%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} %\usepackage{lineno} \usepackage{lscape} \usepackage{rotating} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm %===============================title page============================= \begin{document} % The rest \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle >$}\,} \def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle <$}\,} \newcommand{\trm}{m_{\perp}} \newcommand{\trp}{p_{\perp}} \newcommand{\trmm}{m_{\perp}^2} \newcommand{\trpp}{p_{\perp}^2} \newcommand{\alp}{\alpha_s} \newcommand{\alps}{\alpha_s} \newcommand{\sqrts}{$\sqrt{s}$} \newcommand{\LO}{$O(\alpha_s^0)$} \newcommand{\Oa}{$O(\alpha_s)$} \newcommand{\Oaa}{$O(\alpha_s^2)$} \newcommand{\PT}{p_{\perp}} \newcommand{\JPSI}{J/\psi} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\zpom}{z_{\PO}} \newcommand{\dgr}{^\circ} \newcommand{\gev}{\,\mbox{Ge}} \newcommand{\GeV}{\rm GeV} \newcommand{\xp}{x_p} \newcommand{\xpi}{x_\pi} \newcommand{\xg}{x_\gamma} \newcommand{\xgj}{x_\gamma^{jet}} \newcommand{\xpj}{x_p^{jet}} \newcommand{\xpij}{x_\pi^{jet}} \renewcommand{\deg}{^\circ} \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\rap}{\ensuremath{\eta^*} } \newcommand{\gp}{\ensuremath{\gamma^*}p } \newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} } \newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} } \newcommand {\gapprox} {\, \raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim} \,$}} \newcommand {\lapprox} {\, \raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim} \,$}} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2}, #4 (#3)} \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}} \def\PR{{\em Phys. Rev.} } \def\PRP{{\em Phys. Rep.} } \def\ZPC{{\em Z. Phys.} {\bf C}} \def\ZP{{\em Z. Phys.} } \def\EJC{{\em Eur. Phys. J.} {\bf C}} % \def\EJC{{\em EPJ} {\bf C}} \def\EJA{{\em Eur. Phys. J.} {\bf A}} \def\CPC{\em Comp. Phys. Commun.} \def\SJNP{{\em Sov. J. Nucl. Phys.}} \def\SPJETP{{\em Sov. Phys. JETP}} \def\JETPL{{\em JETP Lett.}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{titlepage} %\linenumbers \noindent \begin{flushleft} DESY 11-166 \hfill ISSN 0418-9833\\ September 2011 \end{flushleft} %\noindent %\today %\noindent %Version 1.0 %\noindent % {\em Editors:} Richard~Polifka~(polir1am@mail.desy.de), Mikhail~Kapishin~(kapishin@mail.desy.de), %\noindent % {\em Referees:} Serguei~Levonian~(levonian@mail.desy.de), Roman~Kogler~(kogler@mail.desy.de) %\noindent %{ \em Comments by:} Monday July 18th % {\em Comments by:} Friday April 23, 2010 \vspace*{2cm} \begin{center} \begin{Large} {\boldmath \bf Measurement of Dijet Production in Diffractive Deep-Inelastic Scattering with a Leading Proton at HERA } \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent The cross section of diffractive deep-inelastic scattering $ep \to e X p$ is measured, where the system $X$ contains at least two jets and the leading final state proton is detected in the H1 Forward Proton Spectrometer. The measurement is performed for fractional proton longitudinal momentum loss $\xpom < 0.1$ and covers the range $0.1 < |t| < 0.7~{\rm GeV}^2$ in squared four-momentum transfer at the proton vertex and $4 0.01$. Higher order QCD radiation is modelled by parton showers. Processes with a resolved virtual photon are also included, with the photon structure function given by the SaS-G 2D LO parameterisation~\cite{2gluphot}. In the two-gluon Pomeron (TGP) model~\cite{bart,bart2}, the diffractive exchange is modelled at LO as the interaction of a colourless pair of gluons with a $q\bar{q}$ or $q\bar{q}g$ configuration emerging from the photon. The model is implemented in the RAPGAP generator. Higher order effects are simulated using parton showers. % The set of the gluon PDFs used in the model is CCFM A0~\cite{RAPGAP} . The unintegrated gluon PDF of set A0~\cite{a0ref} is used. In the soft colour interaction (SCI) model~\cite{lowx3,lowx4}, the diffractive exchange is modelled via non-diffractive DIS scattering with subsequent colour rearrangement between the partons in the final state, which can produce a colour singlet system separated by a large gap in pseudorapidity. A refined version of the SCI model which uses a generalised area law (GAL) for the probability of having a soft colour interaction~\cite{gal} is used in this analysis (SCI+GAL). Predictions for diffractive dijet production within the SCI+GAL model are obtained using the leading order generator program LEPTO~\cite{lepto}. Higher order effects are simulated using parton showers~\cite{leptodglap1, leptodglap2}. The calculations are based on the CTEQ6L~\cite{2gluprot} proton PDFs. The probability for a soft colour interaction, $R$, has been tuned to $0.3$ to describe the total diffractive dijet cross section as measured using the \textquoteleft two central jets' topology. %in this analysis, with $R = 0.3$. In all three models hadronisation is simulated using the Lund string model~\cite{Lund} implemented within the PYTHIA program~\cite{Pythia}. In this analysis the dijet cross section is also compared to NLO QCD calculations. Assuming proton vertex factorisation, NLO QCD predictions for the diffractive partonic dijet cross section are calculated in bins of $x_{I\!\!P}$ using the NLOJET++~\cite{nlojet} program and integrated over the full $x_{I\!\!P}$ range of the measurement. The renormalisation and factorisation scales are set to $\mu_r = \mu_f = \sqrt{Q^2 + \langle P_T^*\rangle^2}$, where $\langle P_T^*\rangle$ is the mean of the transverse momenta of the two leading jets in the hadronic centre-of-mass frame. In order to estimate the uncertainties of the NLO QCD calculations due to missing higher orders, the factorisation scale $\mu_f$ and renormalisation scale $\mu_r$ are varied simultaneously by factors of $0.5$ and $2$. The average uncertainty arising from the variation of the scale is about $40\%$. The DPDFs used in the NLO QCD calculations are %obtained using two fits, H1 2006 Fit B \cite{H1LRG} and H1 2007 Jets \cite{H1DiJets}. The H1 2007 Jets fit is based on the diffractive inclusive and dijet %diffractive data while H1 2006 Fit B is based on inclusive diffractive data only. % and thus provides a better description of the dijet data % the gluon density is *NOT* better constrained, look at the uncertainty bands % the dijet cross-section is better described, which is pretty obvious but also important here %with respect to the DPDF set H1 2006 Fit B. In order to demonstrate the size of the NLO corrections, the QCD calculations are also performed at leading order.