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\title*{Experimental Results and Perspectives\protect\newline
  of Polarized Lepton-Nucleon Scattering}
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\toctitle{Experimental Results and Perspectives \protect\newline
 of Polarized Lepton--Nucleon Scattering}
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\titlerunning{Polarized Lepton-Nucleon Scattering}
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\author{Michael D\"uren}
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\authorrunning{Michael D\"uren}
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\institute{Universit\"at Erlangen-N\"urnberg, Erwin-Rommel-Str. 1,\\
  D-91058 Erlangen, Germany\\}

\maketitle              % typesets the title of the contribution
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}  
   The spin structure of the nucleon and its spin puzzle is introduced
  in this paper, followed by a summary of the recent results on
  polarized lepton nucleon scattering. The spin structure functions of
  the proton and neutron have been measured and their first moments have
  been determined. The recent experiments confirm that the Ellis-Jaffe
  sum rule is violated, whereas the Bjorken sum rule is valid within
  the precision of the measurement.  Results are reported about the
  flavor decomposition of the quark polarization, a first direct
  measurement of a positive gluon polarization, the observation of a
  double-spin asymmetry in diffractive $\rho^0$ production, the
  polarization of $\Lambda$ hyperons, the observation of transverse
  single-spin asymmetries and the measurement of the
  Gerasimov-Drell-Hearn sum rule. Prospects of future fixed target and
  collider facilities are discussed.
\end{abstract}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

The fact that the nucleon has a large anomalous magnetic moment proves
that it is not a fundamental spin-1/2 Dirac particle. The approximate
agreement of the measured magnetic moments of the members of the
baryon multiplets with predictions of the SU(3)$_f\times$SU(2)
symmetric quark-parton model is an important confirmation of the quark
model approach. Additional predictions about the spin structure of the
nucleon were the Bjorken~\cite{BJSR}\index{Bjorken sum rule} and
Ellis-Jaffe~\cite{EJSR}\index{Ellis-Jaffe sum rule} sum rules, which
however were not experimentally accessible in the first two decades of
the quark model. In 1987 the EMC\index{EMC experiment} collaboration
published a measurement of the spin structure function $g^p_1(x)$ of
the proton and of its first moment, the Ellis-Jaffe sum~\cite{emc1}.
The observed violation questioned our understanding of the spin
structure of the nucleon in terms of the quark-parton model. It caused
intense discussion in the community and demanded experimental and
theoretical clarification.

Since then a series of new spin experiments has been performed at
SLAC, CERN and DESY as summarized in~\cite{windmolders}.  They became
feasible by improved experimental techniques to polarize beams and
targets. At CERN and SLAC the improved figure of merit, which is the
product of luminosity and the squared values of the polarization of
beam and target, allowed for a precision measurement of the inclusive
spin structure functions.  The HERMES
experiment~\cite{hermes}\index{HERMES experiment} uses a completely
novel method, a polarized internal storage cell target\index{internal
target} in a storage ring with longitudinally polarized electrons. The
HERMES storage cell\index{storage cell} is a 40~cm long elliptical
tube around the stored electron beam. Polarized atoms are continuously
injected into the storage cell and leave the cell only after an average
of a few hundred wall bounces. The main advantage of the storage cell
technique is the ability to use pure, highly polarized atomic species
(H, D, $^3$He) in contrast to solid state targets where only a small
fraction of the atomic species is polarizable.

The HERMES experiment\index{HERMES experiment} is dedicated to
semi-inclusive measurements, i.e. measurements which detect final
state hadrons in coincidence with the scattered lepton. By tagging
certain final state hadrons with different flavor content, the spin
contributions $\Delta u,\Delta d,\Delta s$ of the up, down and strange
quark flavors can be disentangled\index{spin flavor decomposition}.

