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\newcommand{\sigrd}{\sigma_r^D}
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\newcommand{\sigrdarg}{\sigma_r^{D(3)}(\beta,Q^2,\xpom)}
\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                32nd International Conference 
                on High Energy Physics, ICHEP04},
                August~16,~2004,~Beijing} \\
                 & Abstract:        & {\bf 6-0175}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}


\begin{center}
  \Large
  {\bf 
    Measurement of the Inclusive Cross Section for Diffractive \\
    Deep Inelastic Scattering at High {\boldmath $ Q^2$} \\ 
    }

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}

\noindent
A measurement is presented of inclusive diffractive deep inelastic scattering
extending to the largest $Q^2$ values accessed to date.  
Data taken by the H1 experiment amounting to
an integrated luminosity of $63 \ \invpb$ are used to
investigate the process $ep \rightarrow eXY$ in the kinematic range
where diffractive exchanges are known to dominate. The $Y$ system is a
proton or proton remnant with $M_Y < 1.6\; \GeV$ and $|t| < 1.0 \;
\GeVsq$ and it is separated from the $X$ system by a large gap in
pseudorapidity. 
%caused by a diffractive exchange carrying a fraction of the
%proton's longitudinal momentum $\xpom \leq 0.05$.  
The diffractive
reduced cross-section $\sigrdarg$ is extracted in the
kinematic range $200 \leq Q^2 \leq 1600\; \GeVsq, 
0.1 \leq$ $(\beta~=~x~/\xpom) \leq 0.9$ and 
$0.0036 < \xpom \leq 0.05$.  The data are used together with
other recent measurements at lower $Q^2$ to test
various factorisation properties and models of diffractive DIS.  
Good agreement is found with predictions based on diffractive parton
densities obtained from an 
NLO QCD fit to lower $Q^2$ data, evolved using the DGLAP
equations, and with a model based on soft colour interactions. 


\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}
\label{intro}

In
Diffractive Deep-Inelastic Scattering (DDIS), it is possible to
investigate the parton dynamics of diffractive exchanges with a
hard scale provided by the virtuality $Q^2$ of the point-like virtual
photon.  The presence of the diffractive exchange implies that the
hadronic final state must consist of two distinct systems separated by
a large gap in rapidity, as shown in figure \ref{FIG:DDIS}.  The
differential cross-section for the process $ep \rightarrow eXY$ can be
written as 
\begin{equation}
\frac{{\rm d}^3 \sigma_{ep \rightarrow eXY}}{{\rm d} \beta {\rm d} Q^2 {\rm d} \xpom} = \frac{4 \pi \alpha_{em}^2}{\beta Q^4}
\left(1 - y + \frac{y^2}{2} \right)\sigrdarg \ .
\label{EQN:DiffXSec}
\end{equation}
Here, the standard DIS variable definitions are used, namely
\begin{equation}
Q^2=-q^2 \ ; \qquad y=\frac{P.q}{P.k} \ ; \qquad x=\frac{-q^2}{2P.q} \ ,
\end{equation}
determined by the four-momenta of the photon ($q$), the proton ($P$)
and the incoming
positron ($k$).  The additional diffractive variables
are defined as
\begin{equation}
\xpom=\frac{q.(P-p_Y)}{q.P} \ ; \qquad \beta=\frac{-q^2}{2q.(P-p_Y)} \ ; \qquad t=(P-p_Y)^2 \ ,
\end{equation}
where $p_Y$ is the four-momentum of the $Y$ system. Here, $\xpom$ corresponds
to the fraction of the proton beam energy transferred to the longitudinal
momentum of the diffractive exchange, $\beta$ is the fraction of the exchanged
longitudinal momentum carried by the quark coupling to the virtual photon and
$t$ is the squared 4-momentum transferred at the proton vertex. 
The reduced cross-section 
$\sigrdarg$ is related to the diffractive
structure functions $F_2^{D(3)}(\beta, Q^2, \xpom)$ and 
$F_L^{D(3)}(\beta, Q^2, \xpom)$ by
%\begin{equation}
%\sigma_r^{D(3)}(\beta, Q^2, \xpom) = F_2^{D(3)}(\beta, Q^2, \xpom) 
%- \frac{y^2}{1+(1-y)^2}F_L^{D(3)}(\beta, Q^2, \xpom).
%\label{EQN:sigredF2D3}
%\end{equation}
\begin{equation}
\sigma_r^{D(3)} = F_2^{D(3)} - \frac{y^2}{1+(1-y)^2} \ F_L^{D(3)} \ ,
\label{EQN:sigredF2D3}
\end{equation}
such that $\sigrd \sim F_2^D$ except at very large values of $y$. 
In the analysis
presented here, neither the squared four-momentum transfer between the
virtual photon and the proton, $t$, nor the mass $M_Y$ are well measured 
as the $Y$ system is not detected. The measured cross-section is corrected to 
the region
\begin{equation}
M_Y < 1.6\; \GeV  \ ; \qquad |t|< 1.0\; \GeVsq \ .
\label{eqn:myandt}
\end{equation}