% using the same NLOJET++ program and the DPDF set H1 2007 Jets. % For comparison with the diffractive measurements, The NLO QCD partonic cross sections are corrected to the level of stable hadrons by evaluating effects due to initial and final state parton showering, fragmentation and hadronisation. The hadronisation corrections are defined in each bin as a ratio of the cross section obtained at the level of stable hadrons to the partonic cross sections. Two sets of hadronisation corrections have been obtained using the RAPGAP generator using two different parton shower models: parton showers based on leading logarithm DGLAP splitting functions in leading order $\alpha_s$~\cite{DGLAP,DGLAP2,DGLAP3,DGLAP4} and parton showers based on the colour dipole model as implemented in ARIADNE \cite{cdm}. The nominal set of corrections $(1+\delta_{had})$ is taken as the average of the two sets, while the difference between them is considered as the hadronisation uncertainty. The average hadronisation corrections are of about $0.9$ with an estimated uncertainty of about $7\%$. Uncertainties arising due to scale variations and hadronisation corrections are added in quadrature and quoted as a total uncertainty on NLO QCD predictions. In order to compare with the results of the FPS measurements, NLO and LO QCD predictions as well as predictions of the RP model are scaled down by a factor of $1.20$~\cite{H1FPShera2} due to the fact that the DPDF sets H1 2006 Fit B and H1 2007 Jets use LRG data which contain a proton dissociation contribution. The $t$-dependence of the $\pom$ and $\reg$ fluxes implemented in the H1 DPDF sets and the RP model are tuned to reproduce the $t$-dependence measured in inclusive diffractive DIS with a leading proton in the final state~\cite{H1FPS}. \section{Experimental Technique} The $e^{\pm}p$ data used in this analysis were collected with the H1 detector in the years 2005 to 2007 and correspond to an integrated luminosity of $156.6$~pb$^{-1}$. % and were % collected with the H1 detector in $e^-p$ and $e^+p$ interactions % in the years $2005-2007$ in the HERA II running period, with % integrated luminosities of $77.2$ and $79.4\, {\rm pb}^{-1}$, respectively. During this period the HERA collider was operated at electron and proton beam energies of $E_e=27.6$~GeV and $E_p=920$~GeV respectively, corresponding to an $ep$ centre-of-mass energy of $\sqrt{s} = 319$~GeV. \subsection{H1 detector} \label{detector} A detailed description of the H1 detector can be found elsewhere \cite{h1detector,h1detector2,SPACAL}. Here, the components most relevant for the presented measurement are described briefly. A right-handed coordinate system is employed with the origin at the nominal interaction point, where the $z$-axis pointing in the proton beam or forward direction and the $x(y)$ axis points in the horizontal (vertical) direction. The polar angle $\theta$ is measured with respect to the proton beam axis and the pseudorapidity is defined as $\eta = -\ln \tan(\theta/2)$. The Central Tracking Detector (CTD), with a polar angle coverage of $20\deg<\theta<160\deg$, is used to reconstruct the interaction vertex and to measure the momenta of charged particles from the curvature of their trajectories in the $1.16\,{\rm T}$ field provided by a superconducting solenoid. Scattered electrons with polar angles in the range $154\deg\!\!<\!\!\theta_e^\prime\!\! <\!\!176\deg$ are measured in a lead\,/\,scintillating-fibre calorimeter, the SpaCal \cite{SPACAL}. The energy resolution is $\sigma(E)/E\approx 7\%/\sqrt{E[\GeV]}\oplus 1\%$ %with an energy scale uncertainty of $1\%$. as determined from the test beam measurement~\cite{SPACAL_TEST}. A Backward Proportional Chamber (BPC) in front of the SpaCal is used to measure the electron polar angle. % with a precision %of $1$~mrad. Hadrons are measured in the SpaCal with a precision of the energy scale of $7\%$. The finely segmented Liquid Argon (LAr) sampling calorimeter surrounds the tracking system and covers the range in polar angle $4\deg\!\!<\!\!\theta\!\!<\!\!154\deg$ corresponding to a pseudorapidity range $-1.5\!\!<\!\!\eta\!\!<\!\!3.4$. The LAr calorimeter consists of an electromagnetic section with lead as the absorber and a hadronic section with steel as the absorber. The total depth varies with $\theta$ between $4.5$ and $8$ interaction lengths. The energy resolution, determined from test beam measurements~\cite{LAR,LAR2}, is $\sigma(E)/E\approx 11\%/\sqrt{E[\GeV]}\oplus 1\%$ for electrons and $\sigma(E)/E\approx 50\%/\sqrt{E[\GeV]}\oplus 2\%$ for hadrons. %The absolute electromagnetic energy scale is known to $1\%$ precision. The hadronic final state is reconstructed using an energy flow algorithm which combines charged particles measured in the CTD with information from the SpaCal and LAr calorimeters~\cite{hadroo2}. %The absolute hadronic energy scale is known with a %precision of $2\%$ for the measurements presented here. The luminosity is determined by measuring the rate of the Bethe-Heitler process $ep\rightarrow ep\gamma$ detected in a photon detector located at $z=-103$~m. The energy and scattering angle of the leading proton are obtained from track measurements in the FPS \cite{FPS}. Protons scattered at small angles are deflected by the proton beam-line magnets into a system of detectors placed within the proton beam pipe inside two movable stations, known as Roman Pots. Both Roman Pot stations contain four planes, where each plane consists of five layers of scintillating fibres, which together measure two orthogonal coordinates in the $(x,y)$ plane. The fibre coordinate planes are sandwiched between planes of scintillator tiles used for the trigger. The stations approach the beam horizontally % from outside the proton ring and are positioned at $z = 61$~m and $z = 80$~m. The detectors are sensitive to scattered protons which lose less than $10\%$ of their energy in the $ep$ interaction and are scattered through angles below $1$~mrad. The energy resolution of the FPS is approximately $5$~GeV within