The inclusive as well as the semi-inclusive results show that only a
fraction of the nucleon spin is due to the spin contribution $\Delta
\Sigma=\Delta u+\Delta d+\Delta s$ of the quarks. The rest is due to
the contribution $\Delta G$ of the gluon spin and due to angular
momentum contributions $L_q$ and $L_G$ of quarks and gluons moving
with high speed in the nucleon.  Current experiments show first
evidence of a non-zero contribution by the gluon spin, however further
experiments are needed  to disentangle and understand all the
contributions of the nucleon's spin $s^{\cal N}_z$, which are
summarized in the helicity sum rule\index{helicity sum rule}
\begin{equation}
s^{\cal N}_z=\frac{1}{2}
=\frac{1}{2}\left(\Delta u+\Delta d+\Delta s \right)+L_q+\Delta G+L_G.
\end{equation}
To improve our understanding of the spin structure of the nucleon, in
future not only the collinear spin contributions have to be measured,
but more emphasis has to be given to investigate transverse spin
components, twist-3 contributions, spin-dependent off-forward parton
distributions and spin effects in fragmentation.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Inclusive Deep Inelastic Scattering}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Spin Structure Functions\index{spin structure function}}

The spin dependent part of the inclusive deep inelastic
scattering\index{inclusive polarized DIS}
cross section $e+{\cal N} \to e'+X$ is characterized by two spin
structure functions $g_1(x,Q^2)$ and $g_2(x,Q^2)$. In the quark-parton
model the Bjorken variable $x$ is interpreted as the momentum fraction
carried by the struck quark and $-Q^2$ is the squared four-momentum of
the exchanged virtual photon and is related to the resolution of the
scattering process.  The first spin structure function $g_1(x,Q^2)$ is
interpreted as
\begin{equation}
    \label{eq:g1def}
    g_1(x,Q^2)={1\over 2}\sum_f e_f^2 \Delta q_f(x,Q^2) 
\end{equation}
with $e_f$ being the charge for a quark with flavor $f$ in units of
the elementary charge and $\Delta q_f(x,Q^2)=
q_f^{\uparrow\uparrow}(x,Q^2)-q_f^{\uparrow\downarrow} (x,Q^2)$ is the
polarized quark distribution function\index{polarized quark
  distribution function}.
$q_f^{\uparrow\uparrow(\uparrow\downarrow)}(x,Q^ 2)$ is the
distribution function of quarks with spin orientation parallel
(anti-parallel) to the spin of the nucleon. The second spin structure
function $g_2(x,Q^2)$ is zero in the simple quark model. In general,
$g_2(x,Q^2)$ contains the Wandzura-Wilczek
contribution\index{Wandzura-Wilczek contribution}
$g_2^{WW}(x,Q^2)=-g_1(x,Q^2)+\int_x^1 dx'\, g_1(x',Q^2)/x' $, a pure
twist-3 contribution, and minor contributions from transverse parton
polarizations~\cite{ww}.

The spin structure function $g_1$ has been measured since many years,
and an impressive, precise data set has been collected by the
experiments at SLAC\index{SLAC experiments}, by SMC\index{SMC
experiment} and by HERMES\index{HERMES experiment} as shown in
Fig.~\ref{due-g1}~\cite{windmolders}.  At all three sites the spin
structure function $g_1(x,Q^2)$ was measured for the proton and the
neutron. The neutron spin asymmetry is obtained either from the
subtraction of deuteron and proton data, or directly from a $^3$He
target. In the $^3$He nucleus the spins of the protons are
anti-parallel and do not contribute to the measured asymmetry (except
for a small contribution which can be corrected).  All experimental
results are consistent and agree with the $Q^2$ evolution as predicted
by QCD.

The measurement of $g_2$ is more difficult. Experiments at
SMC\index{SMC experiment} and SLAC have shown that $g_2$ is consistent
with $g_2^{WW}$, but data are also almost consistent with zero.  The
experiment E155x at SLAC ran in spring 1999 with the aim to provide
more precise data on $g_2$ and to gain access to the interesting
twist-3 component of $g_2$ that remains after subtraction of the
Wandzura-Wilczek contribution $g_2^{WW}$.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Sum Rules}

