The $\pi\, N \rightarrow e^+e^- N$ reaction \\ skip close to the vector meson production threshold $^{a}$
% {Madeleine Soyeur$^1$
Matthias F.M. Lutz$^2$ and Bengt Friman$^{2}$% }
[2.812mm] {\normalsize \hspace*{-8pt}$^1$ DAPNIA/SPhN
%D\'{e}partement d'Astrophysique
de Physique des Particules
%de Physique Nucl\'{e}aire et de l'Instrumentation Associ\'{e}e
%Service de Physique Nucl\'{e}aire
CEA/Saclay
F-91191 Gif-sur-Yvette Cedex
France
[0.2ex] % \hspace*{-8pt}$^2$ GSI, Planckstrasse 1, D-64291 Darmstadt, Germany
Institut f\"ur Kernphysik, TU Darmstadt, D-64289 Darmstadt, Germany % }
The $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$ reaction cross sections are calculated below and in the vicinity of the vector meson ($\rho^0$, $\omega$) production threshold. These processes are largely responsible for the emission of $e^+e^-$ pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector meson-nucleon channels. The vector mesons materialize subsequently into $e^+e^-$ pairs. Using $\pi N\rightarrow \rho^0 N$ and $\pi N \rightarrow \omega N$ amplitudes calculated in the center of mass energy interval $1.4<\sqrt s <1.8$ GeV, we compute the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$ reaction cross sections in these kinematics. Below the vector meson production threshold, the $\rho^0 - \omega$ interference in the $e^+e^-$ channel appears largely destructive for the $\pi^-p \rightarrow e^+e^- n$ cross section and constructive for the $\pi^+n \rightarrow e^+e^- p$ cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector meson-nucleon channels to low-lying baryon resonances.
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\def\rightmark{(Short) The $\pi\, N \rightarrow e^+e^- N$ reaction}
\def\leftmark{M. Soyeur et al.}

\title{The $\pi\, N \rightarrow e^+e^- N$ reaction \\
\smallskip
close to the vector meson production threshold $^{a}$}
\authors{
%
{Madeleine Soyeur$^1$, Matthias F.M. Lutz$^2$ and Bengt Friman$^{2}$%
}\\[2.812mm]
{\normalsize
\hspace*{-8pt}$^1$ DAPNIA/SPhN,
%D\'{e}partement d'Astrophysique, de Physique des Particules,\\
%de Physique Nucl\'{e}aire et de l'Instrumentation Associ\'{e}e,\\
%Service de Physique Nucl\'{e}aire,\\
CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France\\[0.2ex]
%
\hspace*{-8pt}$^2$ GSI, Planckstrasse 1,  D-64291 Darmstadt, Germany\\
Institut f\"ur Kernphysik, TU Darmstadt,
   D-64289 Darmstadt, Germany
%
}}



\abstract{The $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$
reaction cross sections are calculated below and in the vicinity
of the vector meson ($\rho^0$, $\omega$) production threshold.
These processes are largely responsible for the emission of
$e^+e^-$ pairs in pion-nucleus reactions and contribute to the
dilepton spectra observed in relativistic heavy ion collisions.
They are dominated by the decay of low-lying baryon resonances
into vector meson-nucleon channels. The vector mesons materialize subsequently
into $e^+e^-$ pairs. Using $\pi N\rightarrow \rho^0 N$ and
$\pi N \rightarrow \omega N$ amplitudes calculated in the
center of mass energy interval $1.4<\sqrt s <1.8$ GeV, we compute
the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$
reaction cross sections in these kinematics. Below the vector meson production threshold, the
$\rho^0 - \omega$ interference in the $e^+e^-$ channel
appears largely destructive for
the $\pi^-p \rightarrow e^+e^- n$ cross section and
constructive for the $\pi^+n \rightarrow e^+e^- p$ cross section.
The pion beam and the HADES detector
at GSI offer a unique possibility to measure these effects. Such data would provide
strong constraints on the coupling of vector meson-nucleon channels to low-lying baryon
resonances.}

\keyword{Vector meson production; Baryon resonances; Dileptons}
\PACS{13.20; 13.75.G; 14.20.G}
\begin{document}

\maketitle

\setcounter{page}{1}

\section{Introduction}\label{intro}


The study of the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+ n \rightarrow e^+e^- p$ processes described
in this work \cite{Lutz2} aims at gaining understanding of the
$\pi N \rightarrow \rho^0 N$ and $\pi N \rightarrow \omega N$
scattering amplitudes for center of mass ener\-gies close and below the
vector meson production threshold ($1.5<\sqrt s <1.8$ GeV) \cite{Lutz1}.
There are well-known baryon resonances in
this energy range, which contribute
to the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+ n \rightarrow e^+e^- p$ scattering

\medskip
\smallskip
\hrule width 15mm
\begin{notes}
\item[a]
This talk is based on the work published in Ref. [1].
\end{notes}
amplitudes through their coupling to the $\pi N$, $\rho^0 N$ and $\omega N$ channels.
These amplitudes involve in addition significant non-resonant processes.
The phenomenological $\rho N N^*$ and $\omega N N^*$
coupling strengths needed to understand the data related to the
$\pi N \rightarrow \rho^0 N$ and $\pi N \rightarrow \omega N$
amplitudes are pivotal quantities
for baryon structure studies \cite{Lutz1}.

