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%===============================title page=============================

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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
%{\it {\large Draft version as of \timestamp}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
                & & & \\
\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03},
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 087} & 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]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
     Dijets in Di{f}fractive Photoproduction at HERA}

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

\begin{abstract}

\noindent
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A measurement is presented of 
di{f}ferential dijet cross sections in low-$|t|$ di{f}fractive
photoproduction processes of the type $ep \rightarrow e X Y$, in which the
photon dissociation system $X$ is separated from a leading low-mass
baryonic system $Y$ by a large rapidity gap. 
The measurement is based on an integrated luminosity of 18 pb$^{-1}$.
Dijet events are identified
using the inclusive $k_T$ cluster algorithm. The cross sections are
given at the level of stable hadrons and correspond to the kinematic
range
\mbox{$Q^2 < 0.01$ GeV$^2$,} \mbox{165 $< W <$ 240 GeV,}
\mbox{$\xpom < 0.03$,} \mbox{$\etjetone > 5$~GeV} and 
\mbox{$\etjettwo > 4$ GeV}.
The measurements are compared with
predictions based on di{f}fractive parton distributions obtained from 
a QCD analysis of inclusive diffractive DIS
and with diffractive dijet production in DIS. 
\end{abstract}

\end{titlepage}

\pagestyle{plain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
An open task in high energy physics is to obtain a consistent
understanding of diffractive hadronic scattering observed in different
processes. Theoretically it is expected that the cross section
$\sigma^D_{\rm incl}$ for inclusive diffractive deep-inelastic
scattering (DIS) factorises into universal diffractive parton
distributions and process dependent hard scattering
coefficients~\bibref{Collins}.
Diffractive parton densities have been determined from DGLAP QCD
fits to inclusive diffractive HERA data~\cite{h1f2d94,h1f2d97} and have been found to be dominated by the gluon distribution.
Diffractive dijet production in DIS~\bibref{disjets} is directly sensitive to the gluon
component of the diffractive exchange and is in
good agreement with the QCD fits to the inclusive diffractive data. 
However, applying the diffractive parton densities to predict
diffractive 
dijet production at the Tevatron, leads to an overestimation of 
the observed rate by one order of magnitude~\bibref{tevjets}.
This discrepancy has been attributed to the presence of the additional
beam hadron
remnant in \ppbar{} collisions which leads to secondary interactions
and a break-down of factorisation.
The suppression, often characterised by a reduced `rapidity gap survival probability,' 
cannot be calculated perturbatively and 
has been parameterised in various ways
(see, e.g.,~\bibref{gapmartin}).

The transition from DIS to hadron-hadron scattering can be studied in
photoproduction at HERA, where the beam lepton emits a
quasi-real photon which interacts with the proton.
Processes in which a real photon participates directly in the hard
scattering are expected to be similar to deep-inelastic scattering of
highly virtual photons. In contrast, processes in which the photon is
first resolved into partons which then initiate the hard scattering
resemble hadron-hadron scattering.
Via resolved photon processes in hard photoproduction,
parton final states are accessible, which are present
in the equivalent \ppbar{} collisions but not in DIS.
Different prescriptions for diffraction can therefore be tested in the regime of hard
diffractive photoproduction.

In this paper, a measurement of diffractive dijet cross sections
in photoproduction is presented, based on data collected with the
H1 detector at HERA. The integrated luminosity is increased by one
order of magnitude with respect to previous results \cite{h1oldjets}.
Jets are defined using the inclusive $k_T$ cluster algorithm with
asymmetric cuts on the jet transverse energies to facilitate future
comparisons with next-to-leading order calculations. The cross sections
are compared with
diffractive dijet production in DIS and with predictions based on
diffractive parton distributions obtained from inclusive $ep$ scattering.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{kinematics}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Kinematics}
\begin{figure}[!h]
\centering
\begin{minipage}[b]{0.5\textwidth}
\centering      
\includegraphics[width=\textwidth,keepaspectratio]{%
H1prelim-02-113.fig1a.eps}\\
{\bf (a)}
\end{minipage}% <- need this comment! 
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[height=4.3cm,keepaspectratio,clip]{%
H1prelim-02-113.fig1b.eps}\\
{\bf (b)}
\end{minipage}
% Caption
\caption{(a) The generic process $ep \rightarrow eXY$, in which the
diffractive system $X$ is separated from the proton system $Y$ by
the largest rapidity gap in the final state particle distribution.
(b) A resolved photon process of diffractive dijet production,
 viewed in terms of the Resolved Pomeron model.}
\label{fig:generic}
\end{figure}

\figref{fig:generic}a shows the generic diffractive process $ep\rightarrow eXY$,
in which the systems $X$ and $Y$ are by definition separated by the 
largest rapidity gap in the hadronic final state, and $Y$ is the proton system.
\figref{fig:generic}b shows a resolved photon diffractive dijet
process.
The beam lepton emits a quasi-real photon which interacts
with the proton, leading to the formation of two jets within the $X$ system.