%\subsection*{Ellis-Jaffe and Bjorken Sum Rules}
Using SU(3)$_f$ symmetry\index{SU(3)$_f$ flavor symmetry} arguments,
the first moment $\Gamma_1$ of the spin structure function $g_1(x)$
can be related to the axial couplings $F$ and $D$ known from baryon
decays:
\begin{equation}
    \label{eq:gammapn}
    \Gamma_1^{p(n)}=+(-)
    {F+D\over 12}+{3F-D\over 36} +{\Delta \Sigma \over 9}+
\mbox{QCD corrections terms}
\end{equation}
In addition, the total spin carried by quark spins can be expressed as
\begin{equation}
 \Delta \Sigma=3F-D+3\Delta s.
\end{equation}
The Ellis-Jaffe\index{Ellis-Jaffe sum rule} sum rule~\cite{EJSR} is
obtained from Eq.~(\ref{eq:gammapn}) by the additional (reasonable but
possibly false) assumption that the spin carried by strange quarks is
negligible: $\Delta s=0$. From this assumption follows that the total
spin carried by quark spins is $\Delta \Sigma=3F-D=58\%$ (modulo QCD
corrections at finite $Q^2$).  Fig.~\ref{due-sr}~\cite{Emlyn}
demonstrates that the Ellis-Jaffe sum rule is violated with the
consequence, that either the strange quark contribution to the proton
spin is significant, or that the SU(3)$_f$ symmetry which was used to
derive Eq.~(\ref{eq:gammapn}) is broken.  The Bjorken sum
rule~\cite{BJSR}\index{Bjorken sum rule}, which is the non-singlet
combination of the first moments of proton and neutron does not
require these two assumptions and is experimentally verified at the
10\% level (see Fig.~\ref{due-sr}).  The precision of the sum rule
tests is limited by theoretical uncertainties in the extrapolation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\begin{center}
\begin{minipage}[b]{.47\textwidth}
\includegraphics[width=\textwidth]{./dueren.1}
\caption[The spin structure function\index{spin structure function} $g_1(x)$]{Recent results for the
  spin structure functions $xg_1(x)$ at $Q^2=5$~GeV$^2$ for the
  proton, deuteron and neutron. The continuous lines are results of a
  QCD fit at NLO.}
\label{due-g1}
\end{minipage}
\hfill
\begin{minipage}[b]{.47\textwidth}
\includegraphics[width=\textwidth]{./dueren.2}
\caption[Experimental results for the Bjorken and for the Ellis-Jaffe
sum rules]{The measured values of the first moments $\Gamma_1^p$ and
  $\Gamma_1^n$ of the spin structure functions $g_1^p$ and $g_1^n$ of
  the proton and neutron are in good agreement with the Bjorken sum
  rule\index{Bjorken sum rule}, but deviate from the prediction of the
  Ellis-Jaffe sum rule\index{Ellis-Jaffe sum rule}.}
\label{due-sr}
\end{minipage}
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\noindent
of
the spin structure functions at low $x$.  Experimentally, the low $x$
range will be accessible only by a future high energy spin experiment
at a new facility as the proposed polarized HERA
collider~\cite{Hughes}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection*{Gerasimov-Drell-Hearn Sum Rule}
A further sum rule, the Gerasimov-Drell-Hearn
(GDH)\index{Gerasimov-Drell-Hearn sum rule} sum rule, relates the
polarization dependent part of the total photoproduction cross section
to the anomalous magnetic moment of the nucleon. This important
relation has been tested by a precision experiment at the tagged
polarized photon beam of the microtron MAMI in Mainz, Germany.  The
energy range accessible by the experiment is 200-800~MeV. A
preliminary analysis of a small subset of the data reports a number of
$230\pm 20 ~$\umu b, which accounts for most of the GDH prediction of
$\int_{m_\pi}^{\infty}(\sigma_{3/2}-\sigma_{1/2})/\nu\, d\nu=204~$\umu
b~\cite{Thomas}. The remaining difference might be due to
contributions at higher energies, which are planned to be measured at
ELSA/Bonn and at Jefferson Lab.

The GDH sum rule can be generalized\index{generalized GDH sum rule}
for electroproduction. Data have been recently published by the
HERMES\index{HERMES experiment} collaboration~\cite{gdh}, and a new
measurement in the important resonance region was performed in spring
1999 as experiment E94-010 at Jefferson Lab~\cite{Meziani}.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Semi-inclusive Deep Inelastic Scattering}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Flavor Decomposition\index{spin flavor decomposition}}

The observed violation of the Ellis-Jaffe sum rule made clear that the
spin structure of the nucleon is not understood. More detailed
experimental information is needed to disentangle the various possible
contributions of quarks and gluons to the spin of the nucleon.
Semi-inclusive\index{semi-inclusive polarized DIS} data can be used to
measure the sea polarization directly and to test SU(3)$_f$ symmetry
by comparing the first moments of the flavor distributions to the
SU(3)$_f$ predictions. In addition, semi-inclusive polarized DIS
experiments can determine the separate spin contributions $\Delta q_f$
of quark and antiquark flavors $f$ to the total spin of the nucleon
not only as a total integral but as a function of the Bjorken scaling
variable $x$.

