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\begin{titlepage}

% \noindent
% Date:          \today      \\
% Version:       0.2   \\
% Editors:       Katharina Mueller, Krzysztof Nowak  \\
% Referees:      Jacek Turnau, Gerhard Brandt  \\
%H1prelim-08-033
\noindent
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%%%%% {\it {\large version of \today}} \\[.3em]
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 \begin{small}
 \begin{tabular}{llrr}
 {\bf H1prelim-08-033} Submitted to & & &
 \epsfig{file=H1logo_bw_small.epsi
 ,width=1.5cm} \\[.2em] \hline
 \multicolumn{4}{l}{{\bf
		XVI International Workshop on Deep-Inelastic Scattering, DIS2008},
                 April 7-11,~2008,~London} \\
%                  Abstract:        & {\bf }    & & \\
                  Parallel Session & {\bf Hadronic Final States and QCD}   & & \\ \hline
   \multicolumn{4}{l}{\footnotesize {\it Electronic Access:https://www-h1.desy.de/publications/H1preliminary.short\_list.html
     %www-h1.desy.de/h1/www/publications/conf/conf\_list.html
     }} \\[.2em]
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\vspace{2cm}
\begin{center}
\begin{Large}

{\bf Prompt Photon Production in Photoproduction \\ at HERA}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{1.0cm}

\begin{abstract}
A measurement of prompt photons in photoproduction in ep collisions 
with the H1 detector is presented. The analysis is based on 
the data taken in the  years 2004-2007, corresponding to a total 
integrated luminosity of  $340 \pbarnt$. 
The photon signal is extracted using a multivariate analysis based on calorimeter cluster 
different shower shape variables. Inclusive and 
exclusive cross sections are presented as a 
function of the transverse energy $E_T^\gamma$ in the range $5$ to $15 \gev$ and 
the pseudorapidity  $\eta^\gamma$ in the range $-1.0$ to $2.4$.
The momentum fractions $x_\gamma$ and $x_{proton}$ of the incident 
photon and proton carried by the constituents participating in 
the hard scattering process are measured as well.
The results are compared to predictions from theoretical calculations.
\end{abstract}

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\newpage
\section{Introduction}

Isolated photons with high transverse momentum in the final state 
are a direct probe of the dynamics of the hard subprocess in ep collisions. 
The measurement provides complemantary information
to the study of jet production with different and generally lower
corrections for hadronisation. The process gives access to parton density functions of both
photon and proton. The ZEUS collaboration has reported measurements of 
prompt photon production \cite{ZEUS,ZEUS1,ZEUS2}. 
The H1 collaboration has performed a measurement of prompt photon 
cross section both in photoproduction \cite{H1gamma} and in Deep 
Inelastic Scattering \cite{H1dis}. Comparison to LO and NLO calculations showed that cross sections
in  DIS  are significantly underestimated. In photoproduction, the
inclusive cross section is slightly underestimated by the calculations but the photon plus jet
cross section is described reasonably well. 

The present preliminary analysis extends the phase 
space of the previous measurement in photoproduction towards larger 
pseudorapidities of the photon and lower event inelasticities. The 
data used for the measurement have been collected by the H1 detector 
during the years 2004-2007 corresponding to a total integrated luminosity of $340 \pbarnt$,
increased by a factor of three over previous measurement.

\section{Experimental Method}
Photons are reconstructed as a compact electromagnetic cluster in the 
liquid argon calorimeter (LAr)\cite{calo}. 
The transverse energy of the cluster is restricted to $5$ \gev$<E_T^\gamma < 15 \gev$ 
and the pseudorapidity region of $-1.0<\eta^{\gamma}<2.4$. The main experimental 
difficulty is the separation of the photons from neutral mesons, mainly $\pi^0$ 
or $\eta$, decaying into multi-photon final states. The number of 
photons is extracted using a multivariate 
analysis (MVA) \cite{tmva} based on six discriminating shower shape variables. The final 
cross sections are corrected for detector effects using prompt 
photon Monte Carlo events.

