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%===============================title page=============================
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% Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4}
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{\em Nucl. Phys.}   {\bf B}}
\def\PLB{{\em Phys. Lett.}   {\bf B}}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.}    {\bf D}}
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\def\CPC{\em Comp. Phys. Commun.}

\pagestyle{empty}
\begin{titlepage}
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\includegraphics[width=2.cm]{/h1/www/images/H1logo_bw_small.epsi}\\[.2em] \hline
\multicolumn{4}{l}{{\bf
                32nd International Conference
                on High Energy Physics, ICHEP04},
                August~16,~2004,~Beijing} \\
                 & Abstract:        & {\bf 6-0177}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}
 
 
\begin{center}
\begin{Large}
 

{\bf Dijets in Diffractive Photoproduction and Deep-Inelastic
  Scattering at HERA}

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

\begin{abstract}

\noindent
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{abstract}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Measurements are  presented of 
differential dijet cross sections in low-$|t|$ diffractive
photoproduction (photon virtuality $Q^2<0.01$~GeV$^2$) 
and deep-inelastic scattering
processes (DIS, $Q^2>4$~GeV$^2$) 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 measurements are based on an integrated luminosity of 18~pb$^{-1}$
and are performed in the same kinematic ranges besides $Q^2$.
Dijet events are identified in the $\gamma p$ rest frame
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{$\xpom < 0.03$,} \mbox{$\etjetone > 5$~GeV} and 
\mbox{$\etjettwo > 4$ GeV}.
The measurements of dijet rates in photoproduction and DIS are
compared with NLO QCD predictions 
 based on diffractive parton distributions previously obtained from 
a NLO QCD analysis of inclusive diffractive DIS. Whereas the
diffractive dijet rate in DIS is in good agreement with QCD factorisation,
the dijet rate in photoproduction is suppressed by about a
factor 0.5 compared to the NLO QCD prediction.
The results are suggestive of a breakdown of factorisation in photoproduction
for both direct and resolved photon interactions.
This is reminiscent of the observed breakdown of
factorisation in diffractive dijet production in \ppbar{} collisions.
\end{abstract}
\end{titlepage}

\pagestyle{plain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}
Quantum Chromodynamics (QCD) predicts that the cross section
for diffractive deep-inelastic
$ep$ scattering (DDIS) factorises into universal diffractive parton
densities (DPDFs) and process-dependent hard scattering
coefficients~\cite{Collins} (QCD factorisation).
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.

Final state configurations for which a partonic cross section is
perturbatively calculable in QCD include dijet and heavy quark
production, which are directly sensitive to the gluon component of the
diffractive exchange.
Previous measurements of diffractive dijet and D$^*$ meson 
production in DIS have been found
to be described by next-to-leading order (NLO) QCD calculations using
DPDFs and assuming QCD factorisation~\cite{nlojets}. 

However, applying this approach in leading order (LO) QCD calculations
to predict diffractive dijet production in \ppbar{} collisions at the
Tevatron leads to an overestimation of 
the observed rate by approximately one order of
magnitude~\cite{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 breakdown 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.,~\cite{gapmartin}).

The transition from DIS to hadron-hadron scattering can be studied at
HERA in a comparison of scattering processes in DIS and in photoproduction. 
In photoproduction, the beam lepton emits a
quasi-real photon which interacts with the proton ($\gamma p$ collision).
Processes in which a real photon participates directly in the hard
scattering are expected to be similar to the deep-inelastic scattering of
highly virtual photons (``point-like photon''). 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 DIS and photoproduction.

In this paper, measurements of diffractive dijet cross sections
in DIS and photoproduction are presented, based on data collected with the
H1 detector at HERA. For photoproduction 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 
comparisons with NLO predictions. 
Apart from the different ranges for the photon virtuality, the two
measurements are performed in the same kinematic ranges to allow the
closest possible comparison of the cross sections.
The cross sections are compared with NLO QCD predictions based on DPDFs.


%Experimental and theoretical uncertainties can be reduced by a direct  
%comparison of the dijet rate in photoproduction to the dijet rate in DIS
%by looking at the ratios of expectations to data in DIS and
%photoproduction. This should allow to conclude on a possible
%breakdown of factorisation for diffractive photoproduction with much 
%reduced experimental and theoretical uncertainties.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{kinematics}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Kinematics}
%===================
The generic diffractive electron-proton interaction $ep \rightarrow e X Y$ is
illustrated in \figref{fig:generic}. The electron\footnote{Throughout the paper, the word `electron' is used
synonymously for positrons.} (4-momentum $k$)
exchanges a photon ($q$) which interacts with the proton ($P$). 
The final state hadrons produced are, by definition, divided into the
systems $X$ and $Y$, separated by the 
largest gap in the hadron rapidity distribution. The system $Y$ 
lies in the outgoing proton beam direction.

Examples of hard diffractive processes leading to jets in the final state at
HERA are given by the diagrams of \figref{fig:feynBGF} for the
photon-gluon fusion production mechanism (``direct'' or ``point-like'' 
photon process)
 and a process in which the
photon develops hadronic structure from which a single parton undergoes
the hard scatter (``resolved'' or ``hadron-like'' photon process).
In photoproduction, the latter process contributes significantly,
whereas in DIS it is suppressed due to the large photon virtuality.

%%%%
%%%
  \begin{figure}[htb]
   \begin{center}
     \includegraphics[width=0.5\linewidth]{H1prelim-04-113.fig1.eps}
     \caption{Illustration of the generic diffractive process $ep \rightarrow e X
       Y$. The systems $X$ and $Y$ are separated by the largest gap in
       the rapidity distribution of the final state hadrons.}
    \label{fig:generic}
  \end{center}
 \end{figure}

 \begin{figure}[htb]
   \begin{center}
     \textbf{a)}
     \includegraphics[width=0.4\linewidth]{H1prelim-04-113.fig2a.eps}
     \hspace{0.4 cm}
     \textbf{b)}
     \includegraphics[width=0.45\linewidth]{H1prelim-04-113.fig2b.eps} \\
     \caption{Leading order diagrams for diffractive dijet
       production at HERA.
       a) Direct (point-like) photon process (photon-gluon fusion),
       b) resolved (hadron-like) photon process.}
    \label{fig:feynBGF}
  \end{center}
 \end{figure}
%%%%%%
%=======================

