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\begin{document}

\title{Effects of $\mathrm{e^\pm}$ Polarization on  Final States at HERA}

\author{U. St\"osslein}

\address{DESY Hamburg\\ Notkestrasse 85, 22607 Hamburg, Germany \\
E-mail: uta.stoesslein@desy.de}

%$\vec{e}^{\,\pm}p$
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\maketitle

\abstracts{At HERA II,   
longitudinally polarized electrons and positrons
collide with unpolarized protons 
at centre-of-mass-energies of 318 GeV and at high luminosities.
This offers unique opportunities for 
testing the Standard Model and 
probing new physics areas.
A brief overview is given of the possibilities offered by
the use of beam charge and polarization dependent final states at HERA,
in particular as regards 
electroweak structure functions,
generalized parton distributions and  $\Lambda$-baryon
production.
}

%-----------------------------------------------------------------------
\section{Polarization and Luminosity}
The need
for luminosity greater than the design value as well as for longitudinally 
polarized beams at HERA 
has been 
anticipated by
a series of physics workshops~\cite{stossl:Wiik}.
After tapping the potential of the HERA I phase, in 2000/2001 
a major upgrade~\cite{stossl:Hoffstaetter} was performed
to the two interaction regions (H1 and ZEUS)
 to improve focussing at the  interaction points and to thus obtain
 higher luminosity values. 
Each interaction region was rebuilt and 
complemented by a pair of spin rotators,
allowing the transverse polarization generated via synchrotron
radiation in  HERA-e to be converted to longitudinal
 polarization.
With one  spin rotator pair, which has been working since 1995  at 
the HERA-e fixed target experiment HERMES, typical polarization values 
of up to 60\% were achieved.
In March 2003,  successful operation with three  spin
 rotator sets was achieved and  the 
longitudinal polarization of the positrons reached values of up to
54\% in colliding mode~\cite{stossl:Hoffstaetter}. 
The HERA-e polarimeters continuously measure
 both the transverse 
and the longitudinal beam polarization. These devices 
are being upgraded to allow polarization measurements of  a relative 
systematic uncertainty of 1\% with negligible statistical 
errors~\cite{stossl:Bohme}, as is required for  precision measurements.
Absolute luminosities of 2.7$\cdot 10 ^{31} \rm{cm}^{-2}\rm{s^{-1}}$ 
have been reached,
suggesting that luminosities of about 
 5$\cdot 10 ^{31} \rm{cm}^{-2}\rm{s^{-1}}$ are 
achievable at full beam currents and design specific luminosity.
This should allow the collection of about 200 pb$^{-1}$ of data per
 year~\cite{stossl:Hoffstaetter}.

This talk discusses briefly the
 effects on the final states
of scattering polarized $\mathrm{e^\pm}$ off unpolarized protons at HERA.
A collider programme of nucleon and photon spin 
physics 
and on electron-ion collisions may be realized after the present  HERA II 
phase~\cite{stossl:Hera3}.

%-----------------------------------------------------------------------
\section{Beam Polarization Effects in Electroweak Interactions}
%-----------------------------------------------------------------------
\begin{figure}[b]
  \vspace*{3mm}
\centerline{\epsfxsize=1.85in\epsfbox{stossl-andy.mehta.dis02.eps}}
\caption{Measured unpolarized (HERA I data) and 
simulated polarized $\rm{e^{\,\pm}p}$ CC 
cross sections as a function of lepton polarization 
assuming  an integrated 
luminosity of 50 pb$^{-1}$ for each of the polarized data sets.
Figure taken from~\protect\cite{stossl:mehta}. 
\label{stossl-andy.mehta.dis02}}
\end{figure}
%
High luminosities and high polarization values allow 
inclusive deep inelastic scattering (DIS)
measurements to be extended 
to large photon virtualities Q$^2$ where the event rates 
are small. Basic quantities of interest are the proton structure 
functions which are effective descriptions of the non-perturbative 
part of the inclusive ep-scattering process. Utilizing the lepton charge
and helicity dependence of the DIS charged
 current (CC) and neutral current (NC)
 cross sections, more 
precise and new information on the proton dynamics can be obtained, or 
alternately, using the knowledge of 
proton structure functions, 
electroweak parameters 
can be tested.

