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%\documentclass[draft]{ws-procs9x6}  
\documentclass{ws-procs9x6}
%
\newcommand{\F}{$ F_{2}(x,Q^2)\,$} 
\newcommand{\FL}{$ F_{L}(x,Q^2)\,$}
\newcommand{\Fc}{$ F_{2}\,$}
\newcommand{\Q}{$ Q^{2}\,$}
\newcommand{\gv}{GeV$^2\,$}
\newcommand{\as}{$\alpha_s\,$}
\newcommand{\amz}{$\alpha_s(M_Z^2)\,$} 
\newcommand{\FLc}{$ F_{L}\,$} 
\newcommand{\xg}{$xg(x,Q^2)\,$}
\newcommand{\xgc}{$xg\,$}
\newcommand{\ipb}{pb$^{-1}\,$}
\newcommand{\pdff}{$\partial F_{2} / \partial \log Q^{2}$}
\newcommand{\bq}{$\overline{q}$}
\newcommand{\bs}{$\overline{s}$}
\newcommand{\bc}{$\overline{c}$}
\newcommand{\bu}{$\overline{u}$}
\newcommand{\bb}{$\overline{b}$}
\newcommand{\bU}{$\overline{U}$}
\newcommand{\bD}{$\overline{D}$}
\newcommand{\bd}{$\overline{d}$} 
\newcommand{\fb}{fb$^{-1}$}
\newcommand{\dbar}{$\overline{d}$\,}
\newcommand{\ubar}{$\overline{u}$\,}
%
\begin{document}

\title{Physics with H1 at HERA II}

\author{M. KLEIN}

\address{DESY, Platanenallee 6,   15738 Zeuthen, Germany\\ 
E-mail: klein@ifh.de}

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% You may repeat \author \address as often as necessary      %
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\maketitle

\abstracts{ A sketch is given of the main results obtained with the H1
  apparatus at HERA as is a summary of where progress is to be
  expected as a result of increased HERA luminosity, the measurement
  of beam charge and polarisation asymmetries, the variation of beam
  energies, improved systematics and extended kinematic range.}
%
\section{The Past}
%
Before the advent of the world's first electron-proton collider HERA,
two decades of experiments on deep inelastic lepton-nucleon scattering
(DIS) using stationary targets established what is now the
conventional picture of nucleon structure: The proton and the neutron
contain valence and sea quarks which are dominant at large Bjorken $x
> 0.3$ and low $x < 0.05$, respectively. Here, $x$ describes the
momentum fraction of the proton carried by the quarks in the infinite
momentum frame. In the Quark Parton Model (QPM), the distribution of
quarks and anti-quarks in the nucleon is described by momentum density
functions, $q(x)$ and $\overline{q}(x)$, which apply universally to
elementary fermion interactions.  The DIS cross section is largely
determined by the proton structure function $F_2 =
x\sum{e_q^2(q+\overline{q})}$, where $e_q$ are the quark electric
charges. The $x$ dependence of the various parton distributions is to
be determined from experiment.

DIS was crucial in establishing Quantum Chromodynamics (QCD) as the
correct field theory of the strong interactions which describes parton
dynamics in terms of the exchange of gluons and includes gluon-gluon
interactions due to its non-Abelian character. In QCD, the structure
functions are a convolution of calculable coefficient functions with
the parton distributions which due to gluon radiation and quark- antiquark pair
production depend both on $x$ and \Q, the square of the four-momentum
transferred by the exchanged virtual photon, $W^{\pm}$ or $Z$ boson.
The strong coupling constant $\alpha_s$ was found to decrease with \Q,
presumably leading to asymptotically free quarks, i.e. to the
restoration of the QPM as a limit of QCD.  In DIS, secondary
particles are emitted which allow the parton dynamics in the formation
of the final state to be investigated in detail.  Polarised $eD$
scattering was instrumental in establishing the electroweak sector of
the Standard $SU(2)_L \times  U(1) \times SU(3)_c$ Model (SM).
%
\section{HERA and H1}
%
HERA was built in the eighties to carry these investigations much
further. The H1 detector~\cite{h1det} is a large, multipurpose device
of nearly $4\pi$ acceptance, comprising tracking and calorimetric
detectors. The range of $x$ and \Q accessible is much wider than that
available to fixed target experiments.
%, see Fig.\ref{kine}.
The kinematics is reconstructed both from the scattered electron and
from the final state. This results in a superior accuracy for the HERA
DIS measurements which need to be precise to reveal the subtleties
of strong interactions. Moreover, due to the high collision energy,
HERA provides much richer information about the final state than is
accessible at fixed target experiments.

