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\begin{document}

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\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
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 984}    &\\
                 & 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 Semi-Inclusive Diffractive Deep-Inelastic
  Scattering with a Leading Proton at HERA}  


  \vspace*{1cm}
    {\Large H1 Collaboration} 
 
  \vspace*{1cm}
%   {\Large Version 27.6./16:00h} 

\end{center}

\begin{abstract}

\noindent

The semi-inclusive cross section for the diffractive deep-inelastic scattering
process $ep \rightarrow eXp'$ is studied 
with a leading proton detected in the H1 forward proton spectrometer. 
The results are presented in terms of the differential cross section $\dx{\sigma}/\dx{t}$ 
and the diffractive structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$ measured in the
kinematic range $2<Q^2<50~\mr{GeV}^2$, $5\cdot10^{-3}<\beta<1$, $\xpom<0.09$ 
and  $-0.45<t<-0.08~\mr{GeV}^2$.
\end{abstract}
\end{titlepage}

\pagestyle{plain}

\section{Introduction}

The observation of events with a large rapidity gap in the distribution of the 
final state hadrons at HERA \cite{first} allows the nature of colour singlet exchange
in strong interactions to be investigated.  Colour singlet
exchange interactions have been successfully modelled in terms of
phenomenological Regge theory \cite{regge} and, at high energy, 
are attributed to diffractive or
pomeron exchange.  HERA allows the partonic nature of diffraction
to be investigated in deep--inelastic scattering (DIS) using the
virtual photon as a probe.

In diffractive DIS events at HERA \cite{h1_f2d,f2dzeus}, where $ep \rightarrow eXY$,  
the photon dissociation system $X$ and the proton remnant 
system $Y$ are separated by a large gap in rapidity. The system $X$ (with mass $\mx$)
is usually reconstructed in the central detector and, by requiring the absence of 
particles in the forward region of the detector, the mass of the proton remnant system $\my$
and the square of the four-momentum transfer at the proton vertex $t$ are restricted
to small values ($|t| < 1 \rm\ GeV^2$, $\my < 1.6 \rm\ GeV$).  Diffractive DIS single dissociation
 events ($ep \rightarrow eXp'$) are also measured at HERA \cite{zeus_lps, h1_f2lp}
by directly observing the final state proton 
using proton spectrometers located close to the
beam-line.  The detection of the final state proton facilitates the measurement
of the differential cross section $\dx{\sigma}/\dx{t}$ and reduces the large
uncertainty in the contribution of proton disociative processes present in the
large rapidity gap method.

The semi-inclusive structure function $F_2^{LP(3)} (\xpom, x, Q^2)$ \cite{h1_f2lp} was measured 
with a leading proton detected by the H1 forward proton spectrometer (FPS) in the 
range $\xpom > 0.1$. 
In this paper a new measurement of the diffractive structure function $F_2^{LP(3)}$ 
is presented which extends the kinematic range to values of $\xpom<0.1$. 
At these low values of $\xpom$ the measurement can be directly compared with 
measurements of $F_2^{D(3)} (\xpom, \beta, Q^2)$ \cite{f2d_new}
obtained using the presence of a rapidity gap in the central detector.
The differential cross section $\dx{\sigma}/\dx{t}$ is also measured for four 
different $\xpom$ values.
  
The present analysis is based on H1 data collected in the running period from January to April 1999, 
when HERA collided 920~GeV protons with 27.5~GeV electrons, and in the running period from August 1999 to 
August
2000, when 27.5~GeV positrons were collided instead of electrons. 
%Resulting $ep$ centre-of-mass energy 
%is $\sqrt{s}=318$~GeV.