The following 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}
The variable $y$ is related to the 
$\gamma p$ centre-of-mass energy $W$ by $W=\sqrt{y\,s - Q^2}$.
With $p_X$ and $p_Y$ representing the 4-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}
The quantities $M_X$ 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 4-momenta
of the partons entering the hard subprocess from the photon and the
proton, respectively (as indicated in \figref{fig:feynBGF}b, 
for the direct process $u=q$), 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 (\xgamma) and the diffractive exchange (\zpomeron) 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}
The measurements are performed in the region of small $\xpom$,
large $t$, and small masses $M_Y$,
where the cross section is dominated by diffractive scattering in
which the proton remains intact.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Diffractive Parton Densities}
\label{sec:models}
\subsection{QCD Factorisation in Diffractive \boldmath{$ep$} Collisions}

QCD predicts that in the leading $\log(Q^2)$
approximation the cross section
for the diffractive process $\gamma^* p \rightarrow Xp$
factorises into universal diffractive parton
distributions of the proton convoluted with process-dependent hard scattering
coefficients~\cite{Collins}.
The DPDFs~\cite{facold,semicl,hautmannsoper} represent probability
distributions for a parton in the proton under the constraint that
the proton remains intact with particular values of
$t$ and $x_\pom$. At leading twist,
\begin{equation}
\frac{{\rm d^2} \sigma(x,Q^2,x_\pom,t)^{\gamma^*p\rightarrow pX}}
{{\rm d} x_\pom \ {\rm d} t} \ = \
\sum_i \int_x^{x_\pom}{\rm d}\xi \
\hat{\sigma}^{\gamma^*i}(x,Q^2,\xi) \
p_i^D(\xi,Q^2,x_\pom,t) \ .
\label{equ:diffpdf}
\end{equation}
The factorisation formula is
valid for large enough $Q^2$ and at fixed $x_\pom$ and $t$.
It also applies to the case of proton dissociation
into a system of fixed small mass $M_Y$.  The partonic cross sections
$\hat{\sigma}^{\gamma^* i}$ are the same as for inclusive DIS and the
diffractive parton distributions $p_i^D$, which are not known from
first principles, should obey the DGLAP evolution equations.
Analogously to inclusive DIS, the diffractive parton
distributions can be determined from measurements by a
DGLAP QCD fit to the inclusive diffractive DIS cross section.  First
analyses of this kind were performed in
\cite{h1f2d94,actw,royonbartelsfits} based on measurements of the
diffractive structure function $F_2^D$ at HERA. 
The test of the QCD factorisation concept in diffractive dijet production
in DIS and photoproduction is the goal of this paper.

\subsection{H1 Diffractive Parton Densities}
\label{sec:h1dpdf}
 Diffractive parton distributions of the
proton have been determined through DGLAP QCD fits to inclusive
diffractive DIS measurements by the H1 collaboration in ~\cite{h1f2d94,h1f2d97}. 
The fits were made under the additional
assumptions that the $\xpom, t$ dependence of the  
parton distributions factorises from the $x, Q^2$ dependence:
\begin{equation}
p_i^D(x_\pom,t,x,Q^2) = f_{\pom/p}(x_\pom,t) \ \, \,
p_{i,\pom}(\beta=x/x_\pom,Q^2).
\label{reggefac}
\end{equation}
This so-called {\em Regge} factorisation assumption, in the literature
often referred to as the {\em resolved pomeron} model~\cite{RPM}, 
implies that the
diffractive exchange can be treated as a quasi-real object with a
partonic structure, given by parton distributions
$p_{i,\pom}(\beta,Q^2)$.  The variable $\beta$ then corresponds to the
longitudinal momentum fraction of the diffractive exchange carried by
the struck parton in the {\em pomeron}. The first term
$f_{\pom/p}(x_\pom,t)$ (also called the {\em pomeron flux factor})
represents the probability for scattering off a pomeron with
particular values of $x_\pom$ and $t$. It should be stressed that no
proof in QCD exists for the assumption of Eq.~(\ref{reggefac}).
At the present level of experimental precision the assumption  is consistent
with inclusive diffractive H1 measurements for $\xpom<0.01$.
At larger $x_\pom$ a contribution from sub-leading meson (``reggeon")
exchange has to be taken into account, such that the diffractive PDFs,
integrated over $t$, are given by:
\begin{equation}
p_i^D(\xpom,\beta,Q^2) = f_{\pom/p}(\xpom)\  p_{i,\pom}(\beta,Q^2) +
                         f_{\reg/p}(\xpom) \ p_{i,\reg}(\beta,Q^2).
\end{equation}
The pomeron and reggeon flux factors are given by
\begin{equation}
f_{\{\pom,\reg\}/p}(\xpom) = \int_{t_{\rm cut}}^{t_{\rm max}}
\frac{e^{B_{\{\pom,\reg\}}t}}{x_\pom^{2\alpha_{\{\pom,\reg\}}(t)-1}} \
{\rm d}t,
\label{eq:fluxfac}
\end{equation}
where $t_{\rm cut}=-1.0 \rm\ GeV^{2}$, $t_{\rm max}$ is the maximum
kinematically allowed value of $t$ and the pomeron and reggeon
trajectories are assumed to be linear functions of $t$:
\begin{equation}
\alpha_{\{\pom,\reg\}}(t)=\alpha_{\{\pom,\reg\}}(0) +
\alpha_{\{\pom,\reg\}}' t.
\label{eq:trajectory}
\end{equation}
The latest DGLAP QCD fits to the most recent available inclusive DDIS
measurements were presented by the H1 Collaboration in \cite{h1f2d97}.
The pomeron parton distributions are composed of a light flavour singlet and a
gluon distribution, which are evolved using the DGLAP equations, both in
leading and in next-to-leading order.  The strong coupling
constant $\alpha_s$ was fixed by setting
$\Lambda^{\overline{\rm MS}}_{\rm QCD}=0.2 \rm\ GeV$ for 4 flavours, using the
1-loop and 2-loop expressions for $\alpha_s$ at LO and NLO, respectively. 
The charm mass is set to $m_c=1.5$~GeV. Pion PDFs are used for the meson.
The result
of the fit is shown in Fig.~\ref{fig:h1pdfs}.
The uncertainty shown for the NLO PDFs includes the
experimental uncertainty arising from the errors of the fitted data
as well as the theoretical uncertainty, estimated by variations of
$m_c$, $\Lambda_{\rm QCD}$ and the parameters used in the pomeron
and reggeon flux factors.
 The total uncertainty of the NLO gluon distribution
is $\approx 30\%$ at a parton
fractional momentum $\zpomeron \approx 0.5$ and increases to more than $50\%$ for
$\zpomeron \gtrsim 0.7$. 
These parton densities are referred to as `H1 2002 fit' in the present paper
and they are used for the
comparison of the measured cross sections with QCD predictions. The
earlier `H1 fit 2' PDFs~\cite{h1f2d94} are used for detector unsmearing.


