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\noindent
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000


\vspace*{3cm}

\begin{center}
  \Large
  {\bf 

Measurement of Dijet Cross-Sections with Leading Neutrons
in Photoproduction at HERA}

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

\begin{abstract}

\noindent
An analysis is presented of dijets in photoproduction
where a leading neutron with an energy 
$E_n >400$~GeV and angle $\theta_n<0.8$~mrad with respect to the proton
direction is detected.
The average photon-proton center-of-mass energy is about 
$<W_{\gamma p}>\approx 200$~GeV.
Differential cross sections ${\rm d}\sigma/{\rm d}E_T^{jet}$ 
and ${\rm d}\sigma/{\rm d}\eta^{jet}$
are measured where $E_T^{jet}$ and $\eta^{jet}$ are jet
transverse energy and pseudorapidity.
Furthermore differential cross--sections in $x_\gamma^{jet}$ and
$x_\pi^{jet}$ are given where $x_\gamma^{jet}$ is the fraction of
the photon momenta entering the hard scattering, and 
$x_\pi^{jet}$ is the fraction of pion momenta in a model where
the interaction proceeds via exchange of a pion.
The  Monte Carlo predictions based on standard
photoproduction processes or based on the one-pion-exchange model and
using different parametrizations for the pion structure function
are compared to the measurements.
\end{abstract}


\vfill
\begin{flushleft}
  {\bf Abstract: 959} \\
  {\bf Parallel session: PA-02} \\
  {\bf Plenary talk: PL-12} 
\end{flushleft}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}

The cloud of virtual pions contained in the proton 
%Hadronic correlations inside the proton in the form of virtual pions are
%is believed to play
plays
an important dynamical role in the structure of the
nucleon.  It has been shown (e.g. in \cite{Holtmann,PovhKop,Przy})
that the pion-pole
contribution to Deep Inelastic Scattering (DIS) can reliably be determined
by studying the production of highly energetic forward neutrons. The
parton distributions of the pion in the region of $x\gsim 0.2$ have been
constrained by fixed target experiments. Additionally, the analysis of
leading neutron data in DIS at HERA performed by the H1
Collaboration~\cite{H1LN} made possible for the first time a measurement
os the pion structure function at small Bjorken-$x$ 
($\sim 10^{-3}- 10^{-2}$).

Another sensitive probe of the structure of interacting particles is
the production of high $p_T$ jets in hard hadronic interactions. Thus, by
tagging dijet events with a leading neutron in the final state, it should be possible to extract information on the parton
distributions in the pion.  In this paper we present
measurements of the jet production differential cross-sections in photoproduction for events with a leading neutron in the final state which has
energy $E_n>400$~GeV and angle $\theta_n<0.8$~mrad. The cross-sections
are measured differentially in jet transverse energy $E_T^{jet}$,
in pseudorapidity $\eta^{jet}$, and in the momentum fractions of the photon and
the pion carried by the interacting partons, $x_\gamma^{jet}$ and 
$x_\pi^{jet}$.
Different predictions in the form of Monte Carlo simulations are compared to the measurements.
% For the POMPYT Monte Carlo model, which is based on One Pion
% Exchange (OPE), predictions are obtained using different
% parameterizations of the pion structure function.

\section{Event selection}

In this analysis data are used which were collected by the H1 detector in
the years 1996--97 corresponding to an integrated luminosity of
$19.2~\rm pb^{-1}$. 
 Photoproduction events are selected by measuring the
scattered electron in the electron detector of the luminosity system. The
scaled photon energy $y \equiv E_e/E_e^0$ is required to be within $0.3<y
<0.65$, where $E_e$ is the energy of the scattered electron in the
electron detector and $E_e^0$ is the electron beam energy ($27.5$~GeV).
 These requirements restrict the photon virtuality to be $Q^2<0.01~\rm GeV^2$
and
the total center-of-mass energy of the photon--proton system to be
$156<W_{\gamma p}<242$~GeV.
Furthermore, the $z$-coordinate of the reconstructed vertex is required to
lie within $30$~cm of the nominal interaction point.  Jets are identified in
the Liquid Argon Calorimeter (LAr) by means of a cone-type algorithm
with a cone size of $R=\sqrt{\Delta\eta^2+\Delta\phi^2}=1$. Finally,
events are selected which
have exactly two jets with transverse energy $E_T^{jet}>4$~GeV and
pseudorapidity $-1<\eta^{jet}<2$.

Leading neutrons are detected in the Forward Neutron Calorimeter
(FNC) which consists of lead and scintillator fibres and which is located $107$~m away from
the nominal H1 interaction point in the proton beam direction.
(for details see~\cite{H1LN}). 
The acceptance of the FNC is defined by the aperture of the HERA beam pipe
magnets and it corresponds to neutron scattering angles of about $\theta_n
\lsim 0.8$~mrad. For this analysis the energy of the neutron in the FNC is
required to be $E_n>400$~GeV.