\begin{figure}[htbp]
\centering
\epsfig{file=H1prelim-03-011.fig1.eps,width=0.65\linewidth}
\caption{
  A schematic illustration of the generic DDIS process at {\sc Hera}, $ep
  \rightarrow eXY$ (four-momenta are shown in brackets).  The positron
  couples to a virtual photon which interacts with the proton via a
  colour-singlet exchange, producing two distinct final state systems,
  $X$ and $Y$. These two systems are separated by a large gap in
  rapidity if their masses are small compared with that of the full
hadronic final state ($W$).}
\label{FIG:DDIS}
\end{figure}

The preliminary results presented here are based on high $Q^2$
data collected with the H1 detector \cite{h1det}
in $e^+p$ interactions at $\sqrt{s}=(k+P)
= 319 \;\GeV$ at {\sc Hera} in 
1999 and 2000. The data correspond to an integrated
luminosity of $63\; \invpb$. Together with two other preliminary analyses at 
intermediate \cite{eps} and low \cite{lowq2} $Q^2$, they complete the
H1 coverage of the accessible kinematic range as shown in figure \ref{fig1}.

An NLO QCD fit \cite{prn} has been made to the intermediate $Q^2$ data,
together with a previous high $Q^2$ measurement based on a smaller
data set ($36 \ {\rm pb^{-1}}$ \cite{andy}).  
This fit was based on the hard scattering QCD factorisation theorem 
for diffraction \cite{collins}, which implies that diffractive parton
densities can be defined for DDIS, such that at fixed $\xpom$ and $t$,
the $Q^2$ and $\beta$ evolution is described by the DGLAP equations. 
In the fit, it was also necessary to assume `Regge factorisation',
whereby the diffractive parton densities do not change in shape as $\xpom$
and $t$ vary and 
their change in normalisation is given by a parameterisation
based on Reggeon flux factors.
Both a leading `pomeron' contribution and a sub-leading `reggeon' component 
are included in the fit, with different flux factors and separately evolving
parton densities. 

The previous measurements have shown no deviation from the diffractive
QCD hard scattering factorisation theorem. The Regge factorisation
assumption also gives a good approximation to the data, though the low $Q^2$
data gave an indication
that the $\xpom$ dependence becomes stronger as $Q^2$ increases \cite{lowq2}. 
The extended range in $Q^2$ and precision of the data presented here
allow tests
of the QCD hard scattering factorisation theorem and Regge factorisation
assumption to be made, by comparing the predictions of the NLO QCD fit,
evolved using the DGLAP equations, with the new data.  

\section{Experimental Method}

\subsection{Selection Criteria and Kinematic Reconstruction}

The data used for the analysis are a subset of the high $Q^2$ inclusive
neutral current DIS sample studied in \cite{inchiq2}.  The diffractive
selection requires a large gap in the pseudorapidity 
distribution of the final state hadrons in the outgoing proton direction,
signalling a colour singlet exchange between the photon and the proton
to produce two well separated systems $X$ (contained in the main detector)
and $Y$ (escaping unobserved into the beampipe). 
The selection is based on an absence of activity in the components of the
H1 detector which are sensitive to energy flow in the proton fragmentation 
region \cite{eps}.