\begin{figure}[t]
\centering
\includegraphics[width=0.7\linewidth]{H1prelim-04-113.fig3.eps} 
\caption{Quark singlet (left) and gluon (right) distribution
  functions at LO (lines) and NLO (bands) of the
  diffractive exchange at several values of $Q^2$, obtained from DGLAP
  QCD analyses of inclusive diffractive DIS data (from~\cite{h1f2d97}).}
\label{fig:h1pdfs}
\end{figure}

\subsection{Diffractive Dijet Production}
The diffractive parton
densities can be used to predict diffractive final state
cross sections, such as dijet production in DIS and photoproduction.
In these predictions the jet transverse momentum is used for the renormalisation and
factorisation scales.
It has been demonstrated in~\cite{disjets} that diffractive dijet
production in DIS is described to within 10\% by the parton distributions
corresponding to `H1~fit~2.'
%The data themselves have an uncertainty of about 20\%.
The `H1 fit 2' parton densities have also been used to predict diffractive 
dijet production in $\ppbar$ collisions
at the Tevatron. There, the measured diffractive
structure function of the anti-proton is overestimated by approximately one order of magnitude
\cite{tevjets}. 
For the recent `H1 2002 fit' DPDFs, this discrepancy diminishes slightly
but is still approximately a factor 7~\cite{h1f2d97}.  
%NOTE: need fit 2 for comparisons with earlier publication and Tevatron!
In the present paper, diffractive dijet production in DIS and
photoproduction are compared with calculations based on the recent 
`H1 2002 fit' DPDFs.

\section{Monte Carlo Simulations}
In the analyses, different Monte Carlo programs 
are used to correct
the measured distributions for
detector inefficiencies and smearing.
%, and to compare the
%cross sections with theoretical predictions.
The program RAPGAP 2.08~\cite{RAPGAP} is used to
obtain predictions
 based on LO H1 diffractive parton densities
convoluted with LO matrix elements for the hard QCD $2 \rightarrow 2$
subprocess. The appropriate partonic cross sections
are also convoluted with the parton densities of the photon. 
In photoproduction
 the leading order GRV '94
parton distribution functions~\cite{GRVgamma} are used for the
resolved photon component.
These parton densities were
found to give a good description of the effective photon structure
function as measured by H1~\cite{Kaufmann}.
For DIS, processes with a resolved virtual photon are generated
in which the structure of the photon is given by the SAS-2D
parameterisation~\cite{sas2d}, which gives a reasonable description of
inclusive dijet production in a similar $Q^2$ range~\cite{lowq2}.
The PDFs are taken at the scale $\mu^2=\hat{p}_T^2 + 4 m_{q\bar{q}}^2$, where $\hat{p}_T$ is the
transverse
momentum of the emerging hard partons and
$m_{q\bar{q}}$ is the invariant mass of the produced quark pair.

To correct the measured distributions for detector smearing 
the `H1 fit 2' DPDFs are used.
To avoid divergences in the calculation of the matrix elements, 
a cut $\hat{p}_T>3$~GeV is applied at the generator level for DIS and
$\hat{p}_T>2$~GeV
for photoproduction.
No significant losses result from these cuts for the selected 
jets with $\etjetone > 5$ GeV and $\etjettwo > 4$ GeV.
Higher order effects are simulated using parton showers~\cite{PS}
in the leading log($\mu$) approximation (MEPS), and the Lund string
model~\cite{LUND} is used for hadronisation. RAPGAP does not include any
factorisation breaking effects due to 
remnant interactions. Photon radiation from the electron lines
is simulated using the program HERACLES~\cite{heracles}.
The PYTHIA 6.1 Monte Carlo program~\cite{PYTHIA} is used to simulate 
inclusive
dijet photoproduction processes to evaluate migrations from 
high $M_Y$ and high \xpom. For the corresponding correction in DIS,
the RAPGAP program is used in inclusive DIS mode.

\section{Next-to-leading Order QCD Calculations}
QCD factorisation in diffractive DIS \cite{Collins} implies that the
hard scattering cross section for the interaction of the
virtual photon with a parton from the DPDFs is identical to the
non-diffractive case. % for the same values of $\hat{s}$ and $\hat{t}$.
Therefore, programs which
calculate fixed order partonic cross sections for dijet
production in ordinary DIS and photoproduction can also be used in the case of
diffraction. 
% The available programs calculate the cross section up to
%the next-to-leading order ($\mathcal{O}(\alpha_s^2)$) of perturbative
%QCD, using DGLAP evolution.

To calculate diffractive dijet cross sections to NLO in QCD for
deep-inelastic electron-proton scattering, the DISENT
\cite{disent} program is used, as suggested in \cite{hautmann}.  It
was demonstrated in \cite{nlocomp} that calculations using this
program agree very well with the results from other programs.
To obtain NLO cross sections for diffractive dijet photoproduction,
the program by Frixione et~al.~\cite{frixione} is used.
Both programs are interfaced to the NLO diffractive 
parton distributions obtained in
\cite{h1f2d97}.
For the Frixione calculation, the 
GRV HO photon PDFs~\cite{GRVgamma} are used for the hadronic component
of the photon.

The NLO programs are adapted to calculate diffractive cross sections
as follows.
The cross section at a fixed value of $\xpom$ and $t=0$
is calculated by reducing the nominal proton beam energy by a factor
$\xpom$. Since the $x_\pom$ and $t$
dependences of the diffractive PDFs factorise from the $\beta$ and
$Q^2$ dependences, the proton PDFs
can be replaced by the PDFs of the diffractive exchange
$p_{i,\pom}(\beta,Q^2)$. The calculated cross sections are
multiplied by the $t$-integrated flux factor
$f_{\pom/p}(x_\pom)=\int
{\rm d}t\, f_{\pom/p}(x_\pom,t)$.
The same prescription is applied to calculate the contribution from
meson exchange using pion PDFs and the flux factor $f_{\reg/p}(x_\pom)$.
 The partonic configurations are
calculated for $t=0$, such that kinematic effects of a finite value of
$t$ are neglected.  Since the measured cross sections correspond to an
interval in $x_\pom$, the integration over $\xpom$ is approximated by
integrating the results obtained for a set of suitably chosen $\xpom$
points (``$\xpom$ slicing").  The number of $\xpom$ points
is chosen to ensure the calculation is of sufficient precision.