%\subsection{Event selection}
Events are triggered by a high energy LAr cluster. Low $Q^2$ DIS events are 
removed by excluding events with an electron in the backward calorimeter (SpaCal).
The inelasticity is restricted to $0.1 <y_{h}=\Sigma(E-p_z)/2E_e<0.7$ 
where $E_e$ is the energy of the incoming electron and the sum runs over the
energy ($E$) and the longitudinal momentum ($p_z$) of all final state particles.
The z-position of the event vertex is required to be within $\rm 40$ cm of the 
nominal vertex position. In order to correctly determine the vertex position
at least two well reconstructed central tracks are required.
At least one jet with transverse momentum larger 
than $3.5 \gev$ is required. The jet is reconstructed using the $k_T$ algorithm \cite{jetalgo}
with cone size $R_0=1$ running over all final state particle 
candidates, including photon candidates.

Photon candidates are defined by electromagnetic clusters with 
transverse energy $5 < E_T^\gamma < 15 \gev$ and 
pseudorapidity $-1.0 < \eta^\gamma < 2.4$. Candidates close to the cracks of 
the calorimeter are rejected. Charged particles are removed by a
combined condition based on the information from the Central Tracking Detector (CTD)
and the Central Inner Proportional chamber (CIP)\cite{cip}. 
The cluster has to be compact with a transverse radius of 
less than 6 cm. In order to suppress background the photon needs to 
be isolated, what is achieved by a cut on the fraction of the transverse energy of the jet
containing the photon carried by the photon,
$z = E_{T}^{\gamma}/E_{T}^{photon-jet} > 0.9$. The invariant mass of the cluster, when combined with the closest
neighbouring electromagnetic cluster with an energy larger than 80 MeV must be 
larger than $0.3 \gev$. This last requirement rejects candidates from $\pi^0$ decays 
with two photons reconstructed in separated clusters.

For the exclusive selection of a photon accompanied by a jet, the selection on 
the transverse momentum of the jet larger than $4.5 \gev$ and pseudorapidity 
$-1.3<\eta^{jet}< 2.4$ is performed.

For both inclusive and exclusive selections the photon signal is extracted by a 
MVA using the shower shape variables.

\subsection{Extraction of the photon signal and systematic errors}
Six different shower shape variables are used to discriminate between photons
 and neutral mesons \cite{H1dis}.
\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 
the highest energy.
\item Transverse radius
%~\footnote{Transverse radius is defined as the square root
%of the second moment of the transverse cell distribution
%$$R_{T}=\sqrt{\mu_{2}}$$}
of the cluster, where the transverse plane is perpendicular 
to the direction of the incoming particle.
\item Energy fraction deposited in the hottest cell of the cluster.
\item Energy fraction deposited in the first layer of the LAr.
\item Transverse kurtosis
%~\footnote{The transverse kurtosis $K_{T}$ is defined 
%as the ratio of the fourth and squared second moment of the transverse energy
%distribution of cluster cells $$K_{T}=\frac{\mu_{4}}{\mu_{2}^{2}}-3$$} 
giving the information how strongly the energy distribution
is peaked.
\item Transverse symmetry, defined as the ratio 
of the spread of the transverse cell 
distributions along the two principal axes.
\end{itemize}

The discrimination power between the prompt photon signal (photons coming from 
direct events, from resolved and photons radiated off the quark) and the background 
(di-jet production events) can be seen in figure~\ref{estimators}. The plot shows 
the distribution of six different shower shape 
variables for the photon candidate clusters
compared to the PYTHIA predictions for the signal (scaled to the
measured cross section) and the background.
The transverse radius and the hot core fraction exhibit the best discrimination 
power, as can be seen by comparing the prompt photon signal (photons coming from 
direct events, from resolved and photons radiated off the quark) to the background 
(di-jet production events) distributions.