An impressive, 'textbook' test of the electroweak theory can be performed
by measuring of the polarized $\rm{e^\pm p}$ CC cross sections  as shown in 
Fig.~\ref{stossl-andy.mehta.dis02}~\cite{stossl:mehta}.
The expected linear dependence of the  
CC cross section on the beam polarization, i.e. the handedness
of the lepton, is a direct consequence of the Standard Model, in which
the massive W$^+$ and W$^-$-particles, the carriers of the weak force, only act
on left-handed particles 
and right-handed antiparticles. Any deviation from a straight line
would point  to 
physics beyond the Standard Model.
%
Presently, the H1 and ZEUS experiments are taking data  with right-handed
positrons and a first  analysis of the CC cross section can be expected soon.
However, to get the complete picture  depicted in 
Fig.~\ref{stossl-andy.mehta.dis02},  
four beam charge and helicity combinations
have to be measured 
 with high polarization values  and integrated luminosities 
of about 50 pb$^{-1}$ per sample.

Competitive searches for new physics can be performed by investigating 
parity violation in NC DIS, where the cross section depends on both beam 
polarization and charge, see e.g.~\cite{stossl:kleinriemann} for a systematic 
consideration of cross sections and their combinations.
The interference of neutral  electromagnetic ($\gamma$) and weak (Z) currents
leads to additional
 vector and axial-vector contributions to the e$^\pm$p
cross section. These are  parameterized in terms of two new structure 
functions, G$_2$ and xG$_3$ (not to be confused with
the well known polarized structure functions).
 Both contain the quark couplings to the
Z-boson.
Since the strength of the $\gamma$Z interference itself is about
 10$^{-4}\cdot$GeV$^2$/Q$^2$, 
high Q$^2$ values are 
preferable if these structure functions are to be measured.
Measuring the asymmetries introduced by electroweak effects has 
the advantage that
 common systematic uncertainties, like 
acceptances and global inefficiencies,
cancel.

Varying the beam polarization for a fixed lepton charge delivers 
a parity-violating asymmetry  ($\propto \rm{G_2/F_2}$), studied 
first at SLAC in 1978 in a high statistics ed-scattering experiment 
at a Q$^2$
 of 1.6 GeV$^2$~\cite{stossl:Prescott}. Measured at large $\Bx $,
the parity-violating asymmetry is dominated by
 the ratio of d to u-valence quarks.
Simulated HERA data covering the  range of Q$^2$ from 
1000 until 30000~GeV$^2$ unveil the feasibility of
a G$_2$ measurement at $\Bx >0.01$ using the excellent knowledge of the
electromagnetic structure function F$_2$ already obtained from
the HERA I data. 
High polarization values, of about 50\%, 
and high luminosity values 
of about 200 pb$^{-1}$ per sample are needed~\cite{stossl:Klein01}. 
Variation of both lepton polarization and charge, first performed 
in $\mu$C-scattering in 1982 at CERN~\cite{stossl:Argento}, allow the 
determination of a beam conjugation asymmetry which is predominantly
sensitive to 
the interference structure function xG$_3$.
At HERA this delivers 
new information on
the behavior of valence quark distributions in the sea quark range, 
$\Bx > 0.01$.

High polarization values of at least 50\% 
and integrated luminosities of about 150 pb$^{-1}$ per sample
 can significantly improve the tests of electroweak parameters,
for example the determination of the aforementioned 
vector and axial-vector 
couplings of the Z-boson to the light quarks~\cite{stossl:Cashmore}.
The best sensitivity to the mass of the W-boson and the value of 
sin$^2\theta_{\rm W}$
can be achieved using the polarization dependent 
neutral to charged current cross section ratio for electrons;
slightly less precise results are obtained using 
positrons~\cite{stossl:bkr87}.


%-----------------------------------------------------------------------
\section{DVCS Cross Section and Asymmetries }
%-----------------------------------------------------------------------
With the advent of HERA, 
a new class of large rapidity gap events was discovered in 
DIS~\cite{stossl:diffraction} at small $\Bx<0.01$. 
These diffractive events  
were not expected in the  quark-parton model (QPM).
An intuitive picture of these events was offered by  
the 
color dipole
model~\cite{stossl:bj70}, a nearly forgotten picture at this time.
With increased luminosity, in 1999 another class of diffractive events 
was discovered at 
HERA~\cite{stossl:zeus.dvcs.talk,stossl:Adloff01,stossl:Chekanov03} 
in which there is a  
large rapidity gap between the recoiling proton and 
a real  photon in the final state, 
see Fig.~\ref{stossl-h1.dvcskine}a.
These deeply virtual, or off-forward, Compton scattering (DVCS)
events  at  small momentum 
transfer t to the proton can also be described by the color dipole model;
see~\cite{stossl:Chekanov03,stossl:Favart03}
 for comparisons with recent ZEUS and H1 data.
Furthermore, the observation of DVCS  
triggered the further development and  
 use of another theoretical concept for diffractive and exclusive processes, 
generalized parton distribution
(GPD)
functions. 
GPDs were revived in 1996 when   the spin physics community
realized the unique potential they have for  unravelling
 the spin structure of the
nucleon~\cite{stossl:Ji97}.
%
\begin{figure}[b]
\centerline{\epsfxsize=3.6in\epsfbox{stossl-h1.dvcskine.eps}}
\caption{a$)$ DVCS graph, b$)$ BH with photon from initial state lepton and
  c$)$ with photon from final state lepton.  
Figure taken from~\protect\cite{stossl:Adloff01}.
\label{stossl-h1.dvcskine}}
\end{figure}
%
Only recently, the  exciting potential of GPDs in the study 
of three dimensional hadron structure
 has been recognized~\cite{stossl:Burkardt00}. In
the  case that
the initial and final state differ
only in their transverse momenta, 
GPDs encode simultaneously  information
on  the longitudinal momentum, determined by $\Bx$, and transverse position 
of partons in the infinite momentum frame, described by an
impact parameter $\mathrm{b} \sim 1/\sqrt{-\mathrm{t}}$.
%
Nowadays,
GPD based model calculations deliver fair descriptions of
the measured,  t-integrated DVCS cross section and its kinematic 
dependence~\cite{stossl:Chekanov03,stossl:Favart03} 
and are theoretically rather 
well understood, see~\cite{stossl:Diehl03} for a review. More,
and more precise,  
measurements are required to pin down the various theoretical model
uncertainties. 