For the (N)LO calculations, the diffractive parton distributions are
used in their respective version. The strong coupling constant
$\alpha_s$ is set to the value assumed in the QCD fit from which the
PDFs were extracted, using the corresponding 1(2)-loop expression and
taking
$\Lambda_{QCD}^{\overline{MS}}=0.2 \rm\ GeV$ for 4 flavours.
The parton configurations resulting from the
calculations are subjected to the same jet algorithm as is used for
the measured cross sections.
The renormalisation scale is set to the transverse energy of the 
leading jet in the photon-proton centre-of-mass frame: $\mu_r=\etjetone$.
For DISENT, the factorisation scale is set to
$\mu_f=6.2$~GeV, corresponding to the average $E_T$ of the
leading jet observed in the DIS measurement.
For the Frixione calculation, the factorisation scale is set to be
equal to the renormalisation scale. 

Since the calculations refer to jets of partons, whereas the
measurements refer to jets of hadrons, the calculated NLO
cross sections have to
be corrected for the effects of hadronisation. In the case of
diffraction, these also influence the diffractive
kinematics, which are defined on the basis of the
largest gap in rapidity in the hadronic final state.
The hadronisation corrections, defined as
\begin{equation}
1+\delta_{\rm had} = \frac{\sigma^{\rm hadron}_{\rm
    dijet}}{\sigma^{\rm parton}_{\rm dijet}} \ ,
\end{equation}
are determined using the Monte Carlo generator RAPGAP with parton
showers enabled to simulate higher orders. 
The parton level cross section is defined in the same way as for the
NLO calculation and is obtained using the same jet
algorithm and the same definitions of the kinematic variables.
Lund string
fragmentation is used for hadronisation.
The size of
the hadronisation corrections in DIS is of the order of a few percent on average,
reaching 20\% in certain regions of the phase space.
The size of the correction decreases with increasing $p_T$ of the jets.
In photoproduction, the correction lowers the parton level cross
section by $\approx 10$~\% on average. The correction is particularly
large in the second highest bin of the \xgammajets{} distribution in
which resolved photon interactions dominate.
Here, events for which  $\xgammajets \approx 1$ at the parton level
are smeared towards lower values due to hadronisation.
Uncertainties on the hadronisation corrections have not yet been
estimated for the results in this paper.
%It can be determined through the use of a different hadronisation model such as e.g. the
%cluster fragmentation~\cite{clusterfrag}.

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

The hadronic final state $X$ is measured by combining information from
 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
\mbox{$-1.5<\eta<1.5$} with a resolution of \mbox{$\sigma(p_T)/p_T \simeq 0.01\, p_T/$GeV.} A
finely segmented electromagnetic and hadronic
 liquid argon calorimeter (LAr) covers the
range \mbox{$-1.5<\eta<3.4$.} The energy resolution is
$\sigma(E)/E \simeq 0.11/\sqrt{E/{\rm GeV}}$
 for electromagnetic showers and $\sigma(E)/E \simeq 0.50/\sqrt{E/{\rm GeV}}$ for hadrons, as
measured in test beams. 
The backward region $-4 < \eta < -1.4$
is covered by a lead/scintillating fibre calorimeter
 (SPACAL,~\cite{spacal})
which is used to identify and measure the scattered electron in DIS events. 

The forward region is covered by the Forward Muon Detector (FMD) and the Proton Remnant Tagger (PRT).
The 3 pre-toroid double layers of 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 (small angle electron detector) and $z=-103$ m
(photon detector), respectively. The small angle electron detector is also used to
tag and measure the scattered electron in photoproduction.

\subsection{Event Selection}
The data used in these analyses were taken in the 1996 and 1997 running
periods, in which HERA collided 820 GeV protons with 27.5 GeV
positrons. The photoproduction data are collected using a trigger which requires the 
scattered electron to be measured in the small angle  electron detector, 
at least 3 tracks
in the central jet chamber and an event vertex. 
A veto cut requiring less than 2 GeV of
energy deposited in the photon detector suppresses
accidental coincidences with Bremsstrahlung events.
DIS events are collected using a trigger which requires the scattered
electron to be detected in the backward electromagnetic calorimeter
(SPACAL) with an energy of at least 6.5 GeV, an event vertex and at least one large transverse  momentum track
in the central region of the detector.

Rapidity gap events are selected by requiring an 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~\cite{kt} 
with a distance parameter of 1.0 in the $\gamma p $ rest frame,
 which for photoproduction is identical to the laboratory frame
 up to a Lorentz boost along the beam axis. 
At least two jets are required, with transverse energies $\etjetone > 5$ GeV
and $\etjettwo > 4$ GeV for the leading and subleading jet,
respectively.\footnote{The `*'
  denotes variables in the $\gamma p$ system.}
The jet axes of the two leading jets are required to lie within the 
region $-1 < \etajetlab < 2$, well within
the acceptance of the LAr calorimeter. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Kinematic Reconstruction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The hadronic system $X$, which contains 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}. 

Cross sections are measured differentially in
the invariant mass $\mjj$ of the dijet system,
the transverse momentum of the leading jet \ptjetone
and the mean pseudorapidity \meanetajetlab{} of the two
jets in the laboratory frame.
The jet separation \deltaetastar{} is reconstructed in the
$\gamma p$ rest frame where it is related to the scattering angle
of the hard subprocess.

\subsubsection{Reconstruction of Photoproduction Events}
In the photoproduction analysis, the energy $E'_e$ of the scattered electron is measured in
the small scattering angle electron detector and $y$ is reconstructed
according to
\begin{equation}
y= 1-E'_e/E_e, 
\end{equation}
where $E_e$ is the electron beam energy. 
The geometrical acceptance of the detector limits the measurement to $Q^2<0.01$~GeV$^2$ and 
$0.3 < y < 0.65$. 

The estimators \xgammajets{} and \zpomeronjets{} of 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}
where the sum runs over the two jets comprising the dijet system and
$E_p$ is the proton beam energy.
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}

The variable \xpom{} is reconstructed according to 
\begin{equation}
     \xpom = \frac{\sum_X \left(E+p_z\right)}{2\, E_p},
\end{equation}
where the sum runs over
all objects in the $X$ system.