The exclusive observation of neutral vector mesons through their $e^+e^-$
decay presents definite advantages over their observation
through final states invol\-ving pions.
Firstly, there are no competing processes, such as $\pi \Delta$ production which leads to the
same $\pi \pi N$ final state and
impairs consequently the identification of the $\rho$-meson in that channel. Se\-condly, both the $\rho^0$- and
$\omega$-mesons decay into the $e^+e^-$ channel.
This leads to a quantum interference pattern which is expected to reflect sensitively
the structure and relative sign of the $\pi N \rightarrow \rho^0 N$
and $\pi N \rightarrow \omega N$ scattering amplitudes.

A proper understanding of the
$\pi^-p \rightarrow e^+e^- n$ and $\pi^+ n \rightarrow e^+e^- p$
reactions appears also as a necessary step
towards a detailed interpretation of the production of lepton pairs off nuclei
induced by charged pions. Such reactions would be particularly sensitive to
the propagation of $\omega$-mesons in nuclei \cite{Schoen}.

In Section 2, we present the relativistic coupled-channel model \cite{Lutz1}
used to des\-cribe the $\pi N \rightarrow \rho^0 N$ and $\pi N
\rightarrow \omega N$ amplitudes and outline the calculation of the
$\pi^-p \rightarrow e^+e^- n$ and
$\pi^+n \rightarrow e^+e^- p$
cross sections in the
Vector Meson Dominance model. Our numerical results
for these cross sections
are displayed in Section 3.
We discuss the $\rho^0-\omega$ quantum interference pattern in the
$e^+e^-$ spectrum for both the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+ n \rightarrow e^+e^- p$
reactions. We conclude briefly in Section 4.

\section{Calculation of the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$ cross sections
close to the vector
meson production threshold}

We describe the $\pi N \rightarrow e^+e^- N$ reaction for
$e^+e^-$ pair invariant masses ran\-ging from $\sim$0.4 to $\sim$0.8 GeV.
Assuming Vector Meson Dominance for the electromagnetic current \cite{Kroll},  the
$\pi N \rightarrow \rho^0 N$ and $\pi N
\rightarrow \omega N$ amplitudes are the basic
quantities entering the calculation of the $\pi N \rightarrow e^+e^- N$
cross section. This assumption is illustrated in Fig. 1, where we
show the diagrams contributing to the $\pi^-p \rightarrow e^+e^- n$
process.
\begin{figure}[t]
%\vspace*{-1.1cm}
                 \insertplot{fig1.eps}
%\vspace*{-1.1cm}
\caption[]{Diagrams contributing to the $\pi^-p \rightarrow  e^+e^- n$
amplitude with intermediate $\rho^0$- and $\omega$-mesons.}
\label{fig1}
\end{figure}

We use the $\pi N \rightarrow \rho^0 N$ and $\pi N \rightarrow \omega N$
amplitudes obtained in the recent relativistic and unitary coupled-channel
approach to
meson-nucleon scattering of Ref. \cite{Lutz1}.
The available data on pion-nucleon elastic and inelastic scatte\-ring and
on meson photoproduction off nucleon targets
are fitted in the energy window $1.4<\sqrt s <1.8$ GeV, using an effective
Lagrangian with quasi-local two-body meson-baryon interactions
and a generalized form of Vector Meson Dominance to describe the coupling
of vector mesons to real photons.
The scheme comprises the $\pi N$, $\pi \Delta$, $\rho N$,
$\omega N$, $K \Lambda$, $K \Sigma$ and $\eta N$ hadronic channels.
The coupling cons\-tants entering the effective Lagrangian are parameters
which are adjusted to reproduce the data. In view of the kinematics,
only s-wave scattering in the $\rho N$ and $\omega N$ channels is included,
restricting $\pi N$ and $\pi \Delta$ scattering to s- and d-waves.
The pion-nucleon resonances in the S$_{11}$, S$_{31}$, D$_{13}$ and D$_{33}$
partial waves are generated dynamically by solving Bethe-Salpeter
equations \cite{Lutz1}. In the $\rho^0 N$- and $\omega N$-channels,
the restriction to s-wave scattering means that the model applies
to situations where the vector meson is basically at rest with
respect to the scattered nucleon $(\sqrt s \simeq M_N + M_V)$.
This assumption implies that the range of validity of the present
calculation is limited to $e^+e^-$ pairs with invariant masses
$m_{e^+e^-}$ close to $(\sqrt s - M_N)$ and to values of $\sqrt s$
below and
very close to threshold i.e. $1.5 <\sqrt s \leq 1.75$ GeV.