The inclusive DIS kinematic variables are
obtained from 
\begin{equation}
y = y_e^2 + y_{da}(1 - y_{da}) \ ; \qquad Q^2 = \frac{4E_e^2(1 - y)}{\tan^2{\frac{\theta_e}{2}}} \ ; \qquad x = \frac{Q^2}{sy} \ ,
\label{eqn:defaultkinerec}
\end{equation}
where $y_e$ is the inelasticity 
determined by the electron method and $y_{da}$ by
the double-angle method \cite{prn,incl}, $E_e$ is the positron beam
energy and $\theta_e$ the polar angle of the scattered positron.  

The reconstruction of the final state system $X$ uses an algorithm
which optimally combines tracking and calorimetric information
without double counting \cite{fixed}.  
The mass of the $X$ system is reconstructed as
\begin{equation}
M_X^2=(E^2 - p_x^2 - p_y^2 - p_z^2)_{hadrons} \cdot \frac{y}{y_h} \cdot \delta(M_X^{rec}) \ .
\label{eqn:mxreccorr}
\end{equation}
Here, $(E, p_x, p_y, p_z)_{hadrons}$ is the 4-vector of the overall
hadronic final state observed in the detector, 
$y$ and $y_h$ are obtained from equation (\ref{eqn:defaultkinerec})
and from the hadron only method, respectively, and 
$\delta(M_X^{rec})$ corrects for the under-reconstruction of $M_X^2$ 
due to losses in the backward direction. This correction
is estimated from the simulation.  At high $M_X$ ($\gapprox 20$ GeV),
$\delta(M_X^{rec})$ is approximately equal to 1.07, increasing at 
lower values of $M_X$. The diffractive kinematic variables are 
then reconstructed as

\begin{equation}
\beta = \frac{Q^2}{Q^2 + M_X^2} \ ; \qquad \xpom = \frac{x}{\beta} \ .
\label{eqn:diffkinerec}
\end{equation}

\subsection{Corrections to the Data}

The RAPGAP \cite{rapgap} 
Monte Carlo generator is designed to describe the DDIS process 
$ep \rightarrow eXp$.  It is used to correct the data for the effects
of the detector acceptance and kinematic migrations due to the finite
detector resolution and imperfections
in the reconstruction. 
RAPGAP uses diffractive parton densities extracted from a LO QCD
fit, similar to that described in section~\ref{intro}, but performed
on earlier H1 data \cite{incl}. The parton densities are 
convoluted with
QCD matrix elements up to order $\alpha_s$. 
Further QCD radiation is
simulated via an interface to the ARIADNE \cite{ariadne} program, which
is an implementation of the Colour Dipole Model \cite{cdm,ariadne}.
As required by the data \cite{incl}, 
a sub-leading exchange is also included, with parton densities obtained
from a parameterisation for the $\pi$-meson \cite{pipdf}. 
QED radiation is simulated via an
interface to the HERACLES \cite{heracl} program.  

The factor $1.08 \pm 0.10$ required to correct the data to the measured
range $\my < 1.6 \ {\rm GeV}$, $|t| < 1 \ {\rm GeV^2}$ was evaluated
using the DIFFVM \cite{diffvm} generator, which simulates
diffractive events both with intact final state protons and with 
proton dissociation.
%equation \ref{eqn:myandt}.
Migrations into the measured range from very large $\xpom > 0.15$ or large
$\my > 5 \ {\rm GeV}$ values 
are estimated using the DJANGO
\cite{django} generator of non-diffractive DIS. This program is 
an interface between the
HERACLES $ep$ event generator and the ARIADNE program. 

