%Title: Radiative return physics program within EURIDICE network
%Author: Henryk Czyz and Agnieszka Grzelinska
%Published: *Contibution to theFinal EURIDICE Meeting: Effective Theories of Colors and Flavors from EURODAPHNE to EURIDICE, * Kazimierz, Poland, 24-27 Aug 2006
%arxiv/0707.1275
\documentclass{appolb}
\usepackage{epsfig}
%------------------------------------------------------
% Include epsfig package for placing EPS figures in the text
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% BEGINNING OF TEXT %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\ta}[1]{#1\hspace{-.42em}/\hspace{-.07em}} % SLASH
\newcommand{\taa}[1]{#1\hspace{-.55em}/\hspace{-.09em}} % SLASH
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\non}{\nonumber}
\newcommand{\eq}[1]{eq.~(\ref{#1})}
\newcommand{\Eq}[1]{Eq.~(\ref{#1})}
\newcommand{\eps}{\varepsilon}
\newcommand{\be}{\beta}
\begin{document}
\date{\today}
\pagestyle{plain}
%% uncomment the following line to get equations numbered by (sec.num)
%\eqsec
\newcount\eLiNe\eLiNe=\inputlineno\advance\eLiNe by -1
\title{ Radiative return physics program within EURIDICE network
\thanks{Presented by H.~Czy\.z
at The Final EURIDICE Meeting "Effective theories of colours
and flavours: from EURODAPHNE to EURIDICE", Kazimierz, Poland,
24-27 August, 2006.
Work supported in part by EC 5th Framework Programme under contract
HPRN-CT-2002-00311 (EURIDICE network),
EC 6-th Framework Program under contract
MRTN-CT-2006-035482 (FLAVIAnet), TARI project RII3-CT-2004-506078
and
Polish State Committee for Scientific Research
(KBN) under contract 1 P03B 003 28.}
}
\author{Henryk Czy\.z$^a$ and Agnieszka Grzeli\'nska$^b$
\address{ a: \ Institute of Physics, University of Silesia,
PL-40007 Katowice, Poland \\ b: \ Institut f\"ur Theoretische Teilchenphysik,
Universit\"at Karlsruhe,\\ D-76128 Karlsruhe, Germany
}}
\maketitle
\begin{abstract}
A short review of both theoretical and experimental aspects
of the radiative return method is presented with the emphasize
on the results obtained within the EURIDICE network. It is shown
that the method gives not only possibility of an independent
from the scan method measurement of the hadronic cross section,
but also can provide information concerning details of the hadronic
interactions.
\end{abstract}
\PACS{13.40.Ks,13.66.Bc}
%***********************************************************************
\section{Introduction}
%***********************************************************************
Four years of a very active physics program of the EURIDICE network was
also very fruitful for the group developing the radiative return method
\cite{Zerwas}
and tools necessary for the physical analysis. Major part of all theoretical
investigations in that topic was done within this network, thus the review
of the theoretical investigations is in fact the review of the results
obtained within the EURIDICE network. Software developed and/or
upgraded within the network:
PHOKHARA\cite{Szopa,rest,Czyz:PH03,Nowak,Czyz:2004nq,PHOKHARA:mu}
and EKHARA \cite{Czyz:2006dm}
generators together with the event generators
developed by the same group (EVA \cite{Binner}, EVA4pi \cite{CK})
prior to the starting date of
the EURIDICE is successfully used by experimental groups working at meson
factories BaBar and KLOE and soon will be used also at BELLE.
The method originally developed for the hadronic cross section
measurement was successfully used by KLOE \cite{KLOE2}
to obtain $\sigma(e^+e^-\to\pi^+\pi^-$) with the precision competitive
to the one obtained by means of the scan method and by BaBar to
obtain cross sections of many hadronic channels which were measured
with poor accuracy or were not measured at all. Let us mention only
few of them: narrow resonances studies \cite{Aubert:2003sv},
big improvement in the accuracy of the three pion \cite{Aubert:2004kj}
and four charged mesons (pions and kaons) \cite{Aubert:2005eg} cross sections
measurements and proton form factors extraction \cite{Aubert:2005cb}.