\subsubsection{Reconstruction of DIS Events}
In DIS, $E'_e$ is measured in the backward calorimeter SPACAL and $y$
and $Q^2$ are reconstructed using in addition the electron scattering
angle $\theta$ according to
\begin{equation}
y = 1- \frac{E'_e}{E_e}\, \sin^2\frac{\theta_e}{2}, \quad Q^2=4 E_e E'_e\cos^2\frac{\theta_e}{2}.
\end{equation}

The quantity $M_X$ is reconstructed from the sum of all observed energy
deposits above noise levels, excluding the scattered electron:
\begin{equation}
M_X^2 = (\sum_i E_i)^2 - ( \sum_i \vec{p_i})^2.
\end{equation}

The variable \xpom{} is reconstructed according to 
\begin{equation}
     \xpom = \frac {Q^2 + M_X^2 }{Q^2 + W^2 }.
\end{equation}

 The estimators \xgammajets{} and \zpomeronjets{}
are reconstructed as 
\begin{equation}
\xgammajets = \frac{\sum_{\rm jets}\, \left( E-p_z
\right)^*}{\sum_{\rm X }\, \left( E-p_z \right)^*}, \qquad
\zpomeronjets = \frac{ \qsq + M^2_{12}}{\qsq + M^2_X}.
\end{equation}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{xsmeasurement}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Cross Section Measurement}
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 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 regions in which the cross sections are measured
are given in \tabref{tab:xsdef}. For the DIS measurement, the
pseudorapidity range $-3<\eta^*<0$ in the $\gamma p$ frame corresponds
approximately to
the range $-1<\eta<2$ in the laboratory frame.

\setlength{\tabcolsep}{0.5cm}
\begin{table}                                                                  
\begin{center}
{\textbf{Kinematic ranges of cross sections}}\\[1em] 
\begin{tabular}{|c|c|}
\hline
\bf Photoproduction & \bf DIS \\
\hline
\hline
$Q^2 < 0.01\ {\rm GeV}^2$ & $ 4 < Q^2 < 80 \ {\rm GeV}^2$ \\
\hline
\multicolumn{2}{|c|}{$ 165 < W < 242$ GeV} \\
\hline
\multicolumn{2}{|c|}{inclusive $k_T$ jet algorithm, distance
  parameter=1} \\
\hline
\multicolumn{2}{|c|}{$N_{\rm jet} \ge 2$} \\
\hline
\multicolumn{2}{|c|}{$\etjetone > 5$ GeV} \\
\hline
\multicolumn{2}{|c|}{$\etjettwo > 4$ GeV} \\
\hline
$-1 < \eta_{\rm jet(1,2)}^{\rm lab} < 2$ & $-3 < \eta_{\rm jet(1,2)}^*
< 0$ \\
\hline
\multicolumn{2}{|c|}{$\xpom <$ 0.03} \\
\hline
\multicolumn{2}{|c|}{$M_Y < 1.6$ GeV} \\
\hline
\multicolumn{2}{|c|}{$-t < 1$ GeV$^2$} \\
\hline
\end{tabular}
\end{center}
\caption{The kinematic ranges defining the measured cross sections.}
\label{tab:xsdef}
\end{table}
Migrations from large \my{} and \xpom{} are corrected for using
PYTHIA for photoproduction and RAPGAP for DIS. 
The net smearing about the measurement boundary $M_Y=1.6$ GeV is evaluated
with the DIFFVM~\cite{DIFFVM} simulation of proton dissociation.

An analysis of systematic uncertainties has been performed in which
the sensitivity of the measurements to variations of the detector
calibration and the Monte Carlo
models used for acceptance and migration corrections are evaluated. 
The dominant systematic error for the photoproduction analysis arises from the 
uncertainty in the LAr calorimeter energy scale and the migrations
about $\my=1.6$~GeV. For the DIS measurement, the dominant
uncertainty arises from the acceptance and migration corrections.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Comparisons at leading and next-to-leading order of
the QCD calculations based on the diffractive parton distributions
obtained from QCD fits to inclusive diffractive DIS
data~\cite{h1f2d97},
with the measured dijet production 
cross sections in diffractive DIS and photoproduction
are presented in \figrange{fig:diszpomeron}{fig:resscale}.
The inner vertical error bars represent the statistical errors and the
outer error bars denote
the quadratic sum of the statistical and uncorrelated systematic errors.
The shaded band around the data points indicates the correlated normalisation uncertainties of the measurements.

\subsection{Diffractive Dijet Production in DIS}
In~\figref{fig:diszpomeron}a, the differential cross section for dijet
production in diffractive DIS is presented as a function of
\zpomeronjets, an estimator of the longitudinal momentum fraction
of the diffractive exchange entering the hard scattering.
The measurement is compared with NLO calculations obtained with the
DISENT program interfaced to the `H1 2002 fit' diffractive PDFs. The
prediction is corrected for hadronisation effects.
The band around the NLO calculation indicates the uncertainty arising from variations of the
renormalisation scale by factors 0.5 and 2. The uncertainty is
$\approx 20$~\% on average. The variation of the factorisation scale
by factors 0.5 and 2 results in a change of the cross section by
$\pm 10\%$ on average. This factorisation scale uncertainty is not
included in the NLO band.
The uncertainty of the NLO calculation does
not yet include the
uncertainty in the diffractive PDFs
and the uncertainty arising due to the imperfect knowledge of the
hadronisation corrections.
The NLO prediction is in good agreement with the measurement at
$\zpomeronjets<0.6$. At higher values the prediction overestimates the
cross section.  
Within the additional PDF uncertainty the calculation is compatible with
the measurement.

The cross section is shown as a function of $\logxpomeron$ in \figref{fig:diszpomeron}b.
It is well described within the uncertainties by the NLO
calculation. 
The cross section differential in the jet variables \ptjetone, \meanetajetlab,
\deltaetastar{} and \mjj{} is shown in \figref{fig:disjets}.
Also shown are the DISENT predictions at NLO with and without
hadronisation corrections and at LO without hadronisation corrections.
The NLO corrections to the LO cross section amount to a factor
$\approx 1.9$ on
average. The NLO correction decreases smoothly with increasing
\ptjetone{} to 1.5 for $\ptjetone>9$~GeV.
The NLO calculation is in good agreement with the measured
distributions. 
For $\etajetlab<-0.4$ the prediction overestimates the
cross section. This is kinematically related to the excess observed at
high $\xgammajets$ which is shown in \figref{fig:disother}d.
The cross section is shown in \figref{fig:disother}a--c as function of
$Q^2$, $y$ and $M_X$. Good agreement between the measurements and the
calculations is found for these variables.
The concept of QCD factorisation is compatible with the measured
diffractive DIS dijet cross section.
Similar results have been found in a previous diffractive dijet
analysis~\cite{nlojets} and in ~\cite{roger} for diffractive heavy quark
production at HERA.