In total, about 320,000 dijet events are selected, from which 3187~events
satisfy $E_n>400$~GeV. If the cut on jet transverse
energy is increased from $4$ to $7$~GeV, then the total dijet data sample
is reduced to about 41,000 events and the neutron sample to 327 events.


\section{Monte Carlo models}

To correct the data distributions for biases and losses due to the
apparatus and to compare the theoretical models with data,
the POMPYT~2.6~\cite{POMPYT} and PYTHIA~5.7~\cite{PYTHIA} Monte Carlo
programs are used. 

POMPYT simulates leading neutron production using pion exchange. In this
program, the cross-section for leading neutron production is proportional
to the product of a pion flux factor and a pion structure function.  In
the present analysis the pion flux factor is taken from
Holtmann et al.~\cite{Holtmann}. The pion parton distributions are
simulated according to the GRV-$\pi$-LO parameterizations~\cite{GRV1}.
For the comparisons with data, additional POMPYT predictions based on different
parton distributions are also used~\cite{others}.

PYTHIA simulates leading neutron production using the JETSET string
fragmentation model. The program includes the possibility for additional
hard interactions between the remnant partons. These {\em multiple
interactions} increase the underlying energy in the event and improve
the description of jets and energy flow in inclusive hard photoproduction
measurements ~\cite{eflow}. When comparing PYTHIA predictions with data,
simulations are used both with and without multiple interactions.

The parton densities in the proton are generated in PYTHIA
according to the GRV-LO parameterization~\cite{GRV2}.
Both PYTHIA and POMPYT use the GRV-LO parameterizations
for the parton densities in the photon~\cite{GRV3}.


\section{Results}

\begin{figure}[h]
\centering
%\epsfig{file=/afs/desy.de/user/b/bunar/public/prel/fig1.en.eps,
\epsfig{file=/afs/desy.de/user/b/bunar/h1/paper/H1prelim-00-015.fig1.eps,
height=100mm}
\caption{The distributions of leading neutron energy $E_n$ 
for data and POMPYT and PYTHIA Monte Carlo.}
\label{tiltnotilt}
\end{figure}

Figure~\ref{tiltnotilt} shows the distributions of the 
energy of the
neutrons measured in the FNC uncorrected for inefficiency and acceptance. Also shown are the expectations from the POMPYT and PYTHIA Monte Carlo simulations
(with and without multiple interactions).
The standard JETSET fragmentation model (used by PYTHIA) fails to reproduce acceptably the neutron energy spectrum,
predicting a distribution which
is shifted towards lower energies.
POMPYT, on the other hand, describes the energy
spectrum well for $E_n\gsim 400$~GeV, thereby demonstrating the necessity in the FNC energy spectrum for a colour singlet component in the proton manifest in the form of pion exchange and its explicit contribution to leading neutron production.  The large difference between data
and Monte Carlo at low $E_n$ is due to background from neutral
electromagnetic particles ($\pi^0,\gamma$-s) which are present in
the data but 
not in the Monte Carlo simulations used for this analysis.
For neutron energies above $E_n>400$~GeV this contribution is
below $1\%$ and is neglected in the following.
%
The high-energy tail of the neutron energy spectrum is due to the small
attenuation length of scintillating fibres ($1.7\pm 0.2$~m) in the FNC which leads to an
over-estimation of the incident particle's energy and worsening
of energy resolution ($\sigma(E)/E \approx 20\%$ for energies
between $300$ and $800$~GeV)~\cite{H1LN}.

To calculate the cross-sections, the data have been corrected for
trigger efficiency, 
%($\sim 90\%\pm 5\%$), 
the neutron detection efficiency of the FNC
($93\%\pm 5\%$)\cite{H1LN} and the acceptances of the FNC
and electron detector. The
corrections for detector effects were calculated using the POMPYT
Monte Carlo simulation which in general describes well all measured distributions.

