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\noindent
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\multicolumn{4}{l}{{\bf
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 1000}    &\\
                 & Parallel Session & {\bf 5, 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\begin{center}
  \Large
  {\bf
      Forward $\pi^0$ Production in DIS at HERA } 

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

\begin{abstract}
The dynamics of QCD evolution at low values of Bjorken-$x$ is studied via 
the measurement of hard $\pi^0$ probes in deeply
inelastic positron proton scattering with the H1 experiment. The $\pi^0$ mesons
are measured in a region of small angles with respect to the proton remnant in
the laboratory frame, the so-called forward region.\\
Differential cross sections for inclusive $\pi^0$-meson production are 
presented as a function of Bjorken-$x$ and $\pi^0$ transverse momentum, in   
different regions of the four momentum transfer  $Q^2$.  
The accompanying transverse energy flow around the $\pi^0$ is also studied. 
The data are used to discriminate between different QCD evolution schemes for 
the parton ladder between proton and photon.
\noindent


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\section{Introduction}
The HERA collider has extended the available kinematic space
for Deep-Inelastic Scattering (DIS) to regions of large values of the four
momentum transfer $Q^2$ ($\leq 10^5$ $GeV^2$) and small Bjorken-$x$
($x\approx 10^{-5}$). A variety of measured processes has made detailed
tests of perturbative QCD possible. In particular, studies
at low $x$ could reveal novel features of parton dynamics. At small 
$x$ it is very probable that the quark struck by the virtual photon
originates from a QCD cascade initiated by a parton in the proton.
In different
regions of the $Q^2$ and $x$ different schemes are expected 
to describe 
the parton evolution: the mostly discussed being 
DGLAP\cite{DGLAP}, BFKL\cite{BFKL} and CCFM\cite{CCFM}.  
At high $Q^2$ and high $x$ the initial state radiation 
is described by the conventional DGLAP evolution equations which
 resum the leading 
%$\alpha_s$$ln(Q^2/Q_{\circ}^2)$ terms. In this scheme a space-like chain of 
$\alpha_s$$\ln(Q^2/Q_{\circ}^2)$ terms. In this scheme a space-like chain of 
subsequent gluon emissions is characterized by a strong ordering in
transverse momenta $k_{T}$. However, at small $x$ the contribution of large 
$\ln$($1/x$) terms may become important. Resummation of these terms
leads to the BFKL evolution
equation. No ordering on transverse momenta $k_{T}$ of emitted gluons is
imposed here. The CCFM evolution 
equation based on angular ordering and colour coherence interpolates between
the BFKL and DGLAP approaches.\\
An extended parton ladder at 
low $x$ leads to high $k_T$ partonic emission in the forward region to which 
measurements of jets and leading particles are sensitive. Production of DIS
events with a single forward particle is a more refined version of forward
jet production: a forward parton is tagged by its single 
energetic fragmentation product. In analogy to the forward jet 
analysis, inspired 
by the proposal of Mueller\cite{Mueller}, selection of a single particle with
transverse momentum squared ${k_T}^2$ of the order 
of $Q^2$, ${k_T}^2 \approx Q^2$,
suppresses the $k_T$ ordered DGLAP evolution and the choice of the fractional
momentum $x_{\pi}=E_{\pi}/E_p$ ($E_p$ is the proton beam energy ) greater
than Bjorken-$x$ enhances the phase
space for BFKL effects. An advantage of studying single particles as opposed
to jets is the potential 
to reach smaller angles, closer to the initial proton direction, than
is possible with jets which have a broad
spatial extension. A disadvantage is that the cross section of the process
is suppressed in comparison to forward jet production, and that fragmentation
effects are more significant.\\ 
Differential cross-sections for inclusive $\pi^0$-meson
production\cite{pi0} have recently been measured by the H1 
Collaboration. A BFKL 
calculation incorporating some of the NLO effects \cite{Outwaite} was found to
be in good agreement with the data, although
the absolute normalization remained strongly affected by the scale 
uncertainty. A reasonable description of the data is also achieved in the
Monte Carlo model RAPGAP\cite{rapgap}, based on the DGLAP formalism
with inclusion of resolved photon processes.\\
In this analysis we present
new results  on high transverse momentum forward 
$\pi^0$ production in DIS with a statistically increased (by a factor 3.5)
sample that allows
for more differential studies. Additional 
characteristics of the hadronic final are also studied. 