\section{The Forward Proton Spectrometer}

The FPS \cite{VanEsch:2000pi} is used to measure the four momentum of the scattered proton. 
Protons scattered at small angles to the incident proton direction are deflected by the magnets of the beam optics 
into a system of detectors placed close to the proton beam. The detectors
consist of fibre hodoscopes, sandwiched between trigger scintillators, installed in 
movable ``Roman Pot'' plunger vessels. 
Two identical stations are installed at 64~m and 80~m away from the interaction point\footnote{At 81~m and 90~m 
two more detectors are installed. Due to a different acceptance these are not used in the present analysis.}. 
The absolute energy scale uncertainty is estimated as $\pm 5.5 \rm\ GeV$, 
which is about $0.6\%$ of the proton beam energy. 
The distance of the detectors from the beam and the beam line aperture 
restrict the FPS acceptance in the squared 4-momentum transferred between the incident proton and the final state
leading proton to $-0.45<t<-0.08 \ \rm{GeV}^2$ and $E_{p'}/E_p>0.9$, where $E_{p'}$ is the energy of
the leading proton and $E_p$ is the proton beam energy.


\section{Event Selection}

The data analysed in this paper were restricted to running periods where the
FPS detectors were in a stable position close to the circulating beam and all 
relevant components of the H1 detector were fully operational. 
The corresponding luminosity amounts to $28.8 \rm\ pb^{-1}$.  
The event selection is based on the reconstruction of a proton track in the FPS, an electron
candidate with energy above $10 \rm\ GeV$ in the backward electromagnetic calorimeter (SPACAL) \cite{spacal}
and at least one reconstructed track in the central H1 detector \cite{H1:det}. At the trigger level, a
signal in each of the components was required.
In order to reject background from interactions of the beam with the residual gas in the beampipe,
the $z$ coordinate of the event vertex was restricted to $|z_{vtx}| < 35 \rm\ cm$. In addition the
quantities  $\sum_i~(E-P_z)$ and $\sum_i~(E+P_z)$ which are calculated using the 
energy  $E_i$  and the longitudinal momentum $p_{z,i}$ of all final state particles including the
scattered positron and proton were required to be greater than $35  \rm\ GeV$ and less than
$1880 \rm\ GeV$ respectively. The contribution from photoproduction
events has been estimated using the PHOJET Monte Carlo \cite{phojet} and found to be negligible.    


The phase space of the analysis is restricted to the range $2<Q^2<50 \ \rm{GeV}^2$, $0.01<y<0.6$ and 
$\xpom<0.09$.
The standard DIS variables $Q^2$, $y$ and $x$ are reconstructed using the double angle method. 
The variable $\xpom$ may be reconstructed using either the scattered proton
measured in the FPS using $\xpom \simeq 1-E_{p'}/E_p$ or the combination of the 
hadronic final state and scattered electron measured in the central detector 
$\xpom \simeq (Q^2 + \mx^2) / (Q^2 + W^2)$.  In order to obtain the best resolution possible
the FPS is used to reconstruct $\xpom$ for values $E_{p'}/E_p<0.99$ and the central
detector is used for values $E_{p'}/E_p>0.99$.
The squared four-momentum transferred at the proton vertex $t$ is reconstructed
from $t~=~-p_t^2/(1-\xpom)-t_{min}$ using $\xpom$ and $p_t^2$ measured in the FPS.
The final data sample, after all cuts, contains about 3100 events.

Monte Carlo simulations are used to correct the data for 
the effects of losses and migrations due to the finite resolution of the H1 detector.
The smeared acceptance is calculated by running the H1 detector 
simulation program on a sample of events generated using an 
implementation of the `Saturation' model \cite{sat_orig} within the
RAPGAP generator \cite{rapgap}. The cross section is corrected to the Born level and the 
radiative corrections are calculated using RAPGAP interfaced to HERACLES \cite{heracles}.


\section{Systematic Uncertainties}

Systematic uncertainties from the following sources are considered:

\begin{itemize}

\item The uncertainty in the FPS track reconstruction efficiency results in an
overall normalisation uncertainty of $10\%$ for the $e^-p$ data, 
$12\%$ for $e^+p$ data collected in 1999 and $20\%$ for $e^+p$ 
data collected in 2000. 

