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\noindent
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%                32st International Conference on High Energy Physics, ICHEP04},
%                Aug.~16-23,~2004,~Beijing} \\
%                 & Abstract:        & {\bf 756,758}    &\\
%                 & Parallel Session & {\bf 4,5}   &\\ \hline
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                 14th International Workshop on Deep Inelastic Scattering,
                 DIS2006, April 20-24, 2006, Tsukuba, Japan}} \\
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\begin{center}
  \Large
  {\bf 
   Inclusive Prompt Photon Production in Deep Inelastic Scattering at HERA}

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

\begin{abstract}

\noindent
 Results are presented on the inclusive production of isolated prompt photons
 in deep inelastic scattering with a four-momentum transfer of $Q^2>4
 \GeV^2$. The cross sections are measured for the transverse momentum range of
 the photons $3 < E_T^\gamma < 10 \GeV$ and for the pseudorapidity range of
 the photons $-1.2 < \eta^\gamma < 1.8$. They are measured differentially as a
 function of $E_T^\gamma$ and $\eta^\gamma$. The results are compared with the
 predictions of a new leading order calculation, which is in reasonable
 agreement with the inclusive measurement. Comparisons with the predictions of
 the event generators PYTHIA and HERWIG are also presented.
\noindent
\end{abstract}


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\section{Introduction}
Isolated photons with high transverse momentum in the final state are a 
direct probe of the dynamics of the hard subprocess, since they are 
directly observable without large corrections due to hadronisation and 
fragmentation. Previously  ZEUS and H1 have measured the prompt photon cross section in photoproduction\cite{ZEUS}\cite{H1}. ZEUS has recently published an analysis of the prompt photon cross section for photon virtualities $Q^2$ larger than 35 GeV$^2$\cite{ZEUSdis}.
The results are compared to a new leading order
calculation\cite{Thomas1}\cite{Thomas}, $\mathcal{O}(\alpha^3)$, that offers
first predictions for the inclusive prompt photon production in Deep
Inelastic Scattering. 

\section{Experimental Technique}
The events have been collected with the H1 detector(\cite{H1det}) at HERA in
the years 99/00 at a center of mass energy of 318 GeV, with a total integrated
luminosity of 70.6 ${\rm pb}^{-1}$. 

Events were selected with the electron reconstucted in the backward calorimeter (SpaCal\cite{Nicholls:1995di}). 
 Photons are identified in the H1 liquid argon calorimeter (LAR)\cite{calo} by a 
compact electromagnetic cluster with no track pointing to it.
The  transverse energy is restricted to 3 GeV$<E_t^\gamma < $ 10
GeV in the pseudorapidity region $-1.2 < \eta_\gamma<1.8$\footnote{The pseudorapidity $\eta$ of a particle with polar angle $\theta$ is given by $\eta = - \ln \tan(\theta/2)$. $\theta$ is measured with respect to the $z$-axis with the positive axis defined by the direction of the proton, hence positive $\eta$ points in the direction of the proton.} 
The main experimental difficulty is the separation of the photons from neutral mesons, mainly $\pi^0$ or $\eta$, since at high energies their decay photons are not resolved but reconstructed in one single electromagnetic cluster.
These mesons are mainly produced in hadronic jets, therefore an isolation criterium is applied for the $\gamma$ candidates.  
To ease the comparison with pQCD calculations we use an infrared-safe definition of the isolation requirement\cite{Glover:1993xc}\cite{Buskulic:1995au}:
 the energy fraction $z$ of the photon energy to the energy of 
the jet which contains the photon (Photonjet) has to be larger than 0.9. 
\begin{equation}
 z=E^\gamma/E^{Photonjet} > 0.9
\end{equation}
%In this approach the final state hadrons are clustered into jets using the
% so-called democratic procedure\cite{Glover:1993xc}\cite{Buskulic:1995au},
% at which the photon is treated like any other hadron.\\
After the selection cuts there is still a large fraction of background from neutral mesons. The photon signal is extracted by a shower shape analysis which uses six discriminating shower shape functions in a likelihood analysis.\\
The data are corrected for detector effects by taking the average of the corrections of  the PYTHIA 6.2\cite{PYTHIA} and the HERWIG 6.5\cite{HERWIG} event generator.
The background from neutral mesons was generated with the RAPGAP\cite{RAPGAP} generator. 
However, the background Monte Carlo was only used to control the sample not
 for the extraction of the signal. This was done using single particles only. 