\section{Experimental setup and data selection }
The data used for this analysis were collected in 1996 and 1997 with the H1
detector at HERA, in collisions of positrons and protons with energies
of 27.5 GeV and 820 Gev, respectively. The data
correspond to an integrated luminosity of 21 pb$^{-1}$. 
A detailed description of the H1 detector can be found elsewhere\cite{detector}.
 DIS events are
selected by identification of scattered positrons in the backward 
lead/scintillating fiber calorimeter, which has an energy resolution of
$\sigma_{E}/E \approx 0.075/\sqrt{E}$ for electrons. 
The analysis is restricted to the kinematical
range $0.1 < y < 0.6$, $2.0 < Q^{2} < 70.0$ GeV$^{2}$, and  
Bjorken-$x$ extends over two orders of magnitude down to
$x\approx10^{-5}$. In this kinematical region the background
from photoproduction is negligible.\\
The $\pi^0$-mesons are measured in the finely segmented liquid argon (LAr)
calorimeter consisting of an electromagnetic section, that provides an energy resolution
of  $\sigma_{E}/E \approx 0.12/\sqrt{E}$, and of a hadronic section which
has an energy resolution for
charged pions of $\sigma_{E}/E \approx 0.50/\sqrt{E}$.    
The absolute energy scales are known to $\pm$ 3\% for electromagnetic showers
in the forward region relevant to this analysis, and to $\pm$ 4\% for
hadrons as measured in test beams.\\
The $\pi^0$-mesons are identified via the dominant decay channel $\pi^0
\rightarrow 2\gamma$ using calorimetric information only. The $\pi^0$
candidates are selected in the HERA laboratory frame
\footnote{ H1 uses a 
a right-handed coordinate system with the $z$-axis defined 
by the incident proton beam.} 
with polar angles in the region
 $5^{\circ} < \Theta_{\pi} <25^{\circ}$ and with $x_{\pi}$ greater than 0.01. 
 The cut on the minimum transverse momentum of the
$\pi^0$-meson, $p_{T,\pi}^*$ defined in the photon-proton center of mass system (CMS) 
is set to 2.5 GeV.
For the  high $\pi^0$ energies requested here, the decay photons
cannot be separated in the LAr calorimeter and their energy deposits
are reconstructed as one calorimetric cluster. 
Photon induced showers
are selected following a detailed analysis of longitudinal and
transverse shower shape development in the LAr calorimeter as described
in\cite{pi0}.
The efficiency for finding $\pi^0$-mesons after all selection cuts
is above 45\%
and the purity of the
selected $\pi^0$-meson sample is about 80\%. In the selected kinematical range
about 5500 (2000) $\pi^0$ candidates are found with
$p_{T,\pi}^* >2.5 (3.5)$ GeV.
Other sources of high energy photons (such as prompt photon production) are 
negligible\cite{prompt}. The small contribution  of $\eta$-meson production is
corrected for using Monte Carlo models LEPTO\cite{lepto} and 
ARIADNE\cite{ariadne}. 
\section{Results}
%
Inclusive forward $\pi^0$ cross-sections for $p_{T,\pi}^*$ $>$ 2.5 GeV and 
$p_{T,\pi}^*$ $>$ 3.5 GeV
are shown as a function of $x$ 
for different regions of $Q^2$ in Fig.\ref{fig1} and 
Fig.\ref{fig2}, respectively . 
All cross-sections are corrected for detector effects and 
for the influence of QED radiation 
by a bin-by-bin unfolding procedure, using two Monte Carlo models LEPTO
and ARIADNE. Systematic errors are dominated
by the model dependence 
of these corrections which gives rise to typically 10-15 \% uncertainty.\\
In the following, the data are compared with predictions of the Monte Carlo
models RAPGAP\cite{rapgap} and CASCADE\cite{cascade}. RAPGAP implements a QCD
model based on LO DGLAP parton showers with (DIR+RES in the figures) and
without (DIR in the figures) resolved photon processes. The RAPGAP 
calculations were made with the CTEQ4M\cite{cteq4m} parton densities
for the proton and with the GRV\cite{grv} parton 
densities for the virtual photon.
CASCADE has been used as an implementation of the CCFM equation.\\
%
The prediction of RAPGAP with a point-like photon is well below the data. 
A reasonable description of the cross-sections is obtained by including in 
RAPGAP an additional resolved photon contribution  and using a renormalisation 
and factorisation scale
of $Q^2 + 4p_T^2$. CASCADE undershoots the data for lower values of $Q^2$.\\
% The fact that 
%CASCADE  describes the forward jet cross-section\cite{forwh1} but not the 
%forward $\pi^0$ production may indicate the
%importance of the quark splitting functions which are not taken into account 
%in CASCADE. \\ 
The $\pi^0$ cross-section as a function of ~the $\pi^0$ transverse momentum
$p_{T,\pi}^*$, in the photon-proton CMS, is presented in Fig.\ref{fig3} for  
different regions of $Q^2$. 
The measurements extend to values of $p_{T,\pi}^*$ of about 15 GeV 
and, again, are best
described by RAPGAP with a renormalisation and factorisation scale set 
to $Q^2+4p_T^2$.\\
Fig.\ref{fig4} shows the transverse energy flow around the forward $\pi^0$ in 
the photon-proton CMS, for different
ranges of the $\pi^0$ pseudorapidity $\eta_{\pi}^*$, as 
a function of the distance from the $\pi^0$ 
direction in units of pseudorapidity. Energies deposited 
at the polar angle $\Theta>4^{\circ}$, limited by the acceptance of
the LAr calorimeter, are counted here.  
The energy flow is highly 
collimated around the 
direction of the $\pi^0$. The $\pi^0$ itself contributes , on average, about
4 GeV of transverse energy
in the bin containing this particle. Large amounts of 
transverse energy are also produced away 
from  the $\pi^0$. The QCD models presented here give similar 
predictions. However, the calculations which include resolved processes
tend to agree better with the data.\\
The transverse energy flow around the $\pi^0$ reflects how 
the transverse momentum of the jet is
compensated along the ladder. It is best seen in the $E_T$ flow distribution 
for the most
forward $\pi^0$'s  shown in the left upper plot of Fig.\ref{fig4}. RAPGAP with 
direct photon contribution only predicts less radiation 
in the vicinity of the $\pi^0$. The transverse
momentum of the forward particle
is mainly compensated far away from the $\pi^0$, as expected 
for $k_T$ ordered DGLAP emissions. In the CCFM approach, there is more 
QCD radiation close to the $\pi^0$ direction. The prediction of RAPGAP  
 with a resolved $\gamma^*$ component lies between
predictions of CASCADE and RAPGAP-DIR.\\      
The mean transverse energy  along the ladder, in the region 
$0.5 < \eta^* - \eta^*_{\pi} < 3.0 $, for different 
ranges of $\eta_{\pi}^*$ in the hadronic CMS as a function of Bjorken $x$ is presented 
in Fig.\ref{fig5}. The data show, within errors, no dependence on
$x$ and are best described  
by RAPGAP with resolved photon interactions.
\section{Summary}
New measurements of the forward $\pi^0$ cross-sections and
their accompanying
energy flow were presented. The data discriminate between
different QCD models and are
best described by an approach in which the partonic substructure of
virtual photons is taken into account.   
The fact that 
CASCADE  describes the forward jet cross-section\cite{forwh1} but not the 
forward $\pi^0$ production may indicate the
importance of the quark splitting functions which are not taken into account 
in CASCADE.  