Also shown in ~\figref{fig:diszpomeron} is the prediction of the 
LO Monte Carlo event generator RAPGAP with
parton showers included as a model for higher order corrections.
The prediction is lower by $\approx 20\%$ compared with the NLO
calculation and is in reasonable agreement with the measured distribution 
within the uncertainties. 

\subsection{Diffractive Photoproduction of Dijets}
The cross section for diffractive dijet photoproduction is presented
in~\figref{fig:gpzpomeron}a as a function of
\zpomeronjets.
The measurement is compared with NLO predictions obtained with the
Frixione et al. program interfaced to the NLO `H1 2002 fit' diffractive PDFs
and the NLO GRV photon PDFs. The
calculation is corrected for hadronisation effects.
The uncertainty shown on the NLO calculation results from simultaneous
variations of the renormalisation and factorisation scales 
by factors 0.5 and 2.
The uncertainty of the NLO calculation does
not yet include the
uncertainty in the diffractive PDFs
and the uncertainty arising from the imperfect knowledge of the
hadronisation corrections.
The NLO prediction overestimates the cross section by a factor
$\approx 2$. 
%Also shown is the LO prediction of the Frixione program using the LO
%`H1 2002 fit' diffractive PDFs and the LO GRV photon PDFs obtained using
%the 1-loop $\alpha_s$. The LO prediction is not corrected for
%hadronisation. 
This is seen also in \figref{fig:gpzpomeron}b
where the cross section is shown as a function of \xgammajets{}.
The same measured cross sections as a function of \zpomeronjets{} and
\xgammajets{} are shown in \figref{fig:gpzpomeronscaled}a and \ref{fig:gpzpomeronscaled}b,
respectively, where an overall normalisation factor 0.5 has been applied to 
the NLO prediction.
With this additional suppression factor for both the
hadron-like and the point-like components, good agreement is obtained
with the measurements except at large $\zpomeronjets$.
The calculation is compatible with the measured cross
section also at large $\zpomeronjets$ when the
uncertainties due to the diffractive PDFs are taken into account.

The cross section is shown as a function of \logxpomeron{} and $y$ in 
\figref{fig:gpzpomeronscaled}c and \ref{fig:gpzpomeronscaled}d, 
respectively. The scaled NLO
prediction describes the measured distributions well within the
experimental uncertainties.
In \figref{fig:gpjetsscaled} the cross section is shown as a function
of the jet variables \ptjet, \meanetajetlab, \deltaeta{} and \mjj. The NLO
prediction with the additional scaling factor 0.5 describes the cross
section well within the experimental and theoretical uncertainties.
All measured distributions can be 
well described if a suppression factor of 0.5 is applied which
suppresses both the direct and the resolved components.


In the following, the effect of a suppression of only those processes
with a significant photon remnant energy is investigated. This is
suggested by models which
attribute factorisation breaking to secondary interactions among spectators.
A suppression factor 0.34 is applied to that part of the
photoproduction NLO calculation for which
at the parton level $\xgammajets<0.9$.
The factor 0.34 has
been calculated in~\cite{kaidalov} as a relative suppression for
resolved photoproduction when the ratios of diffractive to inclusive jet
production are compared in DIS and photoproduction.
The result is shown in \figref{fig:resscale}, where the cross section
is displayed as a function of $\xgammajets$ and $y$.
%To estimate the dependence on the choice of the cut value,
The cut $\xgammajets<0.9$ has been varied between $0.85$ and $0.95$.
For the $\xgammajets$ distribution this leads to changes of the
prediction in the
highest $\xgammajets$ bin of $\pm 10$\%.
This model cannot describe the shapes of the cross section
as a function of $\xgammajets$ and $y$.

Also shown in ~\figref{fig:gpzpomeron} is the prediction of the LO 
Monte Carlo program RAPGAP with
parton showers included as a model for higher order corrections.
The RAPGAP prediction uses the LO versions of the diffractive PDFs and
the photon PDFs. It is in good agreement with the measurement.
In contrast to the situation in DIS where the parton shower
cascade 
significantly increases the cross section,
the
leading order parton level dijet cross section in photoproduction is
reduced by the inclusion of parton showers. 

\subsection{Ratio of Dijet Cross Sections in Diffractive Photoproduction and DIS}
In \figref{fig:ratio} the ratio of the measured cross section to that
predicted by the NLO calculation is shown as a function of the
inelasticity variable $y$ in 
the DIS and photoproduction kinematic regions.
The shown $y$ range corresponds to a
range of $165 < W < 242$~GeV for the $\gamma p$ centre-of-mass
energy $W$.
 The NLO calculations
are based on the `H1 2002 fit' diffractive parton densities and are 
corrected for hadronisation.
The vertical error bars correspond to the quadratic sum of the
statistical errors and the systematic errors of the data
 which are
uncorrelated among the $y$ bins. The error band around the ratio
points specify the normalisation uncertainty on the measurements which
is correlated among the bins.
Shown at the bottom of the figure is the uncertainty on the ratio resulting
from the variation of the renormalisation scale $\mu_r$ in the DIS NLO 
calculation between
$0.5 < \mu_r/\etjetone < 2$. The scale dependence is similar for
the NLO calculation in photoproduction. If the same scale is used for DIS and
photoproduction the scale uncertainty is largely correlated between
the two kinematic ranges.
Not included is the uncertainty resulting from the uncertainty on the
diffractive parton densities and the uncertainty due to the imperfect
knowledge of the hadronisation corrections.

The ratio of data to NLO prediction for DIS is compatible with unity
within the experimental
uncertainties throughout the measured $y$ range.
The ratio for photoproduction is 
around 0.5 throughout the $y$ range indicating a suppression
factor which is independent
of the centre-of-mass energy within the uncertainties.
Integrated over the measured kinematic range the ratio 
of data to NLO expectation for photoproduction is a factor $0.5\pm
0.1$~(exp.) smaller than the same ratio in DIS.
The uncertainty is estimated by adding the total experimental errors of both
measurements in quadrature and does not include uncertainties in the
calculations. 
This factor indicates a breaking of QCD factorisation
in diffractive dijet photoproduction.
The suppression factor found in photoproduction has to be compared with
the factor $\approx 1/7$ needed to account for the suppression in 
single-diffractive dijet
production at the Tevatron~\cite{h1f2d97,tevjets}.

