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\newcommand{\Dstar}{\particle{D^{*}}}
\newcommand{\Dstarplus}{\particle{D^{*+}}}
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\newcommand{\dstdec}{$D^{*+} \rightarrow D^0 \pi^+ \rightarrow (K^- \pi^+) \pi^+$}
\newcommand{\dcdec}{$D^+ \rightarrow K^- \pi^+ \pi^+$}
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\pagestyle{empty}
\begin{titlepage}

\noindent
{\bf  H1-prelim-02-076 \hfill 
  \epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} 
} \\
\noindent April 2002 
\vspace*{3cm}
\begin{center}
  \Large
  {\bf 
        Measurement of Inclusive {\boldmath $D$}-meson Production \\
in Deep Inelastic Scattering at HERA }\\

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


\begin{abstract}
\noindent

The inclusive production of charmed mesons in deep 
inelastic scattering is studied with the H1 detector at HERA.
%
Inclusive production cross sections are measured for the 
vector- $\Dstar$ and for the
pseudoscalar charmed mesons $ \Dzero, \Dsubs$ and, for the first 
time at HERA, also $\Dplus$ mesons.
% through their decay $D^+ \to K^- \pi^+ \pi^+$.
The finite lifetimes of 0.4 to 1 ps for the pseudoscalar mesons
%$\Dzero$ and $\Dplus$ 
lead to a separation of their production and decay vertices, which
is exploited to distinguish signal and background processes and to 
substantially improve the signal qualities. 
%The reconstruction of separation distances of some
%1/10 mm is made possible by exploiting the high-precision tracking
%capabilities of the central H1 silicon detector.
Differential distributions are measured for the $\Dplus$ and $\Dzero$
mesons and compared with predictions, 
based on LO Monte Carlo simulations.

The measured production cross sections are used to test the isospin
invariance of the fragmentation process and to extract 
the strangeness suppression factor $\gamma_s$ and 
the fraction $P_V$ of D-mesons produced in a vector state.
The results are compared with values measured e.g. at
$e^+ e^-$-colliders and allow tests of the assumed 
universality of the charm fragmentation process.


\end{abstract}
\end{titlepage}

\pagestyle{plain}

%
% --------------------
% phoenix- plot

 \newpage
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig1.eps,width=16. cm}
\caption{Comparison of the invariant mass distributions $m(K \pi \pi)$ for
 $D^+ \rightarrow K^- \pi^+ \pi^+$ decay candidates
(a) before and (b) after a cut on the decay length significance $S_l = l/\sigma_l > 8$,
where $l$ is the radial separation distance between the meson production and its decay vertex, 
and $\sigma_l$ the error of $l$.
The background contribution is suppressed by $\cal O$(300) and the signal to background ratio
is improved by a factor $\cal O$(50) when vertexing information measured with the 
H1 central Si vertex detector CST is exploited.}
  \end{center}
\end{figure}

\clearpage

% --------------------
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig2.eps,width=16. cm}
\caption{ a) $K\pi$-invariant mass  distribution for tagged 
$D^0 \rightarrow K^- \pi^+$ decay candidates
({\it tagged} denotes the cases where the $\Dzero$ is explicitly 
known to originate from a $\Dstar$ decay);
b) the decay length distribution composed of the background contribution (yellow)
taken from the sideband in the data (which represents directly the achieved
resolution function), and the signal contribution, the shape of which is taken
from the simulation. 
c,d) decay length significance $S_l$ distributions (linear and logarithmic scale);
  in the fit only the normalisations of signal and background areas are determined;
  the independent extraction methods produce compatible numbers
  of signal events. }

  \end{center}
\end{figure}

\clearpage
% --------------------
\newpage

\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig3.eps,width=16. cm}
\caption{a)  $K\pi$-invariant mass  distribution for tagged  
$D^0 \rightarrow K^- \pi^+$ decay candidates  
 for a decay length significance $S_l > 4$;
b) efficiency distribution as a function of the cut on the
  decay length significance $S_l = l/\sigma_l$; 
  the efficiency is defined as the number of fitted $\Dzero$-mesons 
  after applying the cut on $S_l$ divided by the total number of $\Dzero$-mesons
  without $S_l$ -cuts.
  Data (solid dots) are compared with expectations from the simulation (open squares).}
  \end{center}
\end{figure}

