret_kloeasy2} show very good agreement above 0.35 GeV$^2$. In this case, the asymmetry is dominated fully by the bremsstrahlung-process,
as the other processes do not contribute outside the $\phi$-resonance. The
assumption of point-like pions (sQED) used to describe the bremsstrahlung in
the Monte Carlo generator seems to be valid above 0.35 GeV$^2$, while below it
is difficult to make a statement due to the large statistical errors of the
data points.
However, to obtain a solid quantitative statement on the validity of the models, as needed, e.g., in the radiative return analyses at the KLOE experiment,
one needs to understand how a discrepancy between theory and data in the
forward-backward asymmetry affects the cross section, as it is the
cross section one wants to measure. This requires further work, which
at the moment is still in progress.
It should also be mentioned that the KLOE experiment has taken almost ten times
more data in the years 2004--2005 than what is shown in
Fig.~\ref{fig:radret_kloeasy1}, with DA$\mathrm{\Phi}$NE operating at the $\phi$-peak energy. This is unfortunately not the case for the {\it off-peak} data, which is restricted to the dataset shown in Fig.~\ref{fig:radret_kloeasy2}.
%%%TT
In the future, the larger dataset from 2004--2005 may be used,
together with the results from the neutral channel and the assumption
of isospin symmetry, to determine the parameters of the direct $\phi$
decay and the double resonance contribution with high precision.
\begin{figure}
\begin{center}
\subfigure[]{\includegraphics[width=80mm]{asymmetry_kloe2002.eps}}
\hspace*{0.cm}
\subfigure[]{\includegraphics[width=80mm]{diff_asymmetry_kloe2002.eps}}
\caption{(a) Preliminary Forward--Backward asymmetry for data taken at $\sqrt{s}=M_\phi$ in 2002, and the corresponding Monte Carlo prediction using the PHOKHARA v6.1 generator. (b) Absolute difference between the asymmetries from data and Monte Carlo prediction. Used with permission
of the KLOE collaboration.}
\label{fig:radret_kloeasy1}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\subfigure[]{\includegraphics[width=80mm]{asymmetry_kloe2006.eps}}
\hspace*{0.cm}
\subfigure[]{\includegraphics[width=80mm]{diff_asymmetry_kloe2006.eps}}
\caption{(a) Preliminary Forward--Backward asymmetry for data taken at $\sqrt{s} \simeq 1000$ MeV
in 2006, and the corresponding Monte Carlo prediction using the PHOKHARA v6.1 generator. (b) Absolute difference between the asymmetries from data and Monte Carlo prediction. Used with permission of the KLOE collaboration.}
\label{fig:radret_kloeasy2}
\end{center}
\end{figure}