With $k$ and $P$ denoting the momenta of the incoming
electron\footnote{Throughout the paper, the word `electron' is used
synonymously for positrons.}
and proton, respectively, and $q$ the momentum of the photon,
kinematic variables are defined:
\begin{equation}
s \equiv (k+P)^2; \qquad Q^2 \equiv -q^2; \qquad y\equiv
\frac{q\cdot P}{k\cdot P}.
\end{equation}
$y$ is related to the 
$\gamma p$ centre-of-mass energy $W=\sqrt{y\,s}$.
With $p_X$ and $p_Y$ representing the momenta of the systems $X$ and
$Y$, the data are discussed in terms of 
\begin{equation}
M^2_X\equiv p_X^2; \quad M^2_Y\equiv p_Y^2; \quad t\equiv (P-p_Y)^2;\quad 
\xpom \equiv \frac{q\cdot (P-p_Y)}{q\cdot P}.
\end{equation}
$M_X$ and $M_Y$ are the invariant masses of the systems $X$ and
$Y$, $t$ is the squared 4-momentum transferred between the incoming proton and 
the photon, and \xpom{} is the fraction of the proton beam momentum 
transferred to the system $X$. With $u$ and $v$ denoting the momenta
of the partons entering the hard subprocess from the photon and the
proton, respectively (as indicated in \figref{fig:generic}b), the 
dijet system has squared invariant mass
\begin{equation}
\hat{s} = M^2_{12} = (u+v)^2.
\end{equation}
The longitudinal fractional momenta carried by the partons from
the photon and the diffractive exchange are given by
\begin{equation}
\xgamma=\frac{P\cdot u}{P\cdot q}; \qquad \zpom=\frac{q\cdot v}{q\cdot
(P-p_Y)}.
\end{equation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{models}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Diffractive Parton Distributions}
\label{sec:models}
In ~\cite{h1f2d94,h1f2d97} diffractive parton distributions of the
proton have been determined through DGLAP QCD fits to inclusive
diffractive DIS data. The fits were made under the additional
assumptions that the shapes of the parton distributions do not depend
on \xpom{} and their normalisation is controlled through Regge
phenomenology (resolved pomeron model~\bibref{RPM}). These assumptions
are consistent with the present data.
In~\bibref{h1f2d94}, the leading order (LO) fits which gave the best
description of the data are referred to as `H1 fit 2' and `H1 fit 3.'
Cross sections for diffractive dijet production in DIS have been
presented in~\bibref{disjets}.
The dijet rate in diffractive DIS depends strongly on the diffractive
gluon distribution via boson-gluon fusion.
It has been demonstrated in~\bibref{disjets} that diffractive dijet
production in DIS is described to within 10\% by the parton distributions
corresponding to `H1~fit~2' of the inclusive analysis.
The data themselves have an uncertainty of about 20\%.
The H1 fit 2 parton densities have also been used to predict diffractive 
dijet production
at the Tevatron. There, the measured diffractive
structure function of the anti-proton is overestimated by approximately one order of magnitude
\bibref{tevjets}.

DGLAP QCD
fits to new high precision data for inclusive diffractive DIS
data have been presented in~\bibref{h1f2d97}. 
%For the first time in diffraction,
%the uncertainties in the extracted parton distributions have been
%evaluated. The total uncertainty of the gluon distribution as
%determined in a next-to-leading order (NLO) QCD fit is $\approx 30\%$ at parton
%fractional momentum $\zpomeron \approx 0.5$ and increases to more than $50\%$ for
%$\zpomeron \gtrsim 0.7$. 
The obtained LO parton distributions
lead to
an underestimation of the dijet rate in DIS of about 20\% when $p_T$
is used as the hard scale. These LO parton densities are referred to
as `H1 2002 fit' in the present paper.

The diffractive parton densities can also be used to predict diffractive
dijet cross sections in direct and resolved photoproduction,
where the jet transverse momentum is used for the renormalisation and
factorisation scale and the photon and pomeron parton distributions are convoluted
with standard partonic cross sections. 
Up to now, predictions for dijet rates, based on diffractive parton distributions and the
resolved pomeron model, 
 can only be made in LO QCD and are
subject to large scale uncertainties and model assumptions. It is
therefore useful to compare the dijet rate in photoproduction with
both the new H1 2002 fit to the recent precise inclusive DIS data and, as
directly as possible, to the dijet rate in DIS. The latter can be done
by looking at the ratios of expectations to data in DIS and
photoproduction, or alternatively, by considering H1 fit 2 as an
approximation to the DIS diffractive dijet data within the LO resolved
pomeron model. Note, however, that this comparison suffers from
slightly different kinematic regions and different jet algorithms used
for DIS and photoproduction.