The diffractive electroproduction of a real photon,  depicted in 
Fig.~\ref{stossl-h1.dvcskine}a, interferes  with the Bethe-Heitler (BH)
process shown in Figs.~\ref{stossl-h1.dvcskine}b,c. Both deliver 
the same final states, but these can be distinguished experimentally 
by the different weights they have in different kinematic regions.
Furthermore, the BH process is a  pure QED process  with a  calculable
cross section. This kind of background is well controlled 
and can be subtracted allowing DVCS cross
section measurements~\cite{stossl:Adloff01,stossl:Chekanov03}. 
Moreover, with the advent of HERA II, the complex and rich
angular structure of the DVCS cross section can be employed to access more
observables which may help to unfold GPDs.

In general, the amplitude-squared  of the real photon electroproduction
cross section receives contributions from pure DVCS
 (Fig.~\ref{stossl-h1.dvcskine}a), from pure BH 
(Figs.~\ref{stossl-h1.dvcskine}b,c) and from their interference 
(with a sign governed by the lepton charge): 
$\mathrm{ %\frac{d^4\sigma}{d\Bx dy d|t| d\phi } \propto
|{\mathcal T}|^2 \propto |{\mathcal T}_{DVCS}|^2  + |{\mathcal T}_{BH}|^2  + {\mathcal I}}  $.
%
Each term can be expanded in a Fourier series in the azimuthal
angle  $\phi$
 between the electron scattering plane and the real photon reaction
plane~\cite{stossl:Diehl97}. This can be used to filter out the
relevant information about the Compton process. 
The terms are given by
\begin{eqnarray}
\label{stossl:BH}
&& \mathrm{    |{\mathcal T}_{\rm BH}|^2
\propto \left[ c^{\rm BH}_0
+  \sum_{n = 1}^2
c^{\rm BH}_n \, \cos(n\phi) + s^{\rm BH}_1 \, \sin(\phi)
\right] }
\\
\label{stossl:DVCS2}
&& \mathrm{  |{\mathcal T}_{\rm DVCS}|^2
\propto \Big[
c^{\rm DVCS}_0
+ \sum_{n=1}^2
\left[c^{\rm DVCS}_n \cos (n\phi) + s^{\rm DVCS}_n \sin (n \phi)\right]
\Big] }
\\
\label{stossl:ITerm}
&& \mathrm{ {\mathcal I}
\propto -\mathrm{sign}(e)\Big[
c_0^{\mathcal I}
+ \sum_{n = 1}^3
\left[c_n^{\mathcal I} \cos(n \phi) +  s_n^{\mathcal I} \sin(n \phi)\right]
\Big] }
\end{eqnarray}
According to the detailed formulae 
in~\cite{stossl:Belitsky01},  $\phi$ dependent 
contributions in the  scattering of polarized 
leptons with helicity $\lambda$ off an
unpolarized proton can be  expected to arise from:
\begin{enumerate}
\item[i)] pure BH (Eq.~\ref{stossl:BH})  in addition to the
 known kinematical $\phi$
dependence of the BH propagator giving 
\begin{enumerate}
\item  $\cos \phi$ and $\cos 2 \phi$  terms (leading twist-2)
\item  no $\sin \phi$ term 
(appears only for transversely polarized proton) 
\item  no beam helicity dependence
(appears only for longitudinally or transversely polarized protons) 
\end{enumerate}
\item[ii)] pure DVCS (Eq.~\ref{stossl:DVCS2}) giving
\begin{enumerate}
\item   suppressed $\cos \phi$ and  $\lambda \sin \phi$ terms (twist-3)
\item $\alpha_{\rm S}$ power suppressed $\cos 2 \phi$ term 
(leading twist-2, related to gluon transversity; $\sin 2 \phi$ 
will appear only for longitudinally or transversely polarized protons) 
\end{enumerate}
\item[iii)] DVCS-BH Interference (Eq.~\ref{stossl:ITerm}) 
 in addition to the known kinematical $\phi$
dependence of the BH propagator and the dependence on the sign of the 
lepton charge giving  
\begin{enumerate}
\item  $\cos \phi$ and  $\lambda \sin \phi$ terms (leading twist-2)
\item  suppressed $\cos 2\phi$ and  $\lambda \sin 2\phi$ terms (twist-3)
\item $\alpha_{\rm S}$ power suppressed  $\cos 3 \phi$ and 
 $\sin 3 \phi$ terms 
(leading twist-2, related to gluon transversity). 
\end{enumerate}
\end{enumerate}
The Fourier coefficients ${\rm  c_n} $ and ${\rm  s_n} $ 
                                %${\rm  s_n^{BH,DVCS, \mathcal I}}$ 
in Eqs.~\ref{stossl:DVCS2}-\ref{stossl:ITerm}
are directly related to the amplitudes of the
$\gamma^*$p Compton process which can be parameterized by 
the so-called Compton Form Factors 
(CFF)~\cite{stossl:Belitsky01}.
CFFs for their part are convolutions of QCD coefficient functions and
GPDs denoted  usually by  H, $\tilde{\rm H}$,  E, $\tilde{\rm E}$.
CFFs, and hence the GPDs, 
appear in quadratic combinations in the DVCS cross section,
but in linear combinations in the interference term (Eq.~\ref{stossl:ITerm}).
Particularly  for HERA 
kinematics,  
 measurements of the dominant  interference Fourier 
coefficients ${\rm  c_1}^{\mathcal I} $ and ${\rm  s_1}^{\mathcal I} $ 
gives 
access to, respectively, the real and the imaginary part of the CFF 
$\mathcal H$ and thus to the leading twist-2 GPD H, since 
at small $\Bx$ possible contributions from the
GPDs   $\tilde{\rm H}$ and  E can be  safely neglected~\cite{stossl:Freund03}.
In principle, a complete separation of the four leading twist-2 GPDs 
%from the set of  Fourier coefficients 
would require in addition data taken with  transversely and
longitudinally polarized protons.

