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\begin{document}

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\begin{titlepage}

\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 1009}    &\\
                 & Parallel Session & {\bf 5}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf Measurement of dijet cross-sections at low 
    {\boldmath $Q^2$} at HERA}

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

\begin{abstract}

\noindent

Triple differential dijet cross-sections in $e^\pm p$ interactions
measured with the H1 detector at HERA are presented in the region of
photon virtualities $2~{\GeV}^2 < Q^2 < 80~{\GeV}^2$, inelasticities
$0.1<y<0.85$, low transverse jet momentum 
$E_t^{jet \hspace{0.5mm}1, 2} > 5~\GeV$ with average 
\mbox{$\ \overline{E}_t > 6~\GeV$}, and pseudorapidity 
$-2.5 < \eta^{jet \hspace{0.5mm}1,2} <0$.  
The data are compared to Monte Carlo simulations which differ in
their assumptions about the virtual photon structure and employ DGLAP
or CCFM parton evolution schemes. Indications of effects connected
with the interaction of longitudinally polarized virtual photons via
their resolved hadronic structure are investigated.
\end{abstract}


\end{titlepage}

\pagestyle{plain}

%===========================================================
\section{Dijet Production at HERA}
\label{uvod}
The production of dijet events at HERA is dominated by processes in
which a virtual photon, coupling to the electron, interacts with a
parton in the proton.
% 
If the mediated photon is almost real ($Q^2<\Lambda_{\mathrm QCD}^2$),
the data are usually described by the sum of two types of process.
In the ``direct'' case, the photon interacts as a whole with partons from
the proton, while in the ``resolved'' interaction, the photon behaves as a
hadron, i.e. as a source of partons described by set of parton
distribution functions (PDF).
%
The same approach has been applied in LO models in the past to virtual
photons with $Q^2 < E_t^2$.  The resolved contributions seem to be
present in
data~\cite{Adloff:1998vc,Kcira:2001ah,Tasevsky:1998fq,Baranov:2002ei}.
%
%
However, contrary to the photoproduction regime, we are not obliged to
introduce the concept of resolved photons if 
$Q^2 \gg \Lambda_{\mathrm QCD}^2$.  Since leading order direct
interactions are not able to fully describe the data in the region of
virtuality $\Lambda_{\mathrm QCD}^2 \ll Q^2 \lapprox E_t^2$ explored
in the present analysis, higher order effects need to be included in
some way -- either using next-to-leading order (NLO) calculations,
via $k_t$ unordered initial QCD cascades, or by allowing for
additional interactions with resolved photons.  Only the last two
approaches are investigated here. Comparisons with NLO predictions are
likely to become possible in the future.  In more detail, the present
measurements are compared with the following models:


\vspace{0.8em}
{\bf a) LO direct and resolved interactions} 
     based on the DGLAP evolution equations and parton showers. The
     effects of transversally ($\gamma^*_T$) and also longitudinally
     ($\gamma^*_L$) polarized resolved photon interactions are
     included~\cite{Sedlak:2001pr,chyla,Chyla:2000hp}.  The cross section
     for longitudinal photons vanishes for $Q^2 = 0$ due to gauge
     invariance.  On the other hand, the concept of a resolved photon
     breaks down for $Q^2 > E_t^2$. Therefore the most promising region
     in which to search for the
     $\gamma^*_L$ resolved processes is 
     $\Lambda_{\mathrm QCD}^2 < Q^2 \ll E_t^2$, 
     which is often the case of the present analysis.

