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\newcommand{\dstar}{\ensuremath{D^*}}
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% Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4}
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
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\def\NPB{{\em Nucl. Phys.}   {\bf B}}
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\def\PRD{{\em Phys. Rev.}    {\bf D}}
\def\ZPC{{\em Z. Phys.}      {\bf C}}
\def\EJC{{\em Eur. Phys. J.} {\bf C}}
\def\CPC{\em Comp. Phys. Commun.}

%Die einleitenden Seiten der Arbeit mit römischer Nummerierung: 
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\begin{titlepage}
%%%%%%%%%%%% coment the header and fill the right conference
%%%%% {\it {\large version of \today}} \\[.3em]
\begin{center} %%% you may want to use this line for working versions
 \begin{small}
 \begin{tabular}{llrr}
 {\bf H1prelim-08-073} Submitted to & & &
 \epsfig{file=/h1/iww/ipublications/H1PublicationTemplates/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 Heavy Flavours}   &
& \\ \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]
 \end{tabular}
 \end{small}
 \end{center}
\vspace{2cm}
\begin{center}
\begin{Large}
{\bf Measurement of $\mathbf \dstar$ Meson Production \\ in Photoproduction}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
Inclusive production of \dstar\ mesons in Photoproduction at HERA
is presented. The data was collected with the H1 detector in the end of the year 2006
and in 2007 and corresponds to an integrated luminosity of ~93 pb$^{-1}$.
This analysis covers a kinematic region of small photon virtuality
$Q^2<2\,{\rm GeV}^2$
and photon-proton center-of-mass energies of $100<W_{\gamma p}<285\,{\rm GeV}$.
The \dstar\ meson is measured for $p_t (D^\star) > \mbox{1.8}$ GeV and
$|\eta (D^\star)| < \mbox{1.5}$. Single and double differential cross sections are compared
to the NLO calculation FMNR and the LO MC programs PHYTHIA and Cascade.
\end{abstract}
\end{titlepage}


\clearpage \newpage 
%\setcounter{tocdepth}{1}   % für die finale Version -> Liste nur Chapter und Sections im Verzeichnis 
%\tableofcontents 
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\pagenumbering{arabic}
%\include{Motivation}
%\include{Selection}
%\include{XSecDeterm}
%\include{Results}

\section{Results of the Measurement}
\label{Kap_Ergebnisse}

\subsection{D* - Signal}
The charm quark is tagged by a \dstar\ meson which decays in the golden channel 
$D^{\star \pm}  \rightarrow D^0 \pi^\pm_{\mathrm{slow}} \rightarrow K^\mp \pi^\pm \pi^\pm_{\mathrm{slow}}$.
The slow pion is created just above its mass threshold and therefore its transverse 
momentum $p_t$ is small. In order to calculate the total \dstar\ meson production
cross section the branching ratio from the PDG, $2.59\%$, is used. 
The number of \dstar\ mesons is extracted from the distribution of the mass
difference $\Delta M$, determined as: 
\begin{equation}
\Delta M = M(K\pi\pi_\text{slow})- M(K\pi)   ~. 
\end{equation} 
Applying the complete event selection for Photoproduction 
and for \dstar\ meson candidates one gets the $\Delta M$-distribution
shown in figure \ref{deltaM}. \\
Table \ref{vis_cuts} shows the definition of the visible range for which the  
measured cross sections are quoted. Table \ref{acc_cuts} summarizes the 
selection cuts for which the data are corrected by the selection efficiency
determined from the Monte Carlo simulation.
\begin{table}[htdp]
\begin{center}
\begin{tabular}{ll}
\hline 
Name & Range \\\hline 
$p_t (D^\star)$ & \mbox{$>\mbox{1.8}$ GeV} \\
$|\eta (D^\star)|$ & $< \mbox{1.5}$ \\
%\multicolumn{2}{S} { ~ } \\[-0.38cm] 
Virtuality & $Q^2< 2 ~\text{GeV}^2$ \\ 
Inelasticity & $\mbox{0.1} < y < \mbox{0.8}$ \\ 
\hline 
\end{tabular}
\end{center}
\caption{Definition of the visible range of the measurement.}
\label{vis_cuts}
\end{table}%

