%================================================================ % LaTeX file with preferred layout for the contributed papers to % the ICHEP Conference 98 in Vancouver % process with: latex hep98.tex % dvips -D600 hep98 %================================================================ \documentstyle[12pt,epsfig]{article} %\usepackage{epsfig} %\usepackage{amsmath} %\usepackage{hhline} %\usepackage{amssymb} %\usepackage{times} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \newcommand{\GeV}{\rm GeV} \newcommand{\TeV}{\rm TeV} \newcommand{\pb}{\rm pb} \newcommand{\cm}{\rm cm} \newcommand{\hdick}{\noalign{\hrule height1.4pt}} \newcommand{\PPP}{I\!\!P I\!\!P I\!\!P} \newcommand{\PRR}{I\!\!P I\!\!P I\!\!R} \newcommand{\RRR}{I\!\!R I\!\!R I\!\!R} \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } %===============================title page============================= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % BEGINNING OF TEXT % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} %\begin{table} \pagestyle{empty} \begin{titlepage} \noindent {\bf H1-prelim-02-014 \hfill % \epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} \epsfig{file=H1logo_bw_small.epsi,width=2.cm} } \\ \noindent May 2002 \vspace*{3cm} \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 slope parameter $\alpha_{eff}(0)$ obtained from a triple Regge type parameterization 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} \end{titlepage} \pagestyle{plain} % \section{Introduction} \label{s_intro} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% At the HERA electron-proton collider, a large fraction 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 and the reggeon, 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 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 modeled by combining Regge theory \cite{collins} with Mueller's generalization of the optical theorem \cite{op_theorem}. 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 $d\sigma/dM_X^{2} \propto 1/M_X^{2}$. 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, a triple Regge analysis is presented using measurements of large rapidity gap events at three different $W_{\gamma p}$ values $\left< W_{\gamma p} \right> = 231,187$ and 91 GeV, the latter data becoming available because of the installation of a new electron tagger (eTag44) at 44~m. To get better constraints on the fit parameters, the leading proton data \cite{lp} providing a large range in $M_X^2$ and fixed target data \cite{ft} providing a larger leverarm in $W$, were used in a simultanous triple Regge fit. In the framework of triple Regge theory, the intercept of an effective trajectory is extracted from the $W$ dependence as a function of $M_X$. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \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 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). 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 virtuallity $Q^2$ of less than $0.01$ GeV$^2$ and center of mass energies of $W_{\gamma p}$ of $164 \approx 91~\rm GeV$ \newpage As the leading final state proton 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 $M_Y<1.6~\rm GeV$. The sample also includes a fraction of non-diffractive events with an accidental gap in rapidity due to a random fluctuation. Furthermore the selection limits the square of the 4-momentum transfer from the incident proton to the system $Y$ to $|t|<1$ GeV$^2$. \begin{figure} \begin{center} \epsfig{figure=gen_proc.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 $y$ reconstructed from hadrons. Most of this background in the eTag33 data sample was rejected by imposing the following cut: \[ y_{had} = \sum_{i=e,h} (E - P_z)_i/ 2E_e > 0.2. \] 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} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The mass of the system X is measured using the central components of the H1 detector. The $M_X$ mass is reconstructed using the HFS (Hadronic Final State) method which combines particle track and calorimeter information 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. The value $M_X^2$ given by the righthand side of expression (\ref{e_mxrec}) has the advantage of being insensitive to the loss of very backward going hadrons ($E \simeq -P_z$). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Simulations} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The Monte Carlo model used to correct for detector inefficiencies, acceptance corrections, trigger inefficiencies and smearing due to detector resolution was based on the PHOJET \cite{phojet} and PYTHIA \cite{pythia} generators. The generated processes are: \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, covering a range in $W =[164,251]$ GeV, 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 Carlo's 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 $30\pm 1.5$ \% 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 $\left=231$ and $\left=187$ data have been cross checked on a data sample in which a z-vertex was reconstructed 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 \footnote{Stability is defined as the fraction of all events generated in a mass interval that are also reconstructed in that interval.