Corrections are made for several small background contributions to the data. 
The contamination from hard diffractive
photoproduction processes, in which a particle from the hadronic final state
fakes the signature of the scattered electron,
is estimated from the number of events in the data in which 
the positron candidate has negative instead of positive charge. The
background is statistically removed from the event sample under the assumption
that it is charge-symmetric. More details can be found
in \cite{inchiq2}. The QED-Compton 
($ep \rightarrow ep \gamma$) background is subtracted using the predictions
of the COMPTON \cite{compton} Monte Carlo generator. The background from
photon photon events ($ep \rightarrow ep e^+ e^-$),
where two photons radiated from the 
incoming electron and proton
interact to produce a lepton pair, is subtracted using the LPAIR \cite{lpair}
generator.

Comparisons of the full simulation 
with the uncorrected data for several
kinematic distributions can be seen in figure \ref{FIG:contplots}.
The simulation gives a good description of the data for all variables.

\subsection{Extraction of the Reduced Cross-Section}

After corrections for backgrounds, detector acceptance and migrations
and QED radiation, the diffractive reduced cross section is extracted
from the measured differential cross section using
equation~\ref{EQN:DiffXSec}. Two different binning schemes are used,
in order to extract data at fixed $Q^2$, $\beta$ and $x$ 
(sections \ref{xpsec} and \ref{scisec}) 
and at fixed $Q^2$, $\beta$ and $\xpom$ 
(section \ref{qcdsec}). 
%\begin{equation}
%\sigma_r^{D(3)}(\beta, Q^2, \xpom) = \frac{x Q^4}{4\pi \alpha^2 (1 - y + \frac{y^2}{2})} 
%\frac{d^3 \sigma_{ep\rightarrow eXY}}{dx dQ^2 d\xpom} \ .
%\label{eqn:xsection2}
%\end{equation}
The data are quoted at the centre of each analysis bin after
applying corrections for the cross section variation across the bin,
calculated analytically using the results of the QCD fit in \cite{incl}.
The acceptance, purity and stability\footnote{The purity (stability)
of a bin is defined as the fraction of events reconstructed (generated)
in a bin that were also generated (reconstructed) in that bin, according
to the simulation.}
for each quoted bin is required to be
greater
than 30 \%.
%, corresponding to one standard deviation in each dimension,
%to be used in the cross-section measurement.  The cross-section is
%corrected to the Born-level using the RAPGAP simulation to provide the
%acceptance, bin-centre and radiative corrections and the DIFFVM
%simulation was used to correct the measurement for proton dissociation
%back to the kinematic phase-space defined by equation
%\ref{eqn:myandt}.

A full analysis of the systematic uncertainties of the measurement was
performed.  The sources of systematic uncertainty associated with the
reconstruction of the scattered electron and the final state hadrons
are discussed in \cite{inchiq2}. Those uncertainties 
particular to the diffractive measurement are described in \cite{eps}.
The dominant systematic uncertainties arise from the 
corections for smearing about the $\my$ boundary of the 
measurement, 
the subtraction of
noise in the hadronic final state reconstruction and, at high
$\xpom$, the correction for smearing into the
sample from very large $\xpom$ as described using the DJANGO model.  
The systematic error on the final cross-sections is approximately 15\%
on average, comparable to the statistical error.

\section{Results}

\subsection{The {\boldmath $\xpom$} Dependence of 
{\boldmath $\sigrd$}}
\label{xpsec}

Figure \ref{fig3} shows the $\xpom$ dependence of the data at fixed
$\beta$ and $Q^2$ compared with the previous H1 high $Q^2$ 
data \cite{andy}. The new
measurement extends the kinematic range in $\beta$ and $Q^2$.  
In the region of overlap of
the two measurements there is good agreement.  
The prediction based on the NLO QCD fit to
lower $Q^2$ data yields a good
description after DGLAP evolution of the parton densities. 
A possible exception is the highest $\beta$ region, where the fit tends to
overshoot the data. 
%In this region, it has been suggested that higher
%twist contributions are present at lower $Q^2$ \cite{bekw}. 
Also shown separately is the Pomeron component of the fit,
which dominates the prediction at large $\beta$, but is clearly insufficient
at low $\beta$ and high $\xpom$. When the 
sub-leading Reggeon component is also
included, the description in the low $\beta$ region is much better.