The $\pi N \rightarrow \rho N$ amplitude has isospin 1/2
and isospin 3/2 components while the  $\pi N \rightarrow \omega N$ amplitude
selects the isospin 1/2 channel. Both amplitudes have spin 1/2 and spin 3/2
parts.

The invariant transition matrix elements for the $\pi N \rightarrow \rho N$
and $\pi N \rightarrow \omega N$ reactions are given by

\begin{eqnarray}
\langle \rho^j (\overline{q})\,N(\overline{p})|\,{\mathcal T}\,| \pi^i(q)\, N(p)\rangle & \nonumber \\
= \,(2\pi)^4\,  \delta^4 (q+ &p- \overline{q}- \overline{p})\, \overline u(\overline{p})\, \epsilon^\mu (\overline{q})
\,T^{ij}_{(\pi N\rightarrow \rho N)\,\mu}\,u(p),
\label{eq:e1}
\end{eqnarray}
\begin{eqnarray}
\langle \omega (\overline{q})\,N(\overline{p})|\,{\mathcal T}\,| \pi^i(q)\, N(p)\rangle & \nonumber \\
= \,(2\pi)^4\,  \delta^4 (q+ &p- \overline{q}- \overline{p})\, \overline u(\overline{p})\, \epsilon^\mu (\overline{q})
\,T^i_{(\pi N\rightarrow \omega N)\,\mu}\,u(p),
\label{eq:e2}
\end{eqnarray}

\noindent
where $T^{ij}_{(\pi N\rightarrow \rho N)\,\mu}$ and
$T^{i}_{(\pi N\rightarrow \omega N)\,\mu}$ are functions of the three kinematic variables
$w=p+q=\overline{p}+\overline{q}$ ($\sqrt {w^2}$ = $\sqrt s$), $q$ and
$\overline{q}$.
These scattering amplitudes can be decomposed into isospin invariant components
as
\begin{eqnarray}
T^{ij}_{(\pi N\rightarrow \rho N)\, \mu} (\overline{q},q;w)
\, = \sum_{I}
T^{(I)}_{(\pi N \rightarrow \rho N)\,\mu}(\overline{q},q;w)\, P_{(\rho)}^{(I)\,ij},
\label{eq:e5}
\end{eqnarray}
\begin{eqnarray}
T^{i}_{(\pi N\rightarrow \omega N)\, \mu} (\overline{q},q;w)
\, = \sum_{I}
T^{(I)}_{(\pi N \rightarrow \omega N)\, \mu}\,(\overline{q},q;w) P_{(\omega)}^{(I)\,i},
\label{eq:e6}
\end{eqnarray}
\noindent
in which $P_{(\rho)}^{(I)\,ij}$ and $P_{(\omega)}^{(I)\,i}$ are isospin projectors \cite{Lutz2}.
The isospin invariant amplitudes can be expanded further into
components of total angular momentum,

\begin{eqnarray}
T^{(I)}_{(\pi N\rightarrow V N)\, \mu} (\overline{q},q;w)
\,& = \,
M^{(I,J=\frac {1} {2})}_{\pi N \rightarrow V N}(s)\,
\,{Y}_{(J=\frac {1} {2})\,\mu}(\overline{q},q;w)\nonumber \\
&+ \, M^{(I,J=\frac {3} {2})}_{\pi N \rightarrow V N}(s)\,
\,{Y}_{(J=\frac {3} {2})\,\mu}(\overline{q},q;w).
\label{eq:e10}
\end{eqnarray}
\noindent
V stands for $\rho$ or $\omega$ and ${Y}_{(J=\frac {1} {2})\,\mu}(\overline{q},q;w)$
and ${Y}_{(J=\frac {3} {2})\,\mu}(\overline{q},q;w)$
are relativistic angular momentum
projectors \cite{Lutz2}.
\par
The $\pi N \rightarrow \rho N$ and $\pi N \rightarrow
\omega N$ amplitudes in the S$_{11}$, S$_{31}$, D$_{13}$ and D$_{33}$
channels obtained in Ref. \cite{Lutz1} are  displayed
in Figs. 2 and 3. The quantities shown
are the amplitudes $M^{(I,J)}_{\pi N\rightarrow \rho N}(s)$
and $M^{(I,J)}_{\pi N\rightarrow \omega N}(s)$ defined by
Eq. (\ref {eq:e10}), which depend only on the center of mass
energy $\sqrt s$.


