%   21/10/94 410251939  MEMBER NAME  F2D      (PHYSICS.) M  TEX
%\bibitem{cascade} H. Jung,
% LaTeX file with prefered layout for the H1 publications
%================================================================
% The style is particularly suited for DESY preprints, which are
% printed in two columns (one LaTeX page per column).
%================================================================
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{hhline}
\usepackage{amssymb}
\usepackage{times}
\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight25cm \textwidth16.0cm
\setlength{\dinmargin}{\dinwidth}
\setlength{\unitlength}{1mm}
\addtolength{\dinmargin}{-\textwidth}
\setlength{\dinmargin}{0.5\dinmargin}
\oddsidemargin -1.0in
\addtolength{\oddsidemargin}{\dinmargin}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\marginparwidth}{0.9\dinmargin}
\marginparsep 8pt \marginparpush 5pt
\topmargin -42pt
\headheight 12pt
\headsep 30pt \footskip 24pt
\parskip 3mm plus 2mm minus 2mm
% A useful Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)}
\def\NCA{\em Nuovo Cimento}
\def\NIM{\em Nucl. Instrum. Methods}
\def\NIMA{{\em Nucl. Instrum. Methods} A}
\def\NPB{{\em Nucl. Phys.} B}
\def\PLB{{\em Phys. Lett.}  B}
\def\PRL{\em Phys. Rev. Lett.}
\def\PRD{{\em Phys. Rev.} D}
\def\ZPC{{\em Z. Phys.} C}
% Some other macros used in the sample text
\def\mco{\multicolumn}
\def\epp{\epsilon^{\prime}}
\def\vep{\varepsilon}
\def\ra{\rightarrow}
\def\ppg{\pi^+\pi^-\gamma}
\def\vp{{\bf p}}
\def\ko{K^0}
\def\kb{\bar{K^0}}
\def\al{\alpha}
\def\ab{\bar{\alpha}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\CPbar{\hbox{{\rm CP}\hskip-1.80em{/}}}%temp replacemt due to no font
\def\etal{{\it et~al.}}
\def\black{\special{ps: 0 0 0 setrgbcolor}}
\def\white{\special{ps: 1 1 1 setrgbcolor}}
%\input definitions.tex
%===============================title page=============================
\begin{document}  
% The rest
\newcommand{\pom}{{I\!\!P}}
\newcommand{\slowpi}{\pi_{\mathit{slow}}}
%\newcommand{\gevsq}{\mathrm{GeV}^2}
\newcommand{\fiidiii}{F_2^{D(3)}}
\newcommand{\fiidiiiarg}{\fiidiii\,(\beta,\,Q^2,\,x)}
\newcommand{\n}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)}
\newcommand{\nz}{1.30\pm 0.08 (stat.)^{+0.08}_{-0.14} (syst.)}
\newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)}
\newcommand{\fiipom}{\tilde F_2^D}
\newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)}
\newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)}
\newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)}
\newcommand{\pomflux}{f_{\pom / p}}
\newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)}
\newcommand {\gapprox}
   {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}}
\newcommand {\lapprox}
   {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}}
\def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
\raise 0.55ex\hbox{$\scriptstyle >$}\,}
\def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex%
\raise 0.55ex\hbox{$\scriptstyle <$}\,}
\newcommand{\pomfluxarg}{f_{\pom / p}\,(x_\pom)}
\newcommand{\dsf}{\mbox{$F_2^{D(3)}$}}
\newcommand{\dsfva}{\mbox{$F_2^{D(3)}(\beta,Q^2,x_{I\!\!P})$}}
\newcommand{\dsfvb}{\mbox{$F_2^{D(3)}(\beta,Q^2,x)$}}
\newcommand{\dsfpom}{$F_2^{I\!\!P}$}
\newcommand{\gap}{\stackrel{>}{\sim}}
\newcommand{\lap}{\stackrel{<}{\sim}}
\newcommand{\fem}{$F_2^{em}$}
\newcommand{\tsnmp}{$\tilde{\sigma}_{NC}(e^{\mp})$}
\newcommand{\tsnm}{$\tilde{\sigma}_{NC}(e^-)$}
\newcommand{\tsnp}{$\tilde{\sigma}_{NC}(e^+)$}
\newcommand{\st}{$\star$}
\newcommand{\sst}{$\star \star$}
\newcommand{\ssst}{$\star \star \star$}
\newcommand{\sssst}{$\star \star \star \star$}

\newcommand{\tw}{\theta_W}
\newcommand{\sw}{\sin{\theta_W}}
\newcommand{\cw}{\cos{\theta_W}}
\newcommand{\sww}{\sin^2{\theta_W}}
\newcommand{\cww}{\cos^2{\theta_W}}
\newcommand{\trm}{m_{\perp}}
\newcommand{\trp}{p_{\perp}}
\newcommand{\trmm}{m_{\perp}^2}
\newcommand{\trpp}{p_{\perp}^2}
\newcommand{\alp}{\alpha_s}

\newcommand{\alps}{\alpha_s}
\newcommand{\sqrts}{$\sqrt{s}$}
\newcommand{\LO}{$O(\alpha_s^0)$}
\newcommand{\Oa}{$O(\alpha_s)$}
\newcommand{\Oaa}{$O(\alpha_s^2)$}
\newcommand{\PT}{p_{\perp}}
\newcommand{\JPSI}{J/\psi}
\newcommand{\sh}{\hat{s}}
%\newcommand{\th}{\hat{t}}
\newcommand{\uh}{\hat{u}}
\newcommand{\MP}{m_{J/\psi}}
%\newcommand{\PO}{\mbox{l}\!\mbox{P}}
\newcommand{\PO}{I\!\!P}
\newcommand{\xbj}{x}
\newcommand{\xpom}{x_{\PO}}
\newcommand{\ttbs}{\char'134}
\newcommand{\xpomlo}{3\times10^{-4}}  
\newcommand{\xpomup}{0.05}  
\newcommand{\dgr}{^\circ}
\newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}}
\newcommand{\gev}{\,\mbox{GeV}}
\newcommand{\WBoson}{\mbox{$W$}}
\newcommand{\fbarn}{\,\mbox{{\rm fb}}}
\newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}}
%
% Some useful tex commands
%
\newcommand{\qsq}{\ensuremath{Q^2} }
\newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} }
\newcommand{\et}{\ensuremath{E_t^*} }
\newcommand{\rap}{\ensuremath{\eta^*} }
\newcommand{\gp}{\ensuremath{\gamma^*}p }
\newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} }
\newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} }

\begin{titlepage}

\noindent
{ Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ Osaka, Japan, July 2000}\\
%{\bf  Draft~1.0   \hspace{5mm} \today}\\  
%{\bf  Editors: K. Daum, E. Tzamariudaki} \\ 
%{\bf Referees: C. Niebuhr, T. Sloan} \\