From a comparison of the LO RAPGAP prediction with the cross sections
in DIS and photoproduction no significant suppression is found
in photoproduction. This was previously reported in~\cite{eps03}.

\section{Summary}
Diffractive dijet production has been measured in the same kinematic
regions for DIS and photoproduction using the same jet algorithm to
allow the closest possible comparison of the cross sections.
Next-to-leading order QCD calculations for the production
of dijets have been interfaced with 
diffractive parton distributions determined by H1 from
inclusive diffractive DIS data to test QCD factorisation in
diffraction.
%The parton level QCD calculations have been corrected for
%hadronisation using the leading-order Monte Carlo generator RAPGAP
%with parton showers and the Lund string fragmentation.

The NLO prediction in DIS describes the measured
distributions reasonably well within the theoretical and experimental
uncertainties. The concept of QCD factorisation is compatible with
the measurement results in diffractive DIS.
In photoproduction, the NLO calculation overestimates 
the dijet rate significantly but describes the shapes of the measured
distributions well within the theoretical and experimental
uncertainties. 
The data strongly favour a suppression of both the resolved and the direct
component of the NLO calculation in photoproduction 
by about the same factor $\approx 0.5$ over a model which suppresses
only that part of the calculation for which at the parton level
$\xgammajets<0.9$ by a factor 0.34.
This disfavours models which describe the breaking of factorisation as
the effect of secondary interactions among spectator partons.

The ratio of data to NLO prediction in photoproduction
is a factor $0.5\pm0.1$~(exp.) smaller than the same ratio in DIS.
This shows a breaking of QCD factorisation in diffractive dijet
photoproduction with respect to the same process in DIS.
%The error is determined from the total uncertainty of the
%measurements. Some of the scale uncertainties of the calculations
%cancel in this double ratio if the same scale is used in
%photoproduction and DIS.

%RAPGAP PS vs NLO?

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 31st
Intl. Conf. on High Energy Physics, ICHEP~2002, Amsterdam.
%\bibitem{H195} H1 Collaboration, T.~Ahmed \etal, \Journal{\PLB}{348}{1995}{681}.
%
\bibitem{nlojets}  H1 Collaboration, paper 113 submitted to 
Intl. Europhysics Conference on High Energy Physics, EPS~2003, Aachen.

%
\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}.

%%%%%%%%%%%%%%%%%%%% DPDFs
\bibitem{facold} 
L.~Trentadue, G.~Veneziano, \Journal{\PLB}{323}{1994}{201}; \\
A.~Berera, D.~Soper, \Journal{\PRD}{50}{1994}{4328}; \\
M.~Grazzini, L.~Trentadue, G.~Veneziano, \Journal{\NPB}{519}{1998}{394}.

\bibitem{semicl}
W.~Buchm\"{u}ller, T.~Gehrmann, A.~Hebecker, \Journal{\NPB}{537}{1999}{477}.

\bibitem{hautmannsoper}
F.~Hautmann, Z.~Kunszt, D.~E.~Soper, \Journal{\NPB}{563}{1999}{153}; \\
F.~Hautmann, D.~E.~Soper, \Journal{\PRD}{63}{2000}{011501}.

\bibitem{actw}
L.~Alvero, J.~C.~Collins, J.~Terron, J.~J.~Whitmore, 
\Journal{\PRD}{59}{1999}{074022}.

\bibitem{royonbartelsfits}
C.~Royon, L.~Schoeffel, J.~Bartels, H.~Jung, R.~Peschanski,
\Journal{\PRD}{63}{2001}{074004}.

\bibitem{RPM} G.~Ingelman, P.~Schlein, \Journal{\PLB}{152}{1985}{256}.

\bibitem{disjets} 
H1 Collaboration, C.~Adloff \etal, \Journal{\EJC}{20}{2001}{29}.

%%%%%%%%%%%%%%%%%%%% Kinematics
%\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{sas2d} G.~Schuler, T.~Sj\"ostrand,
\Journal{\PLB}{376}{1996}{193}.

\bibitem{lowq2} H1 Collaboration, C.~Adloff {\em et al.},
\Journal{\EJC}{13}{2000}{397}.

%
\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{heracles} A.~Kwiatkowski, H.~Spiesberger, H.~M\"ohring,
               \Journal{\CPC}{69}{1992}{155}.
\bibitem{PYTHIA} T.~Sj\"ostrand \etal, \Journal{\CPC}{135}{2001}{238}.
%             see also http://www.thep.lu.se/$\tilde$ torbjorn/Pythia.html.
\bibitem{disent} 
S. Catani, M.~H.~Seymour, \Journal{\NPB}{485}{1997}{29}
[erratum-ibid. {\bf B510} (1997) 503].
         
\bibitem{hautmann} 
F.~Hautmann, JHEP {\bf 0210} (2002) 025.

\bibitem{nlocomp}
C.~Duprel, T.~Hadig, N.~Kauer, M.~Wobisch,
``Comparison of next-to-leading order calculations for jet 
cross-sections in deep inelastic scattering" in
A.~Doyle, G.~Grindhammer, G.~Ingelman, H.~Jung (eds.),
Proc. of the Workshop on Monte Carlo Generators for HERA Physics,
DESY-PROC-1999-02 (1999).

\bibitem{frixione}  S.~Frixione, Z.~Kunszt and A.~Signer,
  \Journal{\NPB}{467}{1996}{399};\\
 S.~Frixione, \Journal{\NPB}{507}{1997}{295};\\
see also http://www.ge.infn.it/$\sim$ridolfi/.


%%%%%%%%%%%%%%%%%%% H1 detector
\bibitem{H1det} H1 Collaboration, I.~Abt \etal, \Journal{\NIMA}{386}{1997}{310 and 348}.
\bibitem{spacal} H1 SpaCal Group, T.~Nicholls \etal, \Journal{\NIMA}{374}{1996}{149}; \\
H1 SpaCal Group, T.~Nicholls \etal, \Journal{\NIMA}{386}{1997}{397}.
%%%%%%%%%%%%%%%%%%% 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{roger}  H1 Collaboration, paper 5-0165 submitted to 32nd
Intl. Conf. on High Energy Physics, ICHEP~2004, Beijing.

