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\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
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%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 & & &
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\multicolumn{4}{l}{{\bf
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 1007}    &\\
                 & Parallel Session & {\bf QCD: hard interactions}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\vspace*{2cm}

\begin{center}
  \Large
  {\bf Inclusive
    Prompt Photon Production at HERA }

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

\begin{abstract}

\noindent
Inclusive prompt photons are measured in photoproduction at HERA.
Cross sections are presented as a function of transverse energy
 \Etg
 and pseudorapidity \etag
 for \Etg$ > 5$~GeV and $-1 < $ \etag$ < 0.9$
  in the $\gamma p$ center of mass energy range $142 < W < 266$~GeV.
  The data were taken with the H1 detector in the
  years 1996-2000.
  After selection of prompt photon candidates, a sizable amount of
 background from $\pi^0$ mesons remains and the $\gamma$ signal is extracted by
  a likelihood technique using calorimetric shower shape variables.
% as discriminators.
  The results are compared to a
  NLO-QCD calculation and to the PYTHIA event generator.
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}

   High energy $ep$ collisions at HERA
   are  dominated by electron scattering at small angles where a quasi real
   photon interacts with the proton.
The interaction of the partons of the quasi real photon and of the proton
 can lead to the process of so called prompt photon emission
 which is sensitive
 to their partonic substructures. 
%  Such interactions can lead to the emission of so called
%  prompt photons by the interacting partons of the proton
%  and the exchanged virtual photon and is therefore sensitive
% to their partonic structure.
 An isolated photon at large
  transverse energy \Etg can be measured directly 
 which is in contrast
   to studies with jets
   where the partonic structure is hidden behind the non perturbative
   hadronisation process.
 
   Recent next to leading (NLO) perturbative QCD (pQCD) calculations
   for inclusive production of isolated photons are
 available~\cite{Fontannaz:2001ek,Krawczyk:2001tz,Gordon:1994km}.
% where in leading order in $\alpha_s$ the
%   high $E_T$ photon is accompanied by a quark or gluon jet.
   In such calculations the exchanged photon interacts either directly
   with the partons of the proton or as a resolved photon. Similarily
   the final state photon can be emitted in a hard partonic process
   or be emitted in a fragmentation process of a quark or gluon.

   In this paper we confront measurements of
 inclusive prompt photon cross sections
   with NLO calculations using the program of
   Fontannaz, Guillet and Heinrich~\cite{Fontannaz:2001ek}
%~\cite{gudrun}.
   and with the event generator PYTHIA~\cite{Sjostrand:2000wi}
 based on leading order QCD matrix elements and 
  leading logarithmic parton showers.  
   The results are also compared to data of the
   ZEUS collaboration~\cite{Breitweg:1999su}.
           
\section{Strategy of Data Analysis}

  Prompt photons are identified in the H1 liquid argon (LAr) 
  calorimeter~\cite{Andrieu:1993kh}.
  The main experimental difficulty is the separation of prompt photons 
  from hadronic background, in particular from 
  fake signals due to $\pi^0$ mesons, as for those, at high energies,
  the two energetic decay photons   
  cannot be resolved in the calorimeter.
  The $\pi^0$ mesons are predominantly produced in jets,
  therefore an isolation requirement is applied
  for the $\gamma$ candidates.

  No track is allowed to point to the calorimetric energy cluster
  of the $\gamma$ candidate to exclude events in which the cluster
  is faked by electrons.
 Neutral current (NC)
  deep inelastic scattering (DIS) background events are further
  reduced by requiring a significant energy loss
 in the electron\footnote{The term
  ``electron'' is used for electrons and positrons.} 
  beam direction as
  expected in untagged photoproduction from the electron scattered under small
  angles.


