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\newcommand{\GeV}{\rm GeV}
\newcommand{\TeV}{\rm TeV}
\newcommand{\pb}{\rm pb}
\newcommand{\cm}{\rm cm}
\newcommand{\hdick}{\noalign{\hrule height1.4pt}}
\def\prp{\perp}
\def\Prp{T}
\def\sx{small-$x$}
\def\kt{\ensuremath{k_\prp}}
\def\kti#1{\ensuremath{k_{\prp #1}}}
\def\pt{\ensuremath{p_\prp}}
\def\pti#1{\ensuremath{p_{\prp #1}}}
\def\qt{\ensuremath{q_\prp}}
\def\qti#1{\ensuremath{q_{\prp #1}}}
\def\xbj{\ensuremath{x_{Bj}}}
\def\xjet{\ensuremath{x_{jet}}}
\def\ptjet{\ensuremath{p_{t\;jet}}}
\def\DJANGO{{\sc Django}}
\def\RAPGAP{{\sc Rapgap}}
\def\CASCADE{{\sc Cascade}}
\def\ARIADNE{{\sc Ariadne}}
\def\ldcmc{{\small LDCMC}}
\def\PHOJET{{\sc Phojet}}
\newcommand{\CCFM}{CCFMa,CCFMb,CCFMc,CCFMd}
\newcommand{\BFKL}{BFKLa,BFKLb,BFKLc}
\newcommand{\LDCMC}{LDCa,LDCb,LDCc,LDCd}
\newcommand{\alphasb}{\alb}
\newcommand{\JETSET}{Jetsetnew}
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\newcommand{\PYTHIAMC}{Jetsetc}
\newcommand{\RAPGAPMC}{RAPGAP206}
\newcommand{\DJANGOMC}{DJANGO}
\newcommand{\HERACLESMC}{HERACLESa,HERACLESb}
\newcommand{\PHOJETMC}{PHOJETa,PHOJETb}
\newcommand{\DGLAP}{DGLAPa,DGLAPb,DGLAPc,DGLAPd}

\begin{document}

\pagestyle{empty}
\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 1001}    &\\
                 & Parallel Session & {\bf 5, 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}
  \Large
  {\bf 
    Forward Jet production at HERA
}

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

\begin{abstract}

\noindent

New parton dynamics, characterized by an initial state
cascade which is non-ordered in parton virtuality,
is expected to become important in the kinematic
region of small Bjorken-$\xbj$.
Evidence for this feature of QCD 
is searched for by studying events with 
a forward jet produced close to the direction of the incoming proton 
in the angular
range $7^o < \theta_{jet} < 20^o$. The measurements
are compared with the predictions of simulations assuming ordered
or non-ordered emissions in the initial state cascade.
The cross section for forward  jet
production is presented as a function of $\xbj$, and shows a  significant
deviation to the predictions based on DGLAP evolution. We also present
the forward jet cross section as a function of
the energy fraction the forward jet takes from the initial proton,  
and as a
function of the transverse momentum of the forward jet. 

\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}
HERA has extended the available $\xbj$ region down to values 
of $\xbj > 10^{-5} $, for values of  the momentum transfer, $Q^2$, 
larger than a few GeV,
where  perturbative calculations in  QCD are still expected to be valid. 
In Deep Inelastic Scattering (DIS)
a parton in the proton can induce a QCD cascade consisting of several
subsequent parton emissions, before the final parton interacts with the virtual
photon. 
\par
Several different prescriptions of the QCD dynamics at small values of $\xbj$
have been proposed. These include QCD parton evolution schemes such as the
DGLAP~\cite{\DGLAP} evolution equation, the small $\xbj$ specific
BFKL~\cite{\BFKL} evolution equation as well as the CCFM~\cite{\CCFM} evolution
equation, which forms a bridge between DGLAP and BFKL using the concept of color
coherence.
\par
Differences between the different dynamical approaches to the parton cascade are
expected to be most prominent in the phase space region towards the proton
remnant direction, i.e. away from the scattered quark.
\par
We investigate the parton evolution at small values of $\xbj$ using jet
production in the forward angular region 
(close to the proton remnant direction) in the laboratory  frame. The analysis
presented here is based on 5 times more statistics than our published
one~\cite{H1_fjets_data} and 
 is complementary to a similar analysis \cite{fwdpi0_h1prelim} 
 which used  high energetic
pions  instead of jets. 
 A schematic
diagram for forward jet production is shown if Fig~\ref{fwdjet-diagram}.
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \epsfig{figure=H1prelim-02-133.fig1.eps, 
      width=8cm,height=8.5cm} 
    \caption{{\it  
    Schematic diagram for forward jet production at HERA. The
    evolution from large $\xjet$ to small $\xbj$ is indicated.
    The phase
    space for DGLAP evolution in $Q^2$ is restricted
    by the requirement of $\ptjet^2 \sim
    Q^2$.
\label{fwdjet-diagram}}}
  \end{center}
\end{figure} 