During its first phase of operation, between 1992 and 2000, H1
recorded an integrated luminosity of about 110\ipb of $e^+p$ and
15\ipb of $e^-p$ data with both beams unpolarised.  In its second
phase, termed HERA II, the aim is to record an increased integrated
luminosity of about 1 fb$^{-1}$ with longitudinally polarised leptons
at highest energies, and also to provide data at lower proton beam
energy.  The increase of the luminosity is achieved due to better
focussing of the beams in the interaction region (IR). Thus
superconducting quadrupoles were put close to the $ep$ interaction
point and detectors close to the beam had to be modified.  Bending the
positron beam nearer to H1 caused stronger synchrotron radiation than
in HERA~I. This and the modified IR caused beam induced backgrounds,
mainly from the dynamic interplay of synchrotron radiation with the
proton beam, which initially prevented H1 and the other collider
experiment, ZEUS, from collecting data.  While this article is being
written, early 2004, HERA is delivering beams with increasing
intensity yet a factor of $2 - 3$ below the design value. The
longitudinal positron polarisation is typically about 40\%.  It
remains a challenge to achieve routine operation at the highest
luminosities but the prospects are good.

The H1 detector underwent a major upgrade for HERA II. A new finely
segmented inner proportional chamber will improve the vertex trigger
capabilities. A dedicated trigger uses central drift chamber hits to
reconstruct tracks, e.g. allowing the online identification of charm
in photoproduction events.  New forward and backward silicon detectors
extend the tracking and thus the heavy flavour physics capabilities to
larger and to lower $x$, respectively.  A new forward drift chamber
system improves tracking at large $x$ and high $Q^2$. Downstream along
the proton beam line, a new Roman pot fibre detector extends the
acceptance for diffractive scattering and measures $t$ dependent cross
sections.  A new Compton polarimeter will measure the beam
polarisation with increased precision and for each bunch separately.
These and further improvements represent significant investments and
form, together with the standard components of the H1 apparatus,
calorimeters and chambers, a solid basis for high precision physics
and searches at HERA II.

This paper provides a brief account of the results~\cite{h1dat}
obtained by the H1 Collaboration from the first phase of HERA
operation.  Subsequently, selected topics are described which are
central to physics with HERA II. With much increased luminosity and
improved systematics genuine surprises may be encountered.  New
developments, such as unintegrated parton distributions or parton
correlation functions, may well change our view on proton structure in
a qualitative way. QCD predicts that instantons exist and that
instanton induced cross sections are accessible to DIS experiments at
HERA.  Given that interactions mediated by two gluon, or Pomeron,
exchange have been observed, should odderons exist, i.e. three gluon
exchange?  The excitement of HERA physics is largely due to the
unprecedented richness of Quantum Chromodynamics.
%
\section{Results of the H1 Experiment at HERA}
%
With beam energies of $E_e=27.5$~GeV and $E_p=920$~GeV, corresponding
to a centre of mass energy squared of $s \simeq 10^5$~GeV$^2$, HERA allows the
regions of very high $Q^2 < s$, and of very small Bjorken $x = Q^2/sy
> 10^{-5}$ to be explored in DIS for the first time. Here $y$ is the
inelasticity, which, in the proton rest frame, corresponds to the
relative energy transferred by the exchanged boson.
%
%\begin{figure}[ht]
%\centerline{ \psfig{file=kinheramu.eps,width=7.5cm}}
%\caption{Kinematical region accessed by the muon-proton fixed target 
%experiments NMC and BCDMS and its extension by the HERA $ep$
%collider experiments H1 and ZEUS.
%\label{kine}}
%\end{figure}
%
At large $Q^2$, the standard model predicts that the cross sections
for exchanging neutral ($\gamma, Z_0$) and charged bosons ($W^{\pm}$)
are of similar strength. A major triumph of the electroweak theory and
of HERA was that this indeed could be observed by the H1~\cite{h1dat}
and ZEUS~\cite{zdat} experiments, see Fig.\ref{nccc}.
%
\begin{figure}[ht]
\centerline{\psfig{file=fig1.mklein.eps,width=11cm}}
\caption{Measurements by H1 and ZEUS of the positron (left) and the 
  electron (right) proton scattering cross sections at large $Q^2$ in
  neutral and charged current scattering. The curves represent
  calculations of the DIS cross section using standard model
  electroweak couplings and a set of parton distributions determined
  by the CTEQ Collaboration.
\label{nccc}}
\end{figure}
%
The detailed exploration of weak neutral and charged current
scattering at high $Q^2$ and large $x$ using high statistics and
polarised $e^{\pm}$ beams is a central issue for the future HERA
programme, as described below.

