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\noindent
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%{\it {\large version of \today}} \\[.3em] 
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%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
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\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03}, 
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 091} & Parallel Session & {\bf 5}) & \\
                & & & \\
\multicolumn{4}{l}{{\bf
                XXI International Symposium on  
                Lepton and Photon Interactions, LP03}, 
                August~11-16,~2003,~Fermilab} \\ 
                & & & \\
                \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\begin{center}
  \Large
  {\bf 
        Diffractive dissociation in photoproduction at HERA}\\

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


\begin{abstract}
\noindent
A new measurement of the differential cross section $d \sigma/d M_X^2$ for the process $\gamma p \rightarrow X Y$, with a large rapidity gap between the systems $X$ and $Y$ and with $Y$ a proton or a low mass proton excitation, is presented at three centre-of-mass energies $\langle W \rangle$ = 91,187 and 231 GeV. The trajectory intercept $\alpha_{eff}(0)$ obtained from a Regge parameterization of the $W$ dependence with a single effective trajectory is presented as a function of $M_X^2$. A combined Triple Regge fit is performed over this rapidity gap data, in combination with leading proton data and fixed target data. The pomeron intercept $\alpha_{\pom}(0)$ is extracted from this fit.

\end{abstract}
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\pagestyle{plain}
%
                              \section{Introduction} \label{s_intro}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the HERA electron-proton collider, the bulk of the cross section corresponds
to photoproduction, in which the electron is scattered through a
very small angle and a quasi-real photon interacts with the proton.
These photon proton interactions at high energies exhibit very similar
properties to hadron interactions which can be understood as a photon fluctuating
into a hadronic state \cite{photonfluc} prior to the interaction with the proton.
At high energies, hadron-hadron elastic and total cross sections
have been successfully described in terms of the Regge picture in which
two trajectories exchanged in the t-channel, the pomeron ($\pom$) and the 
``reggeon'' ($\reg$), are important.
At asymptotically large energies pomeron exchange dominates the elastic channel,
resulting in a slow rise of the elastic and total cross section with energy. 
Processes
in which one or both hadrons dissociate also occur (see Fig.~\ref{f_gproc})
and are characterized by a large
rapidity interval in which no hadronic activity is observed. These diffractive
events dominate at large centre of mass energy and have small dissociative masses.
The inclusive photon dissociative mass distribution can be modelled by combining Regge theory \cite{collins} with
Mueller's generalization of the optical theorem \cite{op_theorem}, the
so-called `triple-Regge' approach.


Experimental results on diffractive dissociation processes have been studied
at fixed target experiments \cite{ft}, in $pp$ and $\bar p p$ collisions \cite{ppbar1,ppbar2} and at HERA \cite{p_zeus,p_paul}.
At sufficiently high energies the diffractive dissociation process is dominated
by the triple pomeron amplitude $\PPP$, leading to the differential cross section behavior
$d\sigma/dM_X^{2} \sim 1/M_X^{2}$. It was shown that for a better description
of the data additional terms $\PRR$ \cite{p_zeus,p_paul} and $\RRR$ \cite{p_paul} were required.
The latter results \cite{p_paul} were obtained from a  triple Regge analysis combining
HERA data with fixed target measurements \cite{ft}.

In the present paper, H1 data are presented from measurements of large rapidity gap events
at three different $W$ values  $\left< W_{\gamma p} \right> = 231,187$ and 91 GeV, the latter
data becoming available because of the installation of a new small angle
electron tagger (eTag44) at 44~m.
The data are interpreted in terms of a simple Regge approach to the $W$
dependence at fixed $M_X$ and also in the framework of a full triple Regge
fit. 
To get better constraints on the triple-Regge fit parameters, leading proton data \cite{lp} providing a large range in $M_X^2$ 
and fixed target data \cite{ft} providing a larger lever-arm in $W$, were used in a simultaneous triple Regge fit.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Event selection}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The data for this measurement were taken during a short dedicated run in 1997
in which HERA was colliding 27.5 GeV positrons with 820 GeV protons.
An integrated luminosity of 2 pb$^{-1}$ was collected. The events
were triggered by a minimal total energy deposit 
from the hadrons in the backward SPACAL
calorimeter in coincidence with a tagged electron in either the electron
tagger at $z=-33$~m (eTag33) or in the tagger at $z=-44$~m (eTag44).
Both of these taggers cover the range $Q^2 < 0.01 \ {\rm GeV^2}$.
Bremsstrahlung events ($ep \rightarrow ep\gamma$) were removed by requiring
no energy above 2 GeV in the photon detector for the eTag33 data,
and 0.6 GeV for the eTag44 data.
%In this event sample, the exchanged photon  has a virtuality $Q^2$ of
%less than $0.01$ GeV$^2$ and center of mass energies of $W_{\gamma p}$  of $164 <W_{\gamma p}^{etag33}<251~\rm GeV$
%and  $\left< W_{\gamma p}^{etag44} \right> \approx 91~\rm GeV$