The %DVCS 
real photon production
 observable containing information on the 
 ${\rm  s_1}^{\mathcal I} $ term
is the single beam spin asymmetry (SSA),   
measured at  Q$^2$ of about 2~GeV$^2$ by the  fixed
target experiments  CLAS and HERMES 
for the first time~\cite{stossl:SSA}.
A measurement of the SSA requires high lepton beam and virtual photon
polarizations (high y). A simulation~\cite{stossl:Freund03} 
for the HERA-positron beam reveals
significant negative asymmetry values, 
shown in Fig.~\ref{stossl-freund} (left).
This asymmetry is positive for an electron beam.
Experimentally, the $\phi$ dependence of the difference between
the number of events with
positive beam helicity and  negative beam helicity 
has to be formed.
Using an unpolarized beam sample to get rid of the $\sin \phi$ amplitude
contributions, and  positron and 
electron beam data,  the 
 beam charge asymmetry sensitive to the ${\rm  c_1}^{\mathcal I} $ term
can be formed for 
real photon production events.
Only HERMES has been able to measure the CA so far~\cite{stossl:CA},
 employing HERAs unique feature of
delivering positron and electron beams.
The CA simulation~\cite{stossl:Freund03} 
for  HERA-collider kinematics shows, in Fig.~\ref{stossl-freund} (right),  
encouragingly large asymmetry values.
A further  measurement of the ${\rm  c_1}^{\mathcal I} $ term 
can be performed via an azimuthal angle asymmetry  that is predicted
to have a size similarly to that of the CA~\cite{stossl:Freund03}.
However,  this measurement would require
a detector with excellent $\phi$ resolution and control of
twist-3 contributions whereas the twist-3 effects for 
the CA and SSA have been estimated to be negligible~\cite{stossl:Freund03}.
\begin{figure}[t]
\hspace*{17.5mm}\vspace*{-80.9mm}\epsfxsize=3.8in\epsfbox{stossl-freund.ca.eps}
\hspace*{-48mm}\epsfxsize=3.87in\epsfbox{stossl-freund.ssa.eps}
\caption{DVCS asymmetries  for  HERA kinematics as a function of $\Bx$ 
for two  typical values of Q$^2$ and t$_{max}= -0.5~\rm{GeV}^2$, modeled
in LO and NLO QCD with (w) and
without (wo) twist-3 contributions (Tw-3).
Left: $t$ integrated single beam spin asymmetry (SSA) for a positron beam.
 Right: $t$ integrated beam charge asymmetry (CA).
 Figures taken from~\protect\cite{stossl:Freund03}.  
 }
\label{stossl-freund}
\end{figure}