Soon after the start of HERA operation, H1 and ZEUS discovered 
new features of the strong interactions and of proton structure.
A striking observation from the first 1992 data was that the proton
structure function $F_2(x,Q^2)$ rises strongly towards low $x$, at
fixed $Q^2$. This observation was later confirmed with much improved
accuracy~\cite{h1dat,zdat}, see Fig.\ref{f2der}.
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig2.mklein.eps,width=11cm}}
\caption{Left: Measurements of the proton structure function \F at
  medium $Q^2$ as a function of the proton momentum fraction $x$
  carried by the struck quark. HERA has significantly extended the
  kinematic range of these measurements and discovered a new regime of
  high sea quark densities. This can be attributed to a large gluon
  density as can be inferred from the measured scaling violations of
  \F, right. Further improvements of the measurement accuracy and new
  data are envisaged to accurately determine \xgc and the strong
  coupling constant.
\label{f2der}}
\end{figure}
%
The rise of \Fc in the DIS region implies that the sea quark density
at low $x$ is high while the strong coupling constant,
$\alpha_s(Q^2)$, is rather small. This defines a new regime of parton
dynamics, the theoretical understanding of which is not complete
despite impressive theoretical attempts over the past
decades~\cite{lowxc}. The $x$ dependence of \F~is observed to
change~\cite{h1dat} at momentum transfers \Q $\sim 1\,$\gv,
corresponding to a distance of 0.3\,fm which is where partonic
interactions seem to emerge.  As striking as the $x$ dependence, is
the strong rise of \F with $Q^2$ at low, fixed $x$.  In the classic
evolution equations of perturbative Quantum Chromodynamics (pQCD), the
\Q dependence, characterised by the derivative \pdff, is related to
the gluon density.  It was soon realised that, at low $x < 0.01$, the
quark contribution to the \Fc scaling violations is small for $Q^2 >
3$\,\gv.  Therefore, the measurement of a large derivative \pdff, see
Fig.\ref{f2der}, indicates that the gluon density is large at low $x$.
The experimental investigation of low $x$ physics will be extended at
HERA II as part of the effort to establish the theory of high density
parton dynamics.

Low $x$ physics soon turned out to be much richer than one could
deduce from the inclusive DIS measurements. A further outstanding result
from HERA in the early nineties was the observation~\cite{h1dat,zdat}
that in about 10\% of all DIS events the proton does not dissociate
but remains intact \footnote{Note that the elastic $ep \rightarrow ep$
  scattering cross section decreases like $Q^{-12}$ and is thus
  negligible at HERA \cite{mktrel}.}.  Since then deep
inelastic diffraction has been investigated in much more detail.
Diffraction, which may be related to colour confinement, occurs in a
simplified view, as a two-gluon exchange which is both a fascinating
theoretical problem and may prove to be a means of finding new
particles at hadron-hadron colliders as it gives rise to particularly
clean events, if both hadrons stay intact.

Because of the high energy available for particle production and since
the gluon density is large, HERA is also a laboratory for heavy quark
physics allowing the production mechanisms of charm and beauty
particles to be studied. This has led to the development of heavy
flavour theory~\cite{tungr} in next to leading order (NLO) QCD, as it
turned out that much can be learned about parton dynamics from a
20-40\% charm event fraction.  No consistent view on strong
interactions can be obtained, and no reliable extraction of \amz is
possible, without accurately understanding heavy flavour physics at
HERA. Heavy quarks may be a clue to finding exotic multiquark bound
states~\cite{penta}.