\begin{table}[htdp]
\begin{center}
\begin{tabular}{ll}
\hline 
Name & Range \\\hline 
$p_t (D^\star)$ & $>\mbox{1.8}$ GeV \\
$|\eta (D^\star)|$ & $< \mbox{1.5}$ \\  
$p_t (K)$ & $>\mbox{0.5}$ GeV \\ 
$p_t (\pi)$ & $>\mbox{0.3}$ GeV \\ 
$p_t (\pi_{\text{slow}})$ & $>\mbox{0.120}$ GeV \\ 
$p_t (K) + p_t(\pi)$ & $>\mbox{2.2}$ GeV \\
$ |M(K\pi) - M(D^0)| $ & $< \mbox{0.08} $ GeV \\ 
%$\Delta M $ & $<\mbox{0.170}$ GeV \\  \hline 
$f={p_t (D^\star)}/{\sum_{\theta > 10^{\circ}} E_i \cdot \sin \theta_i}$ & $>\mbox{0.13}$ \\  \hline 
\end{tabular}
\end{center}
\caption{Selection cuts for decay particles of the \dstar\ mesons. 
  The cut on the variable f is used to supress combinatorical background. The
  measured cross sections are corrected for the efficiency of the selection
  cuts.}
\label{acc_cuts}
\end{table}
%%%%
\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig1.eps} 
\caption{Distribution of the  $\Delta M$ of all \dstar\ meson candidates.} 
\label{deltaM}
\end{figure}

\subsection{Cross-Section determination}
For a cross section determination the number of \dstar\ mesons $N_{D^\star}$ and the 
acceptance $\text{A}_\text{Detector}$ and efficiency $\epsilon_\text{Detector}$, 
the trigger efficiency $ \epsilon_\text{Trigger}$ 
and luminosity $ {\cal L}$ have to be determined.
The bin-averaged differential cross-section $d\sigma^\text{vis}/dY$ for a variable $Y$ 
(with a bin width $\Delta Y$) is then given by the following formula: 
%%
\begin{equation}
\frac{d\sigma^\text{vis}}{dY}  = \frac{N_{D^\star} (1-r)} {\Delta Y {\cal L}   \cdot {\cal B} (D^\star \rightarrow K \pi \pi_\text{slow})  \cdot \text{A}_\text{Detector} \cdot \epsilon_\text{Detector} \cdot \epsilon_\text{Trigger}   }   ~. 
\end{equation}
%%
The correction $r=0.04$ is applied to account for reflections from other $D^0$ 
decays within the $D^0$ mass window as determined in the analysis of \dstar\ 
production at low $Q^2$ (H1prelim-08-072) in a very similar visible range of the
\dstar\ meson.

\subsection{Results}
Single- and double differential cross sections are presented in this draft.
The single differential cross-sections are given for the variables $p_t(D^*)$, 
$\eta(D^*)$ and $W_{\gamma p}$. The double differential cross sections are given 
for $\eta(D^*)$ in three different $p_t(D^*)$ ranges.\\

The cross sections are compared to various LO Monta Carlo models as implemented
in Pythia6.2 and Cascade1.2 and a NLO calculation (FMNR). 
The main difference between Pythia6.2 and Cascade1.2 is the treatment of the 
proton structure. Pythia6.2 is based on the DGLAP evolution equations whereas 
Cascade1.2 is based on the CCFM evolution equations.  
In Pythia two possibilities for the treatment of the charm-quark masses 
are given. The charm-quark can be treated as a massless particle or as a massive
particle. In the latter case only the charm quark for the direct 
contribution to the cross section is caclulated massive whereas the mass of the charm 
quark for the resolved contribution is set to zero.\\

FMNR is a massive scheme NLO-calculation. 
The fragmentation of the $D^*$ meson is done by using 
the peterson fragmentation function.\\

The single differential cross section measurement and the comparison to 
LO-MC-models for $p_t(D^*)$, $\eta(D^*)$ and $W_{\gamma p}$ is shown in figures 
\ref{xs_lo_pt}, \ref{xs_lo_eta} 
and \ref{xs_lo_w}, the comparison to the NLO calculation given by the FMNR is shown in 
the figures \ref{xs_nlo_pt}, \ref{xs_nlo_eta} and \ref{xs_nlo_W}. Double differential 
cross sections are presented in figures \ref{xsdd_lo_pteta} and \ref{xsdd_nlo_pteta}.\\

The cross section measurement, black points, is compared to different 
Monte-Carlo Models, represented by the different colored lines. 
The green histogram shows the prediction 
of the MC-Program Pythia6.2 where the charm-quarks are treated as massive particles, whereas 
the blue histogram shows the prediction by Pythia6.2 where the charm-quarks are treated
as massless-particles. The red histogram shows the prediction of the MC-Program Cascade1.2.\\
To compare the shapes of the of the different distributions the ratio $R$ is shown in the lower part 
of these plots. The ratio $R$ is defined as 
\begin{equation}
  R = \frac{\frac{1}{\sigma^{MC}_{vis}} \cdot \frac{d\sigma^{MC}}{dY}}{\frac{1}{\sigma^{data}_{vis}} \cdot \frac{d\sigma^{data}}{dY}}
\end{equation}
where $Y$ denotes the measured variable.\\