In the second phase of HERA, 
it is anticipated that the size of the data samples available
for the DVCS cross
section measurements will be  about 10 times larger than those used so far.
The measurement of the DVCS associated asymmetries will remain challenging 
with the present H1 and ZEUS detectors, since the 
recoiling proton will not generally be observed, making the determination
of $\phi$ and t difficult~\cite{stossl:Stamen02}.
The 
 very forward proton spectrometer (VFPS)~\cite{stossl:VFPS}
recently installed at H1
 may help to further reduce the proton-dissociative background in the DVCS 
sample and to deliver a first measurement of the t-dependence of
 the DVCS cross section at  centre-of-mass energies of the
 $\gamma^*$p-system W of about 20 GeV. 

%-----------------------------------------------------------------------
\section{Beam Spin Transfer to $\Lambda$-Baryons}
%-----------------------------------------------------------------------
Studying 
$\Lambda$ ($\bar{\Lambda}$) baryon production in unpolarized 
and polarized DIS processes, 
allows the exploitation of the 
 'self-analyzing' decay of the  $\Lambda$.
The $\Lambda$-polarization can be
measured by studying the angular distribution of the 
$\Lambda \to p \pi$ decay (in the $\Lambda$ helicity rest frame).
The polarization of the 
fragmenting parton  is determined by the elementary
Standard Model interactions and the initial parton's 
spin state.
Neglecting weak interactions,
there are  four general DIS observables for involving
$\Lambda$'s that employ the
various possible combinations of (un)polarized leptons and nucleons, 
see e.g.~\cite{stossl:Anselmino03}.

Particularly interesting for the upgraded HERA is to consider the 
spin transfer from a longitudinally polarized charged 
lepton  (helicity S) to the $\Lambda$ while the proton 
is unpolarized (helicity 0). In this DIS  process, the scattered quark
will be polarized 
and its spin will be transferred to the baryon produced in the fragmentation
of this quark. In the QPM, the longitudinal spin transfer to the
outgoing $\Lambda$ is given by~\cite{stossl:Anselmino03}:
\be
\mathrm{
P_{S,0} 
=\frac{y(2-y)}{1 + (1-y)^2} \> 
\frac{\sum_q e^2_q \, q(x) \, \Delta D_{\Lambda/q}(z)}
{\sum_q e^2_q \, q(x) \, D_{\Lambda/q}(z)} \>.
}\label{stossl:lambda}
\ee
Here,  P$_{\rm S,0}$ is the 
polarization of the hyperon $\Lambda$ which is measurable in 
semi-inclusive DIS,
and q and  D are the usual unpolarized quark
 distribution and  fragmentation functions. 
The fragmentation of a longitudinally polarized parton into a longitudinally 
polarized $\Lambda$ is described by $\rm{\Delta D_{\Lambda/q}(z)}$.
This polarized fragmentation function may be further related, via
the so-called Gribov-Lipatov relation~\cite{stossl:gribov}, to the  
polarized quark distribution function of the $\Lambda$.

From Eq.~\ref{stossl:lambda}, it follows that a
$\Lambda$-spin transfer measurement  requires high beam polarizations,
high virtual photon 
polarizations (high y values) and a broad range in z, the hadron
momentum fraction in the lab frame.
For $\Lambda$'s produced in the current fragmentation 
region in the DIS process, i.e. originating from the
struck quark,
the spin of the $\Lambda$
is  entirely due to the strange quark within the naive QPM.
On the other hand, e.g. using SU(3)$_{\rm f}$, 
the quark distributions of the $\Lambda$
can be related to those in the proton~\cite{stossl:Ma01ri}, or,
if both the proton and the $\Lambda$ spin structures are known,
SU(3)$_{\rm f}$ symmetry  may be tested.
In recent years, many theoretical
models have been 
proposed for the longitudinal polarization of $\Lambda$ baryons in 
DIS, addressing the question of
the relationships
 between the spin structure of the proton and of the other 
baryons~\cite{stossl:soffer01,stossl:ellis02}.
Recent DIS results
 on  longitudinal  $\Lambda$-polarization have come 
from HERMES~\cite{stossl:Hermes00} in NC charged lepton-nucleon 
scattering and from NOMAD in $\nu_{\rm e}$ charged current 
interactions~\cite{stossl:Naumov02}, but 
all these data are for low W values, which complicates their interpretation.
Here, HERA II data could give a significant input, due to the much larger 
W ranges accessible, although detailed simulations have yet to be performed.
The   production of $\Lambda$ ($\bar{\Lambda}$) baryons in 
polarized charged current e$^\pm$p DIS could provide 
information on  flavor separated polarized  quark fragmentation functions, 
in a manner analogous to the 
scattering of a neutrino beam on a hadronic target.