%%% H1 DIS diffractive dijets   and    Tevatron diffractive dijets
%\begin{figure}[!h]
%\centering
%\begin{minipage}[b]{0.5\textwidth}
%\centering      
%\includegraphics[height=0.95\textwidth]{%
%H1prelim-02-113.fig2a.eps}\\
%{\bf (a)}
%\end{minipage}% <- need this comment! 
%\begin{minipage}[b]{0.5\textwidth}
%\centering
%\includegraphics[bb=60 255 490 670,height=0.9\textwidth,keepaspectratio,clip=]{%
%H1prelim-02-113.fig2b.eps}\\
%{\bf (b)}
%\end{minipage}
% Caption
%\caption{(a) H1 diffractive DIS dijet cross section differential in
%\zpomeronjets. Also shown are predictions based on the new H1 fit,
%labelled `H1 2002 \sigmard{} QCD Fit (prel.),' and the old fits, 
%labelled `H1 Fit 2' and `H1 Fit 3'
%(from \bibref{h1f2d97}). (b) The diffractive structure function of the anti-proton extracted
%from diffractive dijet data at the Tevatron as a function of $\beta
%\equiv \zpomeronjets$ \cite{tevjets,h1f2d97}. The predictions based on
%the H1 fits are also shown, with the same labelling as in (a) and
%`\Reg' denoting the contribution from the subleading Reggeon
%exchange (from \bibref{h1f2d97}).}
%\label{fig:dijets}
%\end{figure}


\section{Monte Carlo Simulations}
In the analysis different Monte Carlo programs were used to correct
the data for
detector inefficiencies and migrations, and to compare the measured
cross sections with model predictions.
The RAPGAP 2.08 Monte Carlo program~\bibref{RAPGAP} is used to
obtain predictions
 based on diffractive parton densities
extracted in inclusive diffractive DIS within the resolved pomeron model.
Leading order matrix elements for the hard QCD 2$\rightarrow$ 2
subprocess are convoluted
with parton distributions of the pomeron and the photon, taken
at the scale $\mu^2=\hat{p}_T^2+m_{q\bar{q}}^2$, where $\hat{p}_T$ is the
transverse
momentum of the emerging hard partons and
$m_{q\bar{q}}$ is the mass of the produced quarks.
For the resolved photon component, the leading order GRV
parton distribution functions~\bibref{GRVgamma} are used, which were
found to give a good description of the effective photon structure
function as measured
by H1~\bibref{Kaufmann}.

For the diffractive exchange, the H1 fit 2 parameterisations 
are used to simulate pomeron and sub-leading reggeon exchange, which
contributes at the highest \xpom.
To avoid divergences in the calculation of the matrix elements, 
a cut $\hat{p}_T>2$ GeV is applied on the generator level.
No significant losses are seen for the selected jets with $\etjetone >
5$ GeV and $\etjettwo > 4$ GeV due to this cut.
Higher order effects are simulated using parton showers~\bibref{PS}
in the leading log($\mu$) approximation (MEPS), and the Lund string
model~\bibref{LUND} is used for hadronisation. RAPGAP does not include
remnant interactions.
The PYTHIA 6.1 Monte Carlo program~\bibref{PYTHIA} is used to simulate 
inclusive
dijet photoproduction processes in order to evaluate migrations from 
high $M_Y$ and high \xpom{}. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{expproc}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Procedure}
\subsection{H1 Detector}
A detailed description of the H1 detector can be found in~\bibref{H1det}.
Here, a brief account of the components most relevant to the present 
analysis is given. The H1 coordinate system convention defines the
outgoing proton beam direction as the positive $z$ axis and the polar 
scattering angle $\theta$ such that the pseudorapidity 
$\eta = -\ln \tan (\theta/2)$ increases along $z$. 

The hadronic final state $X$ is measured with a tracking and a
calorimeter system.
 The central $ep$ interaction region is surrounded by two large concentric drift
chambers, located inside a 1.15 T solenoidal magnetic field. Charged particle momenta are measured in the range
$-1.5< \eta <1.5$ with a resolution of $\sigma/p_T=0.01\, p_T/$GeV. A finely segmented electromagnetic and hadronic liquid argon calorimeter (LAr) covers the
range $-1.5 < \eta < 3.4$. The energy resolution is
$\sigma/E=0.11/\sqrt{E/{\rm GeV}}$
 for electromagnetic showers and $\sigma/E=0.50/\sqrt{E/{\rm GeV}}$ for hadrons, as
measured in test beams. A lead/scintillating fibre calorimeter (SPACAL) covers the backward region $-4 < \eta < -1.4$. 

The forward region is covered by the Forward Muon Detector (FMD) and the Proton Remnant Tagger (PRT).
The 3 pre-toroid drift chambers of the FMD are used to detect
particles directly in the region $1.9 < \eta < 3.7$,
 and from larger pseudorapidities via
beam-pipe scattering. The PRT
consists of a set of scintillators surrounding the beam
pipe at $z=26$ m and covers the
region $6 < \eta < 7.5$.

The $ep$ luminosity is measured via the Bethe-Heitler Bremsstrahlung
process $ep \rightarrow ep \gamma$, the final state electron and photon being detected in
crystal calorimeters at $z=-33$ m (electron detector) and $z=-103$ m (photon detector), respectively. 