\bibitem{kaidalov} 
A.~Kaidalov, V.~Khoze, A.~Martin, M.~Ryskin,
\Journal{\PLB}{567}{2003}{61}.

\bibitem{eps03}  H1 Collaboration, paper 087 submitted to 
Intl. Europhysics Conf. on High Energy Physics, EPS~2003, Aachen.

%\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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%% DIS zpomeron, xpomeron %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig4.eps}   % LO PDFs
%nloxsdis.fig4.86.xpom.eps}  % NLOPDFs
% Caption
\caption{Cross section for the diffractive 
production of two jets in the DIS kinematic region specified in
\tabref{tab:xsdef} as a function of a)
\zpomeronjets{} and b) \logxpomeron.
Also shown is the NLO prediction of the DISENT program interfaced to
the `H1 2002 fit' diffractive NLO PDFs and the RAPGAP prediction which 
contains parton showers and is based on the LO PDFs from the same
fit. Both predictions include models of hadronisation effects.
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 around the data points shows correlated normalisation 
uncertainties.
The band around the NLO prediction indicates the uncertainty resulting
from the variation of the renormalisation scale by factors 0.5 and 2.
Not shown is the uncertainty resulting from the uncertainty on the
diffractive parton densities and the uncertainty due to the imperfect
knowledge of the hadronisation corrections.
}
\label{fig:diszpomeron}
\end{figure}

%%% DIS, jet variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig5.eps}
% Caption
\caption{Cross section for the diffractive 
production of two jets in the DIS kinematic region specified in
\tabref{tab:xsdef} as a function of the jet variables a)
\ptjetone, b) \meanetajetlab, c) \deltaetastar{} and d) \mjj.
Also shown is the DISENT prediction based on
the `H1 2002 fit' diffractive PDFs at NLO with and without
hadronisation corrections and at LO without hadronisation corrections.
For details see the caption of \figref{fig:diszpomeron}.
}
\label{fig:disjets}
\end{figure}

%%% DIS, other variables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig6.eps}
% Caption
\caption{Cross section for the diffractive 
production of two jets in the DIS kinematic region specified in
\tabref{tab:xsdef} as a function of the variables a)
$Q^2$, b) $y$, c) $M_X$ and d) \xgammajets.
Also shown is the DISENT prediction based on
the `H1 2002 fit' diffractive PDFs at NLO with and without
hadronisation corrections and at LO without hadronisation corrections.
For details see the caption of \figref{fig:diszpomeron}.
}
\label{fig:disother}
\end{figure}

%%% gp, zpomeron, xgamma %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig7.eps}
%nloxsgp.fig4.eps}   % NLO PDFs   (both DPDFs and Photon PDFs)
%nloxsgp.fig5.eps}   % NLO DPDFs  (but LO Photon PDFs)
% Caption
\caption{Cross section for the diffractive 
production of two jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef} as a function of a) \zpomeronjets{} and b) \xgammajets.
Also shown is the NLO prediction of the Frixione et al. program interfaced to
the `H1 2002 fit' diffractive NLO PDFs and the RAPGAP prediction, which 
contains parton showers and is based on the LO PDFs from the same
fit. Both predictions include the effects of hadronisation.
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 around the data points shows correlated normalisation 
uncertainties.
The band around the NLO prediction indicates the uncertainty resulting
from simultaneous variations of the renormalisation and
factorisation
scales by factors 0.5 and 2.
Not shown is the uncertainty resulting from the uncertainty on the
diffractive parton densities and the uncertainty due to the imperfect
knowledge of the hadronisation corrections.
}
\label{fig:gpzpomeron}
\end{figure}

%%% gp, zpomeron, xgamma scaled %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig8.eps}
%nloxsgpscaled.fig1.eps}
% Caption
\caption{Cross section for the diffractive 
production of two jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef} as a function of a) \zpomeronjets, b) \xgammajets{},
c) \logxpomeron{} and d) $y$.
Also shown is the NLO prediction of the Frixione et al. program interfaced to
the `H1 2002 fit' diffractive PDFs with and without hadronisation
corrections, scaled by an overall normalisation
factor 0.5.
For details see the caption of \figref{fig:gpzpomeron}.
}
\label{fig:gpzpomeronscaled}
\end{figure}

%%% gp, jets scaled %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig9.eps}
% Caption
\caption{Cross section for the diffractive 
production of two jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef} as a function of the jet variables a)
\ptjet, b) \meanetajetlab, c) \deltaeta{} and d) \mjj.
Also shown is the NLO prediction of the Frixione et al. program interfaced to
the `H1 2002 fit' diffractive PDFs with and without hadronisation
corrections, scaled by an overall normalisation
factor 0.5.
For details see the caption of \figref{fig:gpzpomeron}.
}
\label{fig:gpjetsscaled}
\end{figure}

%%% resscaled %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig10.eps}
% Caption
\caption{Cross section for the diffractive 
production of two jets in the photoproduction kinematic region specified in
\tabref{tab:xsdef} as a function of a) \xgammajets{} and b) $y$.
Also shown is the NLO prediction of the Frixione et al. program interfaced to
the `H1 2002 fit' diffractive PDFs with hadronisation
corrections. The part of the NLO calculation for which at the parton level
$\xgammajets<0.9$ is scaled by 0.34.
For details see the caption of \figref{fig:gpzpomeron}.
}
\label{fig:resscale}
\end{figure}

%%% ratio %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}
\centering
\includegraphics[width=0.8\textwidth,keepaspectratio]{%
H1prelim-04-113.fig11.eps}
% Caption
\caption{Ratio of data to NLO prediction for the diffractive 
production of two jets in the photoproduction and DIS 
kinematic regions specified in
\tabref{tab:xsdef} as a function of $y$.
The vertical error bars indicate the uncorrelated experimental 
uncertainty.
The error band around the ratio points shows an additional experimental
normalisation uncertainty.
The NLO predictions are based on the `H1 2002 fit' diffractive PDFs and 
are corrected for hadronisation effects. The uncertainty arising
from the variation of the renormalisation scale
in the DIS NLO calculation is shown at the bottom and is fully 
correlated between bins. 
The range shown in $y$ corresponds to a range
$165<W<242$~GeV in the $\gamma p$ centre-of-mass energy.} 
\label{fig:ratio}
\end{figure}

\end{document}