%------------------------------------------------------------------------
\section{Conclusion and Outlook}
%-----------------------------------------------------------------------
HERA II, with its high luminosity and with longitudinally polarized 
electrons and positrons, opens new horizons in the 
study of electroweak theory and parton dynamics,
 both in inclusive DIS and 
via the selection of
particular final states.
The experimental prospects have been illustrated in this talk
 by discussing the most promising channels:
electroweak structure functions and charged current interactions, 
real photon electroproduction
which extends the framework
of DIS to the off-forward region of the virtual
Compton process and the study of  $\Lambda$ spin structure
 via its longitudinal  polarization.

Beyond the measurements  mentioned, there are further
 subjects
 awaiting  investigation. One may think of
e.g. an even more detailed mapping of the 
GPDs which can be done by studying the
complex angular dependence of the 
cross section for the electroproduction of lepton pairs off an unpolarized or
 polarized nucleon target~\cite{stossl:Belitsky03fj}. Unfortunately, the cross
section is very low thus requiring very high luminosities, but first studies 
may start at HERA II.
Another interesting test of NLO versus twist-3 effects
  at HERA II may be performed 
by measuring a single-beam 
spin asymmetry in semi-inclusive pion production, as was done recently by CLAS
at low Q$^2$, hence making interpretation difficult~\cite{stossl:Avakian03}.
Single-beam spin and charge asymmetries may  also be observed
 in the 
diffractive electroproduction of a $\pi^+ \pi^-$ pair. 
These observables are 
expected to be sensitive to Pomeron-Odderon  
interference~\cite{stossl:Hagler} and could thus give  first
evidence for the Odderon, which has so far escaped  detection.

HERA II has just started. 
More detailed investigations are required of the huge 
variety of channels available, and
unexpected results may well appear.

%-----------------------------------------------------------------------
\section*{Acknowledgments}
%-----------------------------------------------------------------------
 I would like to thank 
Markus Diehl, Andreas Freund and Henri Kowalski for fruitful discussion
and Tim Greenshaw for carefully reading the manuscript.


%-----------------------------------------------------------------------
\begin{thebibliography}{0}
%-----------------------------------------------------------------------
\bibitem{stossl:Wiik} B.~Wiik,
{\it  Proceedings of the Workshop Future Physics at HERA 1995/96},
%edited by G. Ingelman, A. De Roeck, R. Klanner, 
{\tt http://www.desy.de/~heraws96} (1996).

\bibitem{stossl:Hoffstaetter}
G.~Hoffst\"atter, M.~Vogt, F.~Willeke,
%``Experiences With The Hera Beams,''
{\it ICFA Beam Dyn.\ Newslett.\  } {\bf 30}, 7 (2003).
%%CITATION = 00376,30,7;%%

\bibitem{stossl:Bohme}
J.~B\"{o}hme for the POL2000 group,
%``Polarisation Measurement At Hera Ii,''
{\it Acta Phys.\ Polon.\ } {\bf  B33},  3949 (2002).

\bibitem{stossl:Hera3}
H. Abramowicz et al., MPI-PhE/2003/06 (2003);\\
T. Alexopoulos et al., DESY/03-194 (2003).

\bibitem{stossl:mehta}
A.~Mehta,
talk given at {\it 10th International Workshop on Deep Inelastic Scattering 
(DIS2002), Cracow, Poland, 30 Apr - 4 May 2002} ; 
{\it Acta Phys.\ Polon.\ }{\bf B33},  3937 (2002).
 
\bibitem{stossl:kleinriemann}
M. Klein, T. Riemann,
{\it Z. Phys.} {\bf  C24}, 151 (1984).

\bibitem{stossl:Prescott}
C.~Y.~Prescott {\it et al.},
 %``Further Measurements Of Parity Nonconservation In Inelastic Electron
%Scattering,''
{\it Phys.\ Lett.\ } {\bf B84}, 524 (1979).

\bibitem{stossl:Klein01}
M.~Klein,
%``Future deep inelastic scattering with HERA and THERA,''
%\href{http://www.slac.stanford.edu/spires/find/hep/www?irn=5492483}{SPIRES entry}
{\it Proceedings of  9th International Workshop on Deep Inelastic Scattering (DIS 2001), Bologna, Italy, 27 Apr - 1 May 2001}, 409 (2002)

\bibitem{stossl:Argento}
BCDMS, A.~Argento et al.,
%``Electroweak Asymmetry In Deep Inelastic Muon - Nucleon Scattering,''
{\it Phys.\ Lett.\ } {\bf B120},  245 (1983).