\vspace{4cm}

\begin{center}
\begin{Large}

{\bf Measurement of \boldmath$D^{*\pm}$ Meson Production 
and the Charm Contribution to the Proton Structure $F_2^c$
in Deep Inelastic Scattering at HERA}
\unboldmath
\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}
%   31/01/90 004111624  MEMBER NAME  TURNIER  (TEX.S)    M  TEX                
%\documentstyle[colordvi,epsfig,feynman,12pt,dina4p]{article}
\def\gev{\rm GeV}
\def\ie{\it i.e.}
\def\etal{\hbox{$\it et~al.$}}
\def\clb#1 {(#1 Coll.),}
%
\hyphenation{do-mi-nant
}
%\special{!userdict begin /bop-hook{gsave 200 30 translate
% 65 rotate /Times-Roman findfont 216 scalefont setfont
% 0 0 moveto 0.93 setgray ( DRAFT) show grestore}def end}


\vspace*{1cm}
\begin{abstract}
\noindent
The production of $D^{*\pm}(2010)$ mesons in deep inelastic scattering
is studied with the H1 detector at HERA using an integrated luminosity
of 18.6~pb$^{-1}$.
In the kinematic region $1<Q^2<100$~GeV$^2$, $0.05<y<0.7$
an $e^+p$~cross section for inclusive $D^{*\pm}$ meson production of 
$8.37\pm 0.41(stat.){+1.11\atop -0.82}(syst.){+0.64\atop -0.39}(theo.)$~nb is measured 
in the visible 
%$D^{*\pm}$
 range $1.5~<~p_T(D^{*\pm})~<~15$~GeV and $|\eta(D^{*\pm})|~<~1.5$. 
Single and double differential inclusive $D^{*\pm}$ meson cross sections are 
compared to a DGLAP type next-to-leading-order (NLO pQCD) calculation
and to calculations using the CCFM evolution. 
%using the most recent extraction of parton densities from the
%NLO p-QCD fit to the inclusive proton structure function $F_2$ by H1.
 The charm contribution to the proton structure, 
$F_2^{c}\left(x,Q^2\right)$, is determined by extrapolating the 
visible charm cross section to full phase space.  

\end{abstract}
\vspace{1.5cm}
\begin{flushleft}
{\bf Abstract: 984} \\
{\bf Parallel sessions: 07} \\
{\bf Plenary sessions: 03}
\end{flushleft}
\end{titlepage}
\section{Introduction}
Results on $D^{*+}$ meson \footnote{The charge conjugate is always implied.}
 production in deep inelastic scattering (DIS) and on the charm 
contribution to the proton structure function$F_2^{c}$ at HERA 
have been published by the H1 and the ZEUS collaborations \cite{h1f2c,zeusf2c}.
Several features of these data show that boson gluon fusion is 
the dominant source of open charm production in deep inelastic $ep$ scattering:
(a) a steep rise of $F_2^{c}$ with decreasing Bjorken-$x$,
(b) a steep increase of the open charm contribution to DIS from large
$x$ accessible at the EMC fixed target experiment \cite{emc} towards small 
$x$ at HERA, and (c) the observed dynamics in inclusive charmed meson 
production. Therefore, the process $e^+p\rightarrow e^+D^{*+}X$ is sensitive
to the gluon density in the proton \cite{h1gluon} and allows the 
universality of the gluon density in the proton to be tested by comparing
the sensitivities of $F_2$ and $F_2^{c}$.
  
The early results from the H1 experiment on $F_2^{c}$ were based on 
%the analysis of 
the 1994 data and were therefore statistically limited.
The current analysis uses the data of the 1996 and 1997 HERA running periods,
yielding a significantly larger integrated luminosity of 18.6~pb$^{-1}$.
Furthermore, the improved instrumentation in the backward region 
of the experiment enables the kinematic range in four-momentum transfer 
squared $Q^2$ of the virtual photon to be extended by one order of magnitude 
towards smaller values.  
Hence, more detailed tests of perturbative QCD become possible.

This paper is organized as follows: a short discussion of the different
treatments of open charm production in perturbative QCD is followed by a
description of  the experimental set-up and details of the analysis; the 
inclusive cross sections of $D^{*+}$ meson production are then presented and 
are compared to QCD predictions. Finally these inclusive $D^{*+}$ meson cross
sections are used to derive the charm contribution to the proton structure 
function $F_2^{c}$.
\section{Models of Open Charm Production}
The description of open heavy flavor production is based on perturbative QCD
(pQCD).
In leading order (LO), the photon gluon fusion process  
($\gamma g\rightarrow Q\overline Q$) is the dominant contribution.
%\subsection{DGLAP Evolution}
\subsection{NLO Calculations in the DGLAP Scheme}
\label{dglap}
Several schemes are used to perform NLO calculations. All approaches 
assume the scale to be hard enough to apply pQCD and to guarantee the validity
of the factorization theorem.

Here, the massive approach is adopted which is
a fixed order (in $\alpha_s$) calculation
with massive quarks, i.e. $m_Q\neq 0$, assuming three active flavors in the
proton. The densities of the three light quarks and the gluon in the proton
are obtained by the DGLAP evolution. The heavy quark is assumed to be
produced only at the 
perturbative level \cite{riemersma} via boson gluon fusion. 
These calculations are considered reliable in the regime  $Q^2\approx m_Q^2$. 
However, they break down for $Q^2\gg m_Q^2$ due to large logarithms 
$\ln(Q^2/m_Q^2)$. 
Based on the NLO calculations of order $\alpha_s^2$ in the coefficient
functions 
%in this fixed-flavor-number-scheme, (FFNS) 
\cite{harris} the Monte
Carlo integration program HVQDIS \cite{hvqdis} provides the four-momenta of 
the outgoing partons.
Thus the calculation of visible differential inclusive 
charmed meson production cross sections becomes possible.
% Within this scheme

%In the {\it massless approach} the charm quark mass is assumed to be zero and 
%therefore charm is treated as an additional active flavor in the 
%proton. This ansatz of {\it flavor excitation (FE)} is appropriate for 
%$Q^2\gg m_Q^2$, however it breaks down for $Q^2\le m_Q^2$. 
%At intermediate values of $Q^2$ the two schemes have to be merged. 
%Different prescriptions
%for doing this matching in the variable-flavor-number-scheme (VFNS) 
%are described in Refs. \cite{acot,collins,mrst}.
%Within these approaches the final state collinear
%divergences are absorbed into the fragmentation functions.
%The VFNS has been mainly applied for inclusive quantities such as 
%$\sigma_{tot},~F_2^{Q}$ but recently also attempts were made 
%to calculate differential cross sections of charmed hadrons \cite{kretzer}.

