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\begin{document}

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\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 1002}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
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\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf                  

Measurement of Inclusive Cross-Sections of the
   Photoproduction of Protons at HERA. 


}

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

\begin{abstract}

 The inclusive cross-sections for the photoproduction 
    of protons as a function of transverse momentum and
    rapidity are measured with the H1 detector at the $ep$
    collider HERA. The analysis is performed for scattering
    processes in a kinematic region restricted to  
    inelasticities $0.3 < y_e < 0.7$ and virtuality of the
    exchanged photon $Q^2 < 0.01 \GeV^2$.
    The measurements are compared to expectations from 
    QCD-based models as a means of investigating the 
    sensitivity of baryon production in hadronisation
    to the properties of the QCD perturbative vacuum.

\end{abstract}  



\vspace{1.5cm}

\noindent


\end{titlepage}

\pagestyle{plain}



 
\section{Introduction} 

\noindent 

Measurements by the H1 and ZEUS Collaborations of the hadronic final state 
at the $ep$ collider HERA have proven important in probing  
QCD dynamics and have provided information on the partonic nature of the
proton and the photon\cite{mk}.  This paper continues a series of
studies which are designed to produce a picture of the $ep$ induced 
hadronic final state that is as complete as is experimentally possible.  
Measurements are presented of the kinematic properties of 
low transverse momentum protons\footnote{  
The term proton is used generically in this paper to also refer to an
anti-proton unless stated otherwise or when used in the context of
 the colliding beams.} inclusively photoproduced in
electron-proton
interactions. The aim of this study is to investigate, using QCD-based
models, baryonic production mechanisms and assess the environmental independence
of these processes. 
 
Within the framework of traditional QCD-based $ep$ scattering models, 
baryons are produced in the $ep$-induced hadronic final state through 
the conservation of the baryon number of the incoming 
 proton and a soft hadronisation mechanism in which the partonic 
final state is converted to hadrons. This is achieved by hadronising a
series of colour strings\cite{string} stretched between colour triplet 
charges in the partonic final state. This leads to the
vacuum production of quark, anti-quark ($q,\bar{q}$) and
diquark, anti-diquark  ($qq,\bar{q}\bar{q}$) pairs which eventually form 
 bound states of mesons and baryons.  However, this approach may 
not be valid in gluon-dominated processes at HERA which
give rise to configurations of octet colour charges. 
The hadronisation of such fields 
would be characterised by a lower baryon rate than in fields 
between triplet charges\cite{gunnar}.  

Such a test of this aspect of non-perturbative QCD modelling can be made
by
comparing $ep$ measurements with string model calculations, with free
parameters determined from
 hadronic final state
measurements in    
$e^+e^-$ collisions. This  
prescription described well earlier measurements of the production 
characteristics of $K^0_s$ and $\Lambda$ particles in $ep$ 
interactions\cite{dave1,dave2} albeit with limited statistical precision. 
This paper presents complementary
measurements of protons in the previously uncovered fragmentation-dominated low momentum region
 and uses a data-set five times as great as used in the earlier work.  

 

\section{Event Selection and Detector Description}


Experimental data for this analysis were collected with
the  H1 detector\cite{H1DET} during the
1996 running period, in which HERA collided 27.5 GeV positrons with 820
GeV
protons. The data sample used corresponds to an integrated luminosity of
6.0 pb$^{-1}$. 

Photoproduction events are characterised by the presence of the scattered
electron in the low angle electron tagger. This restricts the kinematic 
region over which this study is made to $Q^2<0.01$ GeV$^2$ and $0.3 <y_e
<0.7$ where $Q^2$ is the virtuality of the exchanged photon and $y_e$ is
the inelasticity of the scattered electron. 

The scattered electrons are identified by a first level trigger which
requires energy
in the electron tagger and the presence of several tracks in the central
tracking chamber which originate from the primary vertex. 

In order to perform the analysis in a region of high trigger acceptance,
an additional requirement is made that there are at least five 
tracks in the central tracking chamber following full event
reconstruction. 

To suppress beam-gas background events, both the summed hadronic
energy in the forward region of the Liquid Argon calorimeter and the total 
electromagnetic energy in the backward detector, the SPACAL, are required
to be greater than $2$ GeV.


Charged particles are measured in the H1 central 
tracker which covers the polar angle range of
$22^{\circ}<\theta<150^{\circ}$, where $\theta$ is defined 
with respect to the incoming proton direction. The specific ionisation
 energy loss 
of the particles, $dE/dx$, is also measured and this 
is used to identify the protons in this study in the high 
acceptance and resolution region of $0.3 < p_T < 0.55$ GeV and $-0.3 <
y < 0.3$, where 
$p_T$ is the transverse momentum relative to the beam-line and $y$ is the
rapidity of the particle. 