} and purities \footnote{Purity is defined as the fraction of all simulated events reconstructed in a mass interval that are also generated in that interval.} are larger than 30\%. Statistical errors arise from the finite data volume, the samples used in the subtraction of the beamgas 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 differernce 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. %%%%%%%%%%%%%%%%%% \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}), 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 represented by 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} %%%%%%%%%%%%%%%%%% \begin{figure}[!htb] \begin{center} \epsfig{figure=f_3regge.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). Under some assumptions 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} The differential cross section, \[ M_{X}^2\frac{d\sigma_{\gamma p \rightarrow X Y}}{dM_{X}^{2}}\mid_{M_{Y}<1.6~GeV,|t|<1~GeV^2} \] 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 proton elastic cross section $d \sigma _{\gamma p \rightarrow X p} / d M_{X}^{2}$ can be 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 phases $\phi_i(t)$ and $\phi_j(t)$ of 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 $\alpha_{i}(t)$ are not predicted by the model and must be determined from experimental measurements. The form (\ref{E_3Regge1}) is fitted to the data using 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 addional 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. The interference terms 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 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 expexted 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 $Q^2$. A possible indication of a rising pomeron intercept is seen in function of $Q^2$. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Conclusion} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The differential cross section $M_{X} \; d \sigma_{\gamma p \rightarrow X Y} / d M_{X}^{2}$ for $M_Y< 1.6$ GeV and $|t|<1.0$ GeV$^2$ is 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 differential cross section measurement of the rapidity gap data in 3 different $W$ bins the dependence of 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 subleading 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. \begin{thebibliography}{99} \bibitem{photonfluc} J. Sakurai, Ann. Phys. {\bf 11} (1960) 1 \newline D. Yennie, Rev. Mod. Phys. {\bf 47} (1975) 311 \bibitem{collins} P. Collins, An introduction to Regge theory and high energy physics \bibitem{op_theorem} A. Mueller, Phys. Rev. {\bf D2} (1970) 2963 \bibitem{ft} T. Chapin et al., Phys. Rev. {\bf D31} (1985) 17 \bibitem{ppbar1} E-710 Collaboration, N. Amos et al., Phys. Lett. {\bf B301} (1993) 313 \bibitem{ppbar2} CDF Collaboration, F. Abe et al., Phys. Rev. {\bf D50} (1994) 5535 \bibitem{p_zeus} Zeus Collaboration, Zeit. Phys. {\bf C75} (1997) 421 \bibitem{p_paul} H1 Collaboration, J. Adloff et al., Zeit. Phys. {\bf C74} (1997) 221 \bibitem{lp} H1 Collaboration, J. Adloff et al., Nucl. Phys. {\bf B619} (2001) 3 \bibitem{phojet} R. Engel, Zeit. Phys. {\bf C66} (1995) 203 \newline R. Engel, J. Ranft, Phys. Rev. {\bf D54} (1996) 4244 \bibitem{pythia} H. Bengtsson, T. Sj\"ostrand, Comp. Phys. Commun. {\bf 46} (1987) 43 \newline H. Bengtsson, T. Sj\"ostrand, Comp. Phys. Commun. {\bf 82} (1994) 74 \bibitem{thesispaul} P. Newman, A study of the Dynamics of Diffractive Photoproduction at HERA. \bibitem{flux} C. Weizs\"acker, Z. Phys. {\bf 88} (1934) 612 \newline E. Williams, Phys. Rev. {\bf 45} (1934) 729 \newline S. Frixione et al., Phys. Lett. {\bf B319} (1993) 339 \bibitem{raco} H1 Collaboration, S. Aid et al., Zeit. Phys. {\bf C69} (1995) 27 \bibitem{kaidalov} A. Kaidalov, Phys. Rep. {\bf 50} (1979) 157 \bibitem{alberi} G. Alberi, G. Goggi, Phys. Rep. {\bf 74} (1981) 1 \bibitem{goulianos} K. Goulianos, Phys. Rep. {\bf 101} (1983) 169 \bibitem{zotov} N. Zotov, V. Tsarev, Sov. Phys. Usp. {\bf 31} (1988) 119 \end{thebibliography} \begin{figure}[htb] \begin{center} \epsfig{figure=H1prelim-02-014.fig3.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 measurment 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.fig4.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 quality of the fit is 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.fig5.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 comaprison, 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} \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}