The comparison between the NLO predictions and the data are performed
using this Monte Carlo integrator.  
%The hadornization of heavy quarks into   
%the fragmentation of the heavy quarks into  
%heavy flavored hadrons is treated independently in this scheme. 
Charmed quarks are fragmented to $D^{*+}$
mesons according to the Peterson fragmentation function \cite{peterson}, which 
is controlled by a single parameter $\epsilon$. In addition, to account for 
the experimentally observed $p_t$ smearing of hadrons with respect to the 
quark direction, the $D^{*+}$ meson is given a transverse momentum 
$p_t$ with respect to the charm quark, according to the function
$\exp(-\alpha p_t^2)$.
The parameter $\alpha$ is chosen such that an average transverse momentum 
$\langle p_t\rangle\approx 350$~MeV is obtained as observed in $e^+e^-$ data.
The fragmentation is performed in the hadronic center mass frame.
%\footnote{The results are not sensitive to the system in which the
%fragmentation is performed}.

\subsection{CCFM Evolution}

The CCFM evolution equation \cite{ccfm} may be most appropriate to describe
the parton evolution at small $x$. In the parton cascade, gluons are
emitted only in an angular ordered region to account for coherence
effects. Due to angular ordering, the unintegrated gluon distribution in
CCFM depends on the maximum allowed angle in addition to the 
momentum fraction $x$ and the transverse momentum of the propagator gluon. 
The cross section is then calculated according to the $k_t$-factorization
theorem by convoluting the unintegrated gluon density with the off-
shell boson gluon fusion matrix element with massive quarks for the hard 
scattering process, well suited for heavy flavor production.  

It has previously been shown \cite{f2cccfm} that $F_2$ and $F_2^{c}$
can be reasonably well described within the CCFM framework.  
Recently. however a solution of the CCFM 
equation has been obtained \cite{cascade}
which provides a description of $F_2$ and simultaneously the cross section of 
forward jet production, a process which is sensitive to non-DGLAP QCD. 
%the most prominent signature for small $x$ processes. 
Using this solution, a full hadron level Monte Carlo generator
CASCADE has been developed \cite{hannes} in which the full generation of
charm events, including the initial state gluon radiation according to
CCFM and Lund string fragmentation (JETSET) is also possible.
The fragmentation of charmed quarks to $D^{*+}$ mesons is performed using 
the Peterson fragmentation function with $\epsilon$ set to 0.078.
 Here, a refined version of CASCADE with the unintegrated gluon density
\cite{uigd} as extracted from the H1 $F_2$ data \cite{h1f296} has been used.
%With help of Monte Carlo program SMALLX \cite{smallx} the unintegrated 
%gluon density in the proton \cite{uigd,cascade} was extracted from the 
%inclusive $F_2$ data from H1 \cite{h1f296}. The Monte Carlo event generator 
%CASCADE \cite{cascade}

\section{Detector and Data Sample}
The data have been collected with the H1 detector at HERA
during the running periods of 1996 and 1997 when
HERA operated with 27.5 GeV positrons and 820~GeV protons colliding 
at a center of mass energy of $\sqrt{s}=300$~GeV.

While the H1 detector and its trigger capabilities have been described in 
detail elsewhere \cite{h1det}, the following detector components are
significant for this analysis:
%The analysis is restricted to events in which
 
The scattered positron is 
identified and measured in the SpaCal \cite{spacal}, a lead-scintillating 
fiber spaghetti type calorimeter situated in the backward region of the H1 
detector. The SpaCal also provides Time-of-Flight information for trigger
purposes. A four-layer backward drift chamber (BDC) \cite{bdc} is mounted in 
front in order to improve the angular measurement of the scattered positron.

Charged particles are measured by 
the cylindrical central jet drift chambers (CJC) \cite{h1det,cjc} mounted 
concentrically around the beam-line with a homogeneous magnetic field of 
1.15 Tesla inside the H1 detector. Particle charge and momenta are measured
from track curvature.
The CJC  also provides trigger information \cite{dcrphi} based on the 
detection of 
%crudely measured 
track segments attributed to particles originating at the
$ep$ interaction region. 
One double layer of cylindrical multi-wire proportional chambers
(MWPC) \cite{mwpc} for triggering purpose is positioned inside and another one
in between the two jet chambers. 
The events of this analysis were triggered by a coincidence of 
an electromagnetic cluster in the SpaCal with a charged track signal from the 
CJC or a crudely reconstructed vertex with the MWPC.

The luminosity is determined from the rate of the Bethe-Heitler reaction
$ep\rightarrow ep\gamma$. 
The luminosity system consists of an electron detector and a photon detector 
located 33~m and 103~m from the interaction point in the electron beam 
direction, respectively.  
The data amount to an integrated luminosity of 
${\cal L}_{int} = 18.6$~pb$^{-1}$. 
%
%--------------  Kinematics
%
\section{Kinematics\label{kine}}
This analysis is restricted to those deep inelastic scattering (DIS)
events which have  a
scattered positron detected in the backward region of the detector.
At fixed center of mass energy, $\sqrt{s}$, the
kinematics of the inclusive scattering process $ep\rightarrow eX$ can be
completely determined by using any two of the independent Lorentz invariant 
variables: the Bjorken scaling variables $x$ and $y$, the four-momentum 
squared $Q^2=-q^2$ of the virtual boson and the invariant mass squared
$W^2$ of the hadronic final state. In this analysis, these variables are 
determined from the measurement of the energy $E^\prime_e$ and the polar 
angle $\Theta_e$ 
 of the scattered positron according to the expressions
\begin{equation}
\begin{array}{ccc}\displaystyle
Q^2=4E_eE^\prime_e\cos^2\left(
\frac{\Theta_e}{2}\right)&\quad\quad&\displaystyle
y=1-\frac{ E^\prime_e}{ E_e}
\sin^2\left(\frac{ \Theta_e}{2}\right)
\cr\cr\displaystyle
x=\frac{ Q^2}{ ys}&\quad\quad&\displaystyle
W^2=Q^2\left(\frac{ 1-x}{ x}\right)\cr
\end{array}
\end{equation}
where $s=4E_eE_p$, and $E_e$ and $E_p$ denote the energies of the incoming
positron and proton, respectively (positron and proton masses are neglected). 
Here the scattering angle $\Theta_e$ is defined with respect to the proton 
beam direction.
%
%-------------- Monte Carlos