  After all selection cuts, the background is still of similar size as
  the prompt photon signal.
  The signal is thus extracted exploiting a combination of
  discriminating shower
  shape functions in a likelihood analysis.
  Distributions of the $\gamma$ candidates are fitted 
  by a sum of contributions of simulated photons, $\pi^0$ and $\eta$ mesons.
  The signal extraction is performed independently in a
  grid of transverse energy \Etg and pseudorapidity $\eta^{\gamma}$.
  \footnote{The pseudorapidity $\eta$ of an object with polar angle $\theta$
   is given by
   $\eta = -\ln \; \tan (\theta/2)$, where $\theta$ is
   measured with respect to the $z$ axis given by the proton beam direction.}

  The data are corrected for detector effects by a detailed simulation
  of prompt photon production in the H1 detector using the
  PYTHIA event generator~\cite{Sjostrand:2000wi}. In contrast,
  the $\pi^0$ background estimate of PYTHIA is not used in the analysis.
  Only the $\eta/\pi^0$ fraction in the background
   ($ \approx 5\%$ after selection)
  is taken from the generator.
  
\section{Event Selection}

The data have been collected with the H1 detector~\cite{Abt:hi}
 at HERA in different data taking periods with electrons or positrons with
 energy $E_e = 27.5$ GeV collided with protons of energies
 $E_p = 820$ GeV or $E_p = 920$ GeV.
The data correspond 
to an integrated luminosity of $102~\pb^{-1}$ of which
 $28.8~\pb^{-1}$ and $58.6~\pb^{-1}$ are recorded in $e^+p$ interactions  
 at center of mass energies $\sqrt{s} = 300~\GeV$ and
 $\sqrt{s} = 318~\GeV$ respectively,
 and $14.9~\pb^{-1}$  in $e^-p$ interactions at $\sqrt{s} = 318~\GeV$.

The main experimental requirements to select
the prompt photon candidates are the following:
\begin{itemize}
\item
The events are triggered by an electromagnetic cluster in the LAr 
calorimeter.

\item 
A compact electromagnetic energy cluster,
consistent with a $\gamma$ shower,
 is reconstructed in the LAr 
calorimeter in the range \Etg $> 5$~GeV and $-1 < \eta^{\gamma} < 0.9$.
No track is allowed to point to this cluster within a distance of 25 cm.
 
\item
%Events with further calorimetric showers consistent with electrons, besides
%the $\gamma$ candidate, are rejected.
% shower sufficient for SPACAL, in LAr a track is needed for rejection.
Events with electron candidates are rejected.

\item 
An event vertex is required to be within $\pm 35$ cm of the nominal
vertex position
to remove non $ep$ background.

\item
At least two tracks in the central tracker are required which assures
good vertex reconstruction and suppresses QED Compton background. 

\item
 For the inelasticity $y = 1 - E_e'/E_e$ we require
 $0.2 < y < 0.7$, where $E_e'$ is the energy of the non-detected scattered
 electron. The inelasticity is evaluated as $y = \sum{(E - p_z)}/2E_e$  
 where the sum runs over all detected final state particles.
  The range of  $y$ corresponds to 
 the $\gamma p$ center of mass energy range $142 < W < 266$~GeV at
 $E_p = 920$~GeV.
% The lower cut
% removes beam gas background, the upper cut reduces NC DIS background.

\item
 The $\gamma$ candidate is required to be isolated. The transverse energy
 in a cone in ($\eta,\phi$) of radius 1
 around the $\gamma$ candidate $E_T^{cone}$ is required not to exceed
 $0.1 \cdot E_T^{\gamma}$, following
 the convention of~\cite{Breitweg:1999su}.
        