\subsection{Event Selection}
The data used in this analysis were taken in the 1996 and 1997 running
periods, in which HERA collided 820 GeV protons with 27.5 GeV
positrons. The data are collected using a trigger which requires the 
scattered electron to be measured in the electron detector 
and at least 3 tracks
in the central jet chamber. The geometrical acceptance of the electron
detector limits the measurement to $Q^2 < 0.01 $ GeV$^2$ and 
$0.3 < y < 0.65$. 
A veto cut requiring less than 2 GeV of
deposited energy in the photon detector suppresses
accidental coincidences with Bremsstrahlung events.

Rapidity gap events are selected by requiring the absence of activity 
in the forward direction. No signals above noise levels 
are allowed in the FMD and PRT.
In the LAr, no cluster with an energy of more than
400 MeV is allowed in the region $\eta > 3.2$ . These
selection criteria ensure that the gap between the systems $X$ and $Y$
spans 
at least the region $3.2 < \eta < 7.5$, and that 
$M_Y < 1.6$ GeV and \mbox{$-t < 1$ GeV$^2$.} A cut $\xpom < 0.03$
 further reduces non-diffractive contributions. 

Jets are formed from the tracks and clusters of the hadronic final state $X$, 
 using the
inclusive $k_T$ cluster algorithm~\bibref{kt}
(with a distance parameter of 1.0) in the laboratory frame.
%, which
%is identical to the rest frame of $X$ up to a Lorentz boost along the
%beam axis. 
At least 2 jets are required, with transverse energies $\etjetone > 5$ GeV
and $\etjettwo > 4$ GeV for the leading and subleading jet,
respectively. 
The jet axes are required to lie within the region $-1 < \etajetlab < 2$, well within
the acceptance of the LAr calorimeter. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{reconstruction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Kinematic Reconstruction}
The energy $E'_e$ of the scattered electron is measured directly in
the small scattering angle electron detector and is used to reconstruct 
the fractional photon energy
\begin{equation}
y=E_\gamma/E_e= 1-E'_e/E_e, 
\end{equation}
where $E_e$ is the electron beam energy. 
The hadronic system $X$, containing the jets,
is measured in the LAr and SPACAL calorimeters
and the central tracking system. Calorimeter cluster energies and
track momenta are combined using algorithms which avoid double
counting~\cite{combobj}. 
\xpom{} is reconstructed according to 
\begin{equation}
     \xpom = \frac{\sum_X \left(E+p_z\right)}{2\, E_p},
\end{equation}
in which $E_p$ denotes the proton beam energy and the sum runs over
all objects in the $X$ system.
 The invariant mass of
the dijet system is given by
\begin{equation}
\mjj \equiv \sqrt{\strut \left( \pjetone + \pjettwo \right)^2}, 
\end{equation}
with $\pjetone$ and $\pjettwo$ being the 4-momenta of the leading and
sub-leading jet, respectively.
The estimators \xgammajets{} and \zpomeronjets{} on the fractional 
momenta of the partons entering the hard
subprocess are reconstructed as: 
\begin{equation}
\xgammajets = \frac{\sum_{\rm jets}\, \left( E-p_z
\right)}{2\,y\,E_e}; \qquad
\zpomeronjets = \frac{\sum_{\rm jets}\, \left( E+p_z
\right)}{2\,\xpom\,E_p}.
\end{equation}
The invariant mass of the hadronic system $M_X$ is reconstructed
      according to
\begin{equation}
      M_X=\sqrt{\strut \frac{M_{12}^2}{\zpomeronjets\ \xgammajets}}.
\end{equation}
Cross sections are also measured differentially
in
the transverse momentum of the leading jet \ptjetone,
the mean pseudorapidity \meanetajetlab{} of the leading and sub-leading jet, 
and the jet separation \deltaeta{}:
\begin{equation}
\meanetajetlab \equiv \frac{1}{2} \left( \etajetone + \etajettwo
\right); \qquad
\deltaeta{} \equiv \left| \etajetone - \etajettwo \right|.
\end{equation}
\deltaeta{} is related to the scattering angle in the
centre-of-mass system of the hard subprocess.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{xsmeasurement}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Cross Section Measurement}
%\vspace{0.5cm}
\setlength{\tabcolsep}{0.5cm}
\begin{table}                                                                  
\begin{center}
{\textbf{Cross Section Definition}}\\[1em] 
\begin{tabular}{|c|}
\hline
$0.3 < y < 0.65$ \\
$Q^2 < 0.01\ {\rm GeV}^2$ \\
\hline
$N_{\rm jet} \ge 2$\\
$\etjetone > 5$ GeV \\
$\etjettwo > 4$ GeV \\
$-1 < \eta_{\rm jet(1,2)}^{\rm lab} < 2$\\
\hline
$\xpom <$ 0.03 \\
$M_Y < 1.6$ GeV \\
$-t < 1$ GeV$^2$ \\
\hline
\end{tabular}
\end{center}
\caption[Definition of Cross Sections]{The kinematic domain in which the
cross sections are measured. The jets are reconstructed using the
inclusive $k_T$ algorithm with the distance parameter set to 1.0.}
\label{tab:xsdef}
\end{table}
%\vspace{0.5cm}

The measured cross sections are defined at the level
of stable hadrons. The data are corrected for detector inefficiencies
and migrations of kinematic quantities in the reconstruction using the 
RAPGAP Monte Carlo program. For generated diffractive events, the 
H1 detector response is simulated in detail and the Monte Carlo events
are subjected to the same analysis chain as the data.
The simulation gives a good description of the shapes of all data 
distributions.
According to the simulations, the detector level observables are well
correlated with the hadron level quantities. 