\item The uncertainties in the reconstruction of the energy and transverse momentum of leading proton
is estimated by shifting $E_{p'}$ by $\pm 2$ GeV and $p_t$ by  $ \pm 10 \rm\ MeV$. 

\item The uncertainty in the reconstruction of the scattered electron is estimated by 
changing the electromagnetic energy scale of the SPACAL by $\pm 2\%$ and 
shifting the electron polar angle by $\pm 2$ mrad. 

\item The uncertainty in the reconstruction of the hadronic final state is
estimated by changing the hadronic energy scale of the LAr calorimeter
by $\pm 4\%$ and the energy fraction carried by the tracks by $\pm 3\%$.

\item The uncertainty in the physics model used to compute the acceptance corrections
is estimated by reweighting the generated $\xpom$ distribution by $\xpom^{\pm0.2}$,
the $\beta$ distribution by $(1 \pm 0.3 \beta)$ and the $t$ distribution by 
$e^{\pm 2t}$.

\item The uncertainty in the trigger efficiency is estimated by comparing the trigger efficiency 
obtained from a sample of independently triggered data events with that in 
the simulation.
\end{itemize}


\section{The Differential Cross Section \boldmath{$\dx{\sigma}/\dx{t}$}}
\label{slopes}

The differential cross section $\dx{\sigma}/\dx{t}$ is measured for 4 ranges of 
$\xpom$ and shown in figure~\ref{fig:bslopes}. For each $\xpom$ range
the dependence of the cross section on $t$ is parameterised as $\dx{\sigma}/\dx{t} \propto e^{Bt}$ 
and is shown as a solid line on the figures.
The extracted slope parameter $B$ is plotted as a function of $\xpom$ in figure~\ref{fig:bslzeus}.  
Within the experimental errors no dependence on $\xpom$ is visible.
The mean value of the slope parameter $B$ in the 
kinematic range $2<Q^2<50~\mr{GeV}^2$ , $0.01<y<0.6$, $-0.45<t<-0.08 \ \rm\GeV$  and
$\xpom~<~0.09$ is $B=5.0 \pm 0.3 \rm{(stat.)} \pm 0.8 \ \rm{(syst.)~GeV^{-2}}$.  
The results are consistent within errors with measurements made using the 
ZEUS LPS \cite{zeus_lps}, made in a similar kinematic range, 
which are also shown in figure~\ref{fig:bslzeus}. 


\section{Measurement of \boldmath{$F_2^{LP(3)}$} and \boldmath{$F_2^{D(3)}$}}

In order to compare with the result of the previous H1 FPS measurement of the
structure function $F_2^{LP(3)}(\xpom,x,Q^2)$
performed at high $\xpom$ \cite{h1_f2lp}, the data are extrapolated into the range $p_t<0.2 \rm \ GeV$ 
using the $t$ dependence measured in section \ref{slopes}.
The results are shown in figure~\ref{fig:f2lp}.  The combined data points cover the $\xpom$ range 
$2 \cdot 10^{-3}$ to $0.27$ and
show the transition from diffractive DIS processes with $\Pom$ exchange 
(`flat' behaviour of $F_2^{D(3)}$ at $\xpom<0.05$) 
to processes which involve dominantly $\Reg$ and $\pi$ exchange (rising $F_2^{LP(3)}$ behaviour at $\xpom>0.05$). 
The prediction of the `Saturation' model \cite{sat_orig}, as implemented in the RAPGAP Monte Carlo 
generator, is compared with the new measurement and is found to be in good agreement with the data.


The H1 FPS data may also be plotted as a function of $\xpom$ at fixed values of $\beta$ and $Q^2$ to give
the diffractive structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$. The structure
function $F_2^{D(3)}$ is presented in figure~\ref{fig:f2dx} integrated over the $t$ range
$-0.45<t<-0.08 \ \rm\GeV^2$. 