The production of final state particles became a further testing
ground for QCD. Going much beyond DIS fixed target final state
physics, at HERA jet physics became a central issue.  Fig.\ref{jets}
shows, as an example, a recent H1 measurement~\cite{h1dat} of the jet
production cross section at low $Q^2 < 1\,$\gv, termed the
photoproduction region.  The cross section, measured as a function of
the transverse energy of the jet, is seen to decrease by 7 orders of
magnitude, a behaviour which is consistently described by NLO QCD
calculations.  Jet measurements are used~\cite{h1dat} to measure \amz
and jet shapes are investigated~\cite{h1dat} in resummed NLO QCD
calculations which also include power corrections.
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig3.mklein.eps,width=7.5cm}}
\caption{Top: Differential cross section for inclusive jet
 production as a function of the jet transverse energy. Bottom:
 relative difference between the data, the LO QCD prediction and the
 NLO calculation including hadronisation corrections.
\label{jets}}
\end{figure}
%

A most exciting aspect of HERA physics is the search for new
interactions and the new particles with which they are associated,
such as leptoquarks and squarks. Outstanding events with high mass
multi-electrons or with large missing transverse momentum, including
flavour changing neutral current events, have been observed by
H1~\cite{h1dat}; somewhat more than expected in the Standard Model.
At high $Q^2$ and large $x$, a rich field of physics has been opened,
allowing, for example, the search for quark-substructure~\cite{h1dat}
and measurements of parton distributions~\cite{h1dat} in the valence
quark region, at $Q^2 \sim M_Z^2$. The physics at large $x$ and high
\Q cannot be explored thoroughly with the luminosity obtained so far,
since the cross section decreases with $x$ as $(1-x)^3$ at large $x$
and, for photon-exchange, with \Q as $1/Q^4$. High luminosity will
lead to new insight and perhaps discoveries at HERA. In this regard,
lepton beam polarisation is an interesting feature, as will be
discussed below.
%
\section{The Programme for HERA II}
\subsection{High Precision Inclusive DIS}\label{subsec:higpre}
%
In QCD, variations are logarithmic, often involving factors of $\ln
Q^2/\Lambda^2$ or $\ln 1/x$ where $\Lambda$ is the scale parameter in
QCD. Tests of QCD therefore need to reach a high level of accuracy,
typically 1\%, if they are to be decisive and if the data are to be of
use for predicting cross sections at other machines, such as the LHC
or for neutrino astrophysics. An important example in this regard
constitutes the measurement of $\alpha_s$ in DIS. The strong coupling
\amz is the least well known of all the coupling constants, but is of
great importance for testing QCD and for the unification pattern of
the fundamental interactions at extremely high energy. Inclusive deep
inelastic scattering is a process particularly well suited to the
measurement of \as because it is calculable to high orders, in
perturbation theory, and independent of the non-perturbative
corrections that arise in jet and other analyses from final state
effects. An accurate measurement of \amz in DIS was obtained by H1,
the result being $\alpha_s(M_Z^2) = 0.1150 \pm 0.0017 (exp) \pm 0.0008
(model)$.  This measurement is based on a systematic analysis of the
BCDMS $\mu p$ and the H1 $ep$ inclusive cross section data. Contrary
to other determinations of \amz, the correlation of \amz with the
gluon distribution is resolved, leading to competitive, consistent
contributions of the data of both experiments to the final result, see
Fig.\ref{chialf}. The HERA~II programme foresees further progress with
this analysis which can be achieved by still improving the measurement
of the $ep$ cross section, using low $E_p$ HERA data to access large
$x$, a better understanding of the model uncertainties like the charm
mass, possibly the use of data with deuterons \cite{loi} and, last but
not least, from the calculation of the splitting and coefficient
functions in NNLO~\cite{josv} or their modification~\cite{guido}.  In
an $ad~hoc$ procedure, the variation of the renormalisation scale
$\mu_r^2$ between $Q^2/4$ and $4Q^2$ leads in NLO to an estimated
uncertainty of about $\pm 0.005$ on \amz.  It is expected that this
will be halved using forthcoming NNLO calculations.  The prescription
of varying $\mu_r$ by factors of $1/2$ and $2$ must be reexamined
since the data exclude the possibility of such big
variations~\cite{h1dat,zeusqcd}.
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig4.mklein.eps,width=5cm}}
\caption{Contributions from the H1 and the BCDMS data to the 
  $\chi^2$ in the minimisation procedure using NLO QCD theory as a
  function of \amz.
\label{chialf}}
\end{figure}
%