The resulting cross-sections for jet production with
$E_T^{jet}>4$~GeV and events with $E_n>400$~GeV and $\theta_n<0.8$~mrad
are shown in Figs.\ref{crsec1}--\ref{crsec2}.  $E_T^{jet}$ and
$\eta^{jet}$ are the jet
transverse energy and pseudorapidity (positive $\eta^{jet}$ corresponds to the proton direction). $x_\gamma^{jet}$ and $x_\pi^{jet}$
are the fractional momenta of the photon and pion carried by the partons
involved in hard interaction. $x_\gamma^{jet}$ and $x_\pi^{jet}$ are
calculated from the jet $E_T^{jet}$ and $\eta^{jet}$ as follows:
$$
x_\gamma^{jet}=(E_{T,1}^{jet}e^{-\eta_1^{jet}}+
                 E_{T,2}^{jet}e^{-\eta_2^{jet}})/2yE_e^0
\hspace*{1cm}
x_\pi^{jet}=(E_{T,1}^{jet}e^{\eta_1^{jet}}+
              E_{T,2}^{jet}e^{\eta_2^{jet}})/2(E_p^0-E_n)
$$
Here $E_e^0=27.5$~GeV and $E_p^0=820$~GeV are the incident electron 
and proton beam energies.
%
In the figures the inner error bars represent the statistical errors,
while the
outer error bars show the quadratic sum of statistical and systematic
errors combined. The total systematic errors are about 27\%.
%The uncorrelated errors arise from the uncertainty on
%the FNC acceptance (20\%) and the trigger efficiency (5\%). The
%correlated errors are due to the uncertainty on the FNC efficiency (5\%),
%the LAr hadronic energy scale (16\%), the electron detector acceptance
%and the luminosity measurement (6\%).

% 20+5 uncorrelated
% 16+6+5 correlated

In Figure~\ref{crsec1} the POMPYT and PYTHIA predictions are compared with the measured cross-sections. Both the PYTHIA simulation without multiple interactions and the
POMPYT simulation predict somewhat higher cross--sections than measured, and they do not
describe the dependence on pseudorapidity in that they predict 
higher cross-section at low pseudorapidities.
% describe the shapes of the distributions well, but predict a
% somewhat higher cross-section. 
When multiple interactions are included in the PYTHIA model the predicted cross-section is higher than the measurements by a factor~3.

In the framework of the one-pion-exchange model in POMPYT, the sensitivity of the
measurement to different choices for the pion structure function
\cite{others} is presented in
Figure~\ref{crsec2}. It is clear that the remedy for the disagreement between the POMPYT prediction and the measurements is not to be found in a different choice of otherwise acceptable parametrisations of the pion structure function.

Figure~\ref{crsec3} shows similar cross-sections but after increasing the
cut on the jet transverse energy from $4$ to $7$~GeV. At higher jet
energies all Monte Carlo models used for comparison describe the data
distributions well, both in shape and normalization. We note that with
this higher $E_T^{jet}$ cut there is a larger fraction of direct
photoproduction ($x_\gamma \approx 1$) as expected kinematically.

Figure~\ref{crsec4} shows the sensitivity of the POMPYT prediction of the cross sections to the same choices as above for the pion structure function. It is clear that the present level of systematic uncertainty in the measurement means that no preference for any of the pion
structure function parameterizations can yet be given.


\section{Summary}

Measurement of the differential jet cross-sections are presented as
function of $E_T^{jet}$, $\eta^{jet}$, $x_\gamma^{jet}$ and $x_\pi^{jet}$
in photoproduction (in the kinematic range $Q^2<0.01~ \rm GeV^2$,
$0.3<y<0.65$)
for events with an energetic forward neutron (leading neutron) in the final state.  

A model which does not include pion exchange fails to describe
the neutron energy spectrum.
A model which includes one pion exchange describes the neutron energy
spectrum well, thereby establishing the need for a colour singlet component of proton structure which is manifest in the form of pion exchange and leading neutron production. The model also reproduces the observed jet differential
production cross sections for $E_T^{jet}>7~$GeV, but fails for lower $E_T^{jet}>4~$GeV. 
Within the present experimental uncertainties of this measurement, it is not yet
possible to discriminate between different parameterizations of the
pion structure function.

%The POMPYT Monte-Carlo model based on one-pion-exchange
%overestimates the cross-sections at low jet energies ($E_T^{jet}>4~$GeV)
%and doesn't describe the shape of jet pseudorapidity distribution.
%For higher jet energies ($E_T^{jet}>7~$GeV) POMPYT describes the data
%distributions well. The PYTHIA Monte-Carlo model  where neutrons
%are produced from the fragmentation process is also able to describe
%the jet distributions but it fails to describe the neutron energy
%distributions.
                            


%
%The POMPYT Monte Carlo model based on One-Pion-Exchange describes the
%data
%distributions well although it slightly overestimates the cross-sections
%at low jet energies ($E_T^{jet}>4$~GeV). The PYTHIA Monte Carlo model
%where neutrons are produced from the fragmentation process also describes
%the jet distributions well but it fails to describe the neutron energy
%distributions.