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\end{thebibliography}

\begin{figure}[htb]
\center
\epsfig{file=fig1.eps,width=16.0cm}
\caption{ Inclusive $\pi^0$-meson production cross-sections as a function of 
Bjorken $x$ for
$p_{T,\pi}^* >$ 2.5 GeV in three regions of $Q^2$.  
The inner error bars are statistical, the outer error bars give 
the statistical and systematic error added quadratically. 
The QCD models RAPGAP
based on LO DGLAP parton showers with (DIR+RES) and without (DIR) resolved photon
processes and CASCADE, as an implementation of the CCFM equation, are compared to the data.}
\label{fig1}
\end{figure}
%
\begin{figure}[htb]
\center
\epsfig{file=fig2.eps,width=16.0cm}
\caption{ Inclusive $\pi^0$-meson production cross-sections as a function of 
Bjorken $x$ for $p_{T,\pi}^* >$ 3.5 GeV in three regions of $Q^2$.  
The inner error bars are statistical, the outer error bars give 
the statistical and systematic error added quadratically. 
The QCD models RAPGAP
based on LO DGLAP parton showers with (DIR+RES) and without (DIR) resolved photon
processes and CASCADE, as an implementation of the CCFM equation, are 
compared to the data.}
\label{fig2}
\end{figure}

%
\clearpage 
\begin{figure}[htb]
\center
\epsfig{file=fig3.eps,width=16.0cm}
\caption{ Inclusive $\pi^0$-meson production cross-sections as a function of 
$p_{T,\pi}^*$ for $p_{T,\pi}^* >$2.5 GeV in three regions of $Q^2$.  
The inner error bars are statistical, the outer error bars give 
the statistical and systematic error added quadratically. 
The QCD models RAPGAP
based on LO DGLAP parton showers with (DIR+RES) and without (DIR) resolved photon
processes and CASCADE, as an implementation of the CCFM equation,  are 
compared to the data.}
\label{fig3}
\end{figure}
%
\begin{figure}[htb]
\center
\epsfig{file=fig4.eps,width=16.0cm}
\caption{Transverse energy flow around the forward $\pi^0$ 
for different ranges of $\pi^0$ pseudorapidity
dity $\eta_{\pi}^*$ in 
the hadronic CMS as a function of the pseudorapidity distance
from the $\pi^0$ direction. The incoming photon direction defines the $+z^*$ direction.
The contribution from the forward $\pi^0$ is included in the distributions.
The QCD models RAPGAP
based on LO DGLAP parton showers with (DIR+RES) and without (DIR) resolved 
photon
processes and CASCADE, as an implementation of the CCFM equation, are 
compared to the data.}
\label{fig4}
\end{figure}
%
\begin{figure}[htb]
\center
\epsfig{file=fig5.eps,width=16.0cm}
\caption{
Mean transverse energy in the region
$0.5 < \eta^* - \eta^*_{\pi} < 3.0 $ for different ranges of $\eta_{\pi}^*$ 
in the hadronic CMS as a function of Bjorken $x$.
The QCD models RAPGAP
based on LO DGLAP parton showers with (DIR+RES) and without (DIR) 
resolved photon
processes and CASCADE, as an implementation of the CCFM equation, are 
compared to the data.}
\label{fig5}
\end{figure}
\end{document}