\section{QCD based models}

QCD-based calculations are confronted with the data via the 
PYTHIA model\cite{jetset74}, employing the GRV-LO proton and photon
parton densities\cite{grv}. 
%PHOJET1.04\cite{phojet} model.
%and PYTHIA5.722\cite{jetset74}. %Both of these
This scheme uses leading order (LO) QCD matrix elements to
 describe the hard
scattering processes and parton shower algorithms to produce
initial
and final state parton radiation. Multiple soft and hard parton interactions are 
also simulated. 


The PHOJET1.06a\cite{phojet} model of photoproduction is also used in this
analysis. This also uses leading order QCD matrix elements with matched 
parton showers and a phenomenological description of soft
photoproduction processes.

%These
%programs, differ, however in their treatment of multiple interactions and
%the transition from hard to soft processes at low transverse parton
%momentum. 

The Lund string model, as
implemented
in
JETSET 7.4\cite{jetset74}, performs the hadronisation step for both of
the above models.


The production of diquarks  within the Lund string model is 
regulated by several parameters, the most important of which in the
context of this work being the diquark suppression factor {\tt PARJ(1)} which
determines the probability of producing a $(qq, \bar{qq})$ pair 
relative to a $(q,\bar{q})$ pair in the colour field. Results from
$e^+e^-$ collisions at LEP favour a value of approximately
0.1\cite{eestudy}. 


\section{Results}

The measurements are made in the laboratory frame of reference and are
presented as the average cross-sections $E {d^3\sigma \over
d^3p}$ for the photoproduction
of protons and antiprotons, that is, half the sum of the proton and
anti-proton cross
sections. Here $E$ and $p$ are the proton energy and
momentum, respectively. 
This cross-section is shown as a function of the
particle transverse momentum  $p_T$ and rapidity $y$ ,  in figures 
\ref{fig1} and \ref{fig2}, respectively. The errors shown are the 
quadratic sum of the statistical and systematic uncertainties.  
The systematic component is dominant. Furthermore, the systematic 
uncertainies are highly correlated. 


Neither of the corrected distributions in figures \ref{fig1} and
\ref{fig2}  
displays a large variation over the kinematic range studied, although 
the data suggest a slow fall-off towards higher transverse momentum
values. 

The predictions of the QCD-based model PYTHIA are presented using diquark
suppression factors of 0.1 and 0.05. The model 
over-estimates the data with the $e^+e^-$-derived value of 0.1 although
it provides a fair description the shape of the spectra. However, 
a  description of both shape and yield is provided if a 
diquark suppression value of $0.05$ is used. 

This could signal an absence of the fragmentation universality of baryon
production within the currently used theoretical framework. However, more
studies are required of different baryon species over a wider range of
phase space range then covered in this work in order to investigate this. 

There are several major sources of systematic uncertainty in these
measurements. 
\begin{itemize}
\item The uncertainty on the acceptance calculations arising from
the forward and backward energy cuts and the cut on the observed
multiplicity of charged tracks was determined using Monte Carlo
simulations of the H1 detector response to different samples of PYTHIA and
PHOJET-generated events, and was found to be about 8\%.
\item The correction due to the inefficiencies in the first
level triggering of photoproduction events containing a proton was
determined to an accuracy of 5\%.
\item The correction due to the acceptance of the low angle electron
tagger also gives rise to a systematic error of 5\%.
\end{itemize}

Corrections to the proton yield arising from
nuclear interactions of inclusively 
produced hadrons with the material of the detector and beam pipe are
evaluated from an analysis of the distributions of the impact parameters
of candidate protons and anti-protons. The uncertainty on this background
removal procedure accounts for a systematic error on the proton yields of
less than 2\%.



\section{Summary}

First measurements are presented of the cross-section of  
protons inclusively produced in the range 
$0.3 < p_T < 0.55$ GeV and $-0.3 < y <0.3$  in photoproduction  
processes confined to the kinematic region $Q^2<0.01$ GeV$^2$ and
$0.3<y_e<0.7$.

The particle cross-sections 
fall off slowly with increasing transverse momentum
while they show very little dependence on rapidity. 

The QCD-based model PYTHIA was confronted with the data and found to give 
a good description of the data if a value of the diquark suppression factor 
of approximately 0.05 was used.  