\section{Monte Carlo Simulation \label{mc}}
Monte Carlo simulation programs
 are used in order to correct the data and to estimate
the systematic uncertainties associated with the measurement.
For the determination of the acceptance of the detector and the 
$D^{*+}$ selection efficiencies, heavy flavor (charm and bottom) DIS events 
are generated using the AROMA 2.2 \cite{aroma} program. 
This simulates neutral current heavy quark 
production via the boson gluon fusion process and  is implemented in leading 
order QCD including heavy quark mass effects. The charmed quark mass is
chosen to be $m_c=1.5\;\gev$ while the factorization and renormalization 
scales were set to $\mu=\hat s$.
The GRV94LO \cite{grvlo} parton density functions (PDF's) are used for the 
proton. The Lund Model \cite{lundf}, as implemented in 
JETSET 7.4 \cite{jetset} including the parton shower option, 
is used for hadronization. The momentum fraction of the charm quark
carried by the $D^{*+}$ meson is determined according to the Peterson model
\cite{peterson} using a fragmentation parameter $\epsilon$ of 0.078.  
In order to study the effect of different fragmentation models on the
acceptance and efficiencies in the AROMA program, the Peterson 
fragmentation parameter is varied between $\epsilon=0.035$ and 
$\epsilon=0.1$, and, in addition, the symmetric Lund fragmentation 
function has been used. Furthermore, the HERWIG 
\cite{herwig} event generator is used with the same charm quark mass 
and the same PDF's for this purpose. 
In order to investigate the effect of the QCD parameters 
%on acceptance and efficiencies
the charm quark mass has been 
varied between $m_c=1.3\;\gev$ and $m_c=1.7\;\gev$
and the renormalization scale is changed to $\mu=Q^2+4m_c^2$. The
influence of QED effects at the leptonic vertex is determined with help of
the RAPGAP \cite{rapgap} program interfaced to HERACLES 4.1 \cite{herakles}.   
All Monte Carlo generated events are fed into the GEANT based 
simulation program \cite{geant} of the H1 detector and are subjected to the 
same reconstruction and analysis chain as used for the data.

%Differential charm production cross sections 
%
%--------------  Event Selection
%
\section{Event Selection}
\subsection{Selection of DIS Events} 

The identification and selection of the scattered positron in the SpaCal 
is performed with minor changes, as described in Ref. \cite{h1f2}.
%These changes are adapted to better suit the current analysis.

The positron is identified as the most energetic cluster with 
$E_e>8$~GeV. 
The cluster radius\footnote{The cluster radius is defined as 
$\sum_i\log(E_i)\cdot d_i/\sum_i\log(E_i)$ 
where the sum runs over all cells in the
cluster: $E_i$ is the energy of the cell $i$ and $d_i$ is the distance of the 
cell $i$ from the cluster center of gravity.} 
is required to be less than 4~cm, consistent with an
electro-magnetic energy deposition, and the cluster center of gravity is 
required  within 1.5~cm of the extension of a 
charged track segment in the backward drift chamber BDC \cite{bdc}. 

The geometrical acceptance cuts for SpaCal and BDC 
impose a limitation 
on the positron scattering angle of 
$\Theta_e<178^\circ$.
% where $\Theta_e$ is defined with respect to the 
%incoming proton direction.
This requirement restricts the accessible range of the negative four momentum
 squared of the photon to 1~GeV$^2<Q^2<$~100~GeV$^2$ and 
%together with the requirement that the $D^{*\pm}$ be reconstructed in the 
%central tracking detector 
the inelasticity to $ 0.05<y<0.7$. 
%Throughout this paper kinematic variables
%$Q^2$ and $y$ 
%are calculated from the energy and angle of the scattered positron.

Figure \ref{scatel} shows the energy and polar angle distributions of the
scattered positron for events with identified $D^{*+}$ mesons. The data
include corrections for QED radiation as described below. The figure also
includes the absolute prediction of the AROMA Monte Carlo for all values
of $Q^2$.
% and separately for the photoproduction regime, i.e. $Q^2<1$~GeV$^2$. 
Good agreement is observed between data and simulation.
The contribution due to photoproduction background, i.e. $Q^2<1$~GeV$^2$,
amounts to less than 1\%.

\subsection{Selection of Events with \boldmath$D^{*+}$\unboldmath Mesons}
$D^{*+}$ mesons are reconstructed using the decay chain  
\begin{equation}
D^{*+}\rightarrow D^0\pi_{slow}^+\rightarrow (K^-\pi^+)\pi_{slow}^+.
\end{equation}   
%which has a branching ratio of 2.63\%~\cite{PDG}. 
The identification of charm production using the $D^{*+}$ tagging technique 
\cite{feldmann} profits from the tight limitation of phase space in the decay
$D^{*+}\rightarrow D^0\pi_{slow}^+$. 

The decay products are detected in the central tracker.
For each observed track passing some quality cuts and fulfilling minimum 
transverse momentum requirements particle identification is applied using the 
measurement of the energy loss ${\rm d}E/{\rm d}x$ in the central tracker. 
A resolution of 
6\% is reached for well measured tracks.
For each track, the probability of the pion, kaon and proton hypothesis is 
calculated from the measurement of the energy loss along the trajectory.
Assuming the observed track to be produced by either of these particle 
species, normalized probabilities are calculated.
Only those tracks are considered which may be interpreted 
as pions or kaons, by passing momentum dependent minimum values for the
corresponding normalized probabilities.  

In order to reconstruct a $D^{*+}$ meson candidate, unlike-sign charged 
tracks are first combined to 
form $K^-\pi^+$ pairs, i.e. one of the tracks should allow 
the kaon interpretation according to its d$E/$d$x$ measurement
while the other must be consistent with the pion 
hypothesis. Among all possible oppositely charged $K^-\pi^+$ pairs,
those with an invariant mass consistent within $\pm$70~MeV  of the $D^0$
are combined 
with a track of a second pion candidate (``$\pi^+_{slow}$'') having a charge
opposite in sign to that of the kaon.  
%$D^{*+}$ production is found as an 
%distinct enhancement in the distribution of the mass difference
%$\Delta m=m_{K\pi\pi}-m_{K\pi}$ around the expected mass difference of 
%145.4~MeV.    