\begin{figure}[h]
\vspace*{-0.5 cm}
                 \insertplot{fig2new.eps}
\vspace*{-0.9 cm}
\caption[]{Real and imaginary parts of
the $\pi N \rightarrow \rho^0 N$ amplitudes
in the pion-nucleon
S$_{11}$, S$_{31}$, D$_{13}$ and D$_{33}$
partial waves [1].}
\label{fig2}
\end{figure}
The coupling to subthreshold resonances is clearly
exhi\-bited in these pictures.
In the S$_{11}$ channel, the N(1535) and the N(1650) resonances lead
to peak structures in the imaginary parts of the amplitudes.
The pion-induced $\omega$ production amplitudes in the D$_{13}$ channel
reflect the strong coupling of the N(1520) re\-sonance to the
$\omega$N channel.
\begin{figure}[h]
\vspace*{-0.5 cm}
                 \insertplot{fig3.eps}
\vspace*{-0.9 cm}
\caption[]{Real and imaginary parts of
the $\pi N \rightarrow \omega N$ amplitudes in the pion-nucleon
S$_{11}$ and D$_{13}$ partial waves [1].}
\label{fig3}
\end{figure}
The $\pi^-p \rightarrow \rho^0 n$ and $\pi^-p \rightarrow \omega n$
amplitudes are obtained from the
isospin 1/2 and isospin 3/2 scattering amplitudes by the
relations,
\noindent
\begin{eqnarray}
M^J_{\pi^-p \rightarrow \rho^0 n} = - \frac {\sqrt 2} {3}
M^{(1/2,J)}_{\pi N\rightarrow \rho N}  +\frac {\sqrt 2} {3}
M^{(3/2,J)}_{\pi N\rightarrow \rho N},
\label{eq:e17}
\end{eqnarray}
\noindent
\begin{eqnarray}
M^J_{\pi^-p \rightarrow \omega n} = \sqrt{\frac {2} {3}}
M^{(1/2,J)}_{\pi N\rightarrow \omega N}.
\label{eq:e18}
\end{eqnarray}

\noindent
Similarly the $\pi^+ n \rightarrow \rho^0 p$ and $\pi^+n \rightarrow \omega p$
amplitudes are given by
\noindent
\begin{eqnarray}
M^J_{\pi^+n \rightarrow \rho^0 p} = \frac {\sqrt 2} {3}
M^{(1/2,J)}_{\pi N\rightarrow \rho N}  -\frac {\sqrt 2} {3}
M^{(3/2,J)}_{\pi N\rightarrow \rho N},
\label{eq:e19}
\end{eqnarray}
\noindent
\begin{eqnarray}
M^J_{\pi^+n \rightarrow \omega p} = \sqrt{\frac {2} {3}}
M^{(1/2,J)}_{\pi N\rightarrow \omega N}.
\label{eq:e20}
\end{eqnarray}

\newpage
The phases of the isospin coefficients appearing in Eqs. (\ref {eq:e17}) and (\ref {eq:e19}) play a crucial
role in determining the $\rho^0-\omega$ interference in the
$\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$
reaction cross sections.
The real and imaginary parts of the $\pi^-p \rightarrow \omega n$
and of the $\pi^+n \rightarrow \omega p$ amplitudes are the same and mostly positive.
In contrast, the $\pi^-p \rightarrow \rho^0 n$ and $\pi^+n \rightarrow \rho^0 p$ amplitudes
have opposite signs. The $\pi^-p \rightarrow \rho^0 n$ amplitudes are predominantly
negative and will therefore interfere destructively with the $\pi^-p \rightarrow \omega n$
amplitudes. The $\pi^+n \rightarrow  \rho^0 p$ and $\pi^+n \rightarrow \omega p$
amplitudes have the same sign over a large $\sqrt s$ interval, leading to a constructive
interference.

The $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$ cross sections are calculated from
the $\pi^-p \rightarrow \rho^0 n$, $\pi^-p \rightarrow \omega n$,
$\pi^+n \rightarrow \rho^0 p$ and $\pi^+n \rightarrow \omega p$
amplitudes, assuming Vector Meson Dominance of the electromagnetic current \cite{Sakurai,Kroll}.
This assumption can be enforced in the effective Lagrangian by introducing
vector meson-photon interaction terms of the form,
\begin{eqnarray}
{\mathcal L^{int}_{\gamma V}}\,&=&\, \frac {f_\rho} {2 M_\rho^2} F^{\mu \nu}\, \rho^0_{\mu \nu}
\,+\,\frac {f_\omega} {2 M_\omega^2} F^{\mu \nu}\, \omega_{\mu \nu},
\label{eq:e21}
\end{eqnarray}
\noindent
where the photon and vector meson field tensors are defined by
\begin{eqnarray}
F^{\mu \nu}\, =\,\partial^\mu A^\nu -\partial^\nu A^\mu,
\label{eq:e22}
\end{eqnarray}
\begin{eqnarray}
V^{\mu \nu}\, =\,\partial^\mu V^\nu -\partial^\nu V^\mu.
\label{eq:e23}
\end{eqnarray}
In equation (\ref {eq:e21}),
$M_\rho$ and $M_\omega$ are the $\rho$- and $\omega$-masses and
$f_\rho$ and  $f_\omega$ are dimensional coupling constants. Their magnitude can be
determined from the $e^+e^-$ partial decay widths of the $\rho$- and
$\omega$-mesons to be \cite{Friman1}
\begin{eqnarray}
|f_\rho|= 0.036\, GeV^2,
\label{eq:e24}
\end{eqnarray}
\begin{eqnarray}
|f_\omega|= 0.011 \,GeV^2.
\label{eq:e25}
\end{eqnarray}
The relative sign of $f_\rho$ and $f_\omega$
is fixed by vector meson photoproduction amplitudes \cite{Lutz1}.
We assume that the phase correlation between isoscalar and isovector currents
is identical for real and virtual photons as in Sakurai's realization
of the Vector Meson Dominance assumption \cite{Sakurai}. With the conventions used
in this paper, both $f_\rho$ and $f_\omega$ are positive.