\section*{Acknowledgements}   
We are grateful to the HERA machine group whose outstanding efforts have
made
and continue to make this experiment possible. We thank the engineers and
technicians for their work constructing and maintaining the H1 detector,
our
funding agencies for financial support, the DESY technical staff for
continual
assistance and the DESY directorate for the hospitality which they extend
to the non-DESY members of the collaboration.



\begin{thebibliography}{99}
\bibitem{mk} See for example: Michael Kuhlen, QCD and the Hadronic Final
State in Deep
Inelastic
Scattering at HERA, Habilitationsschrift, University of Hamburg,
1997 and references therein; \\
 Martin Erdmann, The Partonic Structure of the Photon, 
Photoproduction at the Lepton-Proton collider, HERA, Habilitationsschrift, University of Heidelberg,  
1996 and references therein.


\bibitem{string}
B. ~Andersson et al.,
Phys.\ Rep.\ {\bf 97} (1983) 31.
%\bibitem{cluster} B.R. ~Webber, \Journal{\NPB}{238}{492}{1984}.

\bibitem{gunnar} G. ~Ingelman, DESY-88-014, Feb. 1988, Invited 
talk given at 4$^{th}$ INFN Workshop on Very High Energy Proton-Proton 
Physics, Erice, Italy (1987).

\bibitem{dave1} H1 Collaboration, {S.~Aid et al.},
\Journal{\NPB}{480}{3}{1999}.
\bibitem{dave2} H1 Collaboration, {C.~Adloff et al.},
\Journal{\ZPC}{76}{213}{1997}.



%\bibitem{phojet} {R. Engel, Proc.\ of the XXIXth Rencontre de Moriond
%(1994) 321.}

\bibitem{jetset74}
T. ~Sj\"ostrand, Comp. Phys. Comm.\ {\bf 82} (1994) 74.
 

 





\bibitem{H1DET}
H1 Collaboration, I. Abt et al.,
Nucl. Instrum. Meth. {\bf A386}, (1996) 310.
 
%\bibitem{CJC} J. ~B\"urger et al., \Journal{\NIMA}{279}{217}{1989}.

%\bibitem{SPACA} H1 SPACAL Group, {R. D. Appuhn et al.},  
%\Journal{\NIMA}{386}{397}{1997}.

%\bibitem{lepto} G. Ingelman,
%                Proc. of the HERA workshop, eds W.~Buchm\"uller and
%                G.~Ingelman, Hamburg (1992) Vol. 3, 1366.

%\bibitem{ariadne} {L. L\"onnblad, \Journal{\CPC}{71}{15}{1992}.}


%\bibitem{DELPHI}
%DELPHI Collaboration,
%P. ~Abreu  et al., Zeit.\ Phys.\ {\bf C65} (1995) 587.

%\bibitem{ee}  OPAL Collaboration, D. ~Buskulie et al.,
%\Journal{\ZPC}{66}{355}{1995}.
\bibitem{pp} UA5 Collaboration, G. ~J. ~Alner et al., 
Phys. Rept. {\bf 154}:247-383, 1987  
%\bibitem{emc} EMC Collaboration, M. ~Arneodo et al.,
%\Journal{\PLB}{150}{458}{1985}

\bibitem{grv} M. ~Gl\" uck, E. ~Reya and A. ~Vogt,
\Journal{\PRD}{46}{1973}{1992}; \\
M. ~Gl\" uck, E. ~Reya and A. ~Vogt,
\Journal{\ZPC}{53}{127}{1992}.

%\bibitem{phojet} {R. Engel, Proc.\ of the XXIXth Rencontre de Moriond
%(1994) 321.}

\bibitem{phojet} R. ~Engel and J. ~Ranft, \Journal{\PRD}{54}{4244}{1996}

\bibitem{eestudy} DELPHI Collaboration, P. ~Abreu
{et al} Z.Phys.C73:11-60,1996 


\end{thebibliography}

\begin{figure}[h]
\begin{center}
\epsfig{file=H1prelim-01-134.fig1.eps,height=15cm,width=15.cm}
\caption{The measured cross-section $E {d^3\sigma \over
d^3p}$ as a 
function of transverse momentum, $p_T$, for rapidity values in 
the range $-0.3<y<0.3$. 
The cross-section represents half of the sum of protons and
anti-protons inclusively produced in
photoproduction interactions. Calculations of the PYTHIA  model are shown
with different values
of the diquark suppression factor of 0.1 (upper curve) and 0.05 (lower
curve).
 }
\label{fig1}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\epsfig{file=H1prelim-01-134.fig2.eps,height=15cm,width=15.cm}
\caption{The measured cross-section $E {d^3\sigma \over
d^3p}$ as a
function of rapidity, $y$, for values of transverse momentum in
the range $0.3 < p_T < 0.55$ GeV. The cross-section represents 
half of the sum of protons and anti-protons inclusively produced in
photoproduction interactions. 
Calculations of the PYTHIA  model are shown with different values
of the diquark suppression factor of 0.1 (upper curve) and 0.05 (lower
curve). } 
\label{fig2}
\end{center}
\end{figure}







\end{document}