The paper starts with a description of the radiative return method in
Section~\ref{sec2} and the ingredients necessary for the precision
physics in Section~\ref{sec3}. The basic obstacle in using of the
radiative return method, final state photon emission (FSR), is
discussed in Section \ref{sec4}, together with methods how to handle it
and be able to perform precision physics despite the encountered problems.
Selected topics beyond the hadronic cross section measurements
are described in Section \ref{sec5}.
%*******************************************************************
\section{The basics of the radiative return method \label{sec2}}
Simple and innovative observation made some years ago \cite{Zerwas}
lead, with series of papers which started with \cite{Binner} and \cite{CK},
to a development of a radiative return method giving
today many valuable physical results. The method gives an access to
information contained in the hadronic cross section
$d\sigma(e^+e^-\to{\rm hadrons})$ through a measurement of the hadronic
invariant mass distribution in the reaction
$e^+e^-\to{\rm hadrons}+{\rm photons}$.
Historically the process of $e^+e^-$ annihilation to a pair
(or arbitrary number) of particles
plus one photon was investigated earlier
\cite{Baier:1965jz,Baier:1965bg,Fadin}, but the scope of
that papers was not to provide with a method to measure the hadronic
cross section.
To illustrate in details how the method works lets consider the lowest order
contribution to the radiative return cross section. The contributing
diagrams are shown in Fig. {\ref{LO}}, where only initial state radiation
(ISR) is taken into account. The complications caused by final state radiation
(FSR), as well as the methods to overcome them, are discussed in
Section \ref{sec4}.
\begin{figure}[ht]
\begin{center}
\epsfig{file=Fig1.ps,width=8.cm}
\\
\caption{The leading order diagrams contributing to the radiative return
cross section. }
\label{LO}
\end{center}
\end{figure}
The corresponding ISR matrix element has the following form
\begin{eqnarray}
{\cal M} \sim \bar v\left(p_{+}\right)
\left[ \gamma^{\nu}
\frac{1}
{p_{-}{\kern-12pt}/ \ - k {\kern-5pt}/ - m}
\epsilon^{*}{\kern-9pt}/\ (k)
+ \epsilon^{*}{\kern-9pt}/ \ (k)
\frac{1}{k {\kern-5pt}/ - p_{+}{\kern-12pt}/ \ - m}\gamma^{\nu}
\right] u(p_-) \
\frac{1}{Q^2}\ J^{em}_{\nu} \ ,
\label{matrix}
\end{eqnarray}
\noindent
where $J^{em}_{\nu}$ is the electromagnetic hadronic current present
also in the matrix element describing the process $e^+e^-\to{\rm hadrons}$.
It is clear from it that a factorization, allowing separation
of the hadronic part will take place even for the
squared matrix element. Indeed, integrating the cross section
over the hadrons phase space $d\bar\Phi_n$ ('bar' indicates that all
statistical factors are included in its definition) one gets
%
\begin{eqnarray}
\int \ { J^{em}_\mu (J^{em}_\nu)^*} \ \ d\bar\Phi_n(Q;q_1,\dots,q_n) =
\frac{1}{6\pi} { \left(Q_{\mu}Q_{\nu}-g_{\mu\nu}Q^2\right)}
\ { R(Q^2)} \ ,
\label{hadronict}
\end{eqnarray}
%
\noindent
where
\begin{eqnarray}
R(s)=\frac{\sigma(e^+e^-\rightarrow hadrons)}{\sigma_{\rm point}}
\ , \ \sigma_{\rm point} = \frac{4\pi\alpha^2}{3s} \ .
\label{rratio}
\end{eqnarray}
That leads to the relation between cross sections with and without
photon emission
\begin{eqnarray}
d\sigma(e^+e^- \to \mathrm{hadrons} + \gamma ({\rm ISR})) &=&
\nonumber \\
&&\kern-50pt
H(Q^2,\theta_\gamma) \ d\sigma(e^+e^-\to \mathrm{hadrons}, s=Q^2) \ ,
\label{factorization}
\end{eqnarray}
%
\noindent
where $Q^2$ is the invariant mass of the hadronic system.