\section{Numerical results}

With the $\pi N \rightarrow \rho N$ and $\pi N \rightarrow
\omega N$ amplitudes and the Vector Meson Dominance assumption
discussed in Section 2, we have calculated the differential
cross section $\frac{d\sigma}{d\overline{q}^2}_{\pi N \rightarrow e^+e^- N}$
for the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$
reactions. The magnitude of the 4-vector $\overline{q}$
is the invariant mass m$_{e^+e^-}$ of the $e^+e^-$ pair.
We refer to \cite{Lutz2} for calculational details.

The differential cross sections for the $\pi^-p \rightarrow e^+e^- n$
and the $\pi^+n \rightarrow e^+e^- p$ reactions are
computed for values of the total center of mass energy $\sqrt s$
ranging from 1.5 GeV up to 1.75 GeV. We explore the dependence of the $\rho^0-\omega$ interference
pattern in the $e^+e^-$ channel on $\sqrt s$ in this energy range, in particular
in the vicinity of the $\omega$-meson production threshold ($\sqrt s$=1.72 GeV).
We illustrate our results below threshold by displaying in Figs. 4 and 5
the differential cross sections for the $\pi^-p \rightarrow e^+e^- n$
and the $\pi^+n \rightarrow e^+e^- p$ reactions at $\sqrt s$=1.5 GeV,
where the N(1520) and N(1535) baryon
resonances play a dominant role.
These figures show very clearly
the isospin effects discussed in Section 2.
For the two reactions, the $\omega$ and $\rho^0$ contributions to the cross section are the
same.
The $\rho^0$-$\omega$ interference is destructive for the $\pi^-p \rightarrow e^+e^- n$
reaction and constructive for the $\pi^+n \rightarrow e^+e^- p$ process.
Consequently, the $\pi^-p \rightarrow e^+e^- n$ differential cross section is extremely small
in the range of invariant masses considered in this calculation.
In contrast, the constructive $\rho^0$-$\omega$ interference for the $\pi^+n \rightarrow e^+e^- p$
reaction leads to a sizeable differential cross section.
This is a very striking prediction, linked to the resonant structure of the scattering
amplitudes $M^{1/2}_{\pi N\rightarrow V N}$ and
$M^{3/2}_{\pi N\rightarrow V N}$.
Data on differential cross sections for the $\pi^-p \rightarrow e^+e^- n$
and $\pi^+n \rightarrow e^+e^- p$ reactions at $\sqrt s$=1.5 GeV would be very
useful for making progress in the understanding
of the couplings of both the N(1520) and N(1535) baryon
resonances to the vector meson-nucleon channels.
\begin{figure}[h]
\vspace*{-0.5 cm}
                 \insertplot{fig4.eps}
\vspace*{-0.9 cm}
\caption[]{Differential cross section for the $\pi^-p \rightarrow e^+e^- n$
reaction at $\sqrt s$=1.5 GeV as function of the invariant mass of the $e^+e^-$
pair. The $\rho^0$ and the $\omega$ contributions are indicated by short-dashed
and dotted lines respectively. The long-dashed line shows the $\rho^0-\omega$ interference.
The solid line is the sum of the three contributions.}
\label{fig4}
\end{figure}
\begin{figure}[t]
\vspace*{-0.1 cm}
                 \insertplot{fig5.eps}
\vspace*{-1 cm}
\caption[]{Differential cross section for the $\pi^+n \rightarrow e^+e^- p$
reaction at $\sqrt s$=1.5 GeV as function of the invariant mass of the $e^+e^-$
pair. The $\rho^0$ and the $\omega$ contributions are indicated by short-dashed
and dotted lines respectively. The long-dashed line shows the $\rho^0-\omega$ interference.
The solid line is the sum of the three contributions.}
\label{fig5}
\end{figure}

\newpage
The differential
cross sections for the $\pi^-p \rightarrow e^+e^- n$ and $\pi^+n \rightarrow e^+e^- p$
reactions below threshold have been calculated also at $\sqrt s$=1.55, 1.60, 1.65 and 1.70 GeV \cite{Lutz2}.
The cross sections vary smoothly with the total center of mass energy. They
exhibit the features discussed for $\sqrt s$=1.5 GeV,  reflecting however
dynamics associated with higher-lying resonances.
Just below threshold ($\sqrt s$=1.70 GeV), the $\omega$-contribution begins to increase, while the general
features of the $e^+e^-$ production in the two isospin channels remain the same.