the measured range. The absolute energy scale uncertainty is $1$~GeV. The effective resolution in the reconstruction of the transverse momentum components of the scattered proton with respect to the incident proton is determined to be \,$\sim\!50$~MeV for $P_x$ and \,$\sim\!150$~MeV for $P_y$, dominated by the intrinsic transverse momentum spread of the proton beam at the interaction point. The scale uncertainties in the transverse momentum measurements are $10$~MeV for $P_x$ and $30$~MeV for $P_y$. Further details of the analysis of the FPS resolution and scale uncertainties can be found elsewhere~\cite{H1FPShera2}. For a leading proton which passes through both FPS stations, the track reconstruction efficiency is $48\%$ on average. \subsection{Kinematic reconstruction} %\noindent The inclusive DIS variables $Q^2$, $x$ and the inelasticity $y$ are reconstructed by combining information from the scattered electron and the hadronic final state using the following method~\cite{H1Diff94}: \begin{eqnarray} y = y_e^2+y_d-y_d^2 \ \ \ , \ \ \ Q^2=\frac{4E_e^2 (1-y)}{\tan ^2(\theta_e^\prime/2)} \ \ \ , \ \ \ x=\frac{Q^2}{sy} \ . \label{eq:y} \end{eqnarray} \noindent Here, $y_e$ and $y_d$ denote the values of $y$ obtained from the scattered electron only (electron method) and from the angles of the electron and the hadronic final state (double angle method), respectively~\cite{dameth}. %\noindent The observable $\xpom$ is reconstructed as: %directly from the energy of the leading proton, such that \begin{equation} \xpom = 1 - E'_p/E_p, \label{eq:xpomfps} \end{equation} \noindent where $E'_p$ is the measured energy of the leading proton in the FPS. The quantity $\beta$ is reconstructed as $\beta = x/\xpom$. The squared four-momentum transfer at the proton vertex is reconstructed using the transverse momentum $P_T$ of the leading proton measured with the FPS and $\xpom$ as described above, such that: \begin{eqnarray} t = t_{\rm min} - \frac{P_T^2}{1-\xpom} \ \ \ , \ \ \ t_{\rm min} = - \frac{\xpom^2 m_p^2}{1-\xpom} \ , \label{eq:tdef} \end{eqnarray} \noindent where $|t_{\rm min}|$ is the minimum kinematically accessible value of $|t|$. % and $m_p$ is the proton mass. The absolute resolution in $t$ varies over the measured range from $0.06$~GeV$^2$ at $|t| = 0.1$~GeV$^2$ to $0.17$~GeV$^2$ at $|t| = 0.7$~GeV$^2$. An estimator for the momentum fraction $\zpom$ is defined at the level of stable hadrons as: \begin{equation} \zpom = \frac{Q^2+M_{jj}^2}{\xpom y s}, \label{eq:zpomdef} \end{equation} \noindent where $M_{jj}$ denotes the invariant mass of the dijet system. The cross sections are studied in terms of the DIS variables $y, Q^2, \beta, \zpom$, the proton vertex variables $\xpom$ and $t$, the jet variables $P_{T}^*$ and $\eta$, and % as well as the variables \begin{eqnarray} \langle P_T^*\rangle = \frac{1}{2}(P_{T,1}^* + P_{T,2}^*) \ \ , \ \ |\Delta\eta^*|=|\eta_1^*-\eta_2^*| \ \ , \ \ |\Delta\phi^*|=|\phi_1^*-\phi_2^*| \ , \label{eq:detadef} \end{eqnarray} \noindent where $P_{T,1}^*, \eta_1^*,\phi_1^*$ and $P_{T,2}^*, \eta_2^*,\phi_2^*$ are transverse momenta, pseudorapidities and azimuthal angles of the axes of the leading and next-to-leading jets, respectively, reconstructed in the hadronic centre-of-mass frame. The indices $1$, $2$ stand for the two jets used in the specific analyses. \subsection{Event selection} %This section describes the cut flow of the \textquoteleft two central jets' and \textquoteleft one central + one forward jet' analyses. The events used in the \textquoteleft two central jets' and \textquoteleft one central + one forward jet' analyses are triggered on the basis of a coincidence of a signal in the FPS trigger scintillator tiles and in the electromagnetic SpaCal. The trigger efficiency, calculated using events collected with independent triggers, is found to be $99\%$ on average and is independent of kinematic variables. \subsubsection{DIS selection} % Several selection criteria are applied in order to suppress % beam-related background % and events in which % the incoming electron loses % significant energy through QED % radiation. The selection of DIS events is based on the identification of the scattered electron as the most energetic electromagnetic cluster in the SpaCal calorimeter. The energy $E_e^\prime$ and polar angle $\theta_e^\prime$ of the scattered electron are determined from the SpaCal cluster %, linked to a reconstructed charged particle track in the BPC or CTD, and the interaction vertex reconstructed in the CTD. The electron candidate is required to be in range $154\deg\!<\!\theta^{\prime}_e\!<\!176\deg$ and $E_e^\prime > 10$~GeV. In order to improve background rejection, an additional requirement % on the radius on the % on the energy weighted cluster radius of $r_{\rm clus} < on the transverse cluster radius, estimated using square root energy weighting~\cite{ELAN}, of less then $4$~cm is imposed. The reconstructed $z$ coordinate of the event vertex is required to be within $\pm 35$~cm of the mean position. At least one track originating from the interaction vertex and reconstructed in the CTD is required to have a transverse momentum above $0.1$~GeV. The quantity $\sum(E-P_z)$, summed over the energies and longitudinal momenta of all reconstructed particles including the electron, is required to be between $35$~GeV and $70$~GeV. For neutral current DIS events this quantity is expected to be twice the electron beam energy when neglecting detector effects and QED radiation. This requirement is applied to remove radiative DIS events and photoproduction background. %Finally, the measurement In order to ensure a good detector acceptance the measurement is restricted to the ranges $45$~GeV and $P_{T,2}^*>4$~GeV for the leading and next-to-leading jet, respectively. Asymmetric cuts are placed on the jet transverse momenta to restrict the phase space to %K.D. a region where NLO calculations are reliable. The axes of the jets are required to lie within the pseudorapidity range $-1<\eta_{1,2}<2.5$ in the laboratory frame. The selected event topology is similar to that in the LRG dijet data used in the DPDF fits~\cite{H1DiJets,ZEUSDPDF}. This data selection is used for testing the proton vertex factorisation hypothesis and the DPDFs in processes with a leading proton in the final state. %It also reaches higher values of $\xpom$ than is possible with the LRG method. \renewcommand{\arraystretch}{1.35} \begin{table}[ht] \begin{center} \begin{tabular}{| c | c| c|} \hline % & & \\ Selection & two central jets & one central + one forward jet \\ %& & \\ \hline %& & \\ DIS & \multicolumn{2}{|c|} {$4 5~\GeV$ & $P_{T,c}^*,P_{T,f}^* > 3.5~\GeV$ \\ Jets &$P_{T,2}^* > 4~\GeV$ & $M_{jj} > 12~\GeV$ \\ &$-1 < \eta_{1,2} < 2.5$ & $-1 < \eta_{c} < 2.5$ \\ & & $1 < \eta_{f} < 2.8 , \eta_f > \eta_{c}$ \\ %& & \\ \hline \end{tabular} \end{center} \caption{Phase space of the diffractive dijet FPS measurements.