The diffractive structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$ has also been reecently
measured~\cite{f2d_new}, using the presence of a 
large rapidity gap in the central detector, and corrected to the 
range $\my < 1.6 \ \rm\GeV$ and $|t| < 1 \rm\ GeV^2$.
In order to compare with this data the FPS measurement of $F_2^{D(3)}(\xpom,\beta,Q^2)$ is
extrapolated into the range $|t|<1~ \rm\ GeV$ using the $t$ slope measured in section \ref{slopes}. The
extrapolation in $t$ is about a factor of $2$ with an uncertainty of $15\%$ which comes from the error on the
measurement of the slope parameter $B$. 
Studies using simulations of the DIFFVM \cite{diffvm} generator show 
that the fraction of leading protons from proton dissociation is around $5\%$ in the highest measured $\xpom$ 
bin ($0.05 < \xpom <  0.09$) and negligible for lower $\xpom$ values. 
The comparison of the structure function obtained from the 2 different methods 
is shown in figure~\ref{fig:f2d}. 
Within errors the leading proton data are in good agreement with the data obtained independently from 
the requirement of a rapidity gap in the central detector, indicating that the contribution of
proton dissociation in the range $\my < 1.6 \rm\ GeV$ is small.
In addition, the FPS data extend the kinematic range of $F_2^{D(3)}$ into 
the low $\beta$ ($\beta=0.01$) and low $Q^2$ ($Q^2=2.6~\mr{GeV}^2$) regions.

In figure \ref{fig:sat} the diffractive structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$ with a leading
proton detected in the FPS is compared with the predictions of two versions of the 
`Saturation' model \cite{sat_orig, sat_scale}.  Within the
experimental errors both versions of the model are able to give a reasonable description of the
data over the whole $Q^2$ and $\beta$ range of the measurement.

\section{Conclusions}

The differential cross section $\dx{\sigma}/\dx{t}$ and the structure functions 
$F_2^{LP(3)}(\xpom,x,Q^2)$ and $F_2^{D(3)}(\xpom,\beta,Q^2)$ 
have been measured in diffractive DIS processes with a leading proton detected in the H1 forward proton spectrometer. 
A fit to the differential cross section $\dx{\sigma}/\dx{t} \propto e^{Bt}$ yields a slope parameter 
$B=5.0~\pm~0.3~$(stat.)$~\pm~0.8~$ (syst.)~GeV$^{-2}$ in the range 
$2<Q^2<50~\mr{GeV}^2$ , $0.01<y<0.6$, $-0.45<t<-0.08 \ \rm\GeV$  and
$\xpom~<~0.09$.

Comparison of the data with $F_2^{LP(3)}(\xpom,x,Q^2)$ previously measured by H1 FPS 
in the high $\xpom$ or non-diffractive range show behaviour consistent with the
transition from $\Pom$ exchange at $\xpom~<~0.05$ to the 
dominance of $\Reg$ and $\pi$ exchange at $\xpom~>~0.05$. 

Comparison of the leading proton data with $F_2^{D(3)}(\xpom,\beta,Q^2)$ obtained 
from the presence of a large rapidity gap in the central detector
shows good agreement between the two methods. 
The `Saturation' model is able to give a good description of the new 
leading proton data.


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

\begin{thebibliography}{99}


\bibitem{first}
M.~Derrick {\it et al.}  [ZEUS Collaboration],
%``Observation of events with a large rapidity gap in deep inelastic scattering at HERA,''
Phys.\ Lett.\ B {\bf 315} (1993) 481. \\
%%CITATION = PHLTA,B315,481;%% 
T.~Ahmed {\it et al.}  [H1 Collaboration],
%``Deep inelastic scattering events with a large rapidity gap at HERA,''
Nucl.\ Phys.\ B {\bf 429} (1994) 477.
%%CITATION = NUPHA,B429,477;%%

\bibitem{regge} 
T.~Regge,
%``Introduction To Complex Orbital Momenta,''
Nuovo Cim.\  {\bf 14} (1959) 951. 
%%CITATION = NUCIA,14,951;%%


\bibitem{h1_f2d}
H1 Collaboration, C.Adloff {\it et al.}
Z. Phys. {\bf C~76} (1997) 613.