\clearpage

% --------------------
\newpage
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig4.eps,width=16. cm}
\caption{ $D^{*+} \rightarrow D^0 \pi^+ \rightarrow (K^- \pi^+) \pi^+$ decay
candidate distributions:
  a) $K \pi$-invariant mass distribution after a $3-\sigma$-cut in the
   $\Delta M = m(K^- \pi^+) \pi^+) - m(K^- \pi^+)$ - variable, shown    in b). 
 The total number of $\Dstar$ is determined from a fit to the $m(K \pi)$ distribution, as 
   indicated in a).}
  \end{center}
\end{figure}

\clearpage

% --------------------
\newpage
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig5.eps,width=16. cm}
\caption{$D^+_s \rightarrow \Phi \pi^+ \rightarrow (K^+ K^-) \pi^+$ decay
 candidate distributions: a) invariant mass distribution $m(KK\pi)$
 after restricting the $m(KK)$-invariant mass to the $\Phi$-resonance region as shown in b). }
  \end{center}
\end{figure}

\clearpage

% --------------------
\newpage
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig6.eps,width=10. cm}
\caption{ $D^0 \rightarrow K^- \pi^+$ decay candidate distribution: 
  the decomposition of the data into a Gaussian right sign signal (bright shading),
   the wrong sign charge combination (dark shading, function taken from simulation) 
   and an exponential background is separately indicated.}
  \end{center}
\end{figure}

\clearpage

% --------------------
\newpage
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig7.eps,width=16. cm}
\caption{Differential production cross section for untagged 
  $\Dzero$ mesons as a function of
   the $\Dzero$ transverse momentum and pseudorapidity (left) and the event kinematics (right).
   The dark shaded bands indicate the AROMA Monte Carlo predictions including a scaled 
   beauty contribution,  shown separately as light shaded bands.
   In the simulation the following parameters for the calculations are used:
   proton structure function: GRV 98 (LO), $m_c = 1.5$ GeV, $m_b = 4.75$ GeV, Peterson parameter
  $\epsilon_c = 0.078, \epsilon_b = 0.0069$; beauty cross section scale factor $= 4.3\pm 1.4$, 
  as previously published by H1. 
}
  \end{center}
\end{figure}

\clearpage

% --------------------
\newpage
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig8.eps,width=10. cm}
\caption{Invariant mass $m(K \pi \pi)$ distribution for
  $D^+ \rightarrow K^- \pi^+ \pi^+$ decay candidates:
 the curve indicates the fit to the H1 data using a Gaussian function for the signal
and a linear for the background (solid dots).}
  \end{center}
\end{figure}

\clearpage
% --------------------
\newpage

\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-076.fig9.eps,width=16. cm}
\caption{ Differential production cross section for $\Dplus$ as a function of
   $\Dplus$ transverse momentum and pseudorapidity (left) event kinematic variables (right).
   The dark shaded bands indicate the AROMA MC predictions including a scaled
   beauty contribution, shown separately as light shaded bands.
  The MC parameters are given in the caption of fig.7.}
  \end{center}
\end{figure}

\clearpage

% -------------------- 
\newpage

\begin{table}[h]