\section{Event Selection}

The main experimental requirements for the selection of the events are the following:
\begin{itemize}
\item Events are triggered by an electromagnetic cluster in the SpaCal. The trigger efficiency is close to 100\%.
\item Electron Selection: well identified electron reconstructed in the
  backward calorimeter ($151^{\circ}<\theta_e<177^{\circ}$) with an energy larger than 10 GeV.  
\item $Q^2_e>$ 4 GeV$^2$, inelasticity $y_{e}=1-E_e^{\prime}(1-\cos\theta_e)/2E_e>0.05$, where $E_e^{\prime}$ is the energy of the scattered electron.
\item 35 GeV$< \Sigma( E - p_z) < 70$ GeV, where the sum runs over all the particles and $p_z$ is their longitudinal momentum. This cut suppresses photoproduction background.  
\item Vertex: the event vertex is required to be within $\rm 40$ cm of the nominal vertex position. There has to be at least one good reconstructed track apart from the track pointing to the electron. This ensures a good vertex reconstruction and suppresses background from elastic QED compton events.
\item Jets: at least one jet with transverse momentum larger than 2.5 GeV and
  $\eta_{jet}< 2.1$. The jet is reconstructed using the $k_t$ algorithm with
  cone size $R_0=1$\cite{jetalgo}. If only one jet is found, the jet is bound
  to be the Photonjet.
\item Photon candidate: electromagnetic cluster  with $3 < E_T^\gamma < 10 \GeV$ and pseudorapidity $-1.2 < \eta^\gamma < 1.8$. No track is allowed to point to the photon candidate within 20 cm.
The cluster has to be compact with a transverse radius of less than 6 cm.
The invariant mass of the cluster combined with  the closest electromagnetic neighbour with an energy above 80~MeV must be larger than 0.3 GeV. This requirement rejects candidates from $\pi^0$ decays with the two photons reconstruced in individual clusters. 
Candidates close to the cracks of the calorimeter are rejected.
\item Isolation: the energy fraction of the photon energy to the energy of the photon jet $z$ has to be larger than 0.9.
\end{itemize}

In a first step events are selected with a good electron and a jet which contains a photon candidate as defined above. In a second step the prompt photon signal is extracted
by a likelihood analysis of the shower shapes.

\section{Extraction of the prompt photon signal}

The photon candidate clusters are analysed using six different shower shape variables  to discriminate between the signal of a single photon and neutral mesons.
\begin{itemize}
\item Hot core fraction: fraction of energy deposited in four or eight - depending on the granularity of the calorimeter - contiguous cells including the cell with highest energy.
\item Transverse radius of the cluster (transverse plane is perpendicular
  to the direction of the incoming particle).
\item Energy fraction of the hottest cell.
\item Energy fraction in the first layer.
\item Kurtosis of the transverse energy distribution of the cluster cells.
\item Transverse Symmetry of the cluster: a photon is expected to have a symmetric cluster (S=1), whereas neutral mesons with more than one decay photon are of more asymmetric shape.
\end{itemize}



Figure~\ref{estimators} shows the six different shower shape variables together
with the background from \mbox{RAPGAP} as well as photons radiated off the electron as
predicted by RAPGAP and the signal prediction from PYTHIA (scaled
by 2.3) for photons being radiated off the quark. Both contributions from RAPGAP are used unscaled. All variables are nicely described by the sum of the Monte Carlo predictions.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,90)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,  -5){\epsfig{file=H1prelim-06-031.fig1a.eps,width=0.3\textwidth}}
\put(25,  -5){\epsfig{file=H1prelim-06-031.fig1b.eps,width=0.3\textwidth}}
\put(80,  -5){\epsfig{file=H1prelim-06-031.fig1c.eps,width=0.3\textwidth}}
\put(-30, 40){\epsfig{file=H1prelim-06-031.fig1d.eps,width=0.3\textwidth}}
\put(25,  40){\epsfig{file=H1prelim-06-031.fig1e.eps,width=0.3\textwidth}}
\put(80,  40){\epsfig{file=H1prelim-06-031.fig1f.eps,width=0.3\textwidth}}
\end{picture}
\end{center}
\caption{Shower shape variables used as input for the discrimination between
  the photon and neutral mesons: Transverse kurtosis, symmetry and radius and
  energy fractions of the hottest cell, the hot core and the first layer). The
  measured data points are shown together with the signal Monte Carlo from
  PYTHIA, scaled by a factor 2.3, photons radiated off the incoming or
  outgoing electron (rad) and background from neutral mesons (non-rad) as
  estimated by RAPGAP. The contributions from RAPGAP are used
  unscaled. The sum of the Monte Carlo prediction is indicated by the blue line.}
\label{estimators}
\end{figure}
The estimators are combined  in a likelihood analysis as well as a neural net  and a range search analysis as a cross check.
Monte Carlo studies showed that neutral mesons can be well separated from photons for transverse energies below 10 GeV. Only particles which decay very asymmetrically
are misidentified as photons.

