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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
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 988}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
     Measurement of Dijet Cross-Sections with Leading Neutrons 
     in $ep$ interactions at HERA}

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

\begin{abstract}

\noindent


Measurements are presented of the production in $ep$ 
interactions at HERA of dijets in conjunction with
a leading neutron. The energy of the neutron is required
to be greater than 400 GeV and its angle with respect to
the incoming proton direction less than 0.8 mrad.
    Differential cross-sections have
    been measured in the photoproduction ($Q^2 < 10^{-2} \GeV^2$) 
    and deep inelastic ($2 < Q^2 < 80~ \GeV^2$) regimes. 
    Monte Carlo simulations based on standard $ep$ interaction
    processes or on the one-pion-exchange model and
    using several parameterizations for the pion structure
    function are compared to the measurements.
    Properties of the hadronic final state are further 
    investigated by measuring, for the fraction of dijet events 
    containing a leading neutron in the final state,
    the dependence on jet and kinematical variables.


\end{abstract}


\end{titlepage}

\pagestyle{plain}

%\boldmath
\section{Introduction}

The cloud of virtual pions contained in the proton 
plays an important 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 be 
reliably determined
by studying the production of highly energetic forward neutrons. While the
parton distributions of the pion in the region of Bjorken-$x\gsim 0.2$ 
have been constrained by fixed target experiments, 
the first measurement of pion structure at small $x (\sim 10^{-3}- 10^{-2}$)
was made possible by the analysis of
leading neutron data in DIS at HERA, performed by the H1
Collaboration~\cite{H1LN}.
The parton distributions of the pion can be probed in hard hadronic
interactions, which are characterized by production of jets with high 
transverse momentum $p_T$.
A first measurement of dijet production in events with a leading neutron in 
photoproduction was recently presented by the ZEUS Collaboration~\cite{ZEUSln}.

%
In this paper jet production is studied 
in events which contain in the final state a leading neutron $n$ with
energy $E_n>400$~GeV and polar angle $\theta_n<0.8$~mrad
\footnote{The H1 coordinate system has its 
origin at the nominal interaction point and its $z$ axis 
along the incoming proton direction. Polar angles $\theta$ 
are measured with respect to the $z$ direction.}.
The measurements are 
made in the quasi-real photoproduction ($Q^2<10^{-2}\rm~GeV^2$) and
DIS ($2<Q^2<80~\rm GeV^2$) regimes.
%
The cross-sections
are measured differentially in $Q^2$, jet transverse energy $E_T^{jet}$ 
and pseudorapidity $\eta^{jet}$, and in the momentum fractions of the 
photon and
the pion carried by the interacting partons, $x_\gamma^{jet}$ and 
$x_\pi^{jet}$.
Several 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.

In addition, the factorization properties of leading neutron 
production are studied
% In assumption of factorization no correlations between the hadron 
% production in current and target fragmentation regions are expected.
% The factorization can be tested 
 by comparing the jet production rate in inclusive and leading neutron 
 data samples.
%
%(e.g. jet) production at central rapidities in
%connection with leading baryons in the proton
%fragmentation region.  
%
%by measuring the
%fraction of leading neutrons events in inclusive dijet sample.

\section{Event selection}
The data used in this analysis were collected with the H1 detector 
in the years 1996--97, corresponding to an integrated luminosity of
$19.2~\rm pb^{-1}$. 

In the photoproduction analysis, the final state electron is detected
in the electron detector of the luminosity system, which has an acceptance 
such  that $Q^2<10^{-2}$~GeV$^2$.
The scaled photon energy $y \equiv 1-E'_e/E_e$ 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 $E_e$ is the electron beam energy ($27.5$~GeV).

The final state electrons in DIS are required to have polar scattering 
angles $156^{\rm o}<\theta_{\rm e}<176^{\rm o}$ 
and are identified using the backward
SpaCal calorimeter in combination with a track segment reconstructed in a 
backward drift chamber (BDC). The energy $E'_e$ of the electron candidate
was required to be
greater than 10~GeV. The inclusive kinematic variables are calculated as
$$   \rm
Q^2=4E_eE'_ecos^2\frac{\theta_e}{2}~~~~~~~
y=1-\frac{E'_e}{E_e}sin^2\frac{\theta_e}{2}
$$
This analysis is restricted to the range: 
$2<Q^2<80\rm~GeV^2$ and $0.1<y<0.7$.