The kinematic region for which the cross sections are measured
is given in \tabref{tab:xsdef}.
The cross sections are presented in terms of a model independent
definition of diffraction, where the two hadronic systems $X$ and $Y$
 are separated by the largest gap in rapidity in the hadronic final state.
Migrations from large \my{} and \xpom{} are corrected for using
PYTHIA. 
Smearing across $M_Y=1.6$ GeV is evaluated
with the DIFFVM~\bibref{DIFFVM} simulation of proton dissociation.

An analysis of systematic uncertainties has been performed in which
the sensitivity of the measurement to variations of the detector
calibration and the Monte Carlo
Models used for correction are evaluated. 
The dominant systematic error on the cross sections arises from the 
uncertainty in the LAr calorimeter energy scale.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
In Figures \ref{fig:xszpomeron}--\ref{fig:xsfig2}, differential cross sections are presented 
in the kinematic range specified in \tabref{tab:xsdef}.
%In all figures, the inner error bars represent the statistical
%uncertainty and the outer error bars show the quadratic sum of
%statistical and systematic errors.
%For the absolute cross sections presented in Figures \ref{fig:xszpomeron}--\ref{fig:xsxgamma}, an
%additional normalisation uncertainty, including the calorimeter scale
%uncertainty, is indicated by the shaded
%band.
%For the normalised cross sections shown in Figures
%\ref{fig:xsfig1}--\ref{fig:xsfig2}, the shaded
%band represents the additional uncertainty resulting from the scale
%uncertainty of the LAr calorimeter.
The figures also show the predictions of the RAPGAP
model using LO diffractive parton
densities obtained in DGLAP QCD fits to inclusive diffractive DIS
data. The predictions are based on the new H1 2002 fit as the best
representation of recent inclusive diffraction data
~\bibref{h1f2d97} and on H1 fit 2, which gives a good
description of diffractive DIS dijet data~\bibref{disjets}.

All predictions are made using the LO GRV
photon parton distributions~\bibref{GRVgamma},
which describe photon structure measurements well~\bibref{Kaufmann}. 
Variations of the renormalisation and factorisation scale $\mu$ by a
factor 2 and 0.5 
lead to changes in the predicted cross sections of about
$20\%$. The parameterisation of the photon structure has been varied within the
experimental constraints, leading to negligible changes of the predicted cross
sections.

For the model predictions based on the new H1 2002
fit parton densities, 
\alphas{} is calculated with $\Lambda_{\rm QCD}=0.2$ GeV for 4 flavours.
The same value was used in the QCD fit extraction of the corresponding
parton densities in~\cite{h1f2d97}.
For the model predictions based on H1 fit 2, the same \alphas{} is
used as in the comparison with
diffractive DIS dijets in~\cite{disjets}.

In a previous contributed conference paper~\cite{ichep02}, 
the values used for the strong coupling constant \alphas{} in the
model predictions were erroneously taken to be too large. 
The calculations of the matrix elements for 
the $2\rightarrow 2$ hard parton scattering cross section 
and the parton shower cascade were affected, resulting in 
predicted dijet cross sections which were
too large by a factor of approximately 1.4.
This mistake has been corrected for the predictions shown here. 


%It is noted that direct and resolved photon interactions depend 
%differently on \alphas. For direct photon interactions, 
%$\sigmahat_{\rm dir} \propto \alphas$, whereas for
%resolved photon processes, $\sigmahat_{\rm res} \propto \alpha_s^2$.
%Therefore, the prediction for the shape of the \xgamma{} distribution
%changed because of the smaller \alphas.
%The shapes of the predictions for the other measured variables 
%are not affected.

\subsection{Dependence on fractional momenta
  $\mathbf{\boldzpom}, \mathbf{\xgamma}$ and $\mathbf{\boldxpom}$}
The cross section
differential in the estimator \zpomeronjets{} of the fractional parton
momentum
from the diffractive exchange is presented in \figref{fig:xszpomeron}.
The new H1 2002 fit 
gives a good description of the diffractive photoproduction dijets.
The RAPGAP prediction based on the H1 fit 2 parton densities
overestimates the normalisation of the data by a factor $\approx 1.4$.

\figref{fig:xsxgamma} shows the cross section differential
in the estimator \xgammajets{} of the fractional photon momentum
taking part in the hard scattering.
The prediction based on the parton densities from the
new H1 2002 fit is also shown. 
%The model gives a good description
%of the data.
The contribution from direct
photon processes (\xgammatrue=1) is indicated by the hatched histogram. 
These interactions dominate the dijet cross section
for $\xgammajets>0.6$. The sum of resolved and direct photon processes
in the model
gives a good description of the data both in normalisation and 
in shape throughout the \xgammajets{} range. There is thus no evidence
for any suppression of the diffractive cross section in the 
region dominated by resolved photons, as might be expected on the
basis of data from the Tevatron \cite{tevjets} or phenomenological
models \cite{gapmartin}.