Hadron production in DIS is described by the absorption of a virtual
photon by a point-like quark and the fragmentation into a hadronic
final state. The two processes can be characterized by two functions:
the quark distribution function $q_f(x,Q^2)$, and the fragmentation
function\index{fragmentation
function} $D_f^h(z,Q^2)$.  The semi-inclusive DIS cross section
$\sigma^h(x,Q^2,z)$ to produce a hadron of type $h$ with energy
fraction $z=E_h/\nu$ is then given by
\begin{equation}
    \label{eq:hadronsig}
    \sigma^h(x,Q^2,z)\propto\sum_f e_f^2 q_f(x,Q^2) D_f^h(z,Q^2).
\end{equation}
It is assumed that the fragmentation process is spin independent,
i.e.~that the probability to produce a hadron of type $h$ from a quark
of flavor $f$ is independent of the relative spin orientations of
quark and nucleon.  The spin asymmetry $A_1^h$ in the semi-inclusive
cross section for production of a hadron of type $h$ by a polarized
virtual photon is given by
\begin{equation}
      A_1^h(x,Q^2,z)= {\sum_f e_f^2  \Delta q_f(x,Q^2) D_f^h(z,Q^2)\over
      \sum_f e_f^2 q_f(x,Q^2)D_f^h(z,Q^2)}\cdot{1+R(x,Q^2)\over 1+\gamma^2}.
    \label{eq:hadronasym}
\end{equation}
The term $R=\sigma_L/\sigma_T$ is the ratio of the longitudinal to
transverse photon absorption cross section and appears in this formula
to correct for the longitudinal component.  It is assumed that $R$ is
flavor and target independent and that the contribution from the
second spin structure function $g_2(x,Q^2)$ can be neglected.  The
term $\gamma=\sqrt{Q^2}/\nu$ is a kinematic factor which enters from
the $g_2=0$ assumption.  Eq.~(\ref{eq:hadronasym}) can be used to
extract the quark polarizations $\Delta q_f(x)/q_f(x)$ from a set of
measured asymmetries on the proton and neutron for positively and
negatively charged hadrons.