} \label{kinrange} \end{table} The selection of the \textquoteleft one central + one forward jet' topology is motivated by the study of diffractive DIS processes in a phase space where deviations from DGLAP parton evolution may be present. The requirement of a forward jet suppresses the parton $p_T$ ordering which is assumed by DGLAP evolution. At least one central jet with $-1<\eta_c<2.5$ and one forward jet with $1<\eta_f<2.8$, where $\eta_f > \eta_c$, are required with $P_{T}^*>3.5$~GeV. %The axes of the jets are required to lie within the range $-1<\eta_C<2.5$, % $1<\eta_F<2.8$ and $\eta_F > \eta_C$. In addition, the invariant mass of the central-forward jet system is required to be larger than $12$~GeV to avoid the phase space region in which NLO QCD calculations are unreliable. % less reliable. The selection criteria for the %\textquoteleft two central jets' and \textquoteleft one central + one forward jet' two analyses are summarised in table~\ref{kinrange}. The \textquoteleft two central jets' data sample contains $581$ events and the \textquoteleft one central + one forward jet' data sample contains $309$ events. \section{Corrections to the Data and Cross Section Determination} \subsection{Background subtraction} \label{bgncor} The selected data samples contain background events arising from random coincidences of non-diffractive DIS events, %resulting in activity in the central H1 detector, with off-momentum beam-halo protons producing a signal in the FPS. %Beam-halo background in the FPS also originates from interactions of beam protons with the residual % gas in the beam-pipe or with the beam collimators. The beam-halo background contribution is estimated statistically by combining the quantity $\sum(E+P_z)$ summed over all reconstructed particles in the central detector in DIS events (without the requirement of a track in the FPS) with the quantity $\sum(E+P_z)$ for beam-halo protons from randomly triggered events. The $\sum(E+P_z)$ spectra for leading proton and beam-halo DIS events for both dijet event topologies are shown in figure~\ref{fig:epzplot}. The background distribution %, resulting from the convolution of the $\sum(E+P_z)$ spectra, is normalised to the FPS DIS data distribution in the range $\sum(E+P_z)>1880$~GeV where the beam-halo background dominates. The ratio of signal to background depends on the signal cross section and is found to be considerably larger than in the inclusive diffractive DIS processes measured with the FPS detector~\cite{H1FPShera2}. After the selection cut $\sum(E+P_z)<1880$~GeV the remaining background amounts on average to about $5\%$. The background is determined and subtracted bin-by-bin using this method. \subsection{Detector simulation} \label{mc} Monte Carlo simulations are used to correct the data for the effects of detector acceptance, inefficiencies, migrations between measurement intervals due to finite resolution and QED radiation. The response of the H1 detector is simulated in detail using the GEANT3 program~\cite{Geant3} and the events are passed through the same analysis chain as is used for the data. The reaction $ep \rightarrow eXp$ is simulated with the RAPGAP program~\cite{RAPGAP} using the RP model and the DPDF set H1 2006 Fit B as described in section~\ref{models}. QED radiative effects are simulated using the HERACLES~\cite{HERACLES} program within the RAPGAP event generator. % In the \textquoteleft two central jets' analysis the $\eta_2^*$ distribution %of the softest jet of the Monte Carlo simulation is reweighted in order to describe the experimental data. %For the $\eta_2^*$ distribution in the \textquoteleft two central jets' sample reweighting of the Monte Carlo simulation is applied in order to describe the experimental data. A similar procedure is applied to the $\eta_f^*$ distribution in the \textquoteleft one central + one forward jet' sample. More details of the analysis can be found elsewhere \cite{RPThesis}. A comparison of the FPS data and the RAPGAP simulation is presented in figure~\ref{fig:fpsplots1} for the variables $\xpom$ and $|t|$ reconstructed with the FPS detector. The contributions of light quarks (uds) to $\pom$ and $\reg$ exchanges and of charm quarks to $\pom$ exchange are also shown in the $\log_{10}(\xpom)$ distribution. Figure~\ref{fig:fpsplots2} presents the data and the Monte Carlo distributions of the variables $P_{T,1}^*, |\Delta\eta^*|$ and $\zpom$ for the \textquoteleft two central jets' sample and of the variables $\langle P_T^*\rangle, \eta_f$ and $\zpom$ for the \textquoteleft one central + one forward jet' topology. For this comparison $\zpom$ is reconstructed from the scattered electron and the hadronic final state in the H1 detector. The MC simulation reproduces the data within the experimental systematic uncertainties. \subsection{Cross section determination} \label{xsect} In order to account for migration and smearing effects and to evaluates the dijet cross sections at the level of stable hadrons, matrix unfolding of the reconstructed data is performed~\cite{blobel}. The resolution and acceptance of the H1 detector is reflected in the unfolding matrix {\bf A} which relates reconstructed variables $\vec{y}_{{\rm rec}}$ with variables on the level of stable hadrons $\vec{x}_{{\rm true}}$ via the formula ${\bf A}\vec{x}_{{\rm true}} = \vec{y}_{{\rm rec}}$. The matrix {\bf A}, obtained for each measured distribution using the RAPGAP simulation, is constructed within an enlarged phase space in order to take into account possible migrations from outside of the measured kinematic range. %Simulated dijets with transverse energy reconstructed below the selection criteria and single