A further example of the importance of large data samples at HERA
regards the flavour decomposition of the partonic contents of the
proton. Not much is known about the strange quark and its possible
asymmetry $s -$\bs~ at high $Q^2$ and $x$ which may be important to
the understanding of the electroweak mixing angle
measurements~\cite{tung}. 
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig5.mklein.eps,width=11cm,height=9cm}}
\caption{Simulation of charged current measurements with 250\ipb
  luminosity for 50\% polarisation showing statistical errors only
  for $e^+p$ (grey points) and for $e^-p$ (black points). The curves
  represent the valence quark contributions to the CC cross sections.
\label{ccud}}
\end{figure}
%
 The problem of the ratio of down and up
quark distributions at large $x$ is important for discoveries of high
mass particles \footnote{As was pointed out recently~\cite{loi}, the
H1 detector offers the opportunity of tagging spectator protons in
electron-deuteron scattering, thereby removing the binding corrections
otherwise necessary in the unfolding of the neutron structure.  This
allows both the sea quark asymmetry \bu $-$\bd~ to be extracted
accurately at low $x$, which is not accessible in $ep$ scattering at
HERA~II, and the ratio $d/u$ to be measured at large $x$.}. HERA~II
can contribute to this through improved measurements of the neutral
and charged current cross sections at very high $Q^2$, see
\cite{mkphil} Fig.\ref{ccud}.
%
\subsection{Physics with Polarised $e^{\pm}$ Beams}\label{subsec:polar}
\subsubsection{Parity Violation and Valence Quarks} \label{subsubsec:parity}
%
The increased luminosity and the use of longitudinal lepton
polarisation will allow the electroweak structure functions \cite{kr}
to be measured. For NC interactions, in addition to $F_2$, this
applies to the lepton beam charge asymmetry which essentially
determines $xG_3$, the $\gamma-Z$ interference part of the generalised
structure function $\bf{xF_3}$.  Variation of the lepton beam helicity
determines the structure function, $G_2 =2x \sum{e_q v_q
(q+\overline{q})}$, so far unmeasured, which is the $\gamma-Z$
interference part of the generalised structure function $\bf{F_2}$.
Here, $v_q$ is the weak vector coupling of the quark $q$.  At high
$x$, $G_2(x,Q^2) $ is proportional to the sum $ u_v + d_v$ while $F_2
\propto 4 u_v + d_v$.  Both $G_2$ and \Fc will thus provide
complementary information on the valence-quark distributions,
independent of nuclear binding corrections. A simulated measurement of
$G_2$ was presented in~\cite{mkg2}.
% is shown in Fig.~\ref{g2}. 
Unique information on the valence quarks at rather low $x \geq 0.01$
can be obtained from beam charge asymmetry data determining the
non-singlet structure function $xG_3 \propto 2 u_v + d_v$.  Since the
underlying asymmetries rise with $Q^2$, the charge asymmetry is
proportional to $1-(1-y)^2$ and the valence quark distributions drop
like a power of $(1-x)$, it would be desirable to significantly exceed
the current goal of 1\,\fb with the upgraded HERA collider.
%
%\begin{figure}[ht]