 \Large
 \renewcommand{\arraystretch}{1.2}

\begin{center}
 \begin{tabular}{|c|c|c|c|c|}
  \hline
  {\bf Cross section} & \dc & \dn & \ds & \dst \\
  \hline 
$\sigma_{vis}(ep \rightarrow eDX)$ (nb)  &
 2.16      & 6.53     & 1.67 & 2.90   \\
stat. error on  $ \sigma_{vis}$          &
$\pm 0.19$ & $\pm 0.49$ & $\pm 0.41$ & $\pm 0.20$  \\
syst. error on $ \sigma_{vis}$           &
$^{+0.46}_{-0.35}$ & $^{+1.06}_{-1.30}$ & $^{+0.54}_{-0.54}$ & $^{+0.58}_{-0.44}$ \\
  \hline  
AROMA LO prediction $ \sigma_{vis}$ &
2.45 & 5.54 & 1.15 & 2.61   \\
 \  error on prediction         &
$\pm 0.30$ & $\pm 0.69$ &  $\pm 0.30$&  $\pm 0.31 $  \\
  \hline
 \end{tabular}
   \caption{Inclusive charmed meson electroproduction cross sections for the four 
  meson states
  in the visible kinematic range, defined by 
  $2\, \le \,Q^2 \le 100\, $GeV$^2,\
\ 0.05 \le y  \le  0.7, \ p_t(D) \ge 2.5\,$GeV/$c$ and $|\eta(D)|  \le 1.5. $ 
 }
\end{center}

\end{table}

\clearpage

%%%%--------------------------

\newpage

\section*{Fragmentation Ratios}

In order to determine fragmentation ratios, the fragmentation factors $f(c \to D)$ are 
calculated based on the measured cross sections $\sigma_{vis}$ and the predictions by 
the AROMA leading order Monte Carlo simulation for both charm $\sigma^{MC}_{c\bar{c}}$ 
and beauty $\sigma^{MC}_{b\bar{b}}$ as given below:

\begin{eqnarray}
\Large \nonumber
\displaystyle f^{}(c\rightarrow D) = 
\frac{\displaystyle \sigma_{vis} - 2 \cdot \sigma^{MC}_{b\bar{b}} \cdot
\displaystyle f^{}(b\rightarrow D)}
{\displaystyle 2 \cdot \sigma^{MC}_{c\bar{c}}}
%
= \frac{\displaystyle \sigma_{vis}(ep \rightarrow eDX) - 
\sigma^{MC}_{vis} (ep \rightarrow b\bar{b} \rightarrow eDX)}
%
{  \frac{\displaystyle \sigma^{MC}_{vis} (ep \rightarrow c\bar{c} \rightarrow eDX)} 
        {\displaystyle f_{w.a.}(c \rightarrow D)}
}
\end{eqnarray}

where ${\displaystyle f_{w.a.}}$ denotes the current world average value of 
the relevant fragmentation factor.

%-----------
\begin{table}[h]
 \large
 \renewcommand{\arraystretch}{1.3}
\begin{center}
\hspace*{-1.cm}
 \begin{tabular}{|c|c|c|c|c|}
  \hline
  {\bf Fragmentation Factors and Ratios} & \dc & \dn & \ds & \dst \\
  \hline 
  $ f(c \to D)$         & 0.202 &  0.658  & 0.156 & 0.263 \\
 stat. error            &  $\pm 0.020$ &  $\pm 0.054$ &  $\pm 0.043$ &  $\pm 0.019 $ \\
 syst. error            & $^{+0.045}_{-0.033}$ & $^{+0.115}_{-0.148}$ & $^{+0.036}_{-0.035}$ & $^{+0.056}_{-0.042}$\\
 theo. error            & $^{+0.029}_{-0.021}$ & $^{+0.086}_{-0.048}$ & $^{+0.050}_{-0.046}$ & $^{+0.031}_{-0.022}$ \\
\hline
 $f_{w.a.}$ = world average          & 0.232 $\pm 0.018$ & 0.549 $\pm 0.026$ & 0.101  $\pm 0.027$  & 0.235  $\pm 0.010$  \\
  \hline
 \end{tabular}
   \caption{Fragmentation factors deduced from the measured cross sections. 
The small b-contributions are subtracted. The obtained values compare well with 
present world average numbers.
 }
\end{center}
\end{table}

\clearpage
%%%%--------------------------

\newpage

The fragmentation ratios  $R_{u/d}$, $\gamma_s$, $P_V$ and $P'_V$
are calculated based on the measured cross sections and the well known decay branching ratios $BR$.
Using for convenience the previously introduced fragmentation 
fractions $f(c\rightarrow D)$, the expressions $R_{u/d}$, $\gamma_s$, $P_V$ and $P'_V$ are determined by
the expressions listed below.
The value $P'_V$ is extracted under the isosopin invariance assumption, 
i.e. $f(c \rightarrow D^{*+}) = f(c \rightarrow D^{*0})$.