jet events are treated as a background to the reconstructed dijet sample. %K.D. The following sources of migrations to the analysis phase space are considered: migrations from low $Q^2$, from low $y$, from large $\xpom$, from low $P_T$ jets, from the single jet topology, fulfilling the $P_T$ requirements for the leading jet as given table \ref{kinrange}, and in case of the \textquoteleft one central + one forward jet' analysis from large $\eta_f$. In order to treat %determine the contamination of the measurement %in the visible phase space defined in table \ref{kinrange} by these migrations correctly the analysis is performed in an extended phase space which includes side-bins in $\vec{y}_{rec}$ and $\vec{x}_{true}$ for each of the migration sources listed above. %%For this purposes, the outside bins of the migration matrix are constructed. %Due to the resolution of the H1 detector, following migrations of events are considered: from the phase space of jets with transverse momenta below the selection cuts, events below the $Q^2$ cut, events above the $\xpom$ cut and for the \textquoteleft one central + one forward jet' topology also the migrations in $\eta_f$. In order to estimate the relative normalisation of the migrations correctly, corresponding additional measurements of low $P_T$ dijet events, inclusive monojet events and dijet events with low $Q^2$ have been performed and incorporated into the migration matrix {\bf A} in terms of side-bins. The unfolded true distribution on the level of stable hadrons is obtained from the measured one by minimising a $\chi^2$ function defined as \begin{equation} \chi^2 = \chi^2_A + \tau^2\chi^2_L = 1/2(\vec{y}_{{\rm rec}} - {\bf A}\vec{x}_{{\rm true}})^T{\bf V}^{-1}(\vec{y}_{{\rm rec}} - {\bf A}\vec{x}_{{\rm true}}) + \tau^2\chi^2_L \end{equation} \noindent where $\chi^2_A$ is a measure of a deviation of ${\bf A}\vec{x}_{{\rm true}}$ from the data bins $\vec{y}_{{\rm rec}}$. The matrix ${\bf V}$ is the covariance matrix of the data, based on the statistical uncertainties. In order to avoid statistical fluctuations, the regularisation term $\chi^2_L$ is implemented into the $\chi^2$ function and defined as $\chi^2_L=(\vec{x}_{{\rm true}})^2$. The regularisation parameter $\tau$ is tuned in order to minimise the bin-to-bin correlations of the covariance matrix {\bf V}. Further details of the unfolding method can be found in~\cite{unf,unf2} %Cross sections are obtained at the Born level by applying corrections for QED %radiative effects. These corrections amount to about $5\%$ on average. The Born level cross section is calculated in each bin $i$ according to the formula: \begin{equation} \sigma_i(ep \rightarrow ejjX^{\prime}p) = \frac{x_i}{\mathcal{L}}(1+\delta_{rad}) \end{equation} \noindent where $x_i$ is the number of background subtracted events %corrected for the detector acceptance, trigger and detector % inefficiencies and migrations between measurement intervals as obtained with the unfolding procedure described above, $\mathcal{L}$ is the total integrated luminosity % the $\epsilon_{FPS}$ is the track reconstruction efficiency of the FPS detector and $(1+\delta_{rad})$ are the QED radiative corrections which amount to about 5\% on average. The differential cross sections are obtained by dividing by the bin width. % Matrix unfolding~\cite{unf,unf2,blobel} of the reconstructed data is performed to account for migration and smearing % effects and evaluates the dijet cross sections at the level of stable hadrons. % The cross section is defined at the level of stable hadrons and calculated according to the formula % \begin{equation} % \sigma(ep \rightarrow ejjX^{\prime}p^{\prime}) = \frac{N_{sig}}{\mathcal{L}}(1+\delta_{rad}), % \end{equation} % \noindent % where $N_{sig}$ is the number of background subtracted events % after unfolding % , $\mathcal{L}$ is the total integrated luminosity % and $(1+\delta_{rad})$ are QED % radiative corrections which amount to about $5\%$ on average. % The cross sections are measured integrating over the full kinematic range of the dijet topologies specified in % table~\ref{kinrange} and also % single-differentially as a function of variables which characterise the hard scattering process. \section{Systematic Uncertainties on the Measured Cross Sections} \label{systs} The systematic uncertainties are implemented into the response matrix {\bf A} and propagated through the unfolding procedure. They are considered from the following sources listed below. \begin{itemize} \item The uncertainties on the leading proton energy and on the horizontal and vertical projections of the proton transverse momentum are $1$~GeV, $10$~MeV and $30$~MeV, respectively (section~\ref{detector}). The corresponding average uncertainties on the cross section measurements are $0.5\%$, $5.3\%$ and $2.2\%$. The dominant uncertainty originates from the FPS acceptance variation as a function of the leading proton transverse momentum in the horizontal projection. The above uncertainties result from the run-by-run variations of the incoming proton beam angle and of the FPS detector positions relative to the proton beam, as well as %uncertainties from the imperfect knowledge of the HERA beam magnet optics. \item The uncertainties of the measurements of the scattered electron energy $E'_e$ ($1\%$) and angle $\theta_e^\prime$ ($1$~mrad) on the SpaCal calorimeter lead to an average systematic uncertainty of the cross section of $1.5\%$ and $2.8\%$, respectively. \item The systematic uncertainty arising from the hadronic final state reconstruction is determined by varying the energy scale of the hadronic final state by $\pm 2\%$ as obtained using %with a dedicated calibration~\cite{iter}. The $2\%$ uncertainty of the calibration is confirmed by studies in the region of low jet transverse momenta and low photon virtuality. This source leads to an average uncertainty of the cross section measurements of $6.2\%$ for production of two central jets and $9.5\%$ for production of one central and one forward jet. \item The model dependence of the acceptance and migration corrections is estimated by varying the shapes of the distributions in the kinematic variables $\langle P_{T}^* \rangle$, $\eta_2^*$, $\eta_f^*$, $\xpom$, $\beta$ and $Q^2$ in the RAPGAP simulation within the