The interference pattern changes drastically above the $\omega$-meson threshold.
 Figs. 6 and 7 show the $\pi^-p \rightarrow e^+e^- n$
and $\pi^+n \rightarrow e^+e^- p$ differential cross sections at $\sqrt s$=1.75 GeV.
At this energy,
the differential cross sections for the $\pi^-p \rightarrow e^+e^- n$ and
$\pi^+n\rightarrow e^+e^- p$ reactions are completely dominated by the
$\omega$-contribution. The magnitudes of the cross sections for the two reactions are
comparable. The $\rho^0-\omega$ interference is still destructive
in the $\pi^-p \rightarrow e^+e^- n$ channel and constructive in
the $\pi^+n\rightarrow e^+e^- p$ channel, albeit very small.
In both reactions, crossing the $\omega$-production threshold
leads to a sharp increase in the cross section, by two orders of magnitude
in the $\pi^-p \rightarrow e^+e^- n$ channel and by one order of
magnitude in the $\pi^+n\rightarrow e^+e^- p$ channel.

\newpage

\begin{figure}[h]
\vspace*{-0.5cm}
                 \insertplot{fig6.eps}
\vspace*{-1.8cm}
\caption[]{Differential cross section for the $\pi^-p \rightarrow e^+e^- n$
reaction at $\sqrt s$=1.75 GeV as function of the invariant mass of the $e^+e^-$
pair.}
\label{fig6}
\end{figure}

\begin{figure}[h]
\vspace*{-0.5 cm}
                 \insertplot{fig7.eps}
\vspace*{-1.4 cm}
\caption[]{Differential cross section for the $\pi^+n\rightarrow e^+e^- p$
reaction at $\sqrt s$=1.75 GeV as function of the invariant mass of the $e^+e^-$
pair.}
\label{fig7}
\end{figure}

\section{Conclusion}

We have computed the $e^+e^-$ pair invariant mass distributions for the $\pi^-p \rightarrow e^+e^- n$
and $\pi^+n\rightarrow e^+e^- p$ reactions below and close to the vector meson production threshold.
We took as input the $\pi N\rightarrow\rho^0 N$ and $\pi N\rightarrow\omega N$ amplitudes
obtained in a recent relativistic and unitary coupled-channel approach to
meson-nucleon scattering \cite{Lutz1}.
Using the Vector Meson Dominance assumption, we have shown that the differential cross sections for
the $\pi^-p \rightarrow e^+e^- n$
and $\pi^+n\rightarrow e^+e^- p$ reactions below the $\omega$-threshold are very sensitive to the
coupling of low-lying baryon resonances to vector meson-nucleon
final states contributing to the $\rho^0$- and $\omega$-meson production amplitudes.
We find that the $\rho^0-\omega$ interference is destructive in the
$\pi^-p \rightarrow e^+e^- n$ channel and constructive in the $\pi^+n\rightarrow e^+e^- p$ channel
(see also Ref. \cite{Titov}).
We predict a very small cross section for the $\pi^-p \rightarrow e^+e^- n$ reaction
below threshold and a sizeable cross section for the $\pi^+n\rightarrow e^+e^- p$ reaction
in this energy range. Above the $\omega$-meson production threshold, both cross sections are
comparable and much larger.

The magnitude of the $\pi^-p \rightarrow e^+e^- n$
and $\pi^+n\rightarrow e^+e^- p$  differential cross sections below the $\omega$-threshold depends strongly
on the structure and dyna\-mics of baryon resonances. These reactions deserve
experimental studies. Such a programme could be carried at GSI (Darmstadt) using
the available pion beam and the HADES spectrometer \cite{Schoen}. These measurements
would provide a necessary step towards the understanding of $e^+e^-$ pair
production in pion-nucleus reactions and
in general significant constraints on the propagation of vector mesons in the
nuclear medium.

\begin{thebibliography}{99}

\bibitem{Lutz2}
M.F.M. Lutz, B. Friman and M. Soyeur, nucl-th/0202049.
\bibitem{Lutz1}
M.F.M. Lutz, Gy. Wolf and B. Friman, nucl-th/0112052.
\bibitem{Schoen}
W. Sch\"on et al., Acta Physica Polonica B 27 (1996) 2959.
\bibitem{Sakurai}
J.J. Sakurai, Currents and Mesons, The University of Chicago Press, 1969.
\bibitem{Kroll}
N.M. Kroll, T.D. Lee and B. Zumino, Phys. Rev. 157 (1967) 1376.
\bibitem{Friman1}
B. Friman and M. Soyeur, Nucl. Phys. A 600 (1996) 477.
\bibitem{Titov}
A.I. Titov and B. K\"{a}mpfer, Eur. Phys. J. A. 12 (2001) 217.
\end{thebibliography}