The Cascade prediction describes the shape of the $p_t(\dstar)$ distribution
(fig.~\ref{xs_lo_pt}), but is too low in normalisation. Both Pythia models are 
too steep. The $\eta(\dstar)$ distribution (fig.~\ref{xs_lo_eta}) is described 
in shape and normalisation by the massless Pythia prediction, while Cascade and
the massive treatment in Pythia predict a too strong decrease in the forward
direction, as was already seen in the analysis of HERA I data (DESY-06-110, in 
a different kinematic range). The double differential measurement in 
$p_t(\dstar)$ and $\eta(\dstar)$, fig.~\ref{xsdd_lo_pteta}, shows that all Monte
Carlo programs have difficulties to describe the forward region $\eta > 0$ at 
large transverse momenta. In the $W_{\gamma p}$ distribution, all MC
predicitions have a tendency to fall more steeply than the data.

The comparison to the NLO calculation given by the FMNR is shown in 
the figures \ref{xs_nlo_pt}, \ref{xs_nlo_eta}, \ref{xs_nlo_W}, and 
\ref{xsdd_nlo_pteta}. The theroretical uncertainty is estimated by an 
independently variation of the scales $\mu_f$, $\mu_r$
and the charm mass $m_c$. In general, the FMNR calculation 
gives a reasonable description of the data, but is also lower than the 
data in the forward direction. As for the LO MC predictions, the deficit is
most prominent at large transverse momenta. 

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig2.eps} 
\caption{Differential cross section as a function of $p_t(D^*)$. 
  The result is compared to different LO-MC models. The data are given by the black points.
  The green histogram shows the prediction 
  of the MC-Program Pythia6.2 where the charm-quarks are treated as massive particles, whereas 
  the blue histogram shows the prediction by Pythia6.2 where the charm-quarks are treated
  as massless-particles (for further explanations see text). 
  The red histogram shows the prediction of the MC-Program Cascade1.2.}
\label{xs_lo_pt}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig3.eps} 
\caption{Differential cross section as a function of $\eta(D^*)$. 
  The result is compared to LO-MC models. The data are given by the black points.
  The green histogram shows the prediction 
  of the MC-Program Pythia6.2 where the charm-quarks are treated as massive particles, whereas 
  the blue histogram shows the prediction by Pythia6.2 where the charm-quarks are treated
  as massless-particles (for further explanations see text). 
  The red histogram shows the prediction of the MC-Program Cascade1.2.}  
\label{xs_lo_eta}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig4.eps} 
\caption{Differential cross section as a function of $W_{\gamma p}$. 
  The result is compared to LO-MC models. The data are given by the black points.
  The green histogram shows the prediction 
  of the MC-Program Pythia6.2 where the charm-quarks are treated as massive particles, whereas 
  the blue histogram shows the prediction by Pythia6.2 where the charm-quarks are treated
  as massless-particles (for further explanations see text). 
  The red histogram shows the prediction of the MC-Program Cascade1.2.}  
\label{xs_lo_w}
\end{figure}

%%%%
\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig5.eps} 
\caption{Differential cross section as a function of $p_{t}(D^*)$. 
  The result is compared to a NLO calculation FMNR.}  
\label{xs_nlo_pt}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig6.eps} 
\caption{Differential cross section as a function of $\eta (D^*)$. 
  The result is compared to a NLO calculation FMNR.}  
\label{xs_nlo_eta}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig7.eps} 
\caption{Differential cross section as a function of $W_{\gamma p}$. 
  The result is compared to a NLO calculation FMNR.}  
\label{xs_nlo_W}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig8.eps} 
\caption{Double differential cross section as a function of $\eta (D^*)$ for 
  three bins of $p_{t}(D^*)$. The result is compared to LO-MC models. The data are given by 
  the black points. The green histogram shows the prediction 
  of the MC-Program Pythia6.2 where the charm-quarks are treated as massive particles, whereas 
  the blue histogram shows the prediction by Pythia6.2 where the charm-quarks are treated
  as massless-particles. The red histogram shows the prediction of the MC-Program Cascade1.2.}  
\label{xsdd_lo_pteta}
\end{figure}
  
\begin{figure}[htbp]
\centering
\includegraphics[width=15cm, angle=0]{H1prelim-08-073.fig9.eps} 
\caption{Double differential cross section as a function of $\eta (D^*)$ for 
  three bins of $p_{t}(D^*)$. The result is compared to a NLO calculation FMNR.}  
\label{xsdd_nlo_pteta}
\end{figure}

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