All events which satisfy the selection cuts are subjected to a jet search 
using a cone algorithm
with radius $R=\sqrt{\Delta\eta^2+\Delta\phi^2}=1$. The jet finding 
is performed in the $\gamma^*p$ center of mass frame, with transverse 
energies calculated  relative to the $\gamma^*$ axis in that frame.
Exactly two jets with transverse energy $E_T^{jet}>6~\rm GeV$ are required.
To ensure that the bulk of the jet energy is restricted  to the region
covered by the LAr calorimeter, events are only considered if both jets
lie within  the region of laboratory 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 corresponds to neutron scattering angles of 
$\theta_n \lsim 0.8$~mrad.
For this analysis the energy of the neutron in the FNC is
required to be $E_n>400$~GeV.

The final photoproduction data sample contains about 80,000 dijet events 
of which 605 events satisfy the neutron identification requirement.
In the DIS sample
25,000 dijet events are selected, of which 334 events contain a 
leading neutron.
% 4 gev 317000 (was 320,000)-->2905   66500-->933  
% 5 gev 157000-->1241   36000-->527
% 6 gev  79000-->605    21500-->284
% 7 gev  41000-->327    13000-->179

\section{Monte Carlo models}

In order to correct the data distributions for biases and losses due to the
apparatus, to correct for the effects of QED radiation and 
to compare theoretical 
models with the data, 
%POMPYT~2.6~\cite{POMPYT}, 
%PYTHIA~5.7~\cite{PYTHIA},
%RAPGAP~2.8~\cite{RAPGAP}, 
%DJANGO
several Monte Carlo generator programs are used. 

POMPYT~\cite{POMPYT} and RAPGAP~\cite{RAPGAP} simulate 
leading neutron production using pion exchange. 
In these programs, 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, predictions based on other pion
parton distributions are also used~\cite{others}.

Standard fragmentation mechanisms which produce leading neutrons 
are used in the Monte Carlo event generators
PYTHIA~\cite{PYTHIA}, DJANGO~\cite{DJANGO} and RAPGAP. 

%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}.

In general, the Monte Carlo simulations describe all relevant 
reconstructed distributions well.

\section{Results}

\begin{figure}[h]
\epsfig{file=H1prelim-01-114.fig1.eps,width=0.95\textwidth}
\caption{The distributions of leading neutron energy $E_n$ 
for data and Monte Carlo detector simulations. 
 Figure 1a and 1b correspond to the photoproduction
($Q^2\sim 0$)
and  DIS ($2<Q^2<80~\rm GeV^2$) regimes, respectively.}
\label{tiltnotilt}
\end{figure}


Figure~\ref{tiltnotilt} shows the distributions of the 
energy of the  neutrons measured in the FNC 
before correction for detector inefficiencies and acceptance effects,
together with 
the expectations from Monte Carlo simulations. 
Models which do not explicitly include the pion exchange mechanism
(PYTHIA, RAPGAP) fail to reproduce acceptably the neutron energy spectrum,
predicting distributions which are shifted towards lower energies.
POMPYT and RAPGAP, on the other hand, describe 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 simulations at low $E_n$ is due to the contribution
of processes other than pion exchange and to background from neutral
electromagnetic particles ($\pi^0,\gamma$), which is 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 
deterioration of the FNC energy response
%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.