As the system $Y$ was not tagged, the selection of single
dissociative processes was based on an absence of significant activity in the
forward detector system, comprising the Proton Remnant Tagger (PRT), 
Forward Muon Detector (FMD) and the forward forward part of the Liquid
Argon calorimeter (LAr):
\begin{itemize}
    \item number of pre-toroid FMD paired hits $<$ 3
    \item number of PRT scintillators giving a signal $<$ 1
    \item no LAr clusters ($E >$ 400 MeV) at $\eta >$ 3.2
\end{itemize}
With this selection, the pseudo-rapidity gap spans at least 3.2 $< \eta <$ 7.0.

Using  Fig.~\ref{f_gproc} as the generic representation for
a quasi two body process, in which there is a large rapidity gap between
the $X$ and $Y$ systems, $Y$ being closest to the proton beam direction,
the events selected by the forward detectors correspond to the processes
in which $Y$ is either a proton or 
a low lying nucleon state with $M_Y<1.6~\rm GeV$.
Furthermore the selection limits the square of the 4-momentum transfer
from the incident proton to the system $Y$ to $|t|<1$ GeV$^2$. 
The sample also includes a fraction of non-diffractive events
with an accidental gap in hadronic rapidity distribution
due to a random fluctuation. 

\begin{figure}
 \begin{center}
   \epsfig{figure=H1prelim-02-014.fig1.eps ,height=5cm}
   \caption{\it Illustration of the generic process $\gamma p \rightarrow XY$.
   In the Regge pole picture, a reggeon is exchanged between the photon
                and the proton.}
 \label{f_gproc}
 \end{center}
\end{figure}

An important background 
in the data sample results from  e$^+$ beam interactions
with residual gas or the beam pipe wall, which have
small values of $y = W^2 / s$ reconstructed from hadrons
($s$ is the square of the $ep$ centre of mass energy). 
Most of this background in the eTag33 data sample
was rejected by imposing the following cut:
\[
y_{had} = \sum_{i=h} (E - P_z)_i/ 2E_e > 0.2 \ ,
\]
where the sum runs over all reconstructed hadrons.
Using data from unpaired electron (pilot) bunches the remaining  background
is shown to be negligible.
In  the eTag44 data sample, corresponding to a smaller $W_{\gamma p}$, no such cut
can be applied as the overlap between data and background is large.
The background is subtracted statistically and is of the order of 10\%.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{$M_{X}$ reconstruction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Having applied the forward detector selection, all particles observed in the
central components of the detector are attributed to the system $X$.
The mass of the system X is measured using the central components of the H1 detector.
The $M_X$ mass is reconstructed using an algorithm which
combines particle track and calorimeter information whilst
avoiding double counting.
The invariant mass is then obtained using the expression:
\begin{equation}
    M_X^2 = \left( \sum_{i \in X} E_i \right)^2 - \left(\sum_{i \in X} \vec{p_i} \right)^2
           \simeq 2 E_{\gamma} \sum_{i \in X} \left(E+P_{z} \right)_{i}
   \label{e_mxrec}
\end{equation}
where $i$ runs over all reconstructed objects of the system X and $E_{\gamma}$ is the energy of
the interacting photon, obtained from the measured scattered electron energy.
This method has the
advantage of being insensitive to the loss of very backward going hadrons ($E \simeq -P_z$).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Simulations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The 
PHOJET \cite{phojet} and PYTHIA \cite{pythia} Monte Carlo generators
were used to correct for detector inefficiencies,
acceptance corrections, trigger inefficiencies and smearing due to
detector resolution. Both generators sub-divide diffractive photoproduction
into the following processes:
\begin{itemize}
  \item $\gamma p \rightarrow Vp\; {\rm (elastic \; case \; (EL))}$;
  \item $\gamma p \rightarrow VY\; {\rm (single \; proton \; dissociation \;(PD))}$;
  \item $\gamma p \rightarrow Xp\; {\rm (single \; photon \; dissociation \;(GD))}$;
  \item $\gamma p \rightarrow XY\; {\rm (double \;dissociation \;(DD))}$
\end{itemize}
with $V=\rho,~\omega,~\phi$. Also non-diffractive
%\footnote{events in which net color is exchanged} 
events were simulated.
At fixed W, the photon dissociative events are produced according to
\[
\frac{d\sigma_{GD}}{dM_X^{2}dt} \propto \frac{1}{M_X^{2}} e^{b_{GD}(M_X)t}
\]
where $b_{GD}$, is the slope parameter for the GD process.
Similar expressions exist
for PD and DD \cite{thesispaul}. The events are simulated
in the region for which $M_{X}/W <$ 0.46.