\par
In the DGLAP evolution scheme, the virtualities $k_i$ of the propagator gluons
are strictly increasing from the proton to the photon. 
Thus the cross section for forward jet production with $\ptjet^2 \sim Q^2$ is
expected to be small, since there is 
no phase space  left for further parton radiation between the forward jet and
the virtual photon.
In the BFKL description, however, the
virtualities (and transverse momenta) $\kti{i}$ can perform a so-called random
walk. 
Based on calculations in the LLA of the BFKL kernel, the cross section for 
DIS events 
at low $\xbj$ and large $Q^2$ with a high $\ptjet^2$ jet in the 
proton direction (a forward jet) \cite{Mueller_fjets1,Mueller_fjets2} is 
expected to rise more rapidly with decreasing $\xbj$ than expected 
from DGLAP based calculations. 



\section{Data and analysis method}
The region in which the forward jet measurement is performed is chosen such that
the phase space for jet production according to the DGLAP evolution is 
suppressed
compared to that available for the BFKL evolution. This is achieved by
requiring $\ptjet^2 \sim Q^2$, where $\ptjet^2$ is the transverse momentum
squared of the forward jet. In addition the momentum fraction of the 
forward jet
$\xjet=E_{jet}/E_p$ is required to be large, whereas $\xbj$ is kept as small
as possible, thus enhancing the phase space for evolution in $x$ 
while suppressing the evolution in $Q^2$.
\par
The $e^+p$ scattering data have been collected at 
$\sqrt{s} = 300~\GeV$ with the H1 detector in 1997 and 
correspond to 
an integrated luminosity of  $13.72~\pb^{-1}$.
\par
DIS events are selected by requiring 
 a scattered electron in the backward 
 SPACAL calorimeter with an
energy $E_{e'}>10$~GeV in the angular range of $ 156^o < \theta_e < 175^o$. The
kinematics are determined from the scattered electron:
$ Q^2 = 4 E_e E_{e'}\cos^2(\theta_e /2)$ and $y=1 - (E_{e'}/E_e)\sin^2(\theta_e /2)$
where $E_e$ is the incident positron energy.
In summary the following cuts are applied: 
\begin{center}
\begin{tabular}{c}
$E_{e'} > 10\mbox{ GeV}$\\
$ 156^o < \theta_e < 175^o$\\
$ 0.1 < y < 0.7$ \\
$ 5\mbox{ GeV}^2 < Q^2 < 75 \mbox{ GeV}^2$
\end{tabular}\end{center}
The forward jets are defined using the $k_t$-jet 
algorithm~\cite{kt_2,kt_1} in its inclusive mode
(applied in the Breit-frame) by requiring: 
\begin{center}
\begin{tabular}{c}
$p_{t\,jet} > 3.5$ GeV \\
$7.0^o < \theta_{jet} < 20.0^o $  \\
$ \xjet > 0.035 $\\
$0.5 < \ptjet^2/Q^2 < 2 $
\end{tabular}\end{center}
where $p_{t\,jet}$ is measured in the laboratory frame.
\par
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \epsfig{figure=H1prelim-02-133.fig2.eps,width=12cm,height=10cm} 
    \caption{{\it  
    Distribution of the energy $E_e$ and the angle $\Theta_e$ of the 
    scattered electron variables after the forward jet selection.
    The solid (dashed) line shows the 
    predictions from  CDM (RG)
     Monte Carlo after full detector simulation.
    \label{fwdjet-kin-controla}}}
  \end{center}
\end{figure} 
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \epsfig{figure=H1prelim-02-133.fig3.eps,width=17cm,height=16cm} 
    \caption{{\it  
    Distribution of basic jet variables after the forward jet selection.
    The solid (dashed) line shows the 
    predictions from CDM (RG)
     Monte Carlo after full detector simulation.