\subsection{The {\boldmath $Q^2$} and {\boldmath $\beta$} 
Dependences of {\boldmath $\sigrd$}}
\label{qcdsec}

The $Q^2$ dependence of $\xpom \sigrd$ at fixed $\beta$ and $\xpom$ is
compared with the QCD fit 
in figures \ref{fig4} and \ref{fig5}.  Also
included in these figures are the medium $Q^2$ data used in the fit
and low $Q^2$ data 
which were not included in the fit.  Over most of the $\beta$
range, the data display
large positive scaling violations, indicative of a strongly 
gluon-dominated structure. Exact
scaling occurs at a fractional momentum of around
$\beta \approx 0.65$.
The predictions of the NLO QCD fit to lower
$Q^2$ data are in good agreement with the 
new high $Q^2$ data.
For $\xpom = 0.01$ (figure \ref{fig4}), the sub-leading reggeon component is 
negligible. 
For $\xpom = 0.03$ (figure \ref{fig5}), the data cannot be described without
the admixture of the quark-dominated sub-leading
exchange.

$\xpom \sigrd$ is
shown as a function of $\beta$ at fixed $\xpom$ and $Q^2$ in
figures \ref{fig6} and \ref{fig7}. Again, the new data show that 
the observations from lower $Q^2$ persist into the new kinematic
regime. At relatively low $\xpom = 0.01$ (figure~\ref{fig6}),
the data are approximately flat as a function of $\beta$.  At higher
$\xpom = 0.03$ (figure~\ref{fig7}), the data show a tendency to decrease with
increasing $\beta$. This effect is reproduced by the QCD fit, where
it arises due to the evolution of the pomeron parton densities
to the higher $Q^2$ range accessed and the
increased contribution from the sub-leading exchange.

Figures \ref{fig8and10} and \ref{fig9and11} show the same
distributions as figures~\ref{fig4}-\ref{fig7}, 
but restricted to $\beta$ and $Q^2$ values which contain 
high $Q^2$ data points, 
allowing a closer inspection of the level of agreement between
the predictions of the NLO QCD fit and the data.

\subsection{Comparison with Soft Colour Rearrangement Models}
\label{scisec}

In the Soft Colour Interactions (SCI) model of Edin, Ingelman and
Rathsman \cite{sci}, the underlying hard
interaction is the same for both diffractive and non-diffractive
events.  Soft interactions then take place,
in which colour, but not momentum, is transferred
between the outgoing partons.  
The colour strings connecting the outgoing partons are thus rearranged and
rapidity gaps can be produced where there is no colour connection
between neighbouring partons.
The original SCI model contains just one free parameter,
which is the probability of the soft colour rearrangements occurring.  A
modification to this model uses a Generalised Area Law (GAL)
\cite{gal}, whereby configurations with colour strings spanning
a large area in energy-momentum space are exponentially suppressed.

Figure \ref{fig2} shows the $\xpom$ dependence of the data at fixed
$\beta$ and $Q^2$, compared with both versions of the SCI model. 
%The
%dashed, black curve is the prediction of the original model, the
%solid, blue curve is the model incorporating the generalised area law.
The original SCI model is able to describe the data in the highest $\beta$
bin at high $\xpom$ but undershoots the data almost everywhere
else.  The model incorporating the generalised area law produces a
much better overall description and is able to describe the data well
everywhere except at the lowest $\beta$.