The variables are combined in a MVA producing a final discriminator in bins of transverse 
energy $E_T^{\gamma}$ and pseudorapidity $\eta^{\gamma}$. The signal content is obtained 
by fitting the discriminator distributions of pure signal and pure background samples of single 
particle Monte Carlo to the data. As an example for the fit figure~\ref{fit} shows 
the discriminator for six different energy bins for one $\eta^{\gamma}$ bin. The
figures show the signal and background distributions together with the data.

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 listed below.
\begin{itemize}
\item Description of the shower shape variables in the simulation. Systematic shift 
of shower shape variables between 3.5\% and 8\% (depending on the variable 
and pseudorapidity region) motivated by previous study \cite{H1dis} leads 
to errors up to 30\% on the cross sections.
\item The uncertainty of the description of the  trigger correction together 
with the steep  slope of the trigger efficiency at low  transverse energies 
leads to a systematic error up to 20\% in the lowest $E_{T}^{\gamma}$ bin.
\item The model dependence was studied by comparing acceptance corrections 
obtained with HERWIG and PYTHIA, leading to a systematic error of up to 10\% 
in the most forward $\eta^{\gamma}$ bin.
\item Description of the photon conversion rate in the detector. 
A variation of the conversion rate by factors 0.5 and 1.5
leads to a systematic error of 15\% in the most forward $\eta^{\gamma}$ bin.
\item From the difference between the single particle simulations and the PYTHIA
simulation including the simulation of full hadronic final state systematic error
of 5\% (15\% in the most forward $\eta^{\gamma}$ bin) is assigned.
\end{itemize}

\section{Monte Carlo simulation and calculations}
Monte Carlo (MC) simulations are used in this analysis for the determination of the 
detector acceptance and for the  extraction of the photon signal. The acceptance 
correction is determined from  events generated with PYTHIA 6.2\cite{PYTHIA} event 
generator. The simulated signal contains contributions from direct and resolved 
production of prompt photons as well as photons radiated from the quark in di-jet events. 
The background sample contains genuine di-jet events without high energetic photons 
from the quark.  For the extraction of the photon signal using 
shower-shape-based MVA high statistics single particle 
Monte Carlo samples are used. They consist of single photons (signal part) and 
single hadrons (mainly $\pi^0$ and $\eta$ - background part). All generated events 
are passed through a full GEANT \cite{geant} simulation of
the H1 detector and through the same reconstruction and analysis program
as used for the data.

All the results are compared to two sets of calculations corrected to hadron level and multiple interactions:
\begin{itemize}
\item The FGH (Fontannaz-Guillet-Heinrich) \cite{heinrich,heinrich2} calculation includes 
NLO corrections to the direct and resolved photon production
as well as contribution from quark-to-photon fragmentation and the direct box diagram 
$\gamma g \rightarrow \gamma g$ which is calculated to order $\alpha_{s}^{2}$. The error
is evaluated by varying the fragmentation and renormalisation scales 
together by a factor 0.5 and 2.0 leading to overall error of 
at most $10\%$.
\item The ZL (Zotov-Lipatov) ~\cite{zotov} calculation is based on the $k_{T}$ factorisation 
approach and uses the unintegrated quark and gluon densities  of the proton and the 
photon according to the Kimber-Martin-Ryskin prescription. Direct and resolved 
contributions are taken into account. Estimation of the error has been performed by 
multiplying the $p_{T}^{2}$ scale by a factor $4$ and $1/4$ leading to an error of at most $10\%$.
\end{itemize}



\section{Results}
Differential cross sections for the production of prompt photons in photoproduction 
are measured for $Q^2<1 \gev^2$, $0.1 <y_h< 0.7$ for photons with 
$5 < E_T^\gamma < 15 \gev$,  pseudorapidity  $-1.0 < \eta^\gamma < 2.4$ and the 
transverse energy fraction $z=E_{T}^\gamma/E_{T}^{photon-jet}>0.9$.