As it is clear from Eq. (\ref{matrix}) and Eq. (\ref{hadronict})
the factorization of the Eq. (\ref{factorization}) remains valid
at any order provided that only ISR is considered. The function
$H(Q^2,\theta_\gamma)$ at relatively low energies of meson factories
is given with high accuracy by QED only and thus it is well
known. That means that by measurement of the
differential in $Q^2$ cross section of the reaction
$e^+e^- \to \mathrm {hadrons} + \mathrm{photons}$
one can extract the cross
section $e^+e^- \to \mathrm{hadrons}$ for the energies from the
production threshold to almost the nominal energy of a given experiment,
provided that one is able to overcome complications
described in Section~\ref{sec4}. The cross section
of the reaction with photon emission is lower then the one without
photon emission, thus requires higher luminosity then the ones
necessary for scan experiments for similar statistical accuracy.
However it does not require to build a dedicated experiments
and it can use data collected at any of the meson factories, where
luminosity is not a problem.
%*******************************************************************
\section{Ingredients necessary for a precise analysis \label{sec3}}
An extraction of the hadronic cross section via the radiative return
requires a few basic ingredients:
\begin{itemize}
\item{ an accurate calculation of the ISR
including appropriate radiative corrections}
\item{an adequate, tested experimentally, model of the FSR}
\item{a Monte Carlo event generator to be able to use the theoretical
information in a realistic experimental set up
}
\item{$e^+e^-$ scattering experiment with a high luminosity
and a good detector}
\end{itemize}
The virtual radiative corrections to ISR were calculated in \cite{PHradcor}
while the real emission was included in the developed Monte Carlo generator
PHOKHARA in \cite{Szopa} and \cite{rest}. The estimated
physical accuracy of the ISR contributions, 0.5\%, was adequate at the
time of the release of the generator even for the precise KLOE
pion form factor extraction \cite{KLOE2}.
The new data collected at DAPHNE by KLOE collaboration
\cite{Ambrosino:2007nx,Leone:2006bm}
together with an improvement in the theoretical description of the
Monte Carlo event generator BABAYAGA \cite{Balossini:2006wc} requires however
further work and an inclusion of the NNLO contributions, at least in the
leading logarithmic approximation, is a necessary condition to be able
to fully profit from the new very accurate data.
The FSR modeling requires close collaboration between experimental
and theory groups to reach required precision in a short time and
will be discussed in the next Section.
A development of a reliable Monte Carlo generator requires not only
the precise knowledge of both ISR and FSR, but a continuous work on
efficiency of the generator and its tests for each added hadronic
channel. Only this way one can assure reliability of the developed
product used afterwords by demanding experimental groups.
%*******************************************************************
\section{Final state photon emission: the problems and how to overcome them
\label{sec4}}
The final state emission (FSR) forms a potential problem for the application
of the radiative return method and it has to be studied carefully
to assure adequate accuracy of the description.
At
B- factories the region of
hadronic masses of physical interests,
below 4~GeV, lays far from the nominal energy of the
experiments and an emission of a hard photon is required to
reach it. It means that the typical kinematic configuration of an
event consists of a photon emitted in one direction and hadrons
going opposite to it. That suppresses
the FSR contributions, which are large for photons emitted parallel
to the direction of a charged hadron in the final state, and makes
the measurement of the hadronic cross section easier. For the $\phi$- factory
DAPHNE,
where the region of interest is not far from the nominal
energy of the experiment, that natural separation between the emitted
photon and the hadrons does not take place and one has to suppress FSR
by an appropriate event selection. As a result one has to control
the uncertainty due to the model dependence of the final state emission.
That forms a challenge, as the existing models were not tested
with the adequate
precision prior to the DAPHNE results. Let's discuss that problem
on the basis of the $e^+e^-\to \pi^+\pi^-\gamma(\gamma)$ reaction,
where the accuracy is the most demanding.