\section{Conclusions}

A new measurement of inclusive DDIS at high $Q^2$ has been presented,
which extends the kinematic phase-space compared with previous data
and increases the statistical
precision.
The diffractive reduced cross-section $\sigma_r^{D(3)}(\beta, Q^2,
\xpom)$ was extracted from the data in the kinematic range 
$200 \leq Q^2 \leq 1600\;{\rm GeV^2}, 0.1 \leq \beta \leq 0.9$ and 
$0.0036 < \xpom \leq 0.05$ 
and found to be consistent with previous H1 measurements.  
The new data confirm the
positive scaling violations persisting to large values of
$\beta \sim 0.65$  and the relatively
flat $\beta$ dependence
observed in previous analyses.
The predictions of
an NLO QCD fit to lower $Q^2$ measurements describe the data well.
The data are thus consistent with the diffractive hard scattering 
factorisation theorem and the Regge factorisation assumption. They 
can be described by
a leading heavily gluon dominated `Pomeron' exchange,
complemented by a non-negligible sub-leading Reggeon contribution at
large $\xpom$ and low $\beta$.  
The SCI model incorporating a
generalised area law is found to produce a good description of the
data except at the lowest $\beta$.

\section*{Acknowledgements}

We are grateful to the {\sc Hera} machine group whose outstanding
efforts have made this experiment possible.  We
thank the engineers and technicians for their work in constructing and
now maintaining the H1 detector, our funding agencies for financial
support, the DESY technical staff for continual assistance and the
DESY directorate for support and for
the hospitality which they extend to the non-DESY 
members of the collaboration.

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\bibitem{gal} J. Rathsman, Phys. Lett. B452 (1999) 364-371.

%\bibitem{ddiss} H1 Collaboration,
%\emph{Diffractive Dissociation in Photoproduction at HERA}, paper 985 submitted to this conference.

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\end{thebibliography}

% plots 

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig2.eps,width=0.85\linewidth}
\caption{Reduced cross section $\sigrdthree$ from this measurement, 
compared with recent H1 measurements at lower $Q^2$. 
$\xpom \sigrdthree(\xpom,\beta,Q^2)$ is shown 
as a function of $\xpom$ for fixed $\beta$ and $Q^2$.
Here and elsewhere, the inner error bars represent statistical errors and
the outer error bars correspond to the total error, given by the quadratic
sum of statistical and systematic errors. Normalization uncertainties,
which are of the order of $6-8\%$ for each data set, are not shown.
Also shown is the prediction for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\
GeV$ from the NLO QCD fit performed to the medium $Q^2$ data.
The fit results are shown as solid lines 
for the fitted data ($6.5 \leq Q^2 \leq 120 \ {\rm GeV^2}$ and $M_X>2 \rm\ GeV$).
The extrapolation to low ($Q^2<6.5 \rm\ GeV^2$) and 
high ($Q^2>120\rm\ GeV^2$) values of $Q^2$ is shown as dotted lines.
}
\label{fig1}
\end{figure}


\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig3a.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig3b.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig3c.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig3d.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig3e.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig3f.eps,width=0.49\linewidth}
\caption{
  Distributions of the scattered electron energy (top left), the polar (top
  right) and azimuthal (middle left) angles of the positron, the polar
  angle of the $X$ system (middle right), the reconstructed $\beta$
  (bottom left) and $\log{\xpom}$ (bottom right) of the high $Q^2$
  DDIS event sample. The uncorrected data are compared with the
  predictions of the RAPGAP simulation, the total background simulation 
  and the sum of both.}
\label{FIG:contplots}
\end{figure}



\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig4.eps,width=1.0\linewidth}
\caption{The measured reduced cross section $\xpom\sigrdthree$, plotted
as a function of $\xpom$ at fixed $(\beta,Q^2)$ from the present measurement, 
compared with the previous H1 preliminary measurement
based on 1994-1997 data \cite{andy}. 
Also shown is the prediction for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\
GeV$ from the NLO QCD fit performed to the medium $Q^2$ data.
The solid curves correspond to the sum of ``Pomeron'' and ``Reggeon''
exchange contributions in the fit, whereas the dotted curves represent
the contribution from ``Pomeron'' exchange alone.
}
\label{fig3}
\end{figure}