     The main difference between $\gamma^*_L$ and $\gamma^*_T$ induced 
     interactions arises from the $y$ dependence of the respective fluxes:

     \begin{eqnarray}
       \label{rovnice1}
       f_{\gamma^T/e}(y,Q^2) & 
       = & \frac{\alpha}{2\pi} \left[  \frac{2(1-y)+y^2}{y}
         \frac{1}{Q^2} - \frac{2m_e^2 y}{Q^4} \right] \\
       \label{rovnice2}
       f_{\gamma^L/e}(y,Q^2) & 
       = & \frac{\alpha}{2\pi} \left[  \frac{2(1-y)}{y}
         \frac{1}{Q^2}  \right]
     \end{eqnarray}
     where $\alpha$ is the fine structure constant and $m_e$ the
     electron mass.
%
     While for $y\rightarrow 0$, both transverse and longitudinal
     fluxes are approximately the same, the longitudinal flux vanishes for
     $y\rightarrow 1$.  Also the dependence of the
     point-like~\footnote{The perturbatively non-calculable
       hadron-like part of the photon PDF becomes negligible in our
       kinematical region with respect to the point-like one,
       as has been demonstrated
       in~\cite{Chyla:1999pw}.}  (i.e. perturbatively calculable)
     parts of the photon PDF on \qq and $E_t^2$ differs -- while the
     $\gamma^*_T$ PDF are proportional to $\ln (E_t^2/Q^2)$,
      the $\gamma^*_L$ PDF do not, in the first approximation, 
     depend on either $E_t^2$ or \qq~\cite{chyla}.
     
     Monte Carlo programs HERWIG~5.9~\cite{Herwig} and
     RAPGAP~2.8~\cite{Rapgap} based on the DGLAP evolution scheme were chosen
     for comparisons with the data.  These models differ in the choice
     hadronization model -- a cluster fragmentation is applied in
     HERWIG, the Lund string model in RAPGAP.  Neither of the two
     programs include the resolved interaction of $\gamma^*_L$.  For
     this purpose we used a slightly modified version of HERWIG with the
     longitudinal photon flux according to eq.~(\ref{rovnice2}) and a
     recent $\gamma^*_L$ PDF parameterization~\cite{Chyla:2000hp}.

\vspace{0.8em}
{\bf b) $\mathbf k_t$ unordered initial QCD cascades} 
     accompanying the hard process are present for example in 
     BFKL or CCFM evolution. These evolution schemes 
     can lead to final states in which the
     partons with the largest $k_t$ may come from the cascade, and
     not, as in the DGLAP case, from the hard subprocess. Such events
     may have a similar topology to that for the resolved
     interactions in the DGLAP approximation.
     This possibility is investigated using the CASCADE~1.0
     generator~\cite{Cascade,Cascade2} based on the CCFM evolution
     equations and unintegrated gluon density
     functions~\cite{Unintegr}.  Contrary to DGLAP models, resolved
     photons are not considered in CASCADE.



%================================================================
\section{Measurement of Dijet Cross-Section}

The measurement was done with 16.3 pb$^{-1}$ of data collected in
1999, when the electron-proton center-of-mass energy $\sqrt{s}$
reached 318~\GeV.  A full description of the H1 detector is given
in~\cite{Abt:hi,Abt:1996xv}.

The kinematic variables $x$, \qq and $y$ are determined from the
electron information only, according to 
$Q^2=4 E_e E'_e \cos^2(\theta_e /2)$, 
$\ y=1-(E_e/E'_e) \sin^2(\theta_e /2)$~~and $\ x=Q^2/(ys)$, 
where $E_e$, $E'_e$ and $\theta_e$ are the electron beam
energy, the energy of the scattered electron and the electron scattering
angle, respectively.

The ana\-lysis was performed in $\gamma^*$-proton center-of-mass system,
and jets were found using the $k_t$ longitudinally invariant jet algorithm.
The phase space is defined by the photon virtuality:
 $2~{\GeV}^2 < Q^2 < 80~{\GeV}^2$, 
the electron inelasticity: $0.1 < y < 0.85$,
the transverse energy of two leading jets: $E_t^{jet\,1,2} > 5~\GeV$, 
$\overline{E}_t=(E_t^{jet\,1}+E_t^{jet\,2})/2 > 6~\GeV$ 
and the pseudorapidity of the two leading jets:
$-2.5 < \eta^{jet\,1,2} < 0$.
The $E_t^{jet}$ and $\eta^{jet}$ variables are measured relative to
the $\gamma^* p$ collision axis with positive $\eta^{jet}$ corresponding
to the proton direction.