The solution was first proposed in \cite{Binner}
and further elaborated in \cite{Czyz:PH03}.
A similar
investigations is possible for other hadronic final states,
however till now it
was not performed.
The main tool in the tests of the model(s) of the photon
emission from the final pions is the charge asymmetry.
For ISR emission of any
number of photons the two-pion state is produced in C=-1 and
with an
odd orbital angular momentum.
For one real photon emitted from the final pions
the two-pion state is produced
in C=1 and with an even orbital angular momentum.
As a result, the initial-final
state interference for one photon emission
is odd under $\pi^+\leftrightarrow \pi^-$ interchange
and the integrals for charge blind event selections are equal to zero.
In the same time the interference
is the only source of the charge asymmetry and allows for
tests of the models of the final state emission. The charge asymmetry
depends on the invariant mass of the two-pion system and that
allows for detailed tests of the model(s) of the FSR emission.
In short, the tests should be done in the following way: First
one compares the experimental data for the asymmetry with the Monte Carlo
where the tested model was implemented. That has to be performed
for an event selection which enhance the FSR as compared to the ISR.
Once the implemented model agrees with the data one chooses an
event selection, which suppresses the FSR and makes the
radiative cross section measurement. That guaranties that the
ISR and the FSR contributions are separately well under control.
For the case of untagged photons a specific background,
$e^+e^-\to\pi^+\pi^-e^+e^-$, has to be also taken into account
\cite{Hoefer:2001mx,Czyz:2006dm} as the final leptons are not vetoed and
even if they are, the major part of them escapes detection being emitted
at small angles.
The reaction
$e^+e^-\to \pi^+\pi^-\gamma$,
with the photon emitted from the pions, does contribute also to
dispersion integrals for evaluation of $a_\mu$ and $\alpha_{QED}$
and in the former case its theoretically estimated value \cite{Czyz:PH03}
is about 1.5 times higher then
the size of the present
theoretical uncertainty \cite{Jegerlehner:2007xe,eidelman2007}
and thus numerically
important. The sketched program was successfully undertaken
by KLOE and resulted in a sound extraction of the
$\sigma(e^+e^-\to \pi^+\pi^-)$ \cite{KLOE2} together
with the mentioned photon corrections. The most general form
of the photon emission from scalar particles produced in $e^+e^-$
annihilation, with three form factors was investigated already
in \cite{Baier:1965jz}, where it was shown also that only one
form factor is relevant in the limit of soft photon emission.
Physical program initiated there was undertaken in
\cite{Pancheri:2006cp,Pancheri:2007xt}
with a special emphasize on the FSR tests at KLOE.
Another source of complications for using of
the radiative return method
at DAPHNE are the radiative $\phi$ decays. That problem
was considered for the first
time in \cite{Melnikov:2000gs} and it is discussed in more details
in the next section.
%*******************************************************************
\section{Not only the hadronic cross section \label{sec5}}
%
\begin{figure}[ht]
\begin{center}
\epsfig{file=v_0.3_0.4_asym.ps,width=6cm}
\epsfig{file=v_0.3_0.4_asym_bez.ps,width=6cm}
\caption{ Charge asymmetries for three different models of the radiative
$\phi$ decays compared to the result based on sQED only (no $f_0$).
Left plot with $f_0(980)$ and $f_0(600)$, right plot with $f_0(980)$ only.}
\label{charge_asym}
\end{center}
\end{figure}
%
The study of the $\phi\to\pi\pi\gamma$ decays at DAPHNE is a subject, where
the problem of FSR emission in the pion form factor extraction is interlinked
with the possibility of using of the radiative return method to study
hadronic models of the $\phi\to\pi\pi\gamma$ decays.
In \cite{Czyz:2004nq} charge asymmetries were proposed to test both
topics. The sensitivity to the model parameters, which can be reached
this way is definitely better then the one obtained by the fit to the $Q^2$
spectra. An example is shown in Fig.\ref{charge_asym}, where
charge asymmetries predicted within a number of models of the radiative
$\phi$ decays is shown for models with and without $f_0(600)$ contribution.