    \label{fwdjet-kin-controlb}}}
  \end{center}
\end{figure} 
The \RAPGAP\ ~\cite{\RAPGAPMC} Monte Carlo model  uses LO
matrix elements supplemented with initial and final state DGLAP parton 
showers (DIR-model).
In addition resolved virtual photon processes can be included (RES-model). In
the following  \RAPGAP\ will be labeled as RG. 
The \DJANGO\ ~\cite{\DJANGOMC}  Monte Carlo model is used together with the 
Color-Dipole-Model as
implemented in \ARIADNE\ ~\cite{ariadne} for higher order QCD radiation, 
labeled as CDM.
Simulated events of the RG-DIR and CDM 
Monte Carlo programs have been
processed through the detailed H1 detector simulation. 
In Fig.~\ref{fwdjet-kin-controla} the normalized distributions of the scattered
electron energy and scattering angle, after the forward jet selection, 
are shown.
In Fig.~\ref{fwdjet-kin-controlb} the normalized distributions of basic jet
variables, after the forward jet selection,
are compared to the Monte Carlo predictions.
In both Figs.~\ref{fwdjet-kin-controla} and~\ref{fwdjet-kin-controlb} 
good agreement of the data with the
full detector simulation of the CDM MC is observed. The RG Monte Carlo shows
deviations to the data, as expected from a pure DGLAP type prediction.
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \epsfig{figure=H1prelim-02-133.fig4.eps, width=16cm,height=9cm} 
    \caption{{\it  
    Transverse energy flow around the axis of the selected forward jet as a
    function of $\Delta \eta = \eta_{jet} - \eta_{clus}$ and 
    $\Delta \phi = \phi_{jet} - \phi_{clus}$ in a slice of $|\Delta \phi | =1$ and
    $|\Delta \eta |=1$, respectively. Also shown are the predictions from the
    CDM (solid) and RG (dashed)
    Monte Carlo simulations.
    \label{fwdjet-jetprofiles}}}
  \end{center}
\end{figure} 
In Fig.~\ref{fwdjet-jetprofiles} we show the transverse energy flow around the 
axis of the selected forward jet as a
function of $\Delta \eta = \eta_{jet} - \eta_{clus}$ and 
$\Delta \phi = \phi_{jet} - \phi_{clus}$ in a slice  of $|\Delta \phi |= 1$ and
$|\Delta \eta| = 1$, respectively. Also shown are the predictions from the
Monte Carlo simulations.
\par
The CDM Monte Carlo, which describes best the data at detector level,
 is used for correcting the data to hadron level. 
The difference of the correction factors
obtained by the two Monte Carlos, CDM   and  RG 
is $\sim 8  \%$, and is treated as
systematic error.
\par
The effects of initial state QED radiation are corrected for using HERACLES
interfaced to \DJANGO\ and \RAPGAP .
\par
The following systematic errors are considered:
\begin{itemize}
\item The error on the hadronic energy scale of 4 \% in the LAr- Calorimeter
results in an error of the cross section measurement of  $\sim 6 \%$.
\item The error on the electromagnetic energy scale of 1 \% of the SPACAL
Calorimeter
results in an error of the cross section measurement of $\sim 3 \%$.
\item An error of 1 mrad is assumed 
on the angle measurement of the scattered electron, resulting in
an error of the cross section measurement of $\sim 3 \%$.
\item The error coming from the model dependence between RG and CDM
of $\sim 8 \%$. 
\item The photoproduction background is estimated using the 
\PHOJET ~\cite{\PHOJETMC} Monte Carlo
simulations to $\sim 1$\%.
\end{itemize}
\par
In Fig.~\ref{fwdjet-had-x}-\ref{fwdjet-had-ptjet} we show the forward jet cross section as a function of