The distribution of the mass difference $\Delta m=m_{K\pi\pi}-m_{K\pi}$ is 
shown in Fig. \ref{fig1} for the $K\pi\pi$ combinations in the acceptance range
of pseudorapidity, $\eta(K\pi\pi)=-\ln\tan(\Theta_{K\pi\pi}/2)$, and
 transverse momentum $p_t(K\pi\pi)$. This range is restricted to 
$|\eta(K\pi\pi)|<1.5$, and $p_t(K\pi\pi)>1.5$~GeV. 
A distinct enhancement is visible
around the nominal $D^{*+}-D^0$ mass difference of 145.4 MeV. This figure 
also includes a $\Delta m$ distribution for particle combinations in which
the $K\pi$ pairs are formed by like-sign charged tracks. This distribution
is exclusively determined by track combinatorics.
No enhancement is observed in the $\Delta m$ distribution in this case. 
Furthermore the like-sign distribution gives a perfect description of the
unlike-sign background.
The number of $D^*$ mesons $N_{D^*}$ is extracted from fits to 
both $\Delta m$ distributions with a function taken to be the 
superposition of a Gaussian for the signal and a term 
$N_B(\Delta m-m_\pi)^\alpha$ for the background. 
A total of $973\pm40$ $D^{*+}$ mesons is observed.
%
%--------- Inclusive Cross Sections
%
\section {Inclusive Cross Sections}
%The data are used to extract 
%The results on the  
The integrated and differential cross sections for $D^{*+}$ meson production 
in DIS $ep$ collisions 
%are 
%presented in the kinematic region 1~GeV$^2<Q^2<$~100~GeV$^2$, 
%$ 0.05<y<0.7$ for the visible $D^{*+}$ range $|\eta(D^{*+})|<1.5$ and 
%$p_t(D^{*+})>1.5$~GeV.
%The cross sections 
are calculated from the observed number $ N_{D^*}$ 
of  $D^{*+}$ candidates, according to 
\begin{equation}
\sigma(e^+p \rightarrow e^+D^{*+} X)=
\frac{N_{D^*}~(1-r)}
{ {\cal L}_{int} \cdot B \cdot\epsilon\cdot(1+\delta_{rad})  }~.
\label{sigman}
\end{equation}
Here, $r$ stands for the contribution of reflections in the $D^0$ mass 
window, amounting to 3\%, while 
${\cal L}_{int}$  and $B$  refer to the integrated 
luminosity and the branching ratio 
$B = B(D^{*+} \rightarrow D^0 \pi^+) \cdot B(D^0 \rightarrow K^- \pi^+) =
0.0263$ \cite{PDG}. The efficiency $\epsilon$ is estimated with help of the 
AROMA Monte Carlo program \cite{aroma}. 
The radiative corrections $\delta_{rad}$,
which amount to  $\delta_{rad}=0.03$ for the integrated visible cross 
section, are obtained from the program HECTOR \cite{hector}.

\subsection{Integrated Cross Section}
The inclusive cross section of $D^{*+}$ meson production  
in the kinematic region 1~GeV$^2<Q^2<$~100~GeV$^2$, $ 0.05<y<0.7$ and 
in the visible $D^{*+}$ range $|\eta(D^{*+})|<1.5$ and $p_t(D^{*+})>1.5$~GeV
is found to be
$$\sigma_{vis}(e^+p \rightarrow e^+D^{*+} X)=\left(
8.37\pm 0.41(stat.){+1.11\atop-0.82}(syst.){+0.64\atop-0.39}(theo.)
\right)~\rm{nb}.$$
The errors refer to those from statistics, experimental systematics and an 
additional 
%the statistical error, the experimental systematics and a 
systematic error related to the changes in efficiency obtained using 
different Monte Carlo generators and varying the model parameters. 
%as outlined in section \ref{mc}.
%
%The experimental systematic uncertainties are summarized in Tab.~\ref{expsys}.
%By adding the different contributions in quadrature a total relative errors 
%of ${+12\%\atop-10\%}$ is obtained for the integrated cross section.

The largest contribution 
to the experimental systematic error
is due to the uncertainty in the track reconstruction 
efficiency. Other important sources of systematic errors include uncertainties
in the extraction of the $D^{*+}$ signal, i.e. the determination of the 
background shape in the $\Delta m$ distribution and of the $D^0$ mass 
resolution, and the uncertainty in the branching fraction of the $D^{*+}$ to
$K\pi\pi$ from other experiments. By adding the different contributions in 
quadrature, a total relative error of ${+12\%\atop-10\%}$ is obtained for the 
integrated cross section.
 
The uncertainties due to model dependences 
% Table \ref{modelsys} summarizes the effect on the cross section due to
include our incomplete understanding of the fragmentation process, 
the uncertainty due to the charm quark mass, the sensitivity to the 
factorization and renormalization scales $\mu$ and the change of acceptance
due to QED effects on the lepton side. The largest effect on the
efficiency is observed by 
changing the charm quark mass from $m_c=1.5~\gev$ 
in the reference Monte Carlo dataset to
$m_c=1.3~\gev$.
% while the other model uncertainties contribute almost equally in magnitude. 
A total relative model dependent error of ${+8\%\atop-5\%}$ is 
obtained by adding the different contributions in quadrature.

In the framework of the NLO DGLAP evolution, the visible 
inclusive $D^{*+}$ meson production cross section has been calculated with
the HVQDIS program. The predictions range
%The visible inclusive $D^{*+}$ meson production cross section has to be 
%compared with the QCD predictions, which range 
from 4.98~nb for a charm quark mass $m_c=1.5~\gev$ and Peterson fragmentation 
parameter $\epsilon=0.10$ to 6.61~nb for $m_c=1.3~\gev$ and $\epsilon=0.035$ 
using the GRV-HO 98 parton densities in the proton \cite{grv}. 
The hadronization fraction $f(c\rightarrow D^{*+})$ was set to the
world average $0.235\pm0.007\pm0.007$ \cite{hadro}.
%A hadronization fraction times branching ratio of
%$f(c\rightarrow D^{*+})\times BR(D^{*+}\rightarrow D^0\pi^+)=0.1653\pm0.0053$ 
%was used as determined at LEP \cite{hadro}.
On the other hand calculations based on the CCFM evolution, as implemented in
the CASCADE program, yield a significantly higher cross section, 
8.53~nb for $m_c=1.5~\gev$ and 9.95~nb for $m_c=1.3~\gev$, 
using a fragmentation parameter $\epsilon=0.078$ and the unintegrated gluon 
density as extracted from the H1 $F_2$ data \cite{uigd}.  

The NLO DGLAP prediction does not describe well the
measured values. 
%only in marginal agreement with the measured cross sections. 
In previous publications \cite{h1f2c,h1gluon}
H1 reported much better agreement between data and predictions from
the HVQDIS program. This difference in the interpretation of the measured 
visible $D^{*+}$ meson cross section is due to the new determination of the 
charm quark hadronization fraction $f(c\rightarrow D^{*+})$ which result in
a value 16\% smaller than previously measured. 