%\centerline{ \psfig{file=g2.eps,width=9.5cm,angle=90.}}
%\caption{g2
%\label{g2}}
%\end{figure}
%
\subsubsection{Right Handed Currents} \label{subsubsec:righth}
%
The determination of the helicity structure in neutrino-nucleon
scattering has long been considered an interesting problem. It can
finally be solved using polarised lepton beams at HERA, which provides
the equivalent of neutrino and antineutrino beams on fixed targets of
54\,TeV energy.  The charged current scattering cross section is
predicted to be $\sigma_{CC}^{\pm}(\lambda) \propto (1 \pm
\lambda)$. A departure from this expectation would hint at the
existence of right handed currents.  The accuracy of this measurement
depends mainly on the maximum degree of beam polarisation achievable.
%
\subsubsection{Generalised Parton Distributions} \label{subsubsec:genera}
%
Deeply virtual Compton scattering (DVCS), the hard diffractive
scattering of the virtual photon off the proton, $ep \rightarrow e
\gamma p$, interferes with Bethe-Heitler (BH) scattering.  The
interest in this process arises from the possibility it presents to
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig6.mklein.eps,width=10.5cm}}
\caption{The $\gamma^*p \rightarrow \gamma p$ DVCS cross section as
  a function of $W$ measured by H1 and ZEUS. The data are compared
  with NLO QCD using a GPD parameterisation (solid curve) and with a
  Colour Dipole model prediction (dashed curve).
\label{dvcs}}
\end{figure}
%
measure parton correlations, i.e. to measure generalised, or
non-diagonal parton distributions~\cite{diehl}. It is in this respect
similar to vector meson (VM) production, but avoids the complications
due to the VM wave function.  Large asymmetries are
predicted~\cite{freund}, both in lepton beam charge and polarisation
asymmetry measurements, which access the real and the imaginary part
of the $BH \cdot DVCS$ interference amplitude,
respectively. Improvements in the accuracy of the
measurements~\cite{h1dat,zdat}, see Fig.\ref{dvcs}, is likely to shed
new light on the partonic structure of the proton and on the nature of
the diffractive interaction. Exploitation of this process requires
maximum luminosity.
%
\subsection{Physics with Varied Proton Beam Energy}\label{subsec:lowep}
%
Apart from one adjustment of the proton beam energy, from 820 GeV to
920~GeV, HERA has been operated for 11 years at fixed beam energies.
However, there are good reasons to vary the beam energies.  Increasing
the proton beam energy \footnote{The electron beam energy of 27.6 GeV
is chosen to achieve maximum lepton beam polarisation. HERA could be
operated at somewhat larger $E_e$ depending on the rf. power
available.}, $E_p$, is most desirable when searching for new
phenomena, since all search limits are set by the available energy,
rather than by the luminosity, and are given, e.g. in the mass range for
new particles, roughly by $M \leq \sqrt{s} = 2
\sqrt{E_e E_p} =318$\,GeV at the present  energy settings. An increase
in proton beam energy involves certain  risk, or investment, regarding
the quench protection of the proton machine  dipole magnets. 