Figure~\ref{xsec_incl} shows the single differential inclusive cross sections 
as a function of transverse energy and the pseudorapidity of the photon. 
Both calculations are slightly lower than the data most
significantly at low $E_{T}^{\gamma}$.

Exclusive (photon plus jet) single differential cross sections measurement as a function of 
transverse energy and pseudorapidity of the photon (figure~\ref{xsec_excl}), 
transverse momentum and pseudorapidity of jet (figure~\ref{xsec_exclJet}) 
and momentum fractions $x_{\gamma}^{obs}$ and $x_{proton}^{obs}$ (figure~\ref{xsec_exclX})
show better agreement with the calculations. The largest discrepancy arises 
for the highest bin in $x_\gamma^{obs}$, where both calculations give different
prediction, while data does not favour any of them.

\section{Conclusions}
Results on both inclusive and exclusive prompt photon production in photoproduction 
as measured by the H1 collaboration have been presented. The measurement has been 
compared to two calculations, one using a collinear approach and the other based on $k_t$ 
factorisation. The predictions for the inclusive sample are slightly lower than the data, 
most significantly at low $E_{T}^{\gamma}$ but there is reasonable agreement 
for the photon plus jet sample except at high $x_{\gamma}^{obs}$


\newpage
\begin{thebibliography}{99}
\bibitem{ZEUS} J. Breitweg {\it et al.}
%``Measurement of inclusive prompt photon photoproduction at HERA''
Physics Letters B 472 (2000) 1-2, 175-188 
[arXiv:hep-ex/9910045]
\bibitem{ZEUS1} 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. B511 (2001) 19-32
[arXiv:hep-ex/0104001]
\bibitem{ZEUS2} S. Chekanov {\it et al.} [ZEUS Collaboration], 
%``Measurement of prompt photons with associated jets in photoproduction at HERA''
Eur.Phys.J. C49 (2007) 511-522
[arXiv:hep-ex/0608028]
\bibitem{H1gamma} A. Aktas {\it et al.} [H1 Collaboration], 
% ``Measurement of prompt photon cross sections in photoproduction at HERA''
Eur. Phys. J.{\bf  C38} (2005) 437 
[arXiv:hep-ex/0407018].
\bibitem{H1dis} F.D.Aaron {\it et al.} [H1 Collaboration], 
%`` Measurement of isolated photon production in deep-inelastic scattering at HERA''
0711.4578 [hep-ex].
\bibitem{calo} B. Andrieu {\it et al.} [H1 Calorimeter Group Collaboration], Nucl. Instrum. Meth. A{\bf  336} (1993) 460.
\bibitem{tmva} J. Friedman, T. Hastie and R. Tibshirani, “The Elements of Statistical Learning”, Springer
Series in Statistics, 2001
\bibitem{cip}
  J.~Becker {\it et al.},
  %``A vertex trigger based on cylindrical multiwire proportional chambers,''
  Nucl.\ Instrum.\ Meth.\  A {\bf 586} (2008) 190
  [arXiv:physics/0701002].
  %%CITATION = NUIMA,A586,190;%%
\bibitem{PYTHIA} T. Sj\"ostrand {\it et al.}, PYTHIA 6.2 Physics and Manual [hep-ph/0108264].
\bibitem{geant} GEANT 3, R.Brun {\it et al.}, CERN\_DD/EE/84-1.
\bibitem{H1det}  I. Abt {\it et al.} [H1 Collaboration] Nucl. Instr. and Meth. {\bf A 386} (1997) 310, ibid, 348.
\bibitem{jetalgo} Stephen D. Ellis, Davison E. Soper, Phys.Rev. {\bf D48} (1993) 3160 [hep-ph/9305266].
\bibitem{heinrich}
  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].
\bibitem{heinrich2}
  M.~Fontannaz and G.~Heinrich,
  %``Isolated photon + jet photoproduction as a tool to constrain the gluon
  %distribution in the proton and the photon,''
  Eur.\ Phys.\ J.\  C {\bf 34}, 191 (2004)
  [arXiv:hep-ph/0312009].
\bibitem{zotov}
  A.~V.~Lipatov and N.~P.~Zotov,
  %``Prompt photon photoproduction at HERA in the k(T)-factorization
  %approach,''
  Phys.\ Rev.\  D {\bf 72} (2005) 054002
  [arXiv:hep-ph/0506044].
  %%CITATION = PHRVA,D72,054002;%%