\bibitem{f2dzeus}
J.~Breitweg {\it et al.}  [ZEUS Collaboration],
%``Measurement of the diffractive cross section in deep inelastic  scattering using ZEUS 1994 data,''
Eur.\ Phys.\ J.\ C {\bf 6} (1999) 43
[hep-ex/9807010].
%%CITATION = HEP-EX 9807010;%%


\bibitem{zeus_lps}
ZEUS Collaboration, J.~Breitweg {\it et al.},
Eur. Phys. J.  {\bf C~1} (1998) 81.\\
ZEUS Collaboration,
{\em Diffractive Results from the ZEUS Leading Proton Spectrometer at HERA},
Talk given by B. Smalska at the
{\em $9^{th}$ International Workshop on Deep Inelastic Scattering}, Bologna, 
Italy, April 27-May 1, 2001. 



\bibitem{h1_f2lp}
H1 Collaboration, C.Adloff {\it et al.}
Eur. Phys. J. {\bf C~6} (1999) 587.

\bibitem{f2d_new}
H1 Collaboration,
{\em Measurement of the diffractive structure function $F_2^D(3)$},
Abstract 808, Paper submitted to
{\em International Europhysics Conference on High Energy Physics}, Budapest, 
Hungary, July 12-18, 2001. 


\bibitem{VanEsch:2000pi}
P.~Van Esch {\it et al.},
Nucl.\ Instrum.\ Meth.\ A {\bf 446} (2000) 409.
                             

\bibitem{spacal} 
R.~D.~Appuhn {\it et al.}  [H1 SPACAL Group Collaboration],
%``The H1 lead/scintillating-fibre calorimeter,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 397.
%%CITATION = NUIMA,A386,397;%%

\bibitem{H1:det} 
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 detector at HERA,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310.
%%CITATION = NUIMA,A386,310;%%


\bibitem{phojet}
R.Engel,
Z. Phys. {\bf C~66} (1995) 203.


\bibitem{sat_orig}
K.~Golec-Biernat, M.~W\"{u}sthoff, \Journal{\PRD}{59}{1999}{014017}; \\
K.~Golec-Biernat, M.~W\"{u}sthoff, \Journal{\PRD}{60}{1999}{114023}.


\bibitem{rapgap}
H.Jung,
Comp.Phys.Commun. {\bf 86} (1995) 147.

\bibitem{heracles}
A.Kwiatkowski {\it et al.},
Comp.Phys.Commun. {\bf 69} (1992) 155.

\bibitem{diffvm}
B.List,
Diploma Thesis (Tech. Univ. Berlin, 1993 (unpublished).


\bibitem{sat_scale}
K.~Golec-Biernat, M.~W\"{u}sthoff, \Journal{\EJC}{20}{2001}{313}.

\end{thebibliography}

%%%%%%%%%%%%%%%%%% dsig/dt %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig1.eps,width=17cm}}

\vspace{-3cm}

  \caption{The differential cross section $\dx{\sigma}/\dx{t}$ measured with the H1 FPS 
in the range $2<Q^2<50~\mr{GeV}^2~, 
   0.01<y<0.6~,~ 5 \cdot 10^{-3}<\beta<1$ for four different $\xpom$ bins. 
Results of the fit with a function $\dx{\sigma}/\dx{t} \propto e^{Bt}$ 
are shown. The inner error bars represent the statistical errors, the outer error bars 
the statistical and systematic errors added in quadrature.}
  \label{fig:bslopes}
 \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%% B-slopes %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig2.eps,width=17cm}}