The dijet events are characterized by \Et, which is the mean value of
transverse energy $E_t$ of two jets with the highest $E_t$, and in
terms of the variable \xg defined as:
     \begin{equation}
       \label{rovnice3}
       x_\gamma = \frac{\sum\limits_{{\rm jet}\; 1,2}(E^{jet}-p^{jet}_{z})}
                   {\sum\limits_{\rm hadrons}(E-p_{z})}
     \end{equation}
For a $2 \rightarrow 2$ process involving four massless partons, the above expression
gives exactly the fraction of the photon momentum carried by the parton
entering this process from the photon side.  For hadronic jets,
\xg has only approximately such an interpretation, but still allows us
to separate direct ($ x_\gamma \sim 1$) and resolved ($ x_\gamma < 1$)
components with reasonable accuracy.


The measured data are corrected for the effects of limited detector
acceptance and resolution using the Bayesian unfolding method.  The
distributions of kinematic variables (Fig.~\ref{velfinal1}) and jet
observables (Fig.~\ref{velfinal2}) are sufficiently well described by
HERWIG and RAPGAP, which were used in the correction procedure.  The
largest source of systematic errors, typically 10-20\%, arises from
the model dependence of the detector correction, which was taken as 
half of the difference between HERWIG and RAPGAP.  Another 10\% error
appears due to a 4\% energy scale uncertainty of the main calorimeter.


%================================================================
\section{Results and Discussion}


The corrected triple-differential dijet cross-section measured as a
function of \qq, \Et and \xg is shown in
Fig.~\ref{qex.fin1}-\ref{qex.fin24}, where different model predictions
are compared always to the same data points.


A prediction of HERWIG and RAPGAP with the SaS1D~\cite{Schuler:1995fk}
parameterization of the \gammaT PDF, as well as the pure direct
contributions are compared to the data in Fig.~\ref{qex.fin1}.  In
general, HERWIG and RAPGAP tend to underestimate the measured cross-section.
The decrease of the resolved contribution at high \Et is of kinematic
origin, due to the limited energy of the incoming
partons at low \xg.  The direct contributions almost describe the data
in the highest \qq bin, while a clear need for resolved processes is
observed for $Q^2 \ll \EtEQ$.


In the highest \qq range ($25 < Q^2 < 80 ~\GeV^2$) and
$x_\gamma<0.75$, the HERWIG direct contribution almost describes the
data in the lowest \Et bin, but is significantly below it in the
highest \Et bin.  This indicates that the relevance of the resolved photon
contribution is governed by the ratio $\overline{E}_t^2 /Q^2$, rather
than by $Q^2$ itself.


Standard HERWIG with direct and \gammaT resolved contributions
underestimates the data. The description is improved by adding \gammaL
resolved photon interactions, as demonstrated in Fig.~\ref{qex.fin2}.


On the other hand, a simple enhancement of the PDF of the $\gamma^*_T$
in the resolved contribution could lead to a similar prediction as the
introduction of resolved $\gamma^*_L$.  This is indicated in
Fig.~\ref{qex.fin24}, where a modified version of the
GRV~\cite{Drees:1994eu} parameterization
of the real photon PDF were used for the resolved \gammaT component.
The parameter $\omega$ governs the suppression of the photon PDF 
relative to real photons with increasing virtuality.


To distinguish between a non-optimal choice of $\gamma^*_T$ PDF
and the need for resolved $\gamma^*_L$, the
dijet cross-section has been studied as a function of \qq, \xg\, and
$y$, which is shown in Fig.~\ref{qx4y.fin1}-\ref{qx4y.fin24}.  HERWIG
and RAPGAP are below the data especially at low \xg and low $y\ $
 (Fig.~\ref{qx4y.fin1}). The discrepancy becomes smaller
if the resolved \gammaL is added (Fig.~\ref{qx4y.fin2}).
According to eq.~(\ref{rovnice1}-\ref{rovnice2}), the slope of
inelasticity $y$ of the HERWIG prediction in the region of
$x_\gamma<0.75$ depends significantly on whether $\gamma^*_L$
processes are included or not.  Unlike a pure enhancement of
$\gamma^*_T$ PDF, which would not change the slope of the $y$
distribution, addition of $\gamma^*_L$ brings the $y$ dependence of
HERWIG much closer to the measurement (compare Fig.~\ref{qx4y.fin2}
and~\ref{qx4y.fin24}).