The likelihood distribution which has a good separation power is shown in
 Figure~\ref{likelihood} together with the background from RAPGAP and the
 signal from PYTHIA plus radiative photons from RAPGAP. The data is
 well described by the sum of the predictions. Also the fraction of neutral
 mesons is well predicted by the unscaled RAPGAP background, which accumulates
 at low likelihood values.\\
 The probability densities that are used for the likelihood method are taken from the simulation of single particles. 
 Only the contributing fraction of any neutral meson ($\pi^0$, $\eta^0$, $\eta^\prime$, $K^0$, $\rho$, $\omega$, $K^\star$, $K_L$,$K_s$, $n$ and $\bar{n}$ ) is 
 taken from Monte Carlo simulation (RAPGAP). The likelihood functions are
 calculated separately for different bins in $E_T$ and different wheels of the
 calorimeter\cite{calo} which correspond to different $\eta_\gamma$ ranges. The contribution of photons and neutral mesons is
 then determined by independent fits to the data using likelihood
 distributions obtained from a set of single particle photons and background
 respectively. The advantage of the use of single particles is that they can easily be
 produced in high statistics.

\begin{figure}[htb]
\begin{center}
\begin{picture}(90,90)(0,0)
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\put(0,  0){\epsfig{file=H1prelim-06-031.fig2.eps,width=0.6\textwidth}}
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\caption{Likelihood Distribution of photon candidates that have passed the
  primal event selection.}
\label{likelihood}
\end{figure}

\section{Systematic errors}
Various systematic uncertainties were considered. The total systematic error per bin is obtained by adding all different systematic errors in quadrature. The dominant errors are
\begin{itemize}
\item Photon energy: the energy scale at the energies used in this analysis was checked with the reconstructed $\pi^0$ mass and found to be well calibrated. An error of $1\%-3\%$ (forward region) was assumed. This results in a systematic error of the cross section of at most $12\%$.
\item Electron energy: an uncertainty of $2\% $is applied to the energy of the scattered electron.
\item An important error is the description of the shower shape variables in the simulation. 
The differences between simulation and data were studied using electrons in NC DIS events, systematic errors between $3.5\%$ and $8\%$ were applied.
\item  Model dependence: the model dependence was studied by comparing HERWIG and PYTHIA, in the forward region it leads to an error of up to $22\%$.
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results}
Differential cross sections for the production of isolated photons in deep inelastic scattering are shown for $Q_e^2>$4 GeV$^2$, $y_e>0.05$  for photons with $3 < E_T^\gamma < 10 \GeV$,  pseudorapidity  $-1.2 < \eta^\gamma < 1.8$ and the isolation $z=E_\gamma/E_{\gamma Jet}>0.9$.
The errors in the figures contain the statistical error and the systematic errors added in quadrature.

Figure~\ref{xsec_mc} shows the cross section as a function of transverse energy
and the pseudorapidity compared to the prediction of the PYTHIA and HERWIG
generator (radiation off the quark) plus photon radiation off the electron. Both generators nicely
describe the shape in $E_T$ but are significantly lower in the abolute scale
(factor 2.3 for PYTHIA and 2.6 for HERWIG in order to match the total cross section). The $\eta$ distribution is described somewhat better by PYTHIA. At low $\eta$ the production of isolated photons is dominated by radiation off the electrons, which becomes negligible at pseudorapidities larger than 0.
 