\end{document}
\begin{figure}[htb]
\vspace*{-1.1cm}
                 \insertplot{p2.eps}
%\vspace*{-1.1cm}
\caption[]{The figure caption contains an explanatory text for the figure,
  the meaning of the applied signs, references, explicit data for
  parameters}
\label{fig1}
\end{figure}

\begin{figure}[htb]
\vspace*{-1.1cm}
\hspace*{-0.5cm}
                 \insertplot{vdm.xfig.eps}
\vspace*{-1.1cm}
\caption[]{The figure caption contains an explanatory text for the figure,
  the meaning of the applied signs, references, explicit data for
  parameters}
\label{fig1}
\end{figure}

Phenomenological constraints on the $\rho N N^*$ and $\omega N N^*$
coupling strengths are useful both for baryon structure studies
and for building models of vector meson propagation in the
nuclear medium \cite{Lutz1}.
A historical, methodological or logical scope outlined in the
Introduction helps the readers place the subject of the article in
his/her personal knowledge on it or enables to guess the present stage
of the subject. Ample citation \cite{bib1,bib2,bib3,bib4,bib5,bib9} of
literature that deals with the subject in question is also given in
this section, as a source of information.  In a second part, the
Introduction tells the readers more details about the structure of the
article. It often serves as a guide to introduce the sections that
build up the article.

At the beginning of the \LaTeX\ template file {\tt
budapest-template.tex} there is a block of defining commands for page
numbers.  These should be completed by the Editors.

\section{Technical--Preparatory Section}\label{techno}
The technical or methodological preparatory section of the article
should commence the row of the sections. The experimental description
of measurements or the mathematical introduction of the problem, the
definitions of the concepts or the descriptions of the methods,
procedures applied in the investigations should be treated in this
section to start with the problem \cite{bib1,bib10}.

{\it Citation of references} mentioned in the article will be done as
seen in the previous sentence. Citations referring to some journals
should be given as in item 4 under the References.


\subsection{Subsections dealing with details}\label{details}
Subsections (maybe, the deeper {\tt $\backslash$subsubsection}s) will be
arranged so that they appear as discernible distinct parts within the
whole structure of the article. For too wide tables or figures it may
happen that a ``landscape page'' will be setup.

\subsection{Mathematics}\label{maths}

Mathematics can be e.g.\ embedded $P_1({\bf p})=E_p(dN/d^3p)$ as in
this case, or displayed separately from text rows as (the boldface
letter {\bf p} denotes a vector):
\begin{equation}
   n_\mu(x)=
\int_\Sigma d^3\sigma_\mu(x^\prime)\,\delta^{(4)}(x-x^\prime) \label{eq1}
\end{equation}

Not strange if formulae are arranged in an (vertical or horizontal)
array of terms/factors or equations or in matrices, e.g., if a single
row is too short to accommodate a formula:
\begin{eqnarray}
   \tilde{C}({\rm\bf q},{\rm\bf K}) = 1 \pm \Bigl\{1
   &-&
   q_s^2\langle y^2\rangle
   -\left\langle[q_\perp(x-\beta_\perp t) +
   q_L(z-\beta_L t)]^2\right\rangle
 \nonumber \\
   &+&
   \langle q_\perp(x-\beta_\perp t) +
   q_L(z-\beta_L t)\rangle^2
+ {\cal O}\left[\left\langle(q{\cdot}x)^4\right\rangle\right] \Bigr\} \, ,
\label{eq2}
\end{eqnarray}
{\it Cross references to formulae} will be given as ``as in
Eq.~(\ref{eq2})'' or ``given by (\ref{eq1})'', etc.

\subsection{Tables}\label{tabs}

An example of a simply built table we give below.
\begin{table}[hb]
\vspace*{-12pt}
\caption[]{Title of the table (usually, the first sentence).
An explanatory on the data text may follow; it ranges in the full
width of the table, similarly as for figures.}\label{tab1}
\vspace*{-14pt}
\begin{center}
\begin{tabular}{lllll}
\hline\\[-10pt]
Projectile & Energy & $\bar{E}$ & $\sigma_{KLL}^{\rm rel}$ &
$\sigma_{KLM}/\sigma_{KLL}$\\
&(MeV) & (eV) & (\%) & (\%)\\
\hline\\[-10pt]
Ne$^{3+}$ & 110 & 756.6 $\pm$ 0.3 & {\phantom{$0$}}71.6 $\pm$ 3.8 &
{\phantom{$00$}}8.1 $\pm$ 1.2 \\
Ne$^{10+}$ & 110 & 742.8 $\pm$ 0.2 & 100 & {\phantom{$0$}}10.3 $\pm$ 4.5 \\
Ar$^{6+}$ & 220 & 743.7 $\pm$ 0.3 & 153.5 $\pm$ 10.7 & $<9.2$ \\
Ar$^{17+}$ & 220 & 719.8 $\pm$ 0.4 & 269.2 $\pm$ 21.3 &
{\phantom{$00$}}9.84 $\pm$ 0.35\\
\hline
\end{tabular}
\end{center}
\end{table}