Very distinct asymmetries promise deep insight in the details of
the constructed models.
The asymmetry was partially used by KLOE \cite{Ambrosino:2005wk}
to cross check the fit of the model parameters to the $Q^2$ spectrum
of the pion pair invariant masses. More detailed tests are expected
at KLOE, when both data taken at the $\phi$ resonance and below it
will be analyzed.
%
\begin{figure}[ht]
\begin{center}
\epsfig{file=v_90_cifot.ps,width=8.cm}
\\
\caption{The differential, in the invariant mass of the $\Lambda\bar \Lambda$
pairs ($Q^2$), cross section of the process
$e^+e^- \to \Lambda (\to p\pi^-) \bar \Lambda (\to \bar p \pi^+)\gamma$
at B-factories energy: circles - with no cuts applied, crosses - angular cuts
on the pions and protons only, squares (overlapped with crosses)
- angular cuts on pions, protons and the photon. }
\label{lamtot}
\end{center}
\end{figure}
%
Another example of using of the radiative return method to study
hadron properties is the baryon form factors extraction.
It was shown in \cite{Nowak} that at B-factories it is possible
to extract the nucleon form factors up to their phases for a wide range
of the invariant masses of the nucleon-antinucleon pairs. That is
possible through studies of the nucleon angular distributions. In a
properly chosen reference frame in which they are studied, a rest frame of the
nucleon-antinucleon system with z-axis along the emitted photon, that
studies are particularly simple as the angular distributions resemble
there the nucleon angular distributions
of the process without a photon emission. That measurement
was successfully performed by BaBar collaboration \cite{Aubert:2005cb}.
For the production of unstable baryon pairs,
the decay products carry information about their
spins and serve as spin analyzers providing with complete information
about the production process. In \cite{Czyz:2007wi} it was studied in details
for the process
$e^+e^- \to \Lambda (\to p\pi^-) \bar \Lambda (\to \bar p \pi^+)\gamma$.
The feasibility of such measurement at B-factories is obvious from
Fig.\ref{lamtot} as one expects about one hundred events per 100 fb$^{-1}$
in the range of BaBar detector.
The direction of pions coming from lambda decays is strictly correlated
with the spin of the decaying lambdas and by observing them one can measure
both spin asymmetries and spin correlations in the process of production
of the lambda-antilambda pairs. In Fig.\ref{lamspin} (left)
the spin asymmetry,
which is proportional to the sine of the phase difference of the
magnetic and electric lambda form factors is shown for
$\Delta\phi=\frac{\pi}{2}$. In Fig.\ref{lamspin} (right)
the xz-spin correlation (please look \cite{Czyz:2007wi} for the reference
frames definition),
which is proportional to cosine of the phase difference of the
magnetic and electric lambda form factors is shown for
$\Delta\phi= {\pi}$. It is enough to measure one of them to determine
the phase difference of the lambda form factors up to a twofold sign
ambiguity and the other serve to determine that sign.
The analysis can be applied also to other members of the baryon octet.
As almost nothing is known about their form factors, B-factories
can provide valuable physical information allowing to test symmetries
of the underlying models.
%
\begin{figure}[ht]
\begin{center}
\epsfig{file=v_asym_c4fot.ps,width=6.1cm}
\epsfig{file=v_asym_xzfot.ps,width=6.1cm}
\caption{ Spin asymmetry (left) for the relative phase between
magnetic and electric lambda form factors $\Delta\phi=\frac{\pi}{2}$
and spin correlations (right) for $\Delta\phi={\pi}$ in
the process
$e^+e^- \to \Lambda (\to p\pi^-) \bar \Lambda (\to \bar p \pi^+)\gamma$:
circles - with no cuts applied, crosses - angular cuts
on the pions and protons only, squares
- angular cuts on pions, protons and the photon.}
\label{lamspin}
\end{center}
\end{figure}
%
\section{Summary}
The radiative return research program carried within the EURIDICE network
was outlined. It was shown that just by theoretical and experimental analysis
of the data of the existing
meson factories one can get rich information concerning
hadronic physics, which is not limited to the hadronic cross section
measurement.