 
%
%---- Differential cross sections
%
\subsection{Differential Cross Sections}
In Fig. \ref{fig2} the inclusive single differential $D^{*+}$ cross 
sections in the visible region are shown as a function of the kinematic 
quantities $W$, $x_{Bj}$ and $Q^2$ and
as a function of the $D^{*+}$ observables $p_{t}(D^*)$, 
$\eta(D^*)$
and $z_{D}(D^*)={P\cdot p_{D^*}}/{P\cdot q}={(E-p_z)_{D^*}}/{2yE_e}$
($P$, $q$ and $p_{D^*}$ denote the four-momenta of the incoming proton,
the exchanged photon and the observed $D^{*+}$).
 The errors account for the statistical error (inner error bars) and 
the total error (outer error bars) obtained by adding 
the statistical error and the  systematic uncertainties in quadrature. 
A bin by bin correction due to QED radiation has been applied using 
the HECTOR program \cite{hector} amounting to 3\% for the full kinematic 
range.

%The data are compared to 
Also  shown in Fig.\ref{fig2} are the expectations from
the NLO QCD calculations of the HVQDIS program  using the 
GRV 98 HO parton density parameterization \cite{grv}, a charm quark mass
varying from $m_c=1.3$~GeV to $m_c=1.5$~GeV and a fragmentation parameter 
varying from $\epsilon=0.035$ to $\epsilon=0.10$. The renormalization scale 
and the factorization scale are set to $\mu_r^2=\mu_f^2=Q^2+4m_c^2$.
The dark shaded band indicates the
uncertainties in this calculation for  $m_c=1.3$~GeV
and $\epsilon=0.035$ (upper limit) and $m_c=1.5$~GeV and $\epsilon=0.10$ 
(lower limit). 
Although the predicted visible cross section is smaller
than experimentally observed, the agreement with the data in the shapes of the 
different single differential cross sections is reasonable. 
A difference in shape is observed only in the shape of the d$\sigma$/d$\eta$
cross section. In the forward direction, the observed $D^{*+}$ meson 
production cross section is considerably larger than predicted by the 
calculation.
This excess is also manifest in the larger cross section observed in the
data at small $z_D$. 

A possible cause for this effect could be the simplified implementation 
of fragmentation in the HVQDIS program. This approach 
 does not account for the color force between the charm quark 
and the proton remnant which should result in a migration of the $D^{*+}$
meson from the original charm quark direction towards larger pseudorapidities.
To quantify this `beam drag effect' \cite{norrbin}, a mapping function from  
$\eta(c)$-$p_t(c)$-space to $\eta(D^{*+})$-$p_t(D^{*+})$ space 
has been constructed with help of the AROMA Monte Carlo program. This function
has then been used to replace the Peterson fragmentation with transverse 
momentum smearing in HVQDIS. No significant change in the $\eta$ and $z_D$ 
distributions have been observed by this procedure compared to the
original treatment of fragmentation.
% described in section \ref{dglap}.  

%two dimensional density
%functions in the $\eta(D^{*+})$-$P_t(D^{*+})$ space have been extracted for a
%grid in the  $\eta(c)
%has been quantified by using the AROMA 
%Monte Carlo program. 
%Therefore the AROMA program was used to model this color drag in the  

%In figure \ref{fig2} 
Figure \ref{fig2} also includes 
%The data are also compared to 
the predictions of the 
CCFM calculations using the CASCADE program. Here, the charm quark mass is 
varied from $m_c=1.3$~GeV (upper limit) to $m_c=1.5$~GeV (lower lower) 
while the Peterson fragmentation parameter is fixed to $\epsilon=0.078$. 
The expectations from the CASCADE program are found to agree better with data
in general and especially in the forward $\eta$ region, where the HVQDIS 
program fails to describe the data.
% the CASCADE program reproduces the measurement well.
%leads to a better agreement with the data.
%Especially a better description in $\eta$ is observed. 
It is interesting to note that the CCFM calculation, which starts from 
completely different principles and aims specifically to describe low $x$ 
phenomena, is able to describe open heavy flavor production in the HERA regime
better than the DGLAP based  NLO calculations with the chosen settings.

%Figure \ref{fig4} shows the double differential inclusive $D^{*+}$
%cross sections d$^2\sigma$/d$\eta$d$Q^2$ and  d$^2\sigma$/d$p_t$d$Q^2$. It 
%becomes obvious that the excess at large pseudorapidity observed in the data

 In order to enable the study of correlations among the observables in 
$D^{*+}$ meson production Figures \ref{fig4} and \ref{fig5} show double 
differential inclusive $D^{*+}$ cross sections. 
It is evident that the excess observed in the data with respect to
the HVQDIS expectation at large pseudorapidities ($0.5<\eta<1.5$) 
is independent of $Q^2$ and is concentrated at small $p_t(D^{*+})$ 
and small $z_D$. 
It is especially in this phase space region where the CASCADE program
better represents the data. In general this program leads to a 
better description of the data for small transverse momenta of the $D^{*+}$ 
mesons ($p_t<4~\gev$).
At larger transverse momenta the predictions of the HVQDIS program agree 
better with the data. 

% The inclusive
%visible $D^{*+}$ cross section is obtained in this calculation by convoluting 
%the charm quark production cross section with the Peterson fragmentation 
%function using $\epsilon=0.078$(histograms). 
%The uncertainties in the calculation due to a variation of the charm quark 
%mass between 1.3~GeV and 1.7~GeV is indicated by the shaded area. 
% This calculation is found to be in good 
%agreement with the measured cross section. Slight 
%excesses over the theoretical prediction are observed in the data for 
%$\eta_{D^*}>0$ and $x_{D^*}<0.2$ which are highly correlated. 
%Taking into account the uncertainties due to model parameters not covered by 
%the shaded area of the histograms, e.g. fragmentation, factorization and renor%malization scale, in 
%all distributions 
%the significance of the current analysis 
%does not allow to claim a discrepancy between 
%the data is in agreement with the NLO 
%calculations on the basis of the HVQDIS program with the precision achieved 
%in the current analysis.    

%The systematic error includes all uncertainties due to analysis and detector
%effects as well as various sources of uncertainties due to the AROMA model 
%used for the efficiency calculation. 
%Being explicit, it covers the uncertainties in the determination of the signal
%events in each individual bin coming from the mass resolution, the shape
%of the combinatorial background as well as the contribution due to 
%reflections in the $D^0$ mass window. Furthermore the errors on the
%knowledge of the trigger efficiency, the luminosity determination, the track
%reconstruction efficiency, and
%the energy and angular 
%resolution of the scattered positron are included.
%The contribution of photoproduction events in the selected sample is estimated
%using Monte Carlo simulations and found to be negligible.
%to be negligible from Monte Carlo simulations.