Lowering the beam energy up to about half the present values is possible
at the expense of reducing the luminosity. It makes possible the
extension of the kinematic range for many HERA measurements, such as
the total $\gamma p$ and vector meson cross
sections~\cite{h1dat}. The study of two further, specific questions
requires $E_p$ to be lowered.  The first regards the understanding of
the gluon density and pQCD at low $x$.  Investigations based on
\pdff~only cannot uniquely pin down the behaviour of \xg at low
$x$. More generally, an additional constraint is necessary if QCD is
to be tested to higher order at low $x$.  This requires an accurate
determination of the longitudinal structure function \FL.  Such a
measurement~\cite{bgk}, accurate to about 5\%, can be made with the
present H1 apparatus for $Q^2 > 3$\,\gv in a sequence of runs at low
$E_p$, for example at 460 and 570 GeV, with luminosities of about 10
and 5 \ipb.

The second question concerns access to the medium $Q^2$, large $x$
region with HERA. This is of great interest for a precision
measurement of \amz, for the determination of parton distributions at
large $x$ and perhaps also for the search for an intrinsic heavy
flavour contribution to proton structure. Since the luminosity is
expected to degrade roughly like $E_p^2$, it is presently not
realistic to envisage a luminosity larger than about 30 \ipb.  As is
demonstrated in Fig.\ref{f2loep}, such data would be of considerable
use in extending the kinematic range of the HERA data and achieving a
larger overlap with the data from the BCDMS experiment. The latter have the
peculiar feature of forcing \amz in DIS QCD analyses to small values
unless the BCDMS high $y$ data are excluded, see~\cite{wir}.
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig7.mklein.eps,width=11.cm,height=9.cm}}
\caption{Measurement of the proton structure function \F by the BCDMS
  Collaboration using 4 different muon beam energies, between 120\,GeV
  and 280\,GeV (squares). Simulation of precision low energy run data
  (points), for $E_p=460\,$GeV, $E_e=27.6\,$GeV and 30\,\ipb luminosity,
  with a full simulation of the systematic accuracy (inner error
  bars).  The lines mark the kinematic range limit $Q^2 =
  2ME_{\mu}xy$ for $y=0.3$ and 120\,GeV and 280\,GeV enforced in the
  H1 QCD fit to the BCDMS data. Precision H1 data from extended low
  energy running will have substantial overlap with the BCDMS data. 
\label{f2loep}}
\end{figure}
%
\subsection{Final States, Diffraction and Heavy Flavour}\label{subsec:finsta}
%
Final state physics at HERA allows the parton dynamics to be studied
in detail.  At low $x$ it has been realised that, while collinear
factorisation, as is inherent in DGLAP evolution, seems to be able to
account for the rise of \Fc towards low $x$, data on final state
production may be better described in $k_t$ factorisation
approaches. The phenomenology based on different evolution equations
(DGLAP, BFKL, CCFM) applied to data on forward particle
production~\cite{h1dat} or on azimuthal correlations between
dijets~\cite{h1dat}, for example, promises to yield new
insight~\cite{lowxc} into parton dynamics at low $x$.  Larger data
samples of increased systematic accuracy and extended kinematic range
will be extremely valuable in the pursuit of these studies. It is
noteworthy that currently a major step is being made in these areas.
While previously final state physics, diffraction and heavy flavour
were, and will of course continue to be, considered separately, joint
studies of all these fields and their interdependence using data of
higher luminosity are now being made.  This concerns, for example, the
investigations of how NLO parton distributions in the pomeron,
determined in inclusive diffraction, are applicable to diffractive
charm~\cite{h1dat} or jet production~\cite{h1dat}, see
Fig.\ref{diffr}.  The study of diffraction with H1 will be further
pursued using an upgraded system of proton tagging spectrometers and
high luminosity data permitting the $t$ dependence to be employed.

Jet physics is a major testing ground for QCD. Recently progress was
made in describing consistently event shapes in jet
production~\cite{h1dat} using resummed NLO QCD calculations.  With
high luminosity, the measurement of \amz from jet rates will become
more precise and joint analyses of inclusive DIS with jet production
may help in the determination of the gluon density at large $x$, that
remains unresolved in DIS. The description of multi-jet final states
will be much improved in following the development of parton shower
simulation programs at higher orders~\cite{webber} (MC@NLO).

A consistent theory is necessary to describe charm and beauty
production in DIS.  Describing correctly the effects that occur close
to charm threshold is a nontrivial task in the DGLAP framework which
considers the charm quark to be light at high $Q^2 >> m_c^2$.  The
amount and accuracy of heavy flavour data~\cite{naros} from HERA~I, on charm
mesons~\cite{h1dat}, fragmentation functions~\cite{h1dat}, $J/\Psi$
production~\cite{h1dat} etc., is most remarkable and work is ongoing.
Based on the first observations, see Fig.~\ref{diffr}, one may well
speculate that beauty at HERA II will play the role of charm at
HERA~I.  Accurate beauty data, based on the large transverse momentum
of the b-quarks and on their measurable lifetime, corresponding to
about 0.5\,mm decay lengths, promise to open an important new testing
ground for QCD. New reactions like the production of strange quarks in
CC scattering will be also studied.