The generated mass distributions have been
reweighted using an iterative procedure, until a satisfactory
description of the reconstructed data is obtained.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Extraction of the differential cross section $d\sigma_{\gamma p}/d M_{X}^{2}$}
\label{s_cs}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
From the eTag33 triggered data, two bins in $W$ have
been constructed. The first, 164 $< W <$ 212 GeV, yields a centre of mass energy averaged
over the photon flux distribution of $\left< W \right>$ = 187 GeV. The second range is
212 $< W <$ 251 GeV, corresponding to $\left< W \right>$ = 231 GeV. For the eTag44 data
an averaged centre of mass energy $\left< W \right>$ = 91 GeV is obtained.

The differential cross section at $\left< W \right>$ = 231 GeV, ($\left< W \right>$ = 187 GeV)
is measured in 7,(8)  $M_X^2$ bins covering the range 4.00 $< M_X^2 <$ 862 GeV, (1860 GeV). 
For $\left< W \right>$ = 91 GeV,
%the centre of mass is reduced compared to that of
%$\left< W \right>$ = 231~GeV and $\left< W \right>$ = 187~GeV, such that 
measurements
in the highest $M_X$ region are no longer possible and the measured range 
is reduced to 1.58 $< M_X^2 <$ 186 GeV$^2$.

The PHOJET and PYTHIA Monte Carlos are used to correct  the measured mass distribution for detector
resolution and acceptance losses to a cross section defined in the
kinematic range
\[
M_Y < 1.6~\rm GeV \mbox{   and   } |t| < 1~\rm GeV^2.
\]
The mean acceptances of the electron taggers are
$30\pm 2$ \% for the $\left< W \right> =$ 231 GeV sample,
45 $\pm 2$ \% for $\left< W \right> =$ 187 GeV and
$34\pm$~2\% for $\left< W \right> =$ 91 GeV.

To obtain a $\gamma p$ cross section, the photon flux
given by the Weizs\"acker-Williams formula~\cite{flux} has been used.
Radiative corrections were found to be at the level of 1\% in \cite{raco}
and are neglected here.

The SPACAL trigger efficiencies for the $\left<W\right>=231$ and $\left<W\right>=187$
data have been cross checked 
using a data sample triggered on the basis of a vertex within 
30~cm of the mean interaction point. The trigger efficiency was found to be almost 100\% for
all considered $M_X$ bins.
For the $\left< W \right> =91$ GeV data, the dissociating X-system
is produced more forward
such that the SPACAL trigger efficiency is reduced to about 40\%.
For all measured data points the stabilities and purities  
\footnote{Purity (stability) is defined as the fraction of all simulated
events reconstructed (generated) in a mass interval that are also generated 
(reconstructed) in
that interval.} are larger than 30\%.


Statistical errors arise from the finite data volume, the samples used in
the subtraction of the beam-gas background and the simulation samples used to
make corrections. The statistical error in each interval is formed by adding
the contributions from these three sources in quadrature. Systematic errors
are evaluated on a bin by bin basis. The dominant source is the model 
dependence uncertainty in the acceptance corrections, evaluated from the
difference between the results obtained when correcting with the PYTHIA and
the PHOJET Monte Carlo models. The systematic errors and the statistical
errors are then added in quadrature to give the total error.