\end{itemize}

\section{Signal Extraction}

 A large part of the selected $\gamma$ candidates 
 have showers initiated by $\pi^0$ mesons.
 The fraction of prompt photons in the data is extracted by a shower
  shape analysis where 
 the mean transverse shower radius given by
      $R = \sum_{i} r_i E_i / \sum_{i} E_i$ and the ``shower hot core
   fraction'' ($HCF$) are used to discriminate against background.
  Here $r_i$ is the transverse distance of  
   cell $i$ with energy $E_i$ measured 
   with respect to the axis from the event vertex to the center of gravity
   of the shower.
   $HCF$ is the energy fraction 
   of the cluster which is contained in 4 or 8 contiguous cells
 including the cell of highest energy
  depending on calorimeter granularity.
 Likelihood functions
  based on the distributions of $R$ and $HCF$ are calculated for the data and
  for simulated samples of photons, $\pi^0$ mesons and $\eta$ mesons 
  separately in a grid of $6 \times 6$ bins in $\eta^{\gamma}$ and
  $E_T^{\gamma}$.
  The contribution of the different particle types is then determined by
  independent fits
  to the data distributions. Hereby the $\eta/\pi^0$ fraction
  ($ \approx 5\%$ after selection) is taken from PYTHIA.     
   
%   Fig.~\ref{fig:signal} shows for the example of one $(\eta,E_T)$ bin
    Summing over the full $\eta^{\gamma}$, \Etg range
    we show in Fig.~\ref{fig:signal}
    the measured distributions of $R$ and $HCF$ and the simulated 
   distributions of photons and background from $\pi^0$ and $\eta$ mesons
   with the normalisations taken 
   from the likelihood fits in the different bins. The data distribution is well
   described by the extracted signal and background components.
   The discrimination power
%   is less good at 
   decreases to
   high \Etg where $R$ and $HCF$ distributions
   of $\pi^0$ mesons and photons get more similar.
    Events with \Etg $> 10$ GeV are not included
  in the results presented below. 

\section{Systematic Uncertainties}


 For the prompt photon cross sections various systematic uncertainties  
 were considered and the given total systematic error per bin is obtained 
 by adding the different systematic errors in quadrature.

\begin{itemize}

\item
   The most important systematic errors are due to potentially inadequate
  simulation of the shower shapes. Uncertainties in the simulated
  distributions of $R$ and $HCF$ 
  are established by comparison to electron candidates from NC DIS events.
  The resulting errors of the cross sections are typically
 $\pm 10\%$  to $\pm 20\%$. 

\item 
 The uncertainties of the electromagnetic and hadronic energy scales
 and variations of the
assumed $E_T$ and $\eta$ dependence of the single particles used in
  the shower simulations contribute errors smaller than 10\% altogether.
 
\item
   Background due to DIS electrons
 resulting from  the tracker inefficiency
  (below 0.4\% for the used track selection)
   leads to
   a subtraction of $(3.0 \pm 0.3)\%$
    in the lowest $\eta$ bin and at
   high \Etg , and is negligible otherwise.  

\item
   An  overall uncertainty of $\pm 1.5\%$ of the luminosity measurement is not
   included in the shown results.

\item
   To take account of uncertainties in the detector corrections
   obtained
   by simulation of the measurement using PYTHIA,
   the \Etg dependence in PYTHIA is varied leading to
   uncertainties below 3\%.
   The sensitivity of the correction factors to the
   underlying event activity is studied by changing
   the relative
%   weight of the PYTHIA events as function of
   weight of the PYTHIA events in proportion to
   the transverse energy
   in the isolation cone $E_T^{cone}$ around the photon.
  Allowing a change for the relative event yield at the cut energy
        $E_T^{cone} = 0.1 \cdot E_T^{\gamma}$
by factors 0.5 and 2
 leads to variations of the
   final results below 3\% which are included in the systematic
errors.

 It was verified that PYTHIA describes the dependence
  of the measured cross sections on the chosen cut on the isolation cone.
% Finally, switching off the multiple interactions in PYTHIA changes
% the resulting measured cross sections by less than $ \%$.
 
\end{itemize}
     
\section{Results}
  The results are presented as $ep$ cross sections
 \footnote{The cross sections obtained
    at $\sqrt{s} = 300~\GeV$
   are transformed to  $\sqrt{s} = 318~\GeV$
by corrections of about $4\%$ taken from PYTHIA.}
   at  $\sqrt{s} = 318~\GeV$ and $0.2 < y < 0.7$ for photon virtualities
   $Q^2 < 1 \; \GeV^2$, including the photon isolation condition
 $E_T^{cone} = 0.1 \; \cdot$ \Etg (see above).
  Differential cross sections \dsdE and \dsdeta
 are obtained by summation over the
 \etag and \Etg bins respectively. 
The errors in the figures contain the statistical errors as obtained from 
the likelihood fits and the systematic errors added in quadrature. 