%\vspace{-3cm}

  \caption{The slope parameter $B$ of the differential cross section 
$\dx{\sigma}/\dx{t}\propto e^{Bt}$ as a function of $\xpom$. Results using the  
ZEUS LPS \cite{zeus_lps} are also shown. The inner error bars represent the statistical errors; 
the outer error bars the statistical and systematic errors added in quadrature.}
  \label{fig:bslzeus}
 \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%% F2LP(3) %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig3.eps,width=17cm}}

%\vspace{-3cm}

  \caption{The structure function $F_2^{LP(3)}(\xpom,x,Q^2)$, presented as 
$\xpom F_2^{D(3)}(\xpom,x,Q^2)$ and plotted as a function of $\xpom$ at fixed
values of $x$ and $Q^2$. The circles are
new data measured with a leading proton detected in the FPS extrapolated into the 
range $p_t<0.2 \rm\ GeV$. 
The results of the previous H1 leading proton measurement \cite{h1_f2lp} performed 
at larger values of $\xpom$, in the same $p_t$ range, are shown as triangles. 
The solid curve shows the prediction of the 
`Saturation' model as implemented in the RAPGAP Monte Carlo
generator.  The inner error bars represent the statistical errors; 
the outer error bars the statistical and systematic errors added in quadrature.}  
  \label{fig:f2lp}
 \end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%% F2D(3) NOT EXTRAPOLATED %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig4.eps,width=17cm}}

%\vspace{-3cm}

  \caption{The structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$
presented as $\xpom F_2^{D(3)}(\xpom,\beta,Q^2)$ and plotted as
a function of $\xpom$ at fixed values of $\beta$ and $Q^2$.
The squares are data with a leading proton detected in the FPS, 
in the range $-0.45<t<-0.08 \ \rm\GeV^2$. 
The inner error bars represent the statistical errors; the outer error bars 
the statistical and systematic errors added in quadrature.}  
  \label{fig:f2dx}
 \end{center}
\end{figure}



%%%%%%%%%%%%%%%%%%% F2D(3) WRT RAPIDITY GAP METHOD %%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig5.eps,width=17cm}}

%\vspace{-3cm}

  \caption{The structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$
presented as $\xpom F_2^{D(3)}(\xpom,\beta,Q^2)$ and plotted as
a function of $\xpom$ at fixed values of $\beta$ and $Q^2$.
The squares are data with a leading proton detected in the FPS, 
extrapolated into the range $|t|<1 \rm\ GeV^2$. 
The results of the preliminary H1 measurement of 
$\xpom F_2^{D(3)}$ in processes with a large rapidity gap are shown as circles. 
The leading proton data at $Q^2=20~\mr{GeV}^2$ and $\beta=0.7$ are compared with 
rapidity gap data at $Q^2=18~\mr{GeV}^2$ and $\beta=0.65$ respectively. 
The inner error bars represent the statistical errors; the outer error bars 
the statistical and systematic errors added in quadrature.}  
  \label{fig:f2d}
 \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%% F2D(3) WRT SATURATION MODEL%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[!ht]
 \begin{center}
 {\epsfig{file=H1prelim-01-112.fig6.eps,width=17cm}}

%\vspace{-3cm}

  \caption{The structure function $F_2^{D(3)}(\xpom,\beta,Q^2)$ 
presented as $\xpom F_2^{D(3)}(\xpom,\beta,Q^2)$ and plotted as
a function of $\xpom$ at fixed values of $\beta$ and $Q^2$.
The squares are data with a leading proton detected in the FPS, 
extrapolated into the range $|t|<1 \rm\ GeV^2$. 
The data are compared with two versions of the `Saturation' model \cite{sat_orig, sat_scale}.
 The inner error bars represent the statistical errors; the outer error bars 
   the statistical and systematic errors added in quadrature.}  
  \label{fig:sat}
 \end{center}
\end{figure}


\end{document}