% 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 dijet production with
$E_T^{jet}>6$~GeV and events with $E_n>400$~GeV and $\theta_n<0.8$~mrad
are shown in Figs. \ref{crsec1}--\ref{crsec2}  for the photoproduction and
in Fig. \ref{crsec3}  for the DIS measurements.
$E_T^{jet}$ 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:
$$
x_\gamma^{jet}=(E_{T,1}^{jet}e^{-\eta_1^{jet}}+
                 E_{T,2}^{jet}e^{-\eta_2^{jet}})/2yE_e
\hspace*{1cm}
x_\pi^{jet}=(E_{T,1}^{jet}e^{\eta_1^{jet}}+
              E_{T,2}^{jet}e^{\eta_2^{jet}})/2(E_p-E_n)
$$
Here $E_e=27.5$~GeV and $E_p=820$~GeV are the incident electron 
and proton beam energies.
%
The $ep$ cross-sections are corrected to the Born level using the HERACLES
interface to the RAPGAP Monte Carlo program.
In the figures the inner error bars represent the statistical errors,
while the
outer error bars show the quadratic sum of the statistical and systematic
errors. 
The total systematic errors are about 27\% for the photoproduction 
and about 32\% for the DIS measurements.
In Fig.~\ref{crsec3} (DIS) the overall normalization error of $\sim 25\%$
is not shown.

%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 Figs.~\ref{crsec1}-\ref{crsec3} the different Monte Carlo 
predictions are compared with the measured cross-sections.
All Monte Carlo models used for comparison, also PYTHIA which 
does not simulate
pion exchange,  provide satisfactory descriptions 
of the data distributions, both in shape and normalization. 

In the framework of the one-pion-exchange model as implemented in POMPYT, 
the sensitivity of the
measurement to different choices for the pion structure function
\cite{others} is presented in
Fig.~\ref{crsec2}. 
It is clear that with the present level of experimental uncertainty,
 no preference for any of the pion
structure function parameterizations can yet be given.


%************************************************
\section{Test of factorization}

%In the assumption of factorization
Assuming factorization, 
no correlations between the hadron
production in the current and target fragmentation regions are expected.
Factorization is studied here by measuring the fraction of events with a
leading neutron in the 
inclusive dijet sample as a function of the 
jet kinematical variables.

Results are shown in Fig.~\ref{ratio1} as functions
of jet $E_T^{jet}$ and $x_\gamma^{jet}$.
%and  $x_p^{jet}~(=\Sigma  E_T^{jet}e^{\eta^{jet}}/2E_p)$.
Only the photoproduction data  was used for this measurement.
The inner error bars represent the statistical errors, 
while the outer error bars are the quadratic sum of
statistical and systematic errors.
% syst. errors 20% (FNC acceptance)+5% (FNC efficiency)+15% GENE/REC
The systematic errors are highly correlated, since the
main source of systematic errors is the uncertainty of the FNC
acceptance.
The events with a leading neutron
with $E_n>400~\rm GeV$ amount to about $3-3.5\%$ of the inclusive dijet sample.
The fraction of leading neutron events is almost flat in jet $E_T$, 
while it exhibits a strong dependence 
on $x_\gamma^{jet}$-- at high  $x_\gamma^{jet}$  it is twice as large
as at low  $x_\gamma^{jet}$. Possible explanations of this rise
can be kinematics of the processes, or differences either    
in the remnant interactions or in the parton distributions involved 
in leading neutron events as compared to the
inclusive sample.


In order to study 
the transition from photoproduction to DIS the fraction of leading
neutron events as a function of $Q^2$ was measured. The 
resulting distribution
is shown in Fig.\ref{ratioq2}.
The distribution does not show significant deviations from flatness.
% $\sim 5.5\%$ at $Q^2\sim 30~\rm GeV^2$.
% Fig.\ref{ratioq2} shows the fraction of leading neutron events as function 
% of $Q^2$. 

These observations are in general agreement with the factorization 
hypothesis.

\section{Summary}

Measurements of the differential jet cross-sections are presented as a
function of $E_T^{jet}$, $\eta^{jet}$, $x_\gamma^{jet}$ and $x_\pi^{jet}$
in photoproduction  ($Q^2<10^{-2}\rm GeV^2$)
%(in the kinematic range $Q^2<10^{-2}\rm GeV^2$, $0.3<y<0.65$)   
and in deep inelastic $ep$ scattering 
($2<Q^2<80~\rm GeV^2$) for events with an energetic forward neutron 
(leading neutron) in the final state.  

Models which do not include pion exchange fail to describe
the neutron energy spectrum.
Models which include one pion exchange describe 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 models also reproduce 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 fraction of dijet  events with a leading neutron is in general
%agreement with the factorization assumption. 