    The results are shown in Fig.~\ref{fig:res} and compared to
    the NLO pQCD calculation
 of Fontannaz et al.~\cite{Fontannaz:2001ek}
%~\cite{gudrun}  
  and the PYTHIA event generator~\cite{Sjostrand:2000wi}.
    In the NLO calculation the photon and proton parton densities
    AFG~\cite{Aurenche:1994in}
  and MRST2~\cite{Martin:1999ww}
    are used respectively.
  In PYTHIA the leading order QCD matrix elements are regulated by a minimum
    cut-off in transverse momentum which is set to 3~GeV. 
    The parton densities
     GRV(LO)~\cite{Gluck:1991jc},~\cite{Gluck:1994uf} are used 
    for photon and proton respectively.
    The program simulates 
    multiple parton interactions (MI) and initial and final state radiation
\footnote{Default parameters in
   version 6.15/70 were used, for the intrinsic $k_T$ of initial state
    partons in the proton, $<k_T^2> = 1$ GeV$^2$ was chosen.}.

 The NLO calculation describes the data quite well
 in the presented \Etg and $\eta^{\gamma}$ ranges with a tendency
 to overshoot the data, 
 especially at large $\eta^{\gamma}$.
 The PYTHIA simulation describes the data well in shape,
   is however low in normalisation.
  For comparison we show in Fig.~\ref{fig:pythia} also the PYTHIA
  prediction without multiple interactions. 
 It is interesting to note, that in this case the predictions 
  at $0 <$ \etag $< 0.9$ are about 25\% higher, showing that
  the cross section is reduced by the soft underlying event activity,
 as expected~\cite{Fontannaz:2001ek}, 
  due to the isolation cone condition 
   $E_T^{cone} = 0.1 \; \cdot$ \Etg which is presently applied.
  Fig.~\ref{fig:pythia} also shows besides the full PYTHIA prediction 
  including MI, separately
  the component where a final state quark in di-jet events radiates a photon
  and the resolved interactions of the exchanged photon.
    

   The data are compared\footnote{The H1 data
   are corrected for the extension of the upper edge of $y$ from 0.7 to 0.9
   using PYTHIA.}
   to the results of the ZEUS collaboration
   in  Fig.~\ref{fig:resZ} at $\sqrt{s} = 300~\GeV$ in the range
    $-0.7 < \eta^{\gamma} < 0.9$ and $0.2 < y < 0.9$.
   The data are consistent, but the H1 data are somewhat lower at small
   $\eta^{\gamma}$, where the ZEUS results appear to exceed the 
   NLO calculation.
    
\section{Conclusions}

Results on inclusive prompt photon production have been presented. 
The cross sections
\dsdE and \dsdeta 
 are roughly consistent with results from the ZEUS
collaboration, but tend to be lower at negative \etag.
 The data are quite well described in the covered
  $\eta^{\gamma}$       and
  $E_T^{\gamma}$ range
  by a NLO pQCD calculation, but the prediction is above the data
  in the forward region (\etag $> 0.6$) which could be related to 
  underlying event activity not contained in the NLO calculation.
  The cross sections produced with the 
  PYTHIA event generator describe the data distribution well in shape
  with a normalisation that is about 30\% low.