The differential cross section measurement is shown in Fig.~\ref{f_cs_compare} and is compared for the
two highest $W$-bins with the previous H1 measurement \cite{p_paul}. 
%An additional measurement was performed
%due to the installation of the electron tagger at 44 m from the 
%interaction point at a smaller $\gamma p$ center
%of mass energy $W$= 91 GeV.
The results are consistent within the combined normalisation uncertainties.

%%%%%%%%%%%%%%%%%%
\section{Results}
%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Effective trajectory intercept as a function of $M_X$}
\label{s_alphaeff}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

The $W$ dependence of the data is first tested at fixed $M_X$. Assuming a
single effective trajectory of intercept $\alpha_{eff}(0)$ is 
exchanged, Regge theory predicts a centre
of mass energy dependence for the cross section integrated over the $t$
range of the measurement according to
%In the triple Regge model, the differential cross section is expressed
%as a sum over all contributing trajectories. If we assume that this sum can be
%represented by a single {\it effective} trajectory,  the expression (\ref{E_3Regge1})
%can be rewritten as:
\begin{equation}
\frac{d \sigma}{dM_X^2} \propto
            \left(W^2 \right)^{2 \alpha_{eff}(0) -2} \;
            \frac{e^{-B \mid t_{min} \mid}- e^{-B}}{B}
        \label{E_3Regge2}
\end{equation}
where $|t_{min}|$ is the minimum kinematically accessible vale of $|t|$
and $B$ is the $M_X$ dependent slope parameter. 

Fitting the rapidity gap data to (\ref{E_3Regge2}), with $B$ constrained 
by fixed target data \cite{p_paul}, the value of
$\alpha_{eff}$ as a function of $M_{X}^2$ can be
extracted. Fig. \ref{f_stamp} shows  the quality of the fits for the 6 $M_X^{2}$ bins
considered.
%For the highest $M_X^{2}$ bin, the value of  $\alpha_{eff}$ is obtained
%from an extrapolation. 
Fig. \ref{f_alphaeff} shows the variation of $\alpha_{eff}(0)$ as a
function of $M_X^{2}$. To the figure is also added the value of $\alpha_{eff}(0)$
obtained from fits using slightly different assumptions to H1 data in which
the leading proton is tagged \cite{lp} in which higher
$M_X^{2}$ values are reached. Fig. \ref{f_alphaeff} shows that up to $M_X^{2}$ values of
300 GeV the cross section is dominated by the pomeron 
exchange ($\alpha_{eff}(0) \sim 1$). In the leading proton
data subleading exchanges ($\alpha_R(0)$=0.5 and $\alpha_\pi(0)$=0.0) start to contribute, resulting in
a lower value of the effective intercept. The extraction of the pomeron 
intercept from the triple Regge fit (section~\ref{trb}) is given by the band.



\subsection{Triple Regge model}
\label{trb}
%%%%%%%%%%%%%%%%%%
The differential cross section,
$M_{X}^2 d\sigma / dM_{X}^{2}$
is shown in Fig. \ref{f_reggefit} together with a fit using a triple
Regge model (see Fig.~\ref{f_3regge}) performed on the presented cross section as well as on 
the cross sections from the leading proton data \cite{lp}
and fixed target data  \cite{ft}.
In this model the cross section is
expressed as a
sum of contributions with reggeons i,j and k
\cite{kaidalov,alberi,goulianos,zotov}:
\begin{equation}
\frac{d^{2} \sigma}{d M^{2}_{X} \; dt}
=       \frac{s_{0}}{W^{4}} \sum_{i,j,k} G_{ijk}(t)
        \left( \frac{W^{2}}{M^{2}_{X}}\right)^{\alpha_{i}(t)+\alpha_{j}(t)}
        \left( \frac{M^{2}_{X}}{s_{0}}\right)^{\alpha_{k}(0)}
        \cos \left[ \phi_i(t)-\phi_j(t) \right].
        \label{E_3Regge1}
\end{equation}
The trajectories $\alpha_{i}(t)$ are assumed to take the linear form $\alpha_{i}(t) = \alpha_{i}(0)+\alpha^{'}_{i} t$.
The functions $G_{ijk}(t)$ contain the products of all couplings.
%are factored into products of couplings $\beta_{pi}(t)$, $\beta_{pj}(t)$,
%$\beta_{\gamma k}(t)$ and $g_{ijk}(t)$. 
For photoproduction,
the reggeons
$i$ and $j$ must have the same signature such that $\phi_i(t) - \phi_j(t) = \frac{\pi}{2} \left[  \alpha_j(t)-\alpha_i(t) \right]$.