As motivated in Section~\ref{uvod}, the measured cross-sections are
also compared to a prediction of the CASCADE MC program based on the
CCFM evolution scheme (Fig.~\ref{qex.fin22} and~\ref{qx4y.fin22}).
This theoretical approach does not involve the concept of virtual
photon structure and employs much fewer parameters for tuning than the
usual DGLAP-based MC programs. CASCADE describes the data reasonably
but not perfectly. In particular, the \qq dependence at low \xg
is poorly described (see e.g. Fig.~\ref{qx4y.fin23}).


As indicated by Fig.~\ref{qx4y.fin22}, the $y$ dependence of the dijet
cross-section is better described by CASCADE than by HERWIG without
the $\gamma^*_L$ resolved process, since photon polarization states
are correctly treated in CASCADE for all virtualities (only direct
photon interactions are included).

In Fig.~\ref{qx4y.sch.fin1}-\ref{qx4y.sch.fin24}, simplified
versions of Fig.~\ref{qex.fin1}-\ref{qx4y.fin24} are presented, 
where only a part of the measured phase space is displayed.




%================================================================
\section{Conclusions}

The importance of \gammaT resolved photon interactions within the
DGLAP evolution scheme at leading order is clearly demonstrated in the
region where $\EtEQ > Q^2$, even at rather high $Q^2$.  Additional
\gammaL resolved photon contributions further improve the agreement of
HERWIG with the measured data.

Exploring the CCFM approach, the MC program CASCADE does not
reproduce the data perfectly, the main discrepancy is observed in the
\qq dependence at low \xg. On the other hand, the \xg dependence in CASCADE is
comparable to the sum of the direct and resolved contributions in
DGLAP-based MC programs, showing that non $k_t$ ordered parton cascades
can successfully produce the same observables as resolved virtual photons
in the LO DGLAP evolution scheme.


%================================================================
\begin{thebibliography}{99}

%\cite{Adloff:1998vc}
\bibitem{Adloff:1998vc}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of dijet cross-sections at low Q**2 and the extraction of  an effective parton density for the virtual photon,''
Eur.\ Phys.\ J.\ C {\bf 13} (2000) 397
[arXiv:hep-ex/9812024].
%%CITATION = HEP-EX 9812024;%%

%\cite{Kcira:2001ah}
\bibitem{Kcira:2001ah}
D.~Kcira  [ZEUS Collaboration],
``Virtual photon structure at HERA,''
[arXiv:hep-ex/0110082].
%%CITATION = HEP-EX 0110082;%%

%\cite{Tasevsky:1998fq}
\bibitem{Tasevsky:1998fq}
M.~Tasevsky  [H1 Collaboration],
``Jets as a source of information about photon structure,''
[arXiv:hep-ex/9807023].
%%CITATION = HEP-EX 9807023;%%

%\cite{Baranov:2002ei}
\bibitem{Baranov:2002ei}
S.~P.~Baranov, H.~Jung, L.~Jonsson, S.~Padhi and N.~P.~Zotov,
%``A phenomenological interpretation of open charm production at HERA in  terms of the semi-hard approach,''
[arXiv:hep-ph/0203025].
%%CITATION = HEP-PH 0203025;%%


%\cite{Sedlak:2001pr}
\bibitem{Sedlak:2001pr}
K.~Sedlak  [H1 Collaboration],
``Structure of virtual photons at HERA,''
[arXiv:hep-ex/0111019].
%%CITATION = HEP-EX 0111019;%%

%\bibitem{Sedlak}
%K.~Sedl\'ak for H1 and ZEUS Collab., ``Structure of Virtual Photons at HERA'', 
%to be published in proceedings of Photon 2001 conference, hep-ex/0111019.

\bibitem{chyla}
J.~Ch\'yla and M.~Ta\v{s}evsk\'y,
%``Resolved gamma*(L) in hard collisions of virtual photons: QCD  effects,''
Eur. Phys. J. {\bf C18} (2001), 723.
%, hep-ph/0010254.