In \figref{fig:xsxpomeronalpha}, the normalised differential cross
section is shown as function of \xpom. The H1 2002 fit prediction is
shown
for different values of the pomeron intercept. 
While the extreme choice of \alphapom=1.4 is disfavoured, the data
are compatible with \alphapom=1.17 and \alphapom=1.08.
The small ($\approx 5\%$) contribution from the sub-leading reggeon exchange 
is also shown.

\subsection{Dependence on other variables}
The normalised differential cross section is studied for further
variables in Figures \ref{fig:xsfig1} and \ref{fig:xsfig2}. The dependence on $y$ is shown in
\figref{fig:xsfig1}a. The predictions from the 
H1 2002 fit and \mbox{H1 fit 2} are very similar and
 describe the data well. 
The normalised cross section differential in 
the transverse momentum \ptjetone of the leading jet is shown in \figref{fig:xsfig1}b.
Both H1 fits give similar predictions, which decribe the data well.
Normalised cross sections differential in $M_X$, \mjj, \meanetajetlab and
\deltaeta{} are shown in Figures \ref{fig:xsfig1}c, \ref{fig:xsfig1}d, \ref{fig:xsfig2}a and \ref{fig:xsfig2}b, respectively.
As for $y$ and \ptjetone, the shapes of the data are well described by the
predictions based on the parton densities from the H1 QCD fits.

\subsection{Ratio of dijet cross sections in diffractive photoproduction and DIS}
In this section, a comparison is made between diffractive dijet cross 
sections in DIS and in photoproduction.
As shown above, the $\gamma p$ and DIS cross sections can be described
well in shape for all variables using the same LO diffractive parton
densities. 
The ratio of expectation to data for photoproduction is found to be a factor
$1.3 \pm 0.3$ (exp.) larger than the same ratio in DIS, 
where the
uncertainty is estimated using the total experimental errors of both
measurements. 
The deduced factor is independent of the
diffractive parton distributions used in the comparison.
It is, however, obtained using
the LO resolved pomeron model and the error does not take into
account uncertainties due to the different kinematic ranges and jet algorithms.

At the present level of accuracy, no significant suppression of 
the diffractive dijet cross section in photoproduction is observed.
%As indicated by the good agreement of the
%H1 2002 fit prediction with the data throughout the
%\xgammajets{} range (figure \ref{fig:xsxgamma}) the lack of any significant
%suppression of the photoproduction cross section holds for the
%region dominated by resolved photon interactions, as well as direct. 
This result for diffractive photoproduction dijets is to
be compared with a suppression factor of about 10 for single diffractive dijet
production at the Tevatron \cite{tevjets}.


\section{Summary}
Cross sections are presented for the diffractive production of two jets
in the photoproduction regime \mbox{$Q^2<0.01$~GeV$^2$}.
Compared with previous measurements, the luminosity is increased by
one
order of magnitude to $L=18$ pb$^{-1}$.
The inclusive $k_T$ algorithm is used to select events with at 
least 2 jets with
transverse energies larger than 5~GeV and 4~GeV.
Differential cross sections are measured for various 
characteristic variables.

Diffractive parton densities determined in a recent H1 QCD fit to
inclusive diffractive deep-inelastic scattering data lead to predictions for diffractive
dijet photoproduction which describe the shapes and normalisation
 of the data remarkably well.

The photoproduction data are also compared with dijet production
 in diffractive DIS using a leading order calculation based on the resolved
 pomeron model to relate the two measurements.
The ratio of expectation to data for photoproduction is found to be a factor
$1.3 \pm 0.3$ (exp.) larger than the same ratio in DIS.
This factor does not significantly deviate from unity 
at the present level of precision and there is no evidence that it differs
between direct and resolved photon processes. 

At the present level of experimental and 
theoretical uncertainties, a consistent description of dijets in 
diffractive DIS and photoproduction is obtained using diffractive
parton densities determined in QCD fits to inclusive diffractive DIS data.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgements}
We are grateful to the HERA machine group whose outstanding
efforts have made and continue to make 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 the
hospitality which they extend to the non DESY
members of the collaboration.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{bibliography}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}
\def\Journal#1#2#3#4{{#1}{\bf #2} (#3) #4}
\def\NCA{Nuovo Cim.}
\def\NIM{Nucl. Instrum. Methods}
\def\NIMA{{ Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{Nucl. Phys.}   {\bf B}}
\def\PLB{{Phys. Lett.}   {\bf B}}
\def\PRL{Phys. Rev. Lett. }
\def\PRD{{Phys. Rev.}    {\bf D}}
\def\ZPC{{Z. Phys.}      {\bf C}}
\def\EJC{{Eur. Phys. J.} {\bf C}}
\def\CPC{Comp. Phys. Commun. }
\def\PR{{Phys. Rev. }}
\def\PL{{Phys. Lett. }}
\def\RMP{{Rev. Mod. Phys. }}
\newcommand{\etal}{{\em et al.}}
%\bibitem{Pom93} P.~Bruni, G.~Ingelman, {\bibtitlefont Proc. of
%the Europhysics Conference, Marseilles, France, July 1993} 595; siehe
%auch {\tt http://www3.tsl.uu.se/thep/pompyt/}