\begin{eqnarray}
 \renewcommand{\arraystretch}{1.8}
 \large\nonumber
 \begin{array}{ll}
R_{u/d} & =  \frac
{\displaystyle f(c\rightarrow D^0) -f(c\rightarrow D^{*+})\ BR(D^{*+}\rightarrow D^0\pi^+)}
{\displaystyle f(c\rightarrow D^+) +f(c\rightarrow D^{*+})\ BR(D^{*+}\rightarrow D^0\pi^+)}\\
    &   = 1.26\ \pm 0.20\ (stat)\ \pm 0.13\ (syst) \pm 0.04\ (theory)\qquad \\
    &  (= 1.00\ \pm 0.09\mbox{\qquad world average}) 
 \end{array}
\end{eqnarray}


\begin{eqnarray}
 \renewcommand{\arraystretch}{1.8}
 \large\nonumber
 \begin{array}{ll}
\gamma_s & = \frac{\displaystyle 2\ f(c \rightarrow D_s^+)}
{\displaystyle f(c\rightarrow D^+) +f(c\rightarrow D^o)}\\
     &   = 0.36 \pm 0.10\ (stat)\ \pm 0.01\ (syst)\ \pm 0.08\ (theory)\\
    &   (= 0.26\ \pm 0.07\mbox{\qquad world average}) 
 \end{array}
\end{eqnarray}


\begin{eqnarray}
 \renewcommand{\arraystretch}{1.8}
 \large\nonumber
 \begin{array}{ll}
P_V \ & = \frac{\displaystyle VM}{\displaystyle PS+VM} \\
      & = \frac{\displaystyle f(c \rightarrow D^{*+})}
{\displaystyle f(c\rightarrow D^+) +f(c\rightarrow D^{*+})\ BR(D^{*+}\rightarrow D^0\pi^+)}\\
    &   = 0.693\ \pm 0.045\ (stat)\ \pm 0.004\ (syst) \pm 0.009\ (theory) \\
    &   (= 0.601\ \pm 0.032\mbox{\qquad world average}) \\
 \end{array}
\end{eqnarray}


\begin{eqnarray}
 \renewcommand{\arraystretch}{1.8}
 \large\nonumber
 \begin{array}{ll}
P'_V\ & = \frac{\displaystyle 2\ f(c \rightarrow D^{*+})}
{\displaystyle f(c\rightarrow D^+) +f(c\rightarrow D^o)} \\
    & = 0.613\ \pm 0.061\ (stat)\ \pm 0.033\ (syst) \pm 0.008\ (theory) \\
 \end{array}
\end{eqnarray}
%
\clearpage
%

%%%%--------------------------

\newpage
\Large
{\bf Summary}

\large
Production cross sections are measured for the vector- $\Dstar$ and for the
pseudoscalar charmed mesons $ \Dzero, \Dsubs$ and, for the first 
time at HERA, also $\Dplus$ mesons through their decay $D^+ \to K^- \pi^+ \pi^+$.
The measurements rely on the proper reconstruction of the vertex separation distance and
its error for the $D$-meson decays.

The inclusive  $\Dstar$ production cross sections are within errors in agreement with both previous
measurements, 
and with Monte Carlo predictions, based on the leading order AROMA generator program
including parton shower modelling.

Differential cross sections are measured for $ \Dzero$ and $\Dplus$ mesons as functions 
of the meson transverse momenta and pseudorapidity, and as functions 
of the event kinematic variables $y$ and $Q^2$. The measured cross sections 
are found to be reasonably well described
by the LO Monte Carlo predictions.

Based on the measured cross sections, the fragmentation sensitive parameters 
$P_V$, $R_{u/d}$ and $\gamma_{s}$ are extracted. They compare well with the
present world average values, and as such  support the hypothesis of universality
of charm fragmentation.

\end{document}