%The raw data distribution of $x_{D^*}$ shows a larger 
%production rate of $D^{*+}$ mesons for $x_{D^*}<0.2$ compared to the 
%expectation of the AROMA model. To account for this discrepancy the effect of 
%removing the cut in $x_{D^*}$ on the differential cross sections
%by properly reweighting the efficiency has been investigated and a separate 
%systematic error is attributed to this effect. 
%This is the dominant source of systematic error in all distributions 
%except for $d\sigma/dx_{D^*}$.

%The effect on the efficiency of the model parameters for $D^*$ 
%from charm production in the AROMA simulation, e.g. parton densities, charm 
%quark mass and fragmentation \cite{peterson}, has been studied by different 
%Monte Carlo simulations and has been included in the systematic error. 
%Only the hardness of the fragmentation, i.e.
%going from the Lund fragmentation to a soft Peterson fragmentation 
% using 
%$\epsilon=0.10$, result in a significant change of the efficiency in the 
%visible range, which is accounted for by a systematic error. 

%Finally, following the observation in photoproduction
%of a much higher cross section for beauty production than predicted 
%by the LO Monte Carlo, for the systematic error estimate
%a beauty contribution of 5$\times$ the 
%AROMA Monte Carlo expectation has been considered to our data sample
%\cite{beauty}.
%The latter uncertainty has been added linearly to the systematic error.
%
%----- F2C
%
\section{Charm Contribution to the Proton Structure \boldmath$F_2^c$
\unboldmath}
The charm contribution $F^{c}_2(x,Q^2)$ to the proton structure function
is obtained by using the expression for the  
one photon exchange cross section for charm production
\begin{equation}
\displaystyle
\frac{d^2\sigma^{c}}{dxdQ^2}=\frac{2\pi\alpha^2}{Q^4x}
\left(1+\left(1-y\right)^2\right)\;F^{c}_2(x,Q^2)\;.
\end{equation}
The range of $y$ of the measurements is such that contribution from the second structure function $F_1$ is everywhere negligible.
%Since the NLO QCD calculation \cite{karin} predicts a contribution of $F^c_L$
%to the charm production cross section below 2\% everywhere in the 
%kinematic range of this analysis, the simplification  
%$R=F_2/2xF_1-1=0$ is used. 

The visible inclusive $D^{*+}$ cross sections 
$\sigma_{\rm{vis}}^{\rm{exp}}(x,Q^2)$ in bins of $x$ and $Q^2$ are 
converted to a bin center corrected 
$F_2^{c~\rm{exp}}(\langle x\rangle,\langle Q^2\rangle)$ by the relation:
\begin{equation}
F_2^{c~\rm{exp}}(\langle x\rangle,\langle Q^2\rangle)=
\frac{\displaystyle \sigma_{\rm{vis}}^{\rm{exp}}(x,Q^2)}
{\displaystyle \sigma_{\rm{vis}}^{\rm{theo}}(x,Q^2)}\cdot
F_2^{c~\rm{theo}}(\langle x\rangle,\langle Q^2\rangle)~,
\label{f2cexp}
\end{equation}  
%where the theoretical predictions for the inclusive cross section 
%$\sigma_{\rm{vis}}^{\rm{theo}}$ and $F_2^{c~\rm{theo}}$
%are obtained from the HVQDIS program and the program of Ref. \cite{riemersma}
%in case of the NLO DGLAP evolution, and from the CASCADE program in the case 
%of the CCFM evolution.
%The contributionof open beauty production to the visible $D^{*+}$ meson 
%cross sections is neglected.
where $\sigma_{\rm{vis}}^{\rm{theo}}$ and $F_2^{c~\rm{theo}}$ are the 
theoretical  predictions from the model under consideration.
Following the same line as in previous publications 
\cite{h1f2c,zeusf2c,h1gluon} the HVQDIS program and the program of 
Ref. \cite{riemersma} is used to calculate these quantities in 
next to leading order.
 
In Fig. \ref{fig6}, the charm contribution to the proton structure function
$F^{c}_2$ is shown as a function of $x$ for different bins in $Q^2$ 
with $m_c=1.4~\gev$ as extracted from the inclusive $D^{*+}$ 
cross sections.
The error bars  
%As for the differential cross sections the different error bars 
correspond to the statistical  and total experimental errors.
 Also shown is the expectation using
the result from the H1 NLO DGLAP fit to the inclusive $F_2$ measurement
\cite{h1nlo2000}.
The band indicates the uncertainty in this extraction introduced 
by varying the charm quark mass between 1.3~GeV and 1.5~GeV.
Other sources of uncertainties in the determination of the gluon density in 
the proton are not yet taken into account. 
%Compared to the analysis of the 1994 data the accessible range accessible to
%in $Q^2$ could be extended down to $Q^2=2.5$~GeV$^2$
%due to the enlarged acceptance for the 
%detection of the scattered positron with the new backward calorimeter.
%Good agreement is observed between the two data sets in the region of 
%overlap. 
%, both having the same meaning as those presented 
%with the measurements of the inclusive 
%differential cross sections in the previous section.
%The dominant uncertainties contributing to the systematic error of $F^{c}_2$
%are due to the track efficiency and the charm fragmentation in general. At 
%small $x$ significant additional uncertainties are introduced by the 
%uncertainty in the energy calibration of 
%In the framework of the NLO DGLAP evolution 
The direct measurement of $F^{c}_2$ suggests a steeper rise 
%of $F^{c}_2$ 
at small $Q^2$ than expected from the calculations based on the 
gluon density in the proton extracted from the inclusive $F_2$ measurement.
     