$\xbj$, \xjet\  and \ptjet\  for $\ptjet > 3.5$ GeV and $\ptjet > 5$ GeV corrected
to the hadron level. Also shown are the predictions from a pure DGLAP type Monte
Carlo (RG - DIR), including also a contribution from 
resolved virtual photons (DIR+RES), 
and a simulation using the Color Dipole Model (CDM) as implemented in \ARIADNE\  
(\DJANGO ). In \ARIADNE\ the parton emissions  perform a random walk in
transverse momentum leading to a situation similar to the one expected in BFKL.
Whereas the DGLAP type prediction falls below
the data at small \xbj,  CDM and 
 DGLAP including resolved virtual photons 
give a good description of the
measurement. The \CASCADE\ implementation of the 
 CCFM evolution equation, which is based on
$k_t$-factorization, overestimates the data.
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \rotatebox{0.}{\scalebox{0.37}{\includegraphics*{H1prelim-02-133.fig5a.eps}}}
    \rotatebox{0.}{\scalebox{0.37}{\includegraphics*{H1prelim-02-133.fig5b.eps}}}
    \caption{{\it  
    The cross section for forward jet production on hadron level, as a
    function of $\xbj$ for $\ptjet > 3.5$~GeV (left) and
    $\ptjet > 5 $~GeV (right). Also shown are the 
    predictions from the CDM, 
    RG and CASCADE Monte Carlos.
    \label{fwdjet-had-x}}}
  \end{center}
\end{figure} 
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \rotatebox{0.}{\scalebox{0.37}{\includegraphics*{H1prelim-02-133.fig6a.eps}}}
    \rotatebox{0.}{\scalebox{0.37}{\includegraphics*{H1prelim-02-133.fig6b.eps}}}
    \caption{{\it  
    The cross section for forward jet production on hadron level, as a
    function of \xjet\  for $\ptjet > 3.5$~GeV (left) and
    $\ptjet > 5 $~GeV (right). Also shown are the 
    predictions from the CDM, 
    RG and CASCADE Monte Carlos.
    \label{fwdjet-had-xjet}}}
  \end{center}
\end{figure} 
\begin{figure}[htb]
  \begin{center} 
    \vspace*{1mm} 
    \rotatebox{0.}{\scalebox{0.37}{\includegraphics*{H1prelim-02-133.fig7.eps}}}
    \caption{{\it  
    The cross section for forward jet production on hadron level, as a
    function of \ptjet\  for $\ptjet > 3.5$~GeV (left) and
    $\ptjet > 5 $~GeV (right).  Also shown are the 
    predictions from the CDM, 
    RG and CASCADE Monte Carlos.
    \label{fwdjet-had-ptjet}}}
  \end{center}
\end{figure} 
\section{Conclusion}
A new measurement of the forward jet production cross section 
as a function of \xbj , \xjet\ and \ptjet\ has been performed
using an integrated luminosity of  $13.72$ pb$^{-1}$. The data are up to a factor
of two larger than the predicted cross section based on ${\cal O}(\alpha_s)$ and
QCD calculation in the collinear factorization ansatz (DGLAP). 
\par
Using a hadron
level Monte Carlo model incorporating resolved virtual photon processes in
addition to the usual direct photon processes, the data are reasonably well
described. Also the Color Dipole Model, which simulates higher order QCD
radiation without strong ordering of the transverse momenta of the emitted
partons, describes the measurements well. The more sophisticated CCFM approach,
which is based on angular ordering coming from color coherence, predicts  too
high a rate of forward jet events.
\vspace{3cm}
\raggedright 
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\end{thebibliography}

\end{document}