\vskip 0.5 cm
\centerline{***}
%{\bf Acknowledgements}
The publication is based in a big part on results obtained in collaboration
with
J.~H.~K\"uhn, E.~Nowak-Kubat and G.~Rodrigo. The authors are grateful for
many
useful discussions concerning experimental aspects of the radiative
return method to members of the KLOE and BaBar collaborations, mainly
Cesare Bini, Achim Denig, Wolfgang Kluge, Debora Leone, Stefan M\"uller,
Federico Nguyen, Evgeni Solodov and Graziano Venanzoni.
%*******************************************************************
\begin{thebibliography}{99}
%*******************************************************************
\bibitem{Zerwas}
Min-Shih Chen and P.~M.~Zerwas,
%"SECONDARY REACTIONS IN ELECTRON - POSITRON (ELECTRON) COLLISIONS"
Phys. Rev. D {\bf 11} (1975) 58.
%%CITATION = PHRVA,D11,58;%%
\bibitem{Szopa}
G.~Rodrigo, H.~Czy\.z, J.H.~K\"uhn and M.~Szopa,
%``Radiative return at NLO and the measurement of the hadronic cross-section in electron positron annihilation,''
Eur.\ Phys.\ J.\ C {\bf 24} (2002) 71
[hep-ph/0112184].
%%CITATION = HEP-PH 0112184;%%
\bibitem{rest}
H.~Czy{\.z}, A.~Grzeli{\'n}ska, J.~H.~K{\"u}hn and G.~Rodrigo,
%``The radiative return at Phi- and B-factories: Small-angle photon emission at next to leading order,''
Eur.\ Phys.\ J.\ C {\bf 27} (2003) 563
[hep-ph/0212225];
%%CITATION = HEP-PH 0212225;%%
\bibitem{Czyz:PH03}
H.~Czy{\.z}, A.~Grzeli{\'n}ska, J.~H.~K{\"u}hn and G.~Rodrigo,
%``The radiative return at Phi and B-factories: FSR at next-to-leading order,''
Eur.\ Phys.\ J.\ C {\bf 33} (2004) 333
[hep-ph/0308312].
%%CITATION = HEP-PH 0308312;%%
\bibitem{Nowak}
H.~Czy{\.z}, J.~H.~K{\"u}hn, E.~Nowak and G.~Rodrigo,
% ``NUCLEON FORM-FACTORS, B MESON FACTORIES AND THE RADIATIVE RETURN.''
Eur.~Phys.~J.~C {\bf 35} (2004) 527 [hep-ph/0403062].
%%CITATION = HEP-PH 0403062;%%
\bibitem{Czyz:2004nq}
%{\bf ``Charge asymmetry and radiative Phi decays''}
H.~Czy{\.z}, A.~Grzeli{\'n}ska and J.~H.~K{\"u}hn
Phys.\ Lett.\ B {\bf 611} (2005) 116
[hep-ph/0412239].
%%CITATION = HEP-PH 0412239;%%
\bibitem{PHOKHARA:mu}
H.~Czy{\.z}, A.~Grzeli{\'n}ska, J.~H.~K{\"u}hn and G.~Rodrigo,
%"The radiative return at Phi- and B-factories: FSR for muon
% pair production at next-to-leading order"
Eur. \ Phys. \ J. \ C {\bf 39} (2005) 411 [hep-ph/0404078].
%%CITATION = HEP-PH 0404078;%%
\bibitem{Czyz:2006dm}
H.~Czy{\.z} and E.~Nowak-Kubat,
%``The reaction e+ e- $\to$ e+ e- pi+ pi- and the pion form factor
%measurements via the radiative return method,''
Phys.\ Lett.\ B {\bf 634} (2006) 493
[hep-ph/0601169].