The functions $G_{ijk}(t)$ and $\alpha_{ijk}(t)$ are not predicted by 
the model and must be determined from experimental measurements.
The form (\ref{E_3Regge1}) is fitted to the 
data with the six triple Regge couplings ($G_{\pom \pom \pom}(0)$, 
$G_{\pom \pom \reg}(0)$, $G_{\reg \reg \pom}(0)$, $G_{\reg \reg \reg}(0)$, 
$G_{\pi \pi \pom}(0)$, $G_{\pi \pi \reg}(0)$) and $\alpha_{\pom}(0)$ as 
free parameters. 
The trajectories of the sub-leading exchanges and all $t$ dependences are
obtained from previous soft hadronic data.
A factor of 3 is applied to the coupling for the
isospin 1 $\pi$ exchange in the rapidity gap data  
compared with the leading proton data, accounting for the additional 
possibility
of leading neutron production and corresponding to the appropriate
Clebsch-Gordon coefficient. Since the exchange degenerate $\reg$ trajectory
contains both isospin 1 and isospin 0 exchanges, an additional free parameter
$\cal R$ is introduced to multiply the $\reg$ exchange couplings in the
rapidity gap data.
Interference terms ($i \neq j$) are not 
considered in the fit. 

Fig.~\ref{f_reggefit} shows the result of the fit for the different 
$W$-bins as well as the contributions of diffractive ($\pom \pom \pom$
and $\pom \pom \reg$), non-diffractive ($\reg \reg \pom$ and 
$\reg \reg \reg$) and pion terms ($\pi \pi \pom$ and $\pi \pi \reg$).  
From Fig.~\ref{f_reggefit} it can be seen 
that a significant non-diffractive contribution is needed to explain 
the H1 rapidity gap data at large $M_X$.  
The fit yields the result 
${\cal R} = 11.4 \pm 0.2 \ ({\rm stat}) \ \pm \ 6.8 \ ({\rm syst})$, 
significantly
larger than the maximum expected value of 3. This suggests that a more
complex treatment of the sub-leading exchanges is required for a complete
description, probably including
consideration of interference terms or the production of other 
baryon resonances in 
the rapidity gap data.
%A Triple Regge fit is only possible on the 
%three data samples together if the $\reg$ exchanges generate large contributions 
%from resonances of the proton in the rapidity gap data which are not present in 
%the leading proton data, since $\cal R$ tends to be much large than three which 
%is the value one would expect if the scattered proton can only go into a proton 
%or a neutron.
However, the value obtained for 
$\alpha_{\pom}(0) = 1.127 \ \pm 0.004 \ ({\rm stat}) \ \pm 0.025 \ ({\rm syst})
\ \pm 0.046 ({\rm model})$ 
%is however not dependent 
%on these resonance assumptions. 
is stable with respect to different assumptions concerning the sub-leading
exchanges.
%Since the triple-Regge couplings themselves are highly correlated 
%and have large errors due to the theoretical 
%model uncertainties they are not presented here.
The new measurement of $\alpha_{\pom}(0)$ is shown in Fig.~\ref{f_intercepts} together 
with previous measurements as a  
function of $Q^2$. An indication of a rising 
pomeron intercept is seen as a function of $Q^2$.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
                                                 \section{Conclusion}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The differential cross section $M_{X}^2 \; d \sigma_{\gamma p \rightarrow X Y} / d M_{X}^{2}$
for $M_Y< 1.6$ GeV and $|t|<1.0$ GeV$^2$ has been measured for photoproduction 
data at HERA. The precision is improved at $W \sim 200 \ {\rm GeV}$ and
measurements are made for the first time at $W \sim 100 \ {\rm GeV}$.
From the $W$ dependence of the data, the intercept $\alpha_{eff}(0)$ of 
an {\it effective} trajectory as a function of $M_X^{2}$ is determined. 
It is found that at small $M_X^{2}$ values up to $300 \rm~GeV$, the pomeron 
trajectory dominates.
% while in the leading proton data sub-leading exchanges become important.
The data are also subjected to a 
triple Regge decomposition, in which the $M_X$ and $W$ dependences 
are simultaneously described. The resulting pomeron trajectory intercept
is consistent with the result for the soft pomeron describing other soft
hadronic cross sections. 
%A good description of the $W^2$
%and $M_X^{2}$ dependence is only found for a triple Regge fit performed 
%over the rapidity gap data,
%the leading proton data and the fixed target data without interference  involving $\pom$, $\reg$ and $\pi$
%exchange, if the meson exchanges generate large contributions from resonances in the rapidity gap data which 
%are not present in the leading proton data. 