constraints imposed on those distributions by the presented data. The $\eta_2^*$ and $\eta_f^*$ reweightings are varied within the errors of the parameters of the reweighting function, which amount up to a factor $4$. The $\langle P_T^*\rangle$ distribution is reweighted by $\langle P_{T}^* \rangle^{\pm 0.15}$, the $\xpom$ distribution by $(1/\xpom )^{\pm 0.05}$, the $\beta$ distribution by $\beta^{\pm 0.05}$ and $(1- \beta )^{\mp 0.05}$ and the $Q^2$ distribution by $\log(Q^2)^{\pm 0.2}$. For the \textquoteleft two central jets' selection the largest uncertainty is introduced by the $\eta_2^*$ reweighting ($4\%$), followed by $\beta$ ($2.7\%$), while the reweights in $\xpom$, $\langle P_{T}^* \rangle$ and $Q^2$ result in an overall uncertainty of $2.3\%$. The uncertainties for the \textquoteleft one central + one forward jet' topology are $12.8\%$ for the $\eta_f^*$ reweighting, followed by $\langle P_{T}^* \rangle$ ($2.1\%$), while the reweights in $\xpom$, $\beta$ and $Q^2$ result in an overall uncertainty of $1.8\%$. \item Reweighting the $t$ distribution by $e^{\pm t}$ results in a normalisation uncertainty of $4.2\%$ for the extrapolation in $t$ from the measured range of $0.1 < |t| < 0.7~\GeV^2$ to the region $|t_{\rm min}| < |t| < 1~{\GeV}^2$ covered by the LRG data \cite{H1DiJets}. The uncertainty arising from the $t$ reweighting within the FPS acceptance range of $0.1<|t|<0.7~\GeV^2$ is on average $1.4\%$. \end{itemize} The following uncertainties are considered to influence the normalisation of all measured cross sections in a correlated way: \begin{itemize} \item %The systematics related to the proton beam-halo background has been estimated by varying the amount of % background subtracted from the measured $E+P_z$ spectra. Two sources of systematics related to the background subtraction are taken into account: the energy scale uncertainty and the limited statistics in the data sample without the $\sum(E+p_z)$ cut. Firstly, the beam-halo spectrum is shifted within the quoted uncertainties of the hadronic energy scale and proton energy scale. Secondly, the normalisation of the background spectrum is shifted by $1\pm1/\sqrt{N_{{\rm bkg}}}$, where $N_{{\rm bkg}}$ is the number of events in the FPS data sample in the range $\sum(E+P_z) > 1880$~GeV. The uncertainties from these two sources are combined in quadrature. The uncertainty of the proton beam-halo background is considered as a normalisation error and found to be $3.5\%$ for the production of two central jets and $1.5\%$ for the production of one central and one forward jet. \item A normalisation uncertainty of $1\%$ is attributed to the trigger efficiencies, evaluated using event samples obtained with independent triggers. \item The uncertainty in the FPS track reconstruction efficiency results in a normalisation uncertainty of $2\%$. \item A normalisation uncertainty of $3.7\%$ arises from the luminosity measurement. \end{itemize} \noindent The systematic errors shown in the figures are obtained by adding in quadrature all the contributions except for the normalisation uncertainties, leading to an average uncertainty of $11\%$ for \textquoteleft two central jets' and $17\%$ for \textquoteleft one central + one forward jet'. The overall normalisation uncertainty of the cross section measurement obtained by adding in quadrature all normalisation uncertainties is $7\%$ for \textquoteleft two central jets' and $6.2\%$ for \textquoteleft one central + one forward jet'. %The normalisation uncertainty of t The cross section measurement in $t$ has a normalisation uncertainty $4.6\%$. \section{Results} The $ep$ cross section for diffractive production of two central jets and one central + one forward jet, integrated over the full measured kinematic range (table~\ref{kinrange}), is given in table~\ref{ccftable} together with the predictions obtained with NLO QCD calculations. \begin{table}[ht] \begin{center} \begin{tabular}{| c | c| c|} \hline & two central jets & one central + one forward jet \\ & $\sigma$ [pb] & $\sigma$ [pb] \\ %& & \\ \hline %& & \\ %Data & $254.3 \pm 20.1~ (\rm{stat.}) \pm 26.7~\rm{(syst.)}$ & $150.1 \pm 18.9~ (\rm{stat.}) \pm 25.7~\rm{(syst.)}$ \\ %\hline %NLO QCD &&\\ %H1 2006 Fit B & $269.7~ ^{+133.9}_{-52.7}~\rm{(scale)}~ \pm 15.8~\rm{(hadr.)}$ &$148.3~ ^{+101.5}_{-33.4}~\rm{(scale)} \pm 5.6~\rm{(hadr.)}$ \\ %H1 2007 Jets & $256.9~ ^{+86.8}_{-50.5}~\rm{(scale)}~ \pm 22.2~\rm{(hadr.)}$ &$127.9.2~ ^{+65.5}_{-37.3}~\rm{(scale)} \pm 6.8~\rm{(hadr.)}$ \\ Data & $254 \pm 20~ (\rm{stat.}) \pm 27~\rm{(syst.)}$ & $150 \pm 19~ (\rm{stat.}) \pm 26~\rm{(syst.)}$ \\ \hline NLO QCD &&\\ H1 2006 Fit B & $270~ ^{+134}_{-53}~\rm{(scale)}~ \pm 16~\rm{(hadr.)}$ &$148~ ^{+102}_{-33}~\rm{(scale)} \pm 6~\rm{(hadr.)}$ \\ H1 2007 Jets & $257~ ^{+87}_{-51}~\rm{(scale)}~ \pm 22~\rm{(hadr.)}$ &$128~ ^{+66}_{-37}~\rm{(scale)} \pm 7~\rm{(hadr.)}$ \\ \hline \end{tabular} \end{center} \caption{Total cross section for the \textquoteleft two central jets' and \textquoteleft one central + one forward jet' samples compared to the NLO QCD calculations.} \label{ccftable} \end{table} Within the uncertainties, both cross sections are well described by the NLO QCD calculations. The measured differential cross sections are presented in tables~\ref{dijet}-\ref{cfjet} and figures~\ref{dijnlo1}-\ref{cfmc2}. The tables also include the full covariance matrices of the experimental uncertainties. % are also given. The quoted differential cross sections are averaged over the intervals specified in the tables~\ref{dijet}-\ref{cfjet}. \subsection{Differential cross section for the production of two central jets} \label{2cjxs} % \subsubsection{Comparison to NLO QCD predictions} % The $ep$ cross section for diffractive production of two central jets, integrated over the full % measured % kinematic range (table~\ref{kinrange}), is determined to be % \begin{center} % $\sigma_{c+c} = 269.8 \pm 21.3~ (\rm{stat.}) \pm 28.3~\rm{(syst.)~pb}.$ % \end{center} % \noindent % where $c+c$ denotes \textquoteleft two central jets'. % The predictions obtained with NLO DGLAP QCD calculations are % \begin{center} % $\sigma_{c+c}^{H1 2006 B} = 269.7~ ^{+133.9}_{-52.7}~\rm{(scale)}~ \pm 15.8~\rm{(hadr.)~ pb},$ \\ % \vspace{0.3cm} % $\sigma_{c+c}^{H1 2007 J} = 256.9~ ^{+86.8}_{-50.5}~\rm{(scale)}~ \pm 22.2~\rm{(hadr.)