Results on the decomposition\index{spin flavor decomposition} of the
proton spin into contributions from the valence spin distributions
$\Delta u_v$ and $\Delta d_v$ and from the sea $\Delta q_s$ have been
previously reported by SMC~\cite{smcsemi}\index{SMC experiment}. New,
more precise data from HERMES\index{HERMES experiment} have been
presented recently~\cite{Ruh}. Fig.~\ref{due-flavor} shows the
polarization\index{quark polarization} $\Delta q/q$ of quarks in the
proton, separated into flavors. The {\em up} flavor has a positive
polarization which reaches about 40\% at large $x$, whereas the {\em
  down} flavor has a polarization opposite to the proton spin, in
excess of 20\%. In the sea region at small $x$ the up and down
polarizations do not vanish completely. The sea polarization itself is
compatible with zero as shown in the lower panel. The extraction of
the sea was done under the assumption that the polarization of the sea
quarks is independent of their flavor.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[ht]
%\begin{minipage}[b]{.60\textwidth}
\begin{center}
\includegraphics[width=.65\textwidth]{./dueren.3}
\caption[Flavor decomposition of the spin of the proton]
{The polarization of quarks\index{quark polarization} in the proton
  has been measured by HERMES as a function of $x$, separately for the
  flavors up and down and for the sea. The error bars shown are the
  statistical and the bands the systematic uncertainties.}
\label{due-flavor}
\end{center}
%\vfill
%\end{minipage}
%\hfill
%\begin{minipage}[b]{.43\textwidth}
%
%xxxx
%\end{minipage}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  The first and second moments of the spin distributions have been
  determined by HERMES\index{HERMES experiment}. In the measured
  region, the results of HERMES and SMC\index{SMC experiment} agree
  within the quoted errors. A simple Regge-type extrapolation has
  been applied at low $x$ to obtain the total integrals as quoted in
  Table~\ref{tab:moment}.  The HERMES results for the first and second
  moment of $\Delta u_v$ show a significant discrepancy with a
  prediction from quenched lattice QCD\index{lattice QCD} in
  Ref.~\cite{goeck}. The result for $\Delta u +\Delta \bar u$ is
  inconsistent with the result from the inclusive data based on
  SU(3)$_f$ flavor symmetry\index{SU(3)$_f$ flavor symmetry} as in
  Ref.~\cite{elkarl}. The inconsistency of the up flavor has its
  counterpart in the difference which is observed in the sea results.
  The inclusive analysis obtains a large negative strange sea compared
  to the zero sea in the semi-inclusive analysis.  However, the
  uncertainties of the sea measurements are so large that the result
  is not conclusive.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[b]
\begin{minipage}[b]{.47\textwidth}
  \caption{
    The integrals\index{spin flavor decomposition} of various spin
    distributions as measured by HERMES\index{HERMES experiment} for
    $Q^2=2.5$~GeV$^2$.  Note that the entry for $\Delta s +\Delta
    \bar{s}$ does not represent a direct measurement of the strange
    sea but relies on the assumption that the sea polarization is
    flavor independent.  An uncertainty of the Regge-type
    extrapolation at low $x$ is not included in the quoted error.}
   \label{tab:moment}
~\vfill ~
 \end{minipage}
\begin{minipage}[b]{.47\textwidth}
\vfill
\begin{center}
  \begin{tabular}{|c||r|}
    \hline
    & \multicolumn{1}{c|}{total integral}\\
    \hline\hline
%
    $\Delta u +\Delta \bar{u}$ &
    $ 0.56\pm 0.02\pm 0.03 $\\
%
    $\Delta d +\Delta \bar{d}$ &
    $-0.25\pm 0.06 \pm 0.05$ \\ 
%
    $\Delta s +\Delta \bar{s}$ &
    $-0.02\pm     0.03\pm 0.04 $ \\
%
    \hline
%
    $\Delta q_0$ &
    $  0.28\pm 0.04\pm 0.09                     $   \\
%
    $\Delta q_3$ &
    $ 0.83\pm     0.07\pm 0.06                           $  \\
                                %
    $\Delta q_8$ &
    $  0.32\pm     0.09\pm 0.10                          $  \\
%
    \hline
%
    $\Delta u_{v}$ &
    $ 0.57\pm 0.05\pm 0.08                      $ \\
%
    $\Delta d_{v}$ &
    $-0.21\pm 0.10\pm 0.13                      $\\
%
    \hline
    $ x\Delta u_{v}$ &
    $ 0.12 \pm 0.01 \pm 0.01  $\\
%
     $ x \Delta d_{v}$ &
    $-0.02 \pm 0.02 \pm 0.02  $ \\
    \hline
  \end{tabular}
\end{center}
\vfill
\end{minipage}
\end{table}
%\vspace*{-.7cm}\noindent

Possible explanations of these differences are that either SU(3)$_f$
is violated, which would modify the inclusive result, or that the
assumption about the
flavor independence of the sea is wrong,
which would modify the semi-inclusive result.  To test the
applicability of SU(3)$_f$ and SU(2)$_f$ flavor and isospin symmetry,
the semi-inclusive results for the octet combination $\Delta q_8$ and
the triplet combination $\Delta q_3$ of the polarized quark
distributions have been compared to the predictions $\Delta q_8=3F-D$
and $\Delta q_3=F+D$ (Bjorken sum rule). Both predictions agree with
the HERMES\index{HERMES experiment} results when the appropriate QCD
corrections are taken into account.  For a decisive conclusion about
the origin of the discrepancy, the precision has to be further
improved and the sea assumption has to be tested explicitly.

A significant improvement of the precision of the $\Delta d(x)+\Delta
\bar d$ determination is expected in the near future from HERMES using the
1999 deuterium data set.  The recently installed RICH will allow a
direct measurement of $\Delta s(x)$ using kaon identification.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Transverse Asymmetries\index{transverse spin asymmetries}}

The next step in polarized DIS, beyond the understanding of the
collinear part of the quark and gluon polarization in the nucleon, is
the understanding of the transverse polarization components.
Single-spin asymmetries in polarized hadronic reactions are
interpreted as effects of {\em
  time-reversal-odd}\index{time-reversal-odd functions} distribution
functions (Sivers mechanism) or {\em time-reversal-odd} fragmentation
functions (Collins mechanism)~\cite{collins2}.

SMC\index{SMC experiment} presented recently the first measurement of
semi-inclusive DIS hadron production on a transversely polarized
target~\cite{Bravar}.  Leading hadron production has been analyzed in
terms of the Collins angle and indeed a non-zero asymmetry
$A_N=11\%\pm 6\%$ has been found for positive hadrons, whereas the
negative hadrons yield $-2\%\pm 6\%$.