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\begin{figure}[htb]
  \begin{center}
    \epsfig{figure=H1prelim-02-014.fig2.eps,width=11cm}
    \caption{\it The Differential cross section measurement $M_X^2 \; d \sigma / dM_X^2$ for $M_Y<$ 1.6 GeV and $\mid t \mid<$ 1 GeV$^2$.
                 A comaprison with a previous H1 measurement is made for the $\gamma p$ center of mass energies $W$=231 and 187 GeV. The new measurement
yields additional data at $W$=91 GeV.}
    \label{f_cs_compare}
  \end{center}
\end{figure}

\newpage
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-014.fig3.eps,width=12cm}
\caption{For each fixed $M_x^2$-bin  measured, the $W$ dependence is fitted to extract an effective intercept $\alpha_{eff}(0)$.
         The results of the fits are shown for each $M_x^2$-bin.}
\label{f_stamp}
  \end{center}
\end{figure}

\newpage
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-014.fig4.eps,width=15cm}
\caption{The $M_x^2$ evolution of $\alpha_{eff}(0)$ is shown from H1 data. 
One additional point is added from the leading proton data \cite{lp}.
For comparison, the shaded band shows the result 
for $\alpha_{\pom}(0)$ from the triple Regge fit,
where the $M_X$ dependence is also fitted.}
\label{f_alphaeff}
  \end{center}
\end{figure}

\begin{figure}[!htb]
  \begin{center}
    \epsfig{figure=H1prelim-02-014.fig5.eps ,width=15cm}
    \caption{\it Illustration of the Mueller-Regge approach to the inclusive photon 
                 dissociation cross section. It relates the sum over all final
                 states X to the forward amplitude for the process $\gamma \; 
                 \alpha_i(t) \rightarrow \gamma \;  \alpha_j(t)$ at an effective centre of
                 mass energy $M_X$ (middle diagram). For sufficiently large
$M_X$, a Regge 
                 expansion for the photon-reggeon scattering amplitude is also
                 appropriate, such that the dissociation cross section may be 
                 decomposed into triple-Regge terms 
as shown in the last diagram of 
                 the figure.}
    \label{f_3regge}
  \end{center}
\end{figure}


\newpage
\begin{figure}[h]
  \begin{center}
  \begin{tabular}{c} 
    \epsfig{file=H1prelim-02-014.fig6a.eps,width=11 cm} \\
    \epsfig{file=H1prelim-02-014.fig6b.eps,width=11 cm} \\
  \end{tabular}
\caption{The results of the Triple Regge fit performed over the present H1 
rapidity gap data, the H1 leading proton data \cite{lp} and 
fixed target data \cite{ft}. 
The details are explained in the text. } \label{f_reggefit}
  \end{center}
\end{figure}

\newpage
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-014.fig7.eps,bbllx=0,bblly=0,bburx=270,bbury=330,width=11cm}
    \caption{A summary of H1 $\alpha_{\pom}(0)$ measurements 
versus $Q^2$ for $\gamma^{(\ast)} p \rightarrow X p$. A 
previous ZEUS result \cite{p_zeus} at
$Q^2 = 0$ is also shown.}
    \label{f_intercepts}
  \end{center}
\end{figure}



\end{document}