%
\begin{figure}[ht]
\centerline{ \psfig{file=fig8.mklein.eps,width=11.cm}}
\caption{Left: Diffractive
 dijet production cross section in DIS as a function of the
 longitudinal momentum fraction of the Pomeron. The data are compared
 with predictions, within an uncertainty dominated by the
 renormalisation scale choice, using (N)LO diffractive parton
 distributions determined from inclusive diffractive H1 data. Right:
 Measurements of the beauty jet production cross section in
 photoproduction as a function of the muon rapidity compared with NLO
 QCD calculations including hadronisation corrections. A considerable
 increase of the luminosity is required to perform precision
 measurements of such quantities at HERA II.
\label{diffr}}
\end{figure}
%
\subsection{Searches for Exotic Physics}\label{subsec:search}
%
Dedicated analyses of the H1 data from HERA I, using about 15 \ipb of
$e^-p$ and 110 \ipb of $e^+p$ data, have discovered a few peculiar
events of a type or a rate beyond the expectations of the Standard
Model.  Isolated electrons and muons with large missing transverse
momentum, 10 events with $p_t > 25$\,GeV, are observed and $2.9 \pm
0.5$ are expected.  Furthermore, H1 saw multi-electron production at a
rate above the Standard Model expectations. Three $2e$ and three $3e$
events were observed which is to be compared with an expectation of
$0.30 \pm 0.04$ and $0.23 \pm 0.04$, respectively. Based on a
considerable simulation effort, new effects were also searched for
$generically$ in 28 event classes, e.g. of the type $ej$ or $e \mu
\mu$, using electrons, muons, jets and missing energy (neutrinos) to
characterise the classes. The preliminary H1 result~\cite{h1dat}, using all
available HERA~I data, is shown in Fig.\ref{gener}. It confirms the
excesses in the aforementioned channels but no further significant
departure from the SM expectation is found.  It is obvious that a
larger data sample is required to put such generic studies and
dedicated searches on a firmer ground and possibly to discover new
particles or interactions, a major goal of HERA. If, for example,
leptoquarks were seen, charge and lepton beam polarisation would
enable their spectroscopy to be studied. New ways could be found to
further increase the luminosity beyond the HERA II values. Moreover,
new, LHC type, magnets could be used to double the proton beam energy
\cite{daniel} if findings at HERA, the TeVatron or the LHC would
require $ep$ data in an extended range of energy.
%
\begin{figure}[ht]
\centerline{ \psfig{file=fig9.mklein.eps,width=12cm}}
\caption{Event yields, measured and calculated in the standard
  model using various simulation programs, for all event
  configurations with an expectation larger than 0.1. Four jet
  simulations are not yet reliable and kept separate in the generic
  analysis.
\label{gener}}
\end{figure}
%
\section{Future}
%
As was sketched here, the HERA programme is of fundamental importance
in its own right.  Seen from the perspective of the LHC, which will
take particle physics into the TeV energy region, it is becoming clear
that the results of HERA are of interest in all areas: high precision
measurements will pin down the SM expectations and may be necessary
for the determination of the LHC luminosity; high $x$ parton
distributions are of crucial importance for the understanding of any
state possibly discovered at the LHC; understanding low $x$ and
diffractive phenomena appears also to be important for the LHC,
because of the significance of the quark and gluon distributions in
understanding $pp$ collisions and the possibilities of detecting Higgs
production in double diffractive scattering~\cite{khoze}. It is desirable to
operate HERA when the LHC runs and new questions may be posed which
HERA could answer.

The past and the current programmes have not exhausted HERA's
potential.  Precision studies of high parton density
phenomena near the transition from parton-like to hadron-like
behaviour, at $Q^2 \sim 1\,$\gv and smallest $x$, the investigation of
neutron structure in the range opened up by HERA, the study of nuclear
and thus high density gluon structure with high energy electron probes
and the exploration of the completely new kinematic region accessible
to a polarised $eN$ collider are all scientifically most attractive
elements of a programme to which particle physicists will have to
return to if the study of QCD and nucleon structure is to be brought
to a satisfactory conclusion: they are all topics which HERA allows to
be studied uniquely.
% 
\section*{Acknowledgments}
%
I would like to thank the organisers of the 2003 Ringberg workshop for
the invitation to attend what has been an excellent discussion meeting
of physicists interested in deep inelastic scattering at HERA. The H1
results presented here, and those I had no time to discuss, rely on
the efforts of a large collaboration of physicists and engineers to
whom I want to express my deep gratitude. In particular, I like to
thank Allen Caldwell, Tim Greenshaw, Peter Kostka, Tomas Lastovicka,
Paul Newman, Carsten Niebuhr, Daniel Pitzl, Vladimir Shekelyan and
Ferdinand Willeke for a most faithful and enjoyable collaboration in
recent times.
\newpage
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%
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%
\end{document}