A significant result has been reported by HERMES\index{HERMES
  experiment} on a related quantity~\cite{Avakian}. HERMES measured
the asymmetry of hadron production on a longitudinally polarized
target. Even in this case an asymmetry is expected in the azimuthal
angle between the plane which contains the produced pion and the
virtual photon and the plane which contains the scattered lepton and
the virtual photon.  Fig.~\ref{due-azimuth} shows this single-spin
asymmetry as a function of the azimuthal angle for positive and
negative pions. A sinusoidal fit yields an asymmetry of $A_N=2.0\%\pm
0.4\% $ for the positive and $A_N=-0.1\%\pm 0.5\% $ for the negative
pions.

\begin{figure}[t]
\begin{center}
\begin{minipage}[b]{.47\textwidth}
\includegraphics[width=\textwidth]{./dueren.4}
\caption[Azimuthal pion single-spin asymmetry]{Azimuthal dependence
    of the single-spin asymmetry in the cross section for $\pi^+$
    (top) and $\pi^-$ (bottom). The error bars are statistical
    uncertainties. The curves are sinusoidal fits to the data.}
\label{due-azimuth}

\vfill\vspace*{4mm}

\includegraphics[width=\textwidth]{./dueren.5}
\caption[Double-spin asymmetry in diffractive
$\rho$, $\phi$ and J/$\psi$ production from HERMES] {Double-spin
  asymmetry in diffractive $\rho$, $\phi$ and J/$\psi$ production from
  HERMES\index{HERMES experiment}.}
\label{due-vm}
\end{minipage}
\hfill
\begin{minipage}[b]{.47\textwidth}
\includegraphics[width=0.7\textwidth]{./dueren.6}
\caption[Polarization of $\Lambda$ and $\bar \Lambda$]
{The squares (triangles) indicate the transverse polarization of
  $\Lambda$ ($\bar \Lambda$) in unpolarized photoproduction as
  function of the transverse momentum.}
\label{due-lambda}
\vfill\vspace*{4mm}

\includegraphics[width=\textwidth]{./dueren.7}
\caption[Comparison of the spin asymmetry of hadron pairs with high
$p_T$ with Monte-Carlo predictions] {Spin asymmetry in the production
  of hadron pairs with high $p_T$ and opposite charge. One hadron with
  $p_T>1.5$~GeV is required.  The spin asymmetry is plotted as a
  function of the $p_T$ of the second hadron and compared to
  Monte-Carlo predictions using various assumptions for the gluon
  polarization $\Delta G/G$.}
\label{due-highpt}
\end{minipage}
\end{center}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Diffractive Asymmetries}

Results on double-spin asymmetries in diffractive
$\rho^0$-production\index{diffractive $\rho^0$-production} have been
reported by SMC~\cite{Tripet}\index{SMC experiment} and
HERMES\index{HERMES experiment}~\cite{Meissner}.  Naively, no spin
asymmetry is expected in the approach where diffraction is described
by the exchange of a pomeron with vacuum quantum numbers. In this
frame one should expect that diffractive $\rho^0$ production does not
know about the spin of the target nucleon. The SMC result is in
agreement with this prediction. No significant asymmetry has been
observed.

HERMES\index{HERMES experiment} reported a significant, unexpected
positive asymmetry of $A_1^\rho=0.30\pm 0.11 \pm 0.05$ in exclusive
$\rho^0$ production as shown in Fig.~\ref{due-vm}.  The asymmetry in
the production of other vector mesons, $\phi$ and $J/\psi$, was also
measured, but with much less precision and is compatible with zero
(see Fig.~\ref{due-vm}). The difference of the two results is possibly
due to different reaction mechanisms at the different $W^2$ ranges of
the two experiments: $W^2\approx 225$~GeV$^2$ for SMC, and $W^2\approx
25$~GeV$^2$ for HERMES.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{$\Lambda$ Polarization}

Due to the parity violation of the weak decay of $\Lambda$
hyperons\index{$\Lambda$ polarization}, the angular distribution of
the decay products can be used to extract the spin orientation of the
$\Lambda$ hyperon before its decay. This unique feature was used at
HERMES\index{HERMES experiment} to extract two interesting
quantities~\cite{Belostotski}.