\bibitem{stossl:Cashmore} R. Cashmore et al.,
{\it  Proceedings of the Workshop Future Physics at HERA 1995/96}, 163 (1996).

\bibitem{stossl:bkr87}
J. Bl\"umlein, M. Klein, T. Riemann,
% Testing ew standard model at HERA
{\it Proceedings, HERA Workshop, Hamburg 1987, vol. 2}, 687 (1987). 

\bibitem{stossl:diffraction}
ZEUS Collaboration, M.~Derrick et al.,
 %``Observation of events with a large rapidity gap in deep inelastic scattering
%at HERA,''
{\it Phys.\ Lett.\ } {\bf B315}, 481 (1993). \\
H1 Collaboration, T.~Ahmed et al.,
%``Deep inelastic scattering events with a large rapidity gap at HERA,''
{\it Nucl.\ Phys.\ } {\bf B429}, 477 (1994).

% original paper about QPM and CDM
\bibitem{stossl:bj70}
J.D. Bjorken, J.B. Kogut, D.E. Soper, 
{\it Phys.\ Rev.\ } {\bf D3},  1382 (1970).

\bibitem{stossl:zeus.dvcs.talk}
P.R.B.~Saull for the ZEUS collaboration, 
{\it Proc. of the International Europhysics Conference on
  High-Energy Physics (EPS-HEP 99), Tampere, Finland, 15-21 July
  1999,}  420,  (2000), hep-ex/0003030 (2000).


\bibitem{stossl:Adloff01}
H1 Collaboration, C.~Adloff  et al.,
%``Measurement of deeply virtual Compton scattering at HERA,''
Phys.\ Lett.\ B {\bf 517} (2001) 47, hep-ex/0107005 (2001).
%%CITATION = HEP-EX 0107005;%%

\bibitem{stossl:Chekanov03}
ZEUS Collaboration, S.~Chekanov  et al.,
%``Measurement of deeply virtual Compton scattering at HERA,''
Phys.\ Lett.\ B {\bf 573} (2003) 46, hep-ex/0305028 (2003).
%%CITATION = HEP-EX 0305028;%%

\bibitem{stossl:Ji97}
X.-D. Ji,
{\it Phys. Rev. Lett.} {\bf 78}, 610 (1997), hep-ph/9603249 (1996).
%%CITATION = HEP-PH 9603249;%%


%new H1 EPS data
\bibitem{stossl:Favart03}
L.~Favart for the H1 Collaboration,
 %``Studies of DVCS and photoproduction of photons at high t with the H1
%detector,''
hep-ex/0312013 (2003).
%%CITATION = HEP-EX 0312013;%%

\bibitem{stossl:Diehl03}
M.~Diehl,
%``Generalized parton distributions,''
{\it Phys.\ Rept.\ } {\bf 388}, 41 (2003),   
hep-ph/0307382 (2003).

\bibitem{stossl:Burkardt00}
M.~Burkardt,
 %``Impact parameter dependent parton distributions and off-forward parton
%distributions for zeta $\to$ 0,''
{\it Phys.\ Rev.\ } {\bf D62}, 071503 (2000)
[Erratum-ibid.\  {\bf D66}, 119903 (2002)],
hep-ph/0005108 (2000).

\bibitem{stossl:Diehl97}
M.~Diehl, T.~Gousset, B.~Pire and J.~P.~Ralston,
%``Testing the handbag contribution to exclusive virtual Compton
%scattering,''
{\it Phys.\ Lett.\ } {\bf B411}, 193 (1997),
hep-ph/9706344 (1997).

\bibitem{stossl:Belitsky01}
A.~V.~Belitsky, D.~Muller, A.~Kirchner,
%``Theory of deeply virtual Compton scattering on the nucleon,''
{\it Nucl.\ Phys.\ } {\bf B629}, 323 (2002), 
hep-ph/0112108 (2001).


\bibitem{stossl:Freund03}
A.~Freund,
%``A detailed QCD analysis of twist-3 effects in DVCS observables,''
{\it Phys.\ Rev.\ }  {\bf D68},   096006 (2003), 
hep-ph/0306012 (2003).