% fixed xpom, full 

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig5.eps,width=0.9\linewidth}
\caption{Reduced cross section $\sigrdthree$ from this measurement, 
compared with two recent H1 measurements at lower $Q^2$. 
$\xpom \sigrdthree(\xpom,\beta,Q^2)$ is shown as a function of $Q^2$ at 
fixed $x$ or $\beta$ and $\xpom=0.01$.
Also shown is the prediction for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\
GeV$ from the NLO QCD fit performed to the medium $Q^2$ data.
}
\label{fig4}
\end{figure}

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig6.eps,width=0.9\linewidth}
\caption{Reduced cross section $\sigrdthree$ from this measurement, 
compared with a recent H1 measurement at lower $Q^2$. 
$\xpom \sigrdthree(\xpom,\beta,Q^2)$ is shown as a function of $Q^2$ 
at fixed $x$ or $\beta$ and $\xpom=0.03$.
Also shown is the prediction for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\
GeV$ from the NLO QCD fit performed to the medium $Q^2$ data and the
fit prediction for the pomeron contribution alone.
}
\label{fig5}
\end{figure}

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig7.eps,width=0.9\linewidth}
\caption{Reduced cross section $\sigrdthree$ from this measurement, 
compared with two recent H1 measurements at lower $Q^2$. 
$\xpom \sigrdthree(\xpom,\beta,Q^2)$ is shown as a function of $\beta$ at 
fixed $Q^2$ and $\xpom=0.01$.
Also shown is the prediction for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\
GeV$ from the NLO QCD fit performed to the medium $Q^2$ data.
}
\label{fig6}
\end{figure}

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig8.eps,width=0.9\linewidth}
\caption{Reduced cross section $\sigrdthree$ from this measurement, 
compared with a recent H1 measurements at lower $Q^2$. 
$\xpom \sigrdthree(\xpom,\beta,Q^2)$ is shown as a function of $\beta$ 
at fixed $Q^2$ and $\xpom=0.03$. Also shown is the predicion for 
$\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\ GeV$ from the NLO QCD fit 
performed to the medium $Q^2$ data and the fit prediction for the
pomeron contribution alone.
}
\label{fig7}
\end{figure}

% fixed xpom, zoomed

\begin{figure}

\centering
\epsfig{file=H1prelim-03-011.fig9a.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig9b.eps,width=0.49\linewidth}
\caption{
  Reduced cross section $\sigrdthree$ at fixed $\xpom=0.01$ from this
  measurement, compared with a recent H1 measurement at
  lower $Q^2$. $\xpom \sigrdthree(\xpom,\beta,Q^2)$ is
  shown as a function of $Q^2$ at fixed $x$ or $\beta$ (left) and as a
  function of $\beta$ at fixed $Q^2$ (right). Also shown is the
  predicion for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\ GeV$ from
  the NLO QCD fit performed to the medium $Q^2$ data.
}
\label{fig8and10}
\end{figure}

\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig10a.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-03-011.fig10b.eps,width=0.49\linewidth}
\caption{  Reduced cross section $\sigrdthree$ at fixed $\xpom=0.03$ from this
  measurement, compared with a recent H1 measurement at
  lower $Q^2$. $\xpom \sigrdthree(\xpom,\beta,Q^2)$ is
  shown as a function of $Q^2$ at fixed $x$ or $\beta$ (left) and as a
  function of $\beta$ at fixed $Q^2$ (right). Also shown is the
  predicion for $\xpom \sigrdthree$ for $\sqrt{s}=319 \rm\ GeV$ from
  the NLO QCD fit performed to the medium $Q^2$ data and the prediction
for the pomeron component alone.
}
\label{fig9and11}
\end{figure}


\begin{figure}
\centering
\epsfig{file=H1prelim-03-011.fig11.eps,width=1.0\linewidth}
\caption{
The measured reduced cross section $\xpom\sigrdthree$, plotted
as a function of $\xpom$ at fixed $(\beta,Q^2)$ (green
data points). The data are compared with the predictions
of the original Soft Colour Interactions (SCI) model (dashed curves)
and its refinement based on a generalized area law (solid curves),
both obtained with the LEPTO 6.5.2$\beta$ MC generator.
}
\label{fig2}
\end{figure}

\end{document}