The first one is the measurement of the polarization transfer in DIS
scattering of longitudinally polarized electrons off unpolarized
targets. A $\Lambda$ polarization of $P_\Lambda=0.03\pm 0.06 \pm 0.03$
was reported, a number which however is not precise enough to
distinguish between different predictions.  The naive quark model
which assumes 100\% polarization of s-quarks in $\Lambda$ hyperons
predicts $P_\Lambda=0.018$, whereas a SU(3)$_f$ symmetric model from
Jaffe predicts $P_\Lambda=-0.057$, based on the measured results for
the Ellis-Jaffe sum.

A much more precise result was reported concerning the transverse
polarization of $\Lambda$ hyperons in
quasi-photoproduction\index{photoproduction} off an unpolarized
target:
\begin{equation}
  \label{eq:lambda}
  \gamma^{(*)}p\to \Lambda X.
\end{equation}
The polarization was measured with reference to the plane perpendicular to
the $\Lambda$ production plane.  Fig.~\ref{due-lambda} shows the
polarization as a function of the transverse momentum of the $\Lambda$
and $\bar \Lambda$.  A large positive polarization is observed for
$\Lambda$ hyperons, with the tendency to increase with their transverse
momentum. The $\bar \Lambda$ antihyperons show a negative
polarization.  There is no straight-forward explanation of the
observed asymmetries in QCD; however, similar polarizations have been
found in hadronic collisions.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Gluon Polarization\index{gluon polarization}}

The ``most wanted'' component of the nucleon spin is the polarization
of gluons, as they are probably responsible for the spin deficit of
the quarks. As the virtual photon does not couple directly to gluons,
a measurement of the gluon polarization was up to now only very
indirectly possible by using the QCD evolution equations, which relate
the $Q^2$-dependence of the quark distributions to the gluon
distribution. A QCD NLO analysis of recent data yields a gluon
contribution to the proton spin of $\Delta G\approx 1.8\pm
1.0$~\cite{Emlyn}.

For the first time a more direct measurement of the gluon
polarization\index{gluon polarization} has been
presented~\cite{Amarian}. By selecting events with two hadrons with
opposite charge and with large transverse momentum,
HERMES\index{HERMES experiment} was able to accumulate a sample of
events which is enriched by photon-gluon fusion events. By requiring a
large transverse momentum of 1.5~(1)~GeV/c for the first (second)
hadron, the sub-process, where the gluon splits into two quarks, has a
hard scale and can be treated pertubatively.  HERMES estimates from
Monte-Carlo studies that the average squared transverse momentum of
the quarks is 2.1~(GeV/c)$^2$.  As long as the fragmentation process
is spin independent, the spin asymmetry in the production of the
quark-antiquark pair is the same as the spin asymmetry of the observed
final state. The measured asymmetry is however affected by background
processes. The unique signature of the HERMES result is the negative
sign of the asymmetry.  All background processes have a positive
asymmetry, as long as they are dominated by the positive polarization
of the up-quarks in the proton. The observed negative asymmetry
can be explained by a significant positive gluon polarization. The
change of sign comes from the negative analyzing power of the
photon-gluon fusion diagram.  Using a specific background Monte Carlo,
HERMES obtains a value of the gluon polarization\index{gluon
polarization} of $\Delta G/G=0.41\pm 0.18\pm 0.03$ at
$\left<x_G\right>=0.17$.  The quantitative result depends however
critically on the detailed understanding of the background processes.
Fig.~\ref{due-highpt} shows the asymmetry together with Monte-Carlo
predictions using various assumptions for the gluon polarization
$\Delta G/G$.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Future Facilities}

The future of polarized DIS will consist of both, fixed target~\cite{Kabuss}
and  collider experiments~\cite{Hughes,GotoSaito}.

\subsection{Fixed target}

At SLAC the fixed target inclusive era will end with the precise
measurement of $g_2^{p,d}$ at E155x. At lower energies,
MAMI\index{MAMI} at Mainz, ELSA\index{ELSA} at Bonn and CEBAF at
Jefferson Lab will continue to do spin physics. The main future
players at higher energies will be HERMES\index{HERMES experiment} at
DESY and COMPASS\index{COMPASS experiment} at CERN. Both experiments
will concentrate on semi-inclusive data.

Their main aims  are the measurement of the gluon
polarization\index{gluon polarization}, the flavor
decomposition\index{spin flavor decomposition} of polarized quark
distributions, polarized vector meson production, polarized
fragmentation functions, transversity, and, in the case of COMPASS, also
the angular momentum of quarks and gluons and off-forward parton
distributions\index{off-forward parton distributions}.