\vspace*{14.25pt}

\noindent {\large \bf Acknowledgements}

\noindent
 We are grateful to Gudrun Heinrich for discussions and for providing
 some results of the NLO QCD calculations. 
%
%   References 
%
\begin{thebibliography}{99}
%\cite{Fontannaz:2001ek}
\bibitem{Fontannaz:2001ek}
M.~Fontannaz, J.~P.~Guillet and G.~Heinrich,
%``Isolated prompt photon photoproduction at NLO,''
Eur.\ Phys.\ J.\ C {\bf 21} (2001) 303
[arXiv:hep-ph/0105121].
%%CITATION = HEP-PH 0105121;%%

%\cite{Krawczyk:2001tz}
\bibitem{Krawczyk:2001tz}
M.~Krawczyk and A.~Zembrzuski,
%``Photoproduction of the isolated photon at HERA in NLO QCD,''
Phys.\ Rev.\ D {\bf 64} (2001) 114017
[arXiv:hep-ph/0105166].
%%CITATION = HEP-PH 0105166;%%

%\cite{Gordon:1994km}
\bibitem{Gordon:1994km}
L.~E.~Gordon and W.~Vogelsang,
%``Isolated prompt photon production at HERA,''
Phys.\ Rev.\ D {\bf 52}, 58 (1995).
%%CITATION = PHRVA,D52,58;%%

%\bibitem{gudrun}
%Gudrun Heinrich, private communication.

%\cite{Sjostrand:2000wi}
\bibitem{Sjostrand:2000wi}
T.~Sj\"ostrand, P.~Ed\'en, C.~Friberg, L.~L\"onnblad, G.~Miu,
 S.~Mrenna and E.~Norrbin,
%``High-energy-physics event generation with PYTHIA 6.1,''
Comput.\ Phys.\ Commun.\  {\bf 135} (2001) 238
[arXiv:hep-ph/0010017].
%%CITATION = HEP-PH 0010017;%%

%\cite{Breitweg:1999su}
\bibitem{Breitweg:1999su}
J.~Breitweg {\it et al.}  [ZEUS Collaboration],
%``Measurement of inclusive prompt photon photoproduction at HERA,''
Phys.\ Lett.\ B {\bf 472} (2000) 175
[arXiv:hep-ex/9910045].
%%CITATION = HEP-EX 9910045;%%

%\cite{Chekanov:2001aq}
%\bibitem{Chekanov:2001aq}
%S.~Chekanov {\it et al.}  [ZEUS Collaboration],
%``Study of the effective transverse momentum of partons in the proton  using prompt photons in photoproduction at HERA,''
%Phys.\ Lett.\ B {\bf 511} (2001) 19
%[arXiv:hep-ex/0104001].
%%CITATION = HEP-EX 0104001;%%


%\cite{Fontannaz:2001nq}
%\bibitem{Fontannaz:2001nq}
%M.~Fontannaz, J.~P.~Guillet and G.~Heinrich,
%``Is a large intrinsic k(T) needed to describe photon + jet  photoproduction at HERA?,''
%Eur.\ Phys.\ J.\ C {\bf 22} (2001) 303
%[arXiv:hep-ph/0107262].
%%CITATION = HEP-PH 0107262;%%

%\cite{Andrieu:1993kh}
\bibitem{Andrieu:1993kh}
B.~Andrieu {\it et al.}  [H1 Calorimeter Group Collaboration],
%``The H1 liquid argon calorimeter system,''
Nucl.\ Instrum.\ Meth.\ A {\bf 336} (1993) 460.
%%CITATION = NUIMA,A336,460;%%


%\cite{Abt:hi}
\bibitem{Abt:hi}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 Detector At Hera,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310;
%%CITATION = NUIMA,A386,310;%%
%\cite{Abt:1996xv}
%\bibitem{Abt:1996xv}
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%Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 348.
ibid. A {\bf 386} (1997) 348.
%%CITATION = NUIMA,A386,348;%%