%%CITATION = HEP-PH 0601169;%%
\bibitem{Binner}
S.~Binner, J.~H.~K\"uhn and K.~Melnikov,
%``Measuring sigma(e+ e- --> hadrons) using tagged photon,''
Phys.\ Lett.\ B {\bf 459} (1999) 279
[hep-ph/9902399].
%%CITATION = HEP-PH 9902399;%%
\bibitem{CK}
H.~Czy\.z and J.~H.~K\"uhn,
%``Four pion final states with tagged photons at electron positron colliders,''
Eur.\ Phys.\ J.\ C {\bf 18} (2001) 497
[hep-ph/0008262].
%%CITATION = HEP-PH 0008262;%%
\bibitem{KLOE2}
A.~Aloisio {\it et al.}, [KLOE Collaboration],
Phys.~Lett. B {\bf 606} (2005) 12 [hep-ex/0407048].
%"Measurement of sigma(e+ e- --> pi+ pi- gamma) and
% extraction of sigma(e+ e- --> pi+ pi-) below 1-GeV with
% the KLOE detector"
%%CITATION = HEP-EX 0407048;%%
\bibitem{Aubert:2003sv}
B.~Aubert {\it et al.} [BABAR Collaboration],
%``J/psi production via initial state radiation in e+ e- $\to$ mu+ mu- gamma
%at an e+ e- center-of-mass energy near 10.6-GeV,''
Phys.\ Rev.\ D {\bf 69} (2004) 011103
[hep-ex/0310027].
%%CITATION = HEP-EX 0310027;%%
\bibitem{Aubert:2004kj}
B.~Aubert {\it et al.} [BABAR Collaboration],
%``Study of e+ e- $\to$ pi+ pi- pi0 process using initial state radiation
%with BaBar,''
Phys.\ Rev.\ D {\bf 70} (2004) 072004
[hep-ex/0408078].
%%CITATION = HEP-EX 0408078;%%
\bibitem{Aubert:2005eg}
B.~Aubert {\it et al.} [BABAR Collaboration],
%``The e+ e- $\to$ pi+ pi- pi+ pi- , K+ K- pi+ pi- , and K+ K- K+ K- cross
%sections at center-of-mass energies 0.5-GeV - 4.5-GeV measured with
%initial-state radiation,''
Phys.\ Rev.\ D {\bf 71} (2005) 052001
[hep-ex/0502025].
%%CITATION = HEP-EX 0502025;%%
\bibitem{Aubert:2005cb}
B.~Aubert {\it et al.} [BABAR Collaboration],
%``A study of e+ e- --> p anti-p using initial state radiation with BABAR,''
Phys.\ Rev.\ D {\bf 73} (2006) 012005
[hep-ex/0512023].
%%CITATION = PHRVA,D73,012005;%%
\bibitem{Baier:1965jz}
V.~N.~Baier and V.~A.~Khoze,
%``Radiation accompanying two particle annihilation of an electron - positron
%pair,''
Sov.\ Phys.\ JETP {\bf 21} (1965) 1145.
%%CITATION = SPHJA,21,1145;%%
\bibitem{Baier:1965bg}
V.~N.~Baier and V.~A.~Khoze,
%``Photon emission in muon pair production in electron - positron
%collisions,''
Sov.\ Phys.\ JETP {\bf 21} (1965) 629
[Zh.\ Eksp.\ Teor.\ Fiz.\ {\bf 48} (1965) 946].
%%CITATION = ZETFA,48,946;%%
\bibitem{Fadin}
V.~N.~Baier and V.~S.~Fadin,
Phys. Lett. {\bf 27B} (1968) 223.
\bibitem{PHradcor}
G.~Rodrigo, A.~Gehrmann-De Ridder, M.~Guilleaume and J.~H.~K\"uhn,
%``NLO QED corrections to ISR in e+ e- annihilation and the measurement of sigma(e+ e- $\to$ hadrons) using tagged photons,''
Eur.\ Phys.\ J.\ C {\bf 22} (2001) 81
[hep-ph/0106132].