\bibitem{stossl:SSA}
HERMES Collaboration, A.~Airapetian  et al.,
%``Measurement of the beam spin azimuthal asymmetry associated with
%deeply-virtual Compton scattering,''
{\it Phys.\ Rev.\ Lett.\ }  {\bf 87}, 182001 (2001),
hep-ex/0106068 (2001). \\
CLAS Collaboration, S.~Stepanyan  et al.,
 %``First observation of exclusive deeply virtual Compton scattering in
%polarized electron beam asymmetry measurements,''
{\it Phys.\ Rev.\ Lett.\ } {\bf 87},  182002 (2001),
hep-ex/0107043 (2001). 

\bibitem{stossl:CA}
F.~Ellinghaus  for the HERMES Collaboration,
%``Beam-charge asymmetry associated with DVCS at HERMES,''
{\it Nucl.\ Phys.\ } {\bf A711}, 171 (2002),
hep-ex/0207029 (2002).

\bibitem{stossl:Stamen02}
R. Stamen,
talk given at {\it HERA-III Workshop 2002, Munich, Germany,
18 - 20 Dec 2002}, 
{\tt http://wwwhera-b.mppmu.mpg.de/hera-3/hera3/index.html}.

\bibitem{stossl:VFPS}
L. Favart et al., \\
PRC-01/00 (2000) {\tt http://web.iihe.ac.be/h1/vfps/documents.html}.



\bibitem{stossl:Anselmino03}
M.~Anselmino,
%``Transversity and Lambda polarization,''
hep-ph/0302008 (2003).

\bibitem{stossl:Ma00uu}
B.Q.~Ma, I.~Schmidt, J.~Soffer and J.J.~Yang,
 %``Lambda, Antilambda polarization and spin transfer in lepton  deep-inelastic
%scattering,''
{\it Eur.\ Phys.\ J.\ } {\bf C16}, 657 (2000), 
hep-ph/0001259 (2000).

\bibitem{stossl:gribov}
V.N. Gribov, L.N. Lipatov,
%      Title: Deep Inelastic Electron Scattering In Perturbation Theory
{\it  Phys.Lett. }{\bf B37}, 78 (1971);
%      Title: E+ e- Pair Annihilation And Deep Inelastic E P Scattering In Perturbation Theory
{\it    Sov. J. Nucl. Phys.  }{\bf 15}, 675 (1972).


\bibitem{stossl:Ma01ri}
B.Q.~Ma, I.~Schmidt, J.~Soffer and J.J.~Yang,
%``Quark distributions of octet baryons from SU(3) symmetry,''
{\it Phys.\ Rev.\ } {\bf D65}, 034004 (2002),
hep-ph/0110029 (2001).

\bibitem{stossl:soffer01}
J.~Soffer,
%``New prospects for polarized hyperon fragmentation functions,''
{\it Nucl.\ Phys.\ Proc.\ Suppl.\ } {\bf 105}, 140 (2002)
hep-ph/0111054 (2001).

\bibitem{stossl:ellis02}
J.R.~Ellis, A.~Kotzinian,  D.V.~Naumov,
 %``Intrinsic polarized strangeness and Lambda0 polarization in  deep-inelastic
%production,''
{\it Eur.\ Phys.\ J.\ } {\bf C25}, 603 (2002)
hep-ph/0204206 (2002).

%Measurement of Longitudinal Spin Transfer to Lambda Hyperons in Deep Inelastic Lepton Scattering
\bibitem{stossl:Hermes00}
HERMES Collaboration, A. Airapetian et al., {\it Phys.Rev.  } {\bf D64}, 
 112005 (2001), hep-ex/9911017 (1999). \\
S. Belostotski, O. Grebenyuk, Yu. Naryshkin for the HERMES Collaboration,
{\it Acta Phys.\ Polon.\ } {\bf  B33},  3785 (2002).

\bibitem{stossl:Naumov02}
D.V. Naumov for the NOMAD Collaboration,
{\it Acta Phys.\ Polon.\ } {\bf  B33},  3791 (2002).



\bibitem{stossl:Belitsky03fj}
A.V.~Belitsky and D.~M\"uller,
 %``Probing generalized parton distributions with electroproduction of lepton
%pairs off the nucleon,''
{\it Phys.\ Rev. } {\bf D68}, 116005 (2003),
hep-ph/0307369 (2003).


\bibitem{stossl:Avakian03}
CLAS Collaboration, H.~Avakian  et al., 
 %``Measurement of beam-spin asymmetries for deep inelastic pi+
%electroproduction,''
hep-ex/0301005 (2003).

%\cite{Hagler:2002cq}
\bibitem{stossl:Hagler}
P.~Hagler et al.,
%``Pomeron odderon interference effects in electroproduction of pi+ pi-,''
{\it Nucl.\ Phys.\ Proc.\ Suppl.\ } {\bf 121}, 155 (2003),
hep-ph/0209242 (2002).
%%CITATION = HEP-PH 0209242;%%


\end{thebibliography}

\end{document}