\begin{thebibliography}{99}
\bibitem{Holtmann}
H. Holtmann et al., {\em Phys.Lett}.~{\bf B338}~(1994)~363.
\bibitem{PovhKop}
B. Kopeliovich, B. Povh and I. Potashnikova,
{\em Z. Phys.} {\bf C73} (1996) 125.
\bibitem{Przy}
M. Przybycie\'{n}, A. Szczurek and G. Ingelman,
{\em Z. Phys.} {\bf C74} (1997) 509.
\bibitem{H1LN}
%``Measurement of leading proton and neutron production in deep
%inelastic   scattering at HERA."\\
H1 Collaboration, {\em Eur.~Phys.J}.~{\bf C6}~(1999)~587.
\bibitem{POMPYT}
P.Bruni, G. Ingelman, {\em Proceedings of the Europhysics Conference,
Marseille, France, July 1993, p.595};\\
see also http://www3.tsl.uu.se/thep/pompyt
\bibitem{PYTHIA}
PYTHIA Version 5.722,
T. Sj\"ostrand, {\em Comp. Phys. Comm.} {\bf 82} (1994) 74;
\newline
T. Sj\"ostrand, ``PYTHIA 5.7 and JETSET 7.4'',
CERN-TH.7112/93 (1993) (revised Feb. 1994).                 
\bibitem{GRV1}
M. Gl\"uck, E. Reya and A. Vogt, {\em Z. Phys.} {\bf C53} (1992) 651.          \bibitem{others}
J.F. Owens, {\em Phys.Rev.} {\bf D30} (1984) 943;\\ 
P.J. Sutton et al., {\em Phys.Rev.} {\bf D45} (1992) 2349. 
\bibitem{eflow}
H1 Collaboration, {\em Z. Phys.} {\bf C70} (1996) 17.
\bibitem{GRV2}
M. Gl\"uck, E. Reya and A. Vogt, {\em Z. Phys.} {\bf C53} (1992) 127.
\bibitem{GRV3}
M. Gl\"uck, E. Reya and A. Vogt, {\em Phys. Rev.} {\bf D46} (1992) 1973.

\end{thebibliography}


\begin{figure}[p]
 \centering
\epsfig{file=/afs/desy.de/user/b/bunar/h1/paper/H1prelim-00-015.fig2.ps,
height=160mm,bbllx=20pt,bblly=200pt,bburx=550pt,bbury=740pt,clip= }
\caption{Dijet differential cross-sections as function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>4$~GeV, $-1<\eta^{jet}<2$ and with leading neutrons
$E_n>400$~GeV, $\theta_n<0.8$~mrad. Cross-sections correspond
to kinematic range $Q^2<0.01~\rm GeV^2$ and $0.3<y<0.65$.
The POMPYT and PYTHIA Monte Carlo 
predictions are compared to the measurements.}
\label{crsec1} 
\end{figure} 
 
\begin{figure}[p]
 \centering
\epsfig{file=/afs/desy.de/user/b/bunar/h1/paper/H1prelim-00-015.fig3.ps,
height=160mm,bbllx=20pt,bblly=200pt,bburx=550pt,bbury=740pt,clip= }
\caption{Dijet differential cross-sections as function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>4$~GeV, $-1<\eta^{jet}<2$ and with leading neutrons
$E_n>400$~GeV, $\theta_n<0.8$~mrad. Cross-sections correspond
to kinematic range $Q^2<0.01~\rm GeV^2$ and $0.3<y<0.65$.
The POMPYT Monte Carlo predictions using different parameterizations 
for the parton distributions in the pion
are compared to the measurements.}
\label{crsec2} 
\end{figure}  

\begin{figure}[p]
 \centering
\epsfig{file=/afs/desy.de/user/b/bunar/h1/paper/H1prelim-00-015.fig4.ps,
height=160mm,bbllx=50pt,bblly=200pt,bburx=550pt,bbury=740pt,clip= }
\caption{Dijet differential cross-sections as function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>7$~GeV, $-1<\eta^{jet}<2$ and with leading neutrons
$E_n>400$~GeV, $\theta_n<0.8$~mrad. Cross-sections correspond
to kinematic range $Q^2<0.01~\rm GeV^2$ and $0.3<y<0.65$.
The POMPYT and PYTHIA Monte Carlo 
predictions are compared to the measurements.}
\label{crsec3} 
\end{figure} 
 
\begin{figure}[p]
 \centering
\epsfig{file=/afs/desy.de/user/b/bunar/h1/paper/H1prelim-00-015.fig5.ps,
height=160mm,bbllx=20pt,bblly=200pt,bburx=550pt,bbury=740pt,clip= }
\caption{Dijet differential cross-sections as function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>7$~GeV, $-1<\eta^{jet}<2$ and with leading neutrons
$E_n>400$~GeV, $\theta_n<0.8$~mrad. Cross-sections correspond
to kinematic range $Q^2<0.01~\rm GeV^2$ and $0.3<y<0.65$.
The POMPYT Monte Carlo predictions using different parameterizations 
for the parton distributions in the pion
are compared to the measurements.}
\label{crsec4} 
\end{figure}  

\end{document}