\newpage

\subsection{Figures}\label{figs}

Figure \ref{fig1} shows a typical presentation of data or results. The
figure caption is an inevitable part of the figure.

\begin{figure}[htb]
\vspace*{-1.1cm}
                 \insertplot{fig1.ps}
\vspace*{-2.1cm}
\caption[]{The figure caption contains an explanatory text for the figure,
  the meaning of the applied signs, references, explicit data for
  parameters}
\label{fig1}
\end{figure}
{\it Plots} are expected to be submitted in Encapsulated PostScript.
The {\tt epsf.sty} style file is used in {\tt budapest.sty} to help you
place and size your figures into the ma\-nu\-script. Please submit
each figure as a fig-n\-.eps(f) file separately. If the file is
exceptionally large or in other exceptional cases the {\it compression
  of files\/} is desirable, however, in this case include instructions
for decompressing on a unix computer. {\it Photos} should be converted
to EPS files; for color separation purposes, please keep the TIF (or
good quality JPG) file format if they are colorful photos.

\section{Other Sections}\label{others}
Further sections explaining the subject of the article follow the
starting ones. At the end, Special Sections may follow as below.

\section{Conclusions}\label{concl}
As usual, the Conclusions contain the results achieved and presented
in the article.

\section*{Appendix}\label{app}
Details of mathematical derivations, other technical descriptions are
deferred here from the main text. If more than a single appendix will
be included, they will be enumerated by using capital Latin letters:
Appendix A, Appendix B, etc.


\section*{Acknowledgement(s)}
A section devoted for personal gratitude and/or offered grant
identifications.

\section*{Notes} (footnotes will be typeset in this way)
\begin{notes}
\item[a]
Permanent address: Institute, City, Country;\\
E-mail: author@host.domain.name
\end{notes}


\begin{thebibliography}{99}

\bibitem{Lutz1}
M.F.M. Lutz, Gy. Wolf and B. Friman, nucl-th/0112052.

\bibitem{bib1}A.B. Coalman, D.E. Fiedler and G. Hughes, {\it Rev. Mod.
    Phys.}  {\bf 63} (1991) 545.

\bibitem{bib2}G.J. Banderer and S.M. Mikhalchuk, {\it Phys. Lett.}
  {\bf B54} (1983) 387; {\it Sov. J. Nucl. Phys.} {\bf 19} (1979) 197.

\bibitem{bib3}D. Heinemann and U. S\o renmann, Bergensburg preprint
  BPR-94-31, submitted to {\it Phys. Lett. B.}

\bibitem{bib4}T. Czukor and J. Zel\'enyi, {\it Heavy Ion Phys.} {\bf
    1} (1995) 646.

\bibitem{bib5}I.V. Mileev, K. Plummer and M.M. Gorentchev, {\it Int.
    J. Mod.  Phys.} {\bf A11} (1995) 77.

\bibitem{bib6}S. Trottman and G. Karib, {\it Proceedings of the 5th
    Workshop on High Energy Collision Phenomena}, eds J-P. Condrieu
  and P.  Ch\^{a}teau-Simone, Paris, August 2--6, 1993, Springer,
  Heidelberg, 1994, p.  324.

\bibitem{bib7}W.T. Fogg, Talk presented at Advanced Research Workshop
  ``Hot Hadronic Matter: Theory and Experiment'', Barcelona, June 29
  -- July 1, 1994; to be published in the Proceedings by Plenum Press.

\bibitem{bib9}This was not seen in \cite{bib6}.

\bibitem{bib10}From Eq.~(\ref{eq2}) one sees that in the original frame
  the cross term is given by:
$$
Q_{\perp L}^2 =  \left( <x\;\tau\;{\rm sh}\eta'>-
<x><\tau\;{\rm sh}\eta'>\right)
$$
up to small logarithmic corrections. This clearly vanishes as soon
as the source becomes reflection symmetric under $\eta' = - \eta'$.

\end{thebibliography}
\vfill\eject
\end{document}

nucl-th0207020.extracted_bib
\begin{thebibliography}{99}

\bibitem{Lutz2}
M.F.M. Lutz, B. Friman and M. Soyeur, nucl-th/0202049.
\bibitem{Lutz1}
M.F.M. Lutz, Gy. Wolf and B. Friman, nucl-th/0112052.
\bibitem{Schoen}
W. Sch\"on et al., Acta Physica Polonica B 27 (1996) 2959.
\bibitem{Sakurai}
J.J. Sakurai, Currents and Mesons, The University of Chicago Press, 1969.
\bibitem{Kroll}
N.M. Kroll, T.D. Lee and B. Zumino, Phys. Rev. 157 (1967) 1376.
\bibitem{Friman1}
B. Friman and M. Soyeur, Nucl. Phys. A 600 (1996) 477.
\bibitem{Titov}
A.I. Titov and B. K\"{a}mpfer, Eur. Phys. J. A. 12 (2001) 217.
\end{thebibliography}