~ pb}.$ % \end{center} % \noindent % where $H1 2006 B$ and $H1 2007 J$ denote the DPDF sets H1 2006 Fit B and H1 2007 Jets, respectively. % Within the experimental errors, the data are described by the NLO QCD calculations. The measured differential cross sections are shown as a function of $Q^2$, $y$, $\log_{10}(x_{I\!\!P})$ and $z_{I\!\!P}$ in figure~\ref{dijnlo1}. The calculations obtained with the DPDF sets H1 2006 Fit B and H1 2007 Jets are presented as well as the ratio $R$ of the calculations to the data. Within the uncertainties, the normalisation and shape of the cross sections are reasonably well described by the NLO QCD predictions. %QCD contribution is calculated using the DPDF set H1 2007 Jets % for Since dijet production is directly sensitive to the gluon DPDF, the measured cross sections confirm the normalisation and shape of the gluon DPDFs extracted from the NLO QCD fits to diffractive inclusive and dijet cross sections measured using the LRG method~\cite{H1LRG,H1DiJets}. In figure~\ref{dijnlo2} the differential cross sections are shown as a function of $P^*_{T,1}$ and $|\Delta\eta^*|$. Within the errors, NLO QCD predictions describe the data. %The $|\Delta\eta^*|$ distribution shows that the production of two central jets is well described by %NLO QCD calculations which assumes boson gluon fusion is the dominant production mechanism. A slight deviation of the theory from the data is observed for jets with a small separation in pseudorapidity $|\Delta\eta^*|$. For the differential cross section in $P^*_{T,1}$, %the LO %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% the LO QCD contribution is calculated as well using the DPDF set H1 2007 Jets and is observed to underestimate the measured cross section by a factor of about $2$. Figure~\ref{dijmc1} shows a comparison of the differential cross sections in $Q^2$, $y$, $\log_{10}(x_{I\!\!P})$ and $z_{I\!\!P}$ with MC models based on the leading-logarithm approximation and parton showers. %None of the models succeed in describing both % the shape and normalisation of the data. The ratios of the measured cross sections to the MC predictions show that the RP model gives a good description of the shape, but underestimates the dijet cross section by a factor of $1.5$. For this comparison the reweighting with respect to the $\eta_2^*$ distribution specified in section~\ref{mc} is not applied to the RP model. Since the $\pom$ and $\reg$ fluxes which determine the $\xpom$ dependence in the RP model has been tuned to the inclusive diffractive DIS LRG data~\cite{H1LRG} the good agreement in shape of the RP model with the dijet data supports the hypothesis of the proton vertex factorisation. Both the SCI+GAL and TGP models fail to describe the data. The SCI+GAL model predicts harder spectra in $Q^2$ and $\zpom$ and a softer spectrum in $\log_{10}(x_{I\!\!P})$ than are seen in the data. It should be noted that the probability of soft colour interactions and hence the normalisation of diffractive processes in the SCI+GAL model is adjusted to the measured dijet cross section. The TGP model is in agreement with the data only at low $\xpom$ but underestimates the data significantly at larger $\xpom$ %due to the absence of sub-leading contributions. where the missing sub-leading contributions are expected to be large. Figure~\ref{dijmc2} shows the differential cross sections in $P^*_{T,1}$ and $|\Delta\eta^*|$ %, $\log_{10}(x_{I\!\!P})$, $z_{I\!\!P}$ and $|t|$ for the data and the MC models. The shapes of these %$|\Delta\eta^*|$ distributions are again well described by the RP model. Although the SCI+GAL model is not able to describe the differential cross sections as a function of the diffractive kinematic variables $\xpom$ and $\zpom$ and of the DIS kinematic variable $Q^2$ this model reproduces reasonably well the measurements as a function of the jet variables $P^*_{T,1}$ and $|\Delta\eta^*|$. % The $\log_{10}(x_{I\!\!P})$ and $z_{I\!\!P}$ distributions show the largest sensitivity for distinguishing between the models. %The TGP model is in agreement with the data only %for the lowest $\xpom$ bins, the missing subleading component could help to improve the agreement within the whole measured range. %at low $\xpom$ but underestimates the data significantly at larger $\xpom$ %due to the absence of sub-leading contributions. %where the missing sub-leading contributions are expected to be large. None of the LO Monte Carlo models are able to describe all features of the measured differential cross sections. The best shape description in all cases is provided by the RP model. However, this model is a factor of $1.5$ below the data in normalisation. The TGP and SCI+GAL models fail to describe the shape of the differential cross sections.%, although the SCI+GAL model %can describe some distributions. %\subsubsection{Two central jets: extraction of $t$-dependence} The differential cross section in $|t|$ shown in figure~\ref{tfit}a is fit using an exponential form $\exp(Bt)$ motivated by Regge phenomenology. An iterative procedure is used to determine the slope parameter $B$, where bin centre corrections are applied to the differential cross section in $t$ using the value of $B$ extracted from the previous fit iteration. The final fit results in $B = 5.89 \pm 0.50$~(exp.)~GeV$^{-2}$, where the experimental uncertainty is defined as the quadratic sum of the statistical and systematic uncertainties and the full covariance matrix is taken into account in the fit. As shown in figure~\ref{tfit}b, this $t$-slope parameter is consistent within the errors with the $t$-slope measured in inclusive diffractive DIS with a leading proton in the final state~\cite{H1FPShera2} at the same value of $\xpom$. %= 0.035$.