%\cite{Chyla:2000hp}
\bibitem{Chyla:2000hp}
J.~Ch\'yla,
%``QCD improved parton distribution functions of gamma*(L),''
Phys.\ Lett.\   {\bf B488} (2000), 289.
%, hep-ph/0006232.

%\cite{Chyla:1999pw}
\bibitem{Chyla:1999pw}
J.~Ch\'yla and M.~Ta\v{s}evsk\'y,
%``Interpreting virtual photon interactions in terms of parton  distribution functions,''
Phys.\ Rev.\ D {\bf 62}, 114025 (2000).
%[arXiv:hep-ph/9912514].
%%CITATION = HEP-PH 9912514;%%

\bibitem{Herwig}
 G.~Marchesini, B.R.~Webber, G.~Abbiendi, I.G.~Knowles, 
 M.H.~Seymour and L.~Stanco,
          Comput. Phys. Commun. {\bf 67} (1992), 465.

\bibitem{Rapgap}
H.~Jung, Comput. Phys. Commun. {\bf 86} (1995) 147-161.


\bibitem{Cascade}
H.~Jung, ``The CCFM Monte Carlo Generator Cascade'',
Comput. Phys. Commun. {\bf 143} (2002), 100-111.

\bibitem{Cascade2}
H.~Jung and G.P.~Salam, Eur. Phys. J. {\bf C19} (2001), 351-360.


\bibitem{Unintegr}
H.~Jung, Phys. Rev. {\bf D65} (2002) 034015.

%1) THE CCFM MONTE CARLO GENERATOR CASCADE.
%By H. Jung (Lund U.). DESY-01-114, LUNFD6-NFFL-7202-2001, Sep 2001. 14pp. 
%Published in Comput.Phys.Commun.143:100-111,2002 
%e-Print Archive: hep-ph/0109102 

%\cite{Abt:hi}
\bibitem{Abt:hi}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 Detector At Hera,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310.
%%CITATION = NUIMA,A386,310;%%

%\cite{Abt:1996xv}
\bibitem{Abt:1996xv}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The Tracking, calorimeter and muon detectors of the H1 experiment at HERA ,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 348.
%%CITATION = NUIMA,A386,348;%%


%\cite{Schuler:1995fk}
\bibitem{Schuler:1995fk}
G.~A.~Schuler and T.~Sjostrand,
%``Low and high mass components of the photon distribution functions,''
Z.\ Phys.\ C {\bf 68} (1995) 607
[arXiv:hep-ph/9503384].
%%CITATION = HEP-PH 9503384;%%

%\cite{Drees:1994eu}
\bibitem{Drees:1994eu}
M.~Drees and R.~M.~Godbole,
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Phys.\ Rev.\ D {\bf 50} (1994) 3124
[arXiv:hep-ph/9403229].
%%CITATION = HEP-PH 9403229;%%



\end{thebibliography}


%=====================================================
%                   F I G U R E S
%=====================================================

\pagestyle{empty}

% Control plots

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig1.eps,width=16.0cm}
      \caption{Detector level comparison of the data with HERWIG
        and RAPGAP simulations. Both HERWIG and RAPGAP are
        reweighted to describe the data. All detector level
        selection criteria were applied.}
      \label{velfinal1}
    \end{figure}

    \begin{figure}[ht]  \centering
      \epsfig{file=pict/H1prelim-01-133.fig2.eps,width=16.0cm}
      \caption{Detector level comparison of the data with HERWIG
        and RAPGAP simulations. Both HERWIG and RAPGAP are
        reweighted to describe the data. All detector level
        selection criteria were applied.}
      \label{velfinal2}
    \end{figure}