%\cite{Aurenche:1994in}
\bibitem{Aurenche:1994in}
P.~Aurenche, J.~P.~Guillet and M.~Fontannaz,
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Z.\ Phys.\ C {\bf 64} (1994) 621
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%\cite{Martin:1999ww}
\bibitem{Martin:1999ww}
A.~D.~Martin, R.~G.~Roberts, W.~J.~Stirling and R.~S.~Thorne,
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%\cite{Gl\uck:1991jc}
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%\cite{Gluck:1994uf}
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M.~Gl\"uck, E.~Reya and A.~Vogt,
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\end{thebibliography}

\begin{figure}[p] \unitlength 1pt 
 \begin{center}
\begin{picture}(200,200)
   \put(-130,-15.){\epsfig{file=H1prelim-02-152.fig1a.eps,width=200pt}}
   \put(100,-15.){\epsfig{file=H1prelim-02-152.fig1b.eps,width=200pt}}
 \end{picture}
  \end{center}
  \caption{Distributions of the mean transverse shower radius $R$ (a) and 
   and the hot core fraction $HCF$ (b) for the selected photon candidates
   (solid lines) summing over the full range
   for $ -1 < \eta < 0.9, \; 5 < E_T^{\gamma} < 10$ GeV.
     The simulated distributions for photons (dashed lines) and
     background ($\pi^0 + \eta$, dotted lines)
    are normalised by the likelihood fits.}
  \label{fig:signal}
\end{figure} 

\begin{figure}[ht] \unitlength 1pt 
  \begin{center}
\begin{picture}(200,200)
   \put(-130,-15.){\epsfig{file=H1prelim-02-152.fig2a.eps,width=200pt}}
   \put(100,-15.){\epsfig{file=H1prelim-02-152.fig2b.eps,width=200pt}}
 \end{picture}
  \end{center}
  \caption{Prompt photon differential cross sections
\dsdE for  $-1 < \eta^{\gamma} < 0.9$ (a)
and \dsdeta for $5 <$ \Etg $< 10$ GeV (b)
 at $\sqrt{s} = 318~\GeV$ and $0.2 < y < 0.7$    
compared to the prediction of  
a NLO pQCD calculation~\cite{Fontannaz:2001ek}
and the PYTHIA generator~\cite{Sjostrand:2000wi}.}
  \label{fig:res}
\end{figure} 

\begin{figure}[ht] \unitlength 1pt 
 \begin{center}
\begin{picture}(200,200)
   \put(-130,-15.){\epsfig{file=H1prelim-02-152.fig3a.eps,width=200pt}}
   \put(100,-15.){\epsfig{file=H1prelim-02-152.fig3b.eps,width=200pt}}
 \end{picture}
  \end{center}
  \caption{Prompt photon differential cross sections
\dsdE for  $-1 < \eta^{\gamma} < 0.9$ (a)
and \dsdeta for $5 <$ \Etg $< 10$ GeV (b)
 at $\sqrt{s} = 318~\GeV$ and $0.2 < y < 0.7$
 compared to the PYTHIA prediction including multiple interactions
 (full line)
 with the contributions from di-jet events where a final state
 quark radiates a photon (dashed-dotted) and this component summed with resolved 
 photon events (dotted line). Also shown is the the full
  PYTHIA prediction without multiple interactions (dashed line).
}
  \label{fig:pythia}
\end{figure} 

%

\begin{figure}[ht] \unitlength 1pt  
  \begin{center}
\begin{picture}(200,200)
   \put(-130,-15.){\epsfig{file=H1prelim-02-152.fig4a.eps,width=200pt}}
    \put(100,-15.){\epsfig{file=H1prelim-02-152.fig4b.eps,width=200pt}}
 \end{picture}
  \end{center}
  \caption{Prompt photon differential cross sections
    \dsdE for  $-0.7 < \eta^{\gamma} < 0.9$ (a)
  and \dsdeta for $5 <$ \Etg $< 10$ GeV (b) corrected for 
 $\sqrt{s} = 300~\GeV$ and $0.2 < y < 0.9$  
compared to results of the ZEUS collaboration~\cite{Breitweg:1999su}. 
Also shown is the prediction of  
a NLO pQCD calculation~\cite{Fontannaz:2001ek}.}
  \label{fig:resZ}
\end{figure} 

\end{document}