% which is the averaged value over the $\xpom$ spectrum for diffractive dijet production in DIS. The consistency of the measured $t$ dependence %distribution with that for the inclusive diffractive DIS cross sections supports the validity of the proton vertex factorisation hypothesis. %\subsubsection{Two central jets: comparison of the FPS and LRG measurements} %\label{FPSLRG} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\subsubsection{Two central jets: comparison of the FPS and LRG measurements} %\label{FPSLRG} The cross section for the production of two central jets can be compared with the diffractive dijet measurement obtained using the LRG technique~\cite{H1DiJets}. The LRG measurement includes proton dissociation to states $Y$ with masses $M_Y<1.6$~GeV. To correct for the contributions of proton dissociation processes, the LRG dijet data are scaled down by a factor of $1.20$, taken from the diffractive inclusive DIS measurement~\cite{H1FPShera2}. To compare to the results of the LRG method, dijet events are selected in the same kinematic range. The DIS and jet variables $Q^2$, $y$, $P_{T,1}^*$ and $\eta_{1,2}$ are restricted to the ranges $4 5.5$~GeV, and $-1 < \eta_{1,2} < 2$, respectively. The results are presented in figure \ref{mozlog}. The comparison shows consistency of the results within the experimental errors. Compared to the LRG measurement, the phase space of the present analysis extends to $\xpom$ values that are a factor of three larger. \subsection{Differential cross section for the production of one central + one forward jet} % The measured differential cross sections for the \textquoteleft one central + one forward' are compared to % NLO DGLAP % predictions based on the DPDF sets H1 2006 Fit B and H1 2007 Jets and to the LO MC models, as described in % section~\ref{2cjxs}. % \subsubsection{Comparison to NLO QCD predictions} % The total experimental cross section for diffractive production of \textquoteleft one central + one forward' jet, % integrated over the full measured kinematic range (table~\ref{kinrange}) is determined to be % \begin{center} % $\sigma_{c+f} = 163.1 \pm 20.5~ (\rm{stat.}) \pm 27.9~\rm{(syst.)~pb}.$ % \end{center} % \noindent % where $c+f$ denotes \textquoteleft one central and one forward jet'. % The predictions obtained with NLO QCD calculations are % \begin{center} % $\sigma_{c+f}^{H1_2006_B} = 148.3~ ^{+101.5}_{-33.4}~\rm{(scale)} \pm 5.6~\rm{(hadr.)~pb},$ \\ % \vspace{0.3cm} % $\sigma_{c+f}^{H1_2007_J} = 127.9.2~ ^{+65.5}_{-37.3}~\rm{(scale)} \pm 6.8~\rm{(hadr.)~pb}.$ % \end{center} % \noindent % where $H1_2006_B$ and $H1_2007_J$ denote the DPDF sets H1 2006 Fit B and H1 2007 Jets, respectively. % Within the uncertainties, the data are described by the NLO QCD calculations based on the % DPDF sets H1 2006 Fit % B and H1 2007 Jets. Figure \ref{cfnlo1} shows the differential cross sections for the production of \textquoteleft one central + one forward jet' as a function of $|\Delta\eta^*|$, $\eta_f$ and the mean transverse momentum of the forward and central jets $\langle P_T^*\rangle$ together with the expectations from the NLO QCD. Within the errors, the measured data are described by NLO QCD predictions. %The shape of the $|\Delta\eta^*|$ distribution, %which is shifted towards larger values compared to % the case of two central jets, is consistent with NLO DGLAP predictions. In order to test the predictions in a wider kinematic range, the $\eta_f$ distribution of the forward jet shown in figure \ref{cfnlo1} is extended down to a minimum value of $-0.6$ where the prediction overshoots the data. LO QCD calculations, performed using the DPDF set H1 2007 Jets %as described in section ~\ref{models}. The results are presented as a line in the $\langle P_T^*\rangle$ distribution. % The LO calculations underestimate the measured cross section by a factor of about $2.5$. The differential cross sections measured as a function of $z_{I\!\!P}$, $\log_{10}(\beta)$ and $|\Delta\phi^*|$ are presented in figure~\ref{cfnlo2}. The data are well described by the NLO QCD predictions. %The kinematic variable $\beta$ in diffractive events corresponds to the variable $x_{{\rm Bj}}$ in the non-diffractive DIS, possible discrepancies from DGLAP predictions are expected to be present in the $\log_{10}(\beta)$ distribution. In the BFKL approach~\cite{BFKL,BFKL2,BFKL3}, additional gluons can be emitted in the gap between the two jets, leading to a de-correlation in azimuthal angle $|\Delta\phi^*|$. The observed agreement between the measured cross sections and NLO DGLAP predictions in this distribution shows no evidence for such an effect in the kinematic region accessible in this analysis. %\subsubsection{Comparison to LO MC models} Figure~\ref{cfmc1} presents the differential cross sections for the production of \textquoteleft one central + one forward jet' as a function of the variables $\langle P_T^*\rangle$, $|\Delta\eta^*|$ and $\eta_f$. % As in the case of \textquoteleft two central jets', The RP model is a factor of $2.2$ below the data which is a larger discrepancy in normalisation than that observed in the \textquoteleft two central jets' sample. A similar trend is seen for the LO QCD contributions in the two samples. The normalisation of the SCI+GAL model, tuned to \textquoteleft two central jets', agrees with the cross section for \textquoteleft one central + one forward jet'. The shapes of the distributions are reasonably well described by both the RP and SCI+GAL models. The differential cross sections in $z_{I\!\!P}$, $\log_{10}(\beta)$ and $|\Delta\phi^*|$ are shown in figure~\ref{cfmc2}. The shapes of all distributions are well described only by the RP model. As for the case of the \textquoteleft two central jets' the SCI+GAL model is not able to describe the distributions of the diffractive kinematic variables but it well reproducing the shape of the $|\Delta\phi^*|$ distribution. The TGP model completely fails again to describe the $z_{I\!\!P}$ spectrum. % Predictions of the model for the distributions, integrated over $\zpom$, which is not properly described, are not presented. % The shape of the $|\Delta\phi^*|$ distribution is well described by both the RP and SCI+GAL models. \section{Summary} Integrated and differential cross sections are measured for dijet production in the diffractive DIS process $ep \rightarrow e jjX^{\prime}p$. In the process studied, the scattered proton carries at least $90\%$ of the incoming proton momentum and is measured in the H1 Forward Proton Spectrometer. The presented results are compatible with the previous measurements based on the LRG method and explore a new domain at large $\xpom$. % The data cover the range $\xpom<0.1$ in fractional proton longitudinal % momentum % loss, $0.1<|t|<0.7~\GeV^2$ in squared four-momentum transfer at the proton vertex and $4