%%%%%%%%%%%%%%%%%%%% Introduction
\bibitem{Collins} 
J.~Collins, \Journal{\PRD}{57}{1998}{3051} and erratum-ibid. {\bf D61}
(2000) 019902.
\bibitem{h1f2d94} 
H1 Collaboration, C.~Adloff \etal, \Journal{\ZPC}{76}{1997}{613}.
\bibitem{h1f2d97}  H1 Collaboration, paper 980 submitted to 31.
Intl. Conf. on High Energy Physics, ICHEP~2002, Amsterdam.
%\bibitem{H195} H1 Collaboration, T.~Ahmed \etal, \Journal{\PLB}{348}{1995}{681}.
%
\bibitem{disjets} 
H1 Collaboration, C.~Adloff \etal, \Journal{\EJC}{20}{2001}{29}.
%
\bibitem{tevjets}
CDF Collaboration, T.~Affolder \etal, \Journal{\PRL}{84}{2000}{5043}.
%
\bibitem{gapmartin}
E.~Gotsman, E.~Levin, U.~Maor, \Journal{\PLB}{438}{1998}{229}; \\
B.~Cox, J.~Forshaw, L.~ L\"{o}nnblad, [hep-ph/9908464]; \\
A.~Kaidalov, V.~Khoze, A.~Martin, M.~Ryskin, [hep-ph/0306134].

%
%\bibitem{timneanu}
%R.~Enberg, G.~Ingelman, N.~T\^{\i}mneanu, \Journal{\PRD}{64}{2001}{114015}. 
%
\bibitem{h1oldjets}  H1 Collaboration, C.~Adloff \etal, \Journal{\EJC}{6}{1999}{421}.

%%%%%%%%%%%%%%%%%%%% Kinematics
\bibitem{RPM} G.~Ingelman, P.~Schlein, \Journal{\PLB}{152}{1985}{256}.
%\bibitem{SCI} A.~Edin, G.~Ingelman, J.~Rathsman, 
%              Phys. Lett. {\bf B~366} (1996) 371;\\
%              A.~Edin, G.~Ingelman, J.~Rathsman, 
%              Z. Phys. {\bf C~75} (1997) 57.

%%%%%%%%%%%%%%%%%%%% Diffractive Parton Distributions
%%%%%%%%%%%%%%%%%%%% Monte Carlo Simulations
\bibitem{RAPGAP} H.~Jung, \Journal{\CPC}{86}{1995}{147}.
%             see also http://www.desy.de/$\tilde$ jung/rapgap.html.
%
\bibitem{GRVgamma} M.~Gl\"uck, E.~Reya, A.~Vogt,
\Journal{\PRD}{46}{1992}{1973};\\
M.~Gl\"uck, E.~Reya, A.~Vogt,
\Journal{\PRD}{45}{1992}{3986}.
%M.~Gl\"uck, E.~Reya, A.~Vogt,
%\Journal{\ZPC}{53}{1992}{127}.
\bibitem{Kaufmann} H1 Collaboration, C.~Adloff {\em et al.},
\Journal{\PLB}{483}{2000}{36}.
%
\bibitem{PS}   M.~Bengtsson, T.~Sj\"ostrand, \Journal{\ZPC}{37}{1988}{465}.
%
\bibitem{LUND} T.~Sj\"ostrand, \Journal{\CPC}{39}{1986}{347};\\
               T.~Sj\"ostrand, M.~Bengtsson, \Journal{\CPC}{43}{1987}{367}.
\bibitem{PYTHIA} T.~Sj\"ostrand \etal, \Journal{\CPC}{135}{2001}{238}.
%             see also http://www.thep.lu.se/$\tilde$ torbjorn/Pythia.html.