HERMES has upgraded its particle identification recently to achieve
pion, kaon and proton separation in the full kinematic region, using a
RICH detector. An improved muon acceptance and identification will
allow for a better $J/\Psi$ detection. A wheel of silicon detectors
just behind the target cell will be installed, which improves the
acceptance especially for $\Lambda$ decay products. A recoil detector
system is dedicated to low energy, large angle target fragments and
spectator nucleons.

COMPASS will start in 2000 in the experimental area where the
SMC\index{SMC experiment} experiment has been, however with an
improved beam, improved target, high luminosity and, compared to the
SMC experiment, with a much better and larger hadron acceptance and
particle identification. In the final stage COMPASS will have two
spectrometer magnets, two RICH detectors, two hadron and two
electromagnetic calorimeters.  Compared to HERMES, the high beam
energy of COMPASS of 100-200~GeV enables measurements at smaller $x$
and larger $Q^2$ and $W^2$. The large $W^2$ allows for charm
production well above threshold and for the generation of hadrons
with large transverse momentum. The production of open charm allows
for a direct measurement of the gluon polarization.

A future fixed target machine is ELFE\index{ELFE}, a possible new
European electron machine in the 15-30 GeV range, which is discussed
in connection with the TESLA project at DESY and also at CERN as a
machine which could re-use the cavities from LEP. Two further
experiments, which both aimed for the measurement of the gluon
polarization via charm production in photoproduction, were proposed
some years ago, and are still discussed: E-156 at SLAC and
APOLLON\index{APOLLON experiment} at ELFE.

\subsection{Collider}

Two colliders will govern the high energy part of spin physics in the
future: the polarized proton collider RHIC\index{RHIC} at
BNL~\cite{GotoSaito}, and possibly the HERA collider\index{polarized
  HERA} at DESY which may have polarized protons in
future~\cite{Hughes}.

In both machines, the acceleration and storage of polarized protons is
a major challenge to machine physicists. Several Siberian
snakes\index{Siberian snakes} will be needed which compensate
depolarizing resonances of the beam polarization.

RHIC will start its physics program in 2000. Main points on the
program are the measurement of the antiquark polarization and the
gluon polarization. The antiquark polarization can be extracted using
Drell-Yan production via $W^+$ and $W^-$. As $W$-production depends on
flavor and on helicity, the experiment can extract $\Delta u$, $\Delta
\bar u$, $\Delta d$ and $\Delta \bar d$ separately.  The gluon
polarization is approached by the production of prompt photons,
$\pi^0$'s, jets and heavy quarks (charm).

The main aims of a polarized HERA collider are the measurement of the
spin structure functions at low $x$, which will improve the precision
of the verification of the fundamental Bjorken sum rule, and the
polarization of the gluon\index{gluon polarization}.
Fig.~\ref{due-herag1} shows the anticipated precision of this
measurement. As at RHIC, the gluon polarization can be extracted from
the production of heavy flavors and from jet production.
Fig.~\ref{due-deltag}~\cite{Hughes} summarizes the anticipated
precision of the measurement of the gluon polarization at RICH, HERA,
and COMPASS. Also included is the HERA-N option, which is a proposal
to scatter HERA protons off a fixed target.

\begin{figure}[t]
\begin{center}
\begin{minipage}[b]{.47\textwidth}
\includegraphics[width=\textwidth]{./dueren.8}
\caption[Statistical precision of possible future measurements of
$g_1^p$ at HERA.]{The statistical uncertainty on $g_1^p$ from possible
  measurements at HERA with 500 pb$^{-1}$ is shown along with
  different theoretical predictions at low $x$. The center of the
  figure is expanded to show the low-$x$ SMC points.}
\label{due-herag1}
\end{minipage}
\hfill
\begin{minipage}[b]{.47\textwidth}
{\rotatebox[units=360]{90}{\includegraphics[width=8cm]{./dueren.9}}}\\
\vspace*{-4cm}
\caption[Precision of the gluon polarization in future experiments]
{ Comparison of the statistical accuracy of $x\Delta G$ of the
  proposed future experiments as a function of $x$ along with
  predictions from various theoretical models.}
\label{due-deltag}
\end{minipage}
\end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}
%
\addcontentsline{toc}{section}{References}

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\end{thebibliography}

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