The observed fraction of dijet events with a leading neutron
shows no significant dependence on values of the jet 
$E_T$ or on the scale $Q^2$, in agreement with the
hypothesis that the proton-pion and pion-photon vertices are
independent.


\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, C. Adloff et al.,  {\em Eur.~Phys.J}.~{\bf C6}~(1999)~587.
\bibitem{ZEUSln}
ZEUS Collaboration, J. Breitweg et al., {\em Nucl.~Phys.}.~{\bf B596}~(2001) 3.
\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{RAPGAP}
RAPGAP,
H. Jung, {\em Comp. Phys. Comm.} {\bf 86} (1995) 147;\\
(see also http://www.desy.de/\~jung/rapgap.html)
\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{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{DJANGO}
DJANGO, G.A. Schuler and H. Spiesberger, Proceedings pf the Workshop
\it Physics at HERA, \rm Eds. W. Buchm\"uller and G. Ingelman, Vol.3
(1991) 1419.
                                                             
%\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.
%\bibitem{absorpt}
%N. Nikolaev, J. Speth, B. Zakharov, KFA-IKP-TH-1997-17, $hep-ph/9708290$.
%\bibitem{h1fps}
%H1 Collaboration, ``Measurement of the Photoproduction Cross-Sections
%with Leading Proton at HERA", in preparation

\end{thebibliography}


\begin{figure}[p]
 \centering
\epsfig{file=H1prelim-01-114.fig2.eps,width=0.95\textwidth}
\caption{Dijet differential $ep$ cross-sections as a function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>6$~GeV, $-1<\eta^{jet}<2$ and with a leading neutron
$E_n>400$~GeV, $\theta_n<0.8$~mrad. The cross-sections correspond
to the kinematical range $Q^2<10^{-2}\rm GeV^2$ and $0.3<y<0.65$.
POMPYT, RAPGAP and PYTHIA Monte Carlo 
predictions are compared to the measurements.}
\label{crsec1} 
\end{figure} 
 
\begin{figure}[p]
 \centering
\epsfig{file=H1prelim-01-114.fig3.eps,width=0.95\textwidth}
\caption{Dijet differential $ep$ cross-sections as a function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$x_\gamma^{jet}$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>6$~GeV, $-1<\eta^{jet}<2$ and with a leading neutron
$E_n>400$~GeV, $\theta_n<0.8$~mrad. The cross-sections correspond
to the kinematical range $Q^2<10^{-2}\rm GeV^2$ and $0.3<y<0.65$.
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=H1prelim-01-114.fig4.eps,width=0.95\textwidth}
\caption{Dijet differential cross-sections as function of
 jet $E_T^{jet}$, $\eta^{jet}$,
$Q^2$ and $x_\pi^{jet}$ for events with
$E_T^{jet}>6$~GeV, $-1<\eta^{jet}<2$ and with a leading neutron
$E_n>400$~GeV, $\theta_n<0.8$~mrad. The cross-sections correspond
to the kinematical range $2<Q^2<80\rm GeV^2$.
RAPGAP Monte Carlo predictions, in which pion exchange is included, 
are compared to the measurements.}
\label{crsec3} 
\end{figure}  

\begin{figure}[h]
 \centering
\epsfig{file=H1prelim-01-114.fig5.eps,width=0.95\textwidth}
\caption{The fraction of dijet events 
with a leading neutron in photoproduction
as a function of $E_T^{jet}$ and
$x_\gamma^{jet}$ 
for events with
$E_T^{jet}>6~GeV$, $-1<\eta^{jet}<2$.} 
% and $E_n>400~GeV$, $\theta_n<0.8mrad$.}
\label{ratio1} 
\end{figure}  
\vspace*{-1cm}

\begin{figure}[h]
 \centering
\epsfig{file=H1prelim-01-114.fig6.eps,height=100mm}
\caption{The fraction of dijet events with a leading neutron
as a function of  $Q^2$. The first point ($Q^2\sim 0$) corresponds to 
photoproduction.}
\label{ratioq2} 
\end{figure}  

\end{document}