%%%%%%%%%%%%%%%%%%% H1 detector
\bibitem{H1det} H1 Collaboration, I.~Abt \etal, \Journal{\NIMA}{386}{1997}{310 and 348}.
%%%%%%%%%%%%%%%%%%% Event Selection
\bibitem{kt} S.~Ellis, D.~Soper, \Journal{\PRD}{48}{1993}{3160}; \\
S.~Catani, Y.~Dokshitzer, M.~Seymour, B.~Webber,
\Journal{\NPB}{406}{1993}{187}.
%%%%%%%%%%%%%%%%%%% Kinematic Reconstruction
\bibitem{combobj} H1 Collaboration, C.~Adloff \etal, \Journal{\ZPC}{74}{1997}{221}.
%%%%%%%%%%%%%%%%%%% Cross Section Measurement
\bibitem{DIFFVM} B.~List, 
                 Diploma Thesis, Techn. Univ. Berlin, Germany, (1993),
unpublished;\\
B.~List, A.~Mastroberardino, {\em DIFFVM: A Monte Carlo Generator for
diffractive processes in $ep$ scattering} in {\em Monte Carlo
Generators for HERA Physics}, \mbox{A.~Doyle,} \mbox{G.~Grindhammer}, \mbox{G.~Ingelman,}
\mbox{H.~Jung} (eds.), DESY-PROC-1999-02 (1999) 396.
%%%%%%%%%%%%%%%%%%% Results
\bibitem{ichep02}  H1 Collaboration, paper 987 submitted to 31.
Intl. Conf. on High Energy Physics, ICHEP~2002, Amsterdam.
%\bibitem{GRVproton98}  M.~Gl\"uck, E.~Reya, A.~Vogt, hep-ph/9806404.
%\bibitem{GRVproton}  
%M.~Gl\"uck, E.~Reya, A.~Vogt, \Journal{\ZPC}{48}{1990}{471};\\
%M.~Gl\"uck, E.~Reya, A.~Vogt, \Journal{\ZPC}{53}{1992}{127};\\
%M.~Gl\"uck, E.~Reya, A.~Vogt, \Journal{\PLB}{306}{1993}{391}.
%Z. Phys. {\bf C67} (1995) 433.
%\bibitem{LAC} H.~Abramowicz, K.~Charchula, A.~Levy, \Journal{\PLB}{269}{1991}{458}.
%%%%%%%%%%%%%%%%%%% Summary
\end{thebibliography}

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{figures}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% XS absolute in zpomeron %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-02-113.fig2.eps}
% Caption
\caption{Cross section differential in 
\zpomeronjets{} for the diffractive 
production of 2 jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef}.
The inner error bars represent the statistical errors and the outer error bars
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded band shows correlated normalisation uncertainties of the data.
Also shown are two predictions of the RAPGAP model with
LO diffractive parton densities from the new H1 2002
fit (solid histogram) and
the H1 fit 2 
(dashed histogram).
For both predictions, the LO GRV parton distributions of the photon
are used.}
\label{fig:xszpomeron}
\end{figure}

%%% XS absolute in xgamma %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-02-113.fig3.eps}
% Caption
\caption{Cross section differential in 
\xgammajets{} for the diffractive 
production of 2 jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef}.
The inner error bars represent the statistical errors and the outer error bars
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded band shows correlated normalisation uncertainties of the data.
Also shown is the prediction of the RAPGAP model with
LO diffractive parton densities from the new H1 2002
fit. The direct photon contributions (boson gluon fusion and QCD
compton) are indicated by the hatched histogram.
The LO GRV parton distributions of the photon
are used.
}
\label{fig:xsxgamma}
\end{figure}

%%% XS normalised in xpomeron %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-02-113.fig4.eps}
% Caption
\caption{Normalised cross section differential in 
\xpomeron{} for the
diffractive production of 2 jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef}.
The inner error bars represent the statistical errors and the outer error bars
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded band shows the uncertainty of the data resulting from
the uncertainty of the calorimeter energy scale.
Also shown are predictions of the RAPGAP model with
LO diffractive parton densities from the H1 2002 fit, with
intercepts \alphapom=1.17, labelled `H1 2002 fit (prel.),' \alphapom=1.08 (dotted
histogram), and \alphapom=1.4 (dash-dotted histogram). The sub-leading
Reggeon contribution is shown as the hatched histogram.
The LO GRV parton distributions of the photon
are used. 
}
\label{fig:xsxpomeronalpha}
\end{figure}

%%% XS normalised summary 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth,keepaspectratio]{%
H1prelim-02-113.fig5.eps}
% Caption
\caption{Normalised differential cross sections for the
diffractive production of 2 jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef}: (a) $y$, (b) \ptjet, (c) \mx{} and (d) \mjj.
The inner error bars represent the statistical errors and the outer error bars
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded bands show correlated normalisation uncertainties of the data.
Also shown are two predictions of the RAPGAP model with
LO diffractive parton densities from the new H1 2002 fit 
(solid histogram) and
the H1 fit 2 
(dashed histogram).
For both predictions, the LO GRV parton distributions of the photon
are used.
}
\label{fig:xsfig1}
\end{figure}


%%% XS normalised summary 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth,keepaspectratio]{%
H1prelim-02-113.fig6.eps}
% Caption
\caption{Normalised differential cross sections for the
diffractive production of 2 jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef}: (a) \meanetajetlab{} and 
(b) \deltaetalab.
The inner error bars represent the statistical errors and the outer error bars
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded bands show correlated normalisation uncertainties of the data.
Also shown are two predictions of the RAPGAP model with
LO diffractive parton densities from the new H1 2002 
fit (solid histogram) and
the H1 fit 2
(dashed histogram).
For both predictions, the LO GRV parton distributions of the photon
are used.
}
\label{fig:xsfig2}
\end{figure}


\end{document}