J.~H.~K\"uhn and G.~Rodrigo,
%``The radiative return at small angles: Virtual corrections,''
Eur.\ Phys.\ J.\ C {\bf 25} (2002) 215
[hep-ph/0204283].
%%CITATION = HEP-PH 0106132;%%
%%CITATION = HEP-PH 0204283;%%
\bibitem{Ambrosino:2007nx}
F.~Ambrosino {\it et al.} [By KLOE Collaboration],
%``New results from KLOE,''
{\it In the Proceedings of International Conference on Heavy Quarks and Leptons (HQL 06), Munich, Germany, 16-20 Oct 2006, pp 009}
[hep-ex/0701008].
%%CITATION = ECONF,C0610161,009;%%
\bibitem{Leone:2006bm}
D.~Leone [KLOE Collaboration],
%``Measuring The Pion Form Factor Via Radiative Return At Large Photon Angles
%With Kloe,''
Nucl.\ Phys.\ Proc.\ Suppl.\ {\bf 162} (2006) 95.
%%CITATION = NUPHZ,162,95;%%
\bibitem{Balossini:2006wc}
G.~Balossini, C.~M.~Carloni Calame, G.~Montagna, O.~Nicrosini and F.~Piccinini,
%``Matching perturbative and parton shower corrections to Bhabha process at
%flavour factories,''
Nucl.\ Phys.\ B {\bf 758} (2006) 227
[hep-ph/0607181].
%%CITATION = NUPHA,B758,227;%%
\bibitem{Hoefer:2001mx}
A.~Hoefer, J.~Gluza and F.~Jegerlehner, Eur.~Phys.~J.~C{\bf 24} (2002) 51,
%``Pion pair production with higher order radiative corrections
% in low energy e+ e- collisions,''
[hep-ph/0107154].
%%CITATION = HEP-PH 0107154;%%
\bibitem{Jegerlehner:2007xe}
F.~Jegerlehner, these proceedings,
%``Essentials of the Muon g-2,''
[hep-ph/0703125].
%%CITATION = HEP-PH/0703125;%%
\bibitem{eidelman2007}
S.~Eidelman, these proceedings
\bibitem{Pancheri:2006cp}
G.~Pancheri, O.~Shekhovtsova and G.~Venanzoni,
%``Test of FSR in the process e+ e- --> pi+ pi- gamma at DAFNE and extraction
%of the pion form factor at threshold,''
Phys.\ Lett.\ B {\bf 642} (2006) 342
[hep-ph/0605244].
%%CITATION = PHLTA,B642,342;%%
\bibitem{Pancheri:2007xt}
G.~Pancheri, O.~Shekhovtsova and G.~Venanzoni,
%``Final state radiation and a possibility to test a pion-photon interaction
%model near two-pion threshold,''
[hep-ph/0706.3027].
%%CITATION = ARXIV:0706.3027;%%
\bibitem{Melnikov:2000gs}
K.~Melnikov, F.~Nguyen, B.~Valeriani and G.~Venanzoni,
%``Contribution of the direct decay phi $\to$ pi+ pi- gamma to the process e+
%e- $\to$ pi+ pi- gamma at DAPHNE,''
Phys.\ Lett.\ B {\bf 477} (2000) 114
[hep-ph/0001064].
%%CITATION = HEP-PH 0001064;%%
\bibitem{Ambrosino:2005wk}
F.~Ambrosino {\it et al.} [KLOE Collaboration],
%``Study of the decay Phi --> f0(980) gamma --> pi+ pi- gamma with the KLOE
%detector,''
Phys.\ Lett.\ B {\bf 634} (2006) 148
[hep-ex/0511031].
%%CITATION = PHLTA,B634,148;%%
\bibitem{Czyz:2007wi}
H.~Czy\.z, A.~Grzeli\'nska and J.~H.~K\"uhn,
%``Spin asymmetries and correlations in Lambda-pair production through the
%radiative return method,''
Phys.\ Rev.\ D {\bf 75} (2007) 074026
[hep-ph/0702122].
%%CITATION = PHRVA,D75,074026;%%
\end{thebibliography}
\end{document}