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,70)(0,0)
\setlength{\unitlength}{1 mm}
\put(-40,  -5){\epsfig{file=H1prelim-06-031.fig3a.eps,width=0.5\textwidth}}
\put(50,  -5){\epsfig{file=H1prelim-06-031.fig3b.eps,width=0.5\textwidth}}\end{picture}
\end{center}
\caption{Prompt photon differential cross sections $d\sigma/dE_T^\gamma$ for
  $-1.2 < \eta^\gamma < 1.8$ (a) and $d\sigma/dE_\eta^\gamma$ for  $3 <
  E_T^\gamma < 10 \GeV$ (b), for photon virtualities $Q^2>$4 GeV$^2$ and
  $y_e>0.05$. The measured cross section is compared to the prediction of
  PYTHIA (scaled 2.3) and HERWIG (scaled 2.6) plus radiation off the electron,
  Rapgap(rad). }
\label{xsec_mc}
\end{figure}

Figure~\ref{xsec_lo2} shows the comparison with a new LO ($\alpha^3$) calculation\cite{Thomas1}\cite{Thomas} which gives a good description of the data. 
At large pseudorapidities the dominant contribution comes from 
radiation off the quark line (QQ), whereas in the backward region the radiation off
the electron line (LL) dominates the cross section. The data is slightly higher than the calculation.
Figure~\ref{xsec_lo} shows the differential cross section $d\sigma/dE_T^\gamma$
in five different $\eta$-regions which correspond to individual wheels of the
calorimeter. In all five $\eta$ regions the data is well described by the LO ($\alpha^3$) calculation. 
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,70)(0,0)
\setlength{\unitlength}{1 mm}
\put(50,  -5){\epsfig{file=H1prelim-06-031.fig4a.eps,width=0.5\textwidth}}
\put(-40,  -5){\epsfig{file=H1prelim-06-031.fig4b.eps,width=0.5\textwidth}}

\end{picture}
\end{center}
\caption{Prompt photon differential cross sections  $d\sigma/dE_T^\gamma$ for
  $-1.2 < \eta^\gamma < 1.8$ (a) and $d\sigma/d\eta^\gamma$ (b) for    $3 <
  E_T^\gamma < 10 \GeV$, for photon virtualities $Q^2>$4 GeV$^2$ and
  $y_e>0.05$ compared to a LO calculation\cite{Thomas1}\cite{Thomas}. LL
  and QQ show the contribution of radiation off the electron and the quark
  line respectively. As the interference is very small it is not shown, but included in the sum.}
\label{xsec_lo2}
\end{figure}

\begin{figure}[htb]
\begin{center}
\begin{picture}(90,90)(0,0)
\setlength{\unitlength}{1 mm}
\put(-45,  50){\epsfig{file=H1prelim-06-031.fig5a.eps,width=0.35\textwidth}}
\put(15,  50){\epsfig{file=H1prelim-06-031.fig5b.eps,width=0.35\textwidth}}
\put(75,  50){\epsfig{file=H1prelim-06-031.fig5c.eps,width=0.35\textwidth}}
\put(-25,  0){\epsfig{file=H1prelim-06-031.fig5d.eps,width=0.35\textwidth}}
\put(35,  0){\epsfig{file=H1prelim-06-031.fig5e.eps,width=0.35\textwidth}}
\end{picture}
\end{center}
\caption{Prompt photon differential cross sections $d\sigma/dE_T^\gamma$ in five different bins in $\eta$ for photon virtualities $Q^2>$4 GeV$^2$ and $y_e>0.05$ compared to a LO calculation\cite{Thomas1}\cite{Thomas}. }
\label{xsec_lo}
\end{figure}


\section{Conclusion}
Results on inclusive prompt photon production in deep inelastic scattering
have been presented. The data is nicely described in shape by PYTHIA generator
plus  radiation off the electron line as modelled by RAPGAP, though the
absolute scale is too low. The HERWIG generator together with radiative photons shows a somewhat stronger $\eta$ dependence than the data and is also too low in scale. The data is reasonably described in the covered
$\eta^\gamma$ and E$_T^\gamma$ range by a new perturbative LO ($\alpha^3$) calculation.

{\bf Acknowledgements}\\
We'd like to thank Aude Gehrmann-de Ridder, Thomas Gehrmann and Eva Poulsen
for providing the LO calculations and many fruitful discussions.
\newpage
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\end{thebibliography}

\end{document}