\end{thebibliography}

\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig1.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Shower shape variables used to discriminate between 
photons and neutral mesons: transverse kurtosis, transverse symmetry, transverse radius,
energy fraction in the first layer, energy fraction in the hottest cell and 
energy fraction in the hot core of cluster. The measured data points are 
shown together with the radiated, resolved and direct signal Monte Carlo 
and remaining background, as estimated by PYTHIA. The MC prediction is scaled to the measured cross section.}
\label{estimators} 
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig2.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Examples of the MVA discriminator distributions: $\eta^{\gamma}$ bin $0.23 <\eta^{\gamma}< 0.96$
and six transverse energy intervals. The fitted distributions of the single particle 
signal and background are also shown.}
\label{fit}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% inclusive xsections
\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig3.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Inclusive prompt photon single differential cross sections as function of $E_T^\gamma$ 
(left) and $\eta^\gamma$ (right). The cross sections are measured in visible range defined by
$5 < E_T^\gamma < 15 \gev$, $Q^2< 1 \gev^2$, $0.1 < y_h< 0.7$ and 
$z=E_{T}^{\gamma} / E_{T}^{photon-jet} > 0.9$. The inner errors in the figures represent 
the statistical errors, while the outer are the statistical and the systematical errors added 
in quadrature. The measured cross section is compared to the 
Fontannaz-Guillet-Heinrich (continuous red) and Zotov-Lipatov (dashed blue) calculations.}
\label{xsec_incl} 
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exclusive xsections 1
\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig4.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Exclusive prompt photon single differential cross sections as function of $E_T^\gamma$ 
(left) and $\eta^\gamma$ (right). The cross sections are measured in range defined in caption of
figure~\ref{xsec_incl}. In addition jet with transverse momentum $p_T^{jet}>4.5 \gev$ and 
pseudorapidity $-1.3<\eta^{jet}<2.4$ is required. The inner errors in the figures represent 
the statistical errors, while the outer are the statistical and the systematical errors added 
in quadrature. The measured cross section is compared to the Fontannaz-Guillet-Heinrich 
(continuous red) and Zotov-Lipatov (dashed blue) calculations.}
\label{xsec_excl} 
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exclusive xsections 3
\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig5.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Exclusive prompt photon single differential cross sections as function of $p_{T}^{jet}$ (left) 
and $\eta^{jet}$ (right). The cross sections are measured in range defined in caption of
figure~\ref{xsec_excl}. The inner errors in the figures represent 
the statistical errors, while the outer are the statistical and the systematical errors added 
in quadrature. The measured cross section is compared to the Fontannaz-Guillet-Heinrich 
(continuous red) and Zotov-Lipatov (dashed blue) calculations.}
\label{xsec_exclJet} 
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% exclusive xsections 2
\newpage
\begin{figure}[hhh]
\center
\epsfig{file=H1prelim-08-033.fig6.eps,width=15cm}
\setlength{\unitlength}{1cm}
\caption{Exclusive prompt photon single differential cross sections as function of 
$x_\gamma^{obs}$ (left) and $x_{p}^{obs}$ (right). 
The cross sections are measured in range defined in caption of
figure~\ref{xsec_excl}. The inner errors in the figures represent 
the statistical errors, while the outer are the statistical and the systematical errors added 
in quadrature. The measured cross section is compared to the Fontannaz-Guillet-Heinrich 
(continuous red) and Zotov-Lipatov (dashed blue) calculations.}
\label{xsec_exclX} 
\end{figure}


\end{document}