% Physics plots



    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig3.eps,width=16.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of \xg, \Et and $Q^2$. The data are
        compared to HERWIG and RAPGAP MC predictions. 
        Separately shown are the direct (dir) and the resolved
        component of transversally polarized $\gamma$  (res$_T$).}
      \label{qex.fin1}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig4.eps,width=16.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of \xg, \Et and $Q^2$. The data are
        compared to HERWIG with an additional contribution of the
        longitudinally polarized photon processes (res$_L$).}
      \label{qex.fin2}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=H1prelim-01-133.fig5.eps,width=16.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of \xg, \Et and $Q^2$. The data are
        compared to HERWIG and CASCADE MC predictions.
        CASCADE is based on the CCFM evolution scheme.}
      \label{qex.fin22}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig6.eps,width=16.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of \xg, \Et and $Q^2$. A combination of
        the theoretical predictions in 
        Figure~\ref{qex.fin2} and~\ref{qex.fin22} is plotted here.}
      \label{qex.fin23}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig7.eps,width=16.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of \xg, \Et and $Q^2$. The data are
        compared to HERWIG with different $\gamma_T^*$ PDFs.
        $\omega$ is a parameter from the Drees-Godbole 
        factor~\cite{Drees:1994eu},
        which suppresses the GRV $\gamma$ PDFs with $Q^2$.}
      \label{qex.fin24}
    \end{figure}




    \begin{figure}[ht] \centering 
      \epsfig{file=pict/H1prelim-01-133.fig8.eps,width=14.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of $y$, \xg and $Q^2$. The data are
        compared to HERWIG and RAPGAP MC predictions. Both
        MC models underestimate the data, especially in
        the low \xg and low $y$ range.}
      \label{qx4y.fin1}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig9.eps,width=14.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of $y$, \xg and $Q^2$. The data are
        compared to HERWIG with an additional contribution of the
        longitudinally polarized resolved photon processes.
        The additional longitudinal photon contributions
        lead to a better description of the slope of the 
        $y$ distribution.}
%        bring the steepness of the $y$ dependence in the HERWIG 
%        prediction much closer to the measured one.}
      \label{qx4y.fin2}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=H1prelim-01-133.fig10.eps,width=14.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of $y$, \xg and $Q^2$. The data are
        compared to HERWIG and CASCADE MC models.}
%        CASCADE gives
%        very similar prediction to the sum of direct and
%        transversally polarized resolved processes of HERWIG,
%        however the $Q^2$ dependence is not described very well.}
      \label{qx4y.fin22}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig11.eps,width=14.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of $y$, \xg and $Q^2$. A combination of the model
        comparisons from 
        Figure~\ref{qx4y.fin2} and~\ref{qx4y.fin22} is plotted here.}
      \label{qx4y.fin23}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig12.eps,width=14.0cm}
      \caption{Triple differential dijet cross-section as 
        a function of $y$, \xg and $Q^2$. The data are
        compared to HERWIG with different $\gamma_T^*$ PDFs
        (see caption to Fig.~\ref{qex.fin24}).
        The slope of $y$ distributions are steeper in the
        data than in any of the HERWIG predictions plotted.}
      \label{qx4y.fin24}
    \end{figure}




    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig13.eps,width=16.0cm}
      \caption{Simplified version of Fig.~\ref{qex.fin1} and~\ref{qx4y.fin1}.}
      \label{qx4y.sch.fin1}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig14.eps,width=16.0cm}
      \caption{Simplified version of Fig.~\ref{qex.fin2} and~\ref{qx4y.fin2}.}
      \label{qx4y.sch.fin2}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=H1prelim-01-133.fig15.eps,width=16.0cm}
      \caption{Simplified version of Fig.~\ref{qex.fin22} and~\ref{qx4y.fin22}.}
      \label{qx4y.sch.fin22}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig16.eps,width=16.0cm}
      \caption{Simplified version of Fig.~\ref{qex.fin23} and~\ref{qx4y.fin23}.}
      \label{qx4y.sch.fin23}
    \end{figure}

    \begin{figure}[ht] \centering
      \epsfig{file=pict/H1prelim-01-133.fig17.eps,width=16.0cm}
      \caption{Simplified version of Fig.~\ref{qex.fin24} and~\ref{qx4y.fin24}.}
      \label{qx4y.sch.fin24}
    \end{figure}

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\end{document}