The extraction of $F^{c}_2$ according to Equation \ref{f2cexp} is faced with an
intrinsic problem. Since the determination of $F^{c~exp}_2$ includes the 
extrapolation from the visible range of $D^{*+}$ meson production to full 
phase space, the measured value $F^{c~exp}_2$ depends on the predicted 
acceptance of the theoretical calculation for a given choice of parameters.
%To be more explicit, two different calculations may yield the same value for
%$F_2^{c~\rm{theo}}(\langle x\rangle,\langle Q^2\rangle)$ but may have 
%different acceptances and thereby may predict for a bin in $x$ and $Q^2$
%different cross sections $\sigma_{\rm{vis}}^{\rm{theo}}(x,Q^2)$. 
%As a 
%consequence the experimental value $F^{c~exp}_2$ would be different for the 
%comparison with the two models. 
%To account for this, each data point in figure \ref{fig6} obtains 
%a third ``error bar''. The differences between the outer ``errors'' and the   
%second inner errors show the linear displacements which have to be applied to 
%the data points by changing from  $m_c=1.4~\gev$ to $m_c=1.3~\gev$ (up) and
% $m_c=1.5~\gev$ (down).
%Since the extraction of the charm contribution to the proton structure 
%$F^{c}_2$ may heavily depend on the underlying theory as discussed above
%Therefore the result on the measurement of $F^{c}_2$ in the framework of 
%the CCFM evolution is shown separately in Fig. \ref{fig7} as a function of $x$
%for different bins in $Q^2$.
Therefore the results on $F^{c}_2$ are shown also in the framework of
the CCFM evolution separately in Fig. \ref{fig7} as a function of $x$
for different bins in $Q^2$.
As in the previous figure, $F^{c}_2$ is shown for $m_c=1.4~\gev$. However,
the CASCADE program is used to 
extract $F^{c}_2$ from the inclusive $D^{*+}$ cross sections in this case. 
The figure includes also the prediction according to the CCFM evolution
using the unintegrated gluon density \cite{uigd}
as extracted from the inclusive $F_2$ measurement of H1.
The band indicates the uncertainty on this prediction due to the 
variation of the charm quark mass between 1.3~GeV and 1.5~GeV.
%As in Fig. \ref{fig6} linear displacements which have to be applied to 
%the data points by changing from  $m_c=1.4~\gev$ to $m_c=1.3~\gev$ (up) and
%$m_c=1.5~\gev$ (down) is indicated by the differences between the outer 
%``errors'' and the second inner errors.

The comparison of Fig. \ref{fig6} and Fig. \ref{fig7} reveals a steeper rise in
the predicted charm contribution to the proton structure towards small $x$
in the CCFM evolution than obtained by the NLO DGLAP 
evolution. Using the acceptances as calculated with the CASCADE program 
the measured values of $F^{c}_2$ are found to be systematically smaller than 
those determined with the HVQDIS program. Especially at small $x$ 
differences up to almost 20\% are observed, significantly larger than the
statistical uncertainty on the data. 
%In general, the 
%determination of $F^{c}_2$ is found to be in better agreement with the 
%expectation in the CCFM framework.
% compared to the NLO DGLAP case.

In Fig. \ref{fig8} the charm contribution to the proton structure function
$F^{c}_2$ is shown as a function of $Q^2$ for different bins in $x$ in the
NLO DGLAP picture. As in Fig. \ref{fig6} the bands indicate the NLO 
predictions for $m_c$ varying between $1.3~\gev$ and $1.5~\gev$ and
using the parton densities in the 
proton obtained from the H1 NLO fit to the inclusive $F_2$.
% and of the CCFM 
%evolution based on the unintegrated gluon density in the proton extracted 
%from a CCFM fit to the inclusive $F_2$. 
%Although the number of data points in 
%the $x$-$Q^2$ plane is small and the errors on the measurements are still
%quite large, 
%The data show large scaling violation effects.
The variation of the slope of the $Q^2$ dependence of $F_2^c$ with $x$
tends to be stronger for the data
%The data indicate a stronger variation with $x$ of the slope of the $Q^2$ 
%dependence of $F_2^c$ 
than expected by this calculation.
%which means that
% based on the 
%parton densities in the proton as extracted from the H1 NLO DGLAP fit to the 
%inclusive $F_2$. Therefore, 
%scaling violation effects in open charm production seem to be larger than 
%predicted.
%On the other hand, in the framework of the CCFM evolution equations the size 
%of the predicted scaling violations of the charm contribution to the proton 
%structure function agrees well with the data. The size of the scaling violation
%effects on $F^{c}_2$ is not expected to be significantly different in the
%kinematic range of the current analysis for the NLO DGLAP and the CCFM 
%evolution. The difference observed among these two calculations is essentially
%due to a larger $F^{c}_2$ values in general for the CCFM case.  
%The better agreement of these calculation with the
%measurements is mainly due differences in acceptance corrections necessary to
%extract $F^{c}_2$. 
 
%expected by the NLO DGLAP calculation based on the parton densities in the
%proton as extracted from the H1 NLO DGLAP fit to the inclusive $F_2$.
%The data indicate a stronger variation with $x$ of the slope of the $Q^2$ 
%dependence of $F_2^c$  
%that the slopeXS of the $Q^2$ dependence of $F_2^c$ 
%varies stronger with $x$ 
%than predicted by the NLO DGLAP calculations
%scaling violation effects in open charm production seem to be la   
%than predicted by the NLO DGLAP evolution
%The data also indicate that the amount of scaling violation is even larger
%than expected from the NLO DGLAP calculations  slope of 
%the $Q^2$ dependence of $F_2^c$ varies stronger with $x$ 
%than predicted by the NLO DGLAP evolution.\newline
%{\Large{\bf Missing: discussion of CCFM, needs the corresponding figure}}
%\normalsize

%Apart from the sources of systematic error included in the 
%differential $\sigma(ep\rightarrow D^{*+}X)$ distributions,
%the changes of $F_2 ^c$ due to a variation of $m_{c}$ between 
%1.3~GeV and 1.7~GeV, due to the scale, the parton density 
%parameterization in the 
%HVQDIS program and in the theoretical calculation of   
%$F_2 ^{c \ \rm{theo}}$ have been considered. The effect of the hardness of
%the fragmentation on $\sigma_{\rm{vis}}^{\rm{theo}}$ has also been 
%investigated. 
%The 
%systematic error on $F_2 ^c$ is dominated by the uncertainty on 
%$\sigma_{\rm {vis}}^{\rm{exp}}(x,Q^2)$ due to the extrapolation in 
%$x_{D^*}$, the 
%uncertainty on $\sigma_{\rm {vis}}^{\rm{theo}}$ due our ignorance 
%of the charm fragmentation function in deep inelastic $ep$ scattering and due 
%to the effect of our lack of knowledge of the charm quark mass on  
%$\sigma_{\rm{vis}}^{\rm{theo}}$ and $F_2 ^{c \ \rm{theo}}$.

%Fig. \ref{fig5} also includes the prediction for $F^{c}_2$ from the 
%determination of the gluon density from a NLO QCD fit to the H1 inclusive
%$F_2$ data. 

%This expectation is found to be in good agreement with the direct measurement 
%of  $F^{c}_2$. \newline


\section{Conclusions}

New results on differential inclusive $D^{*+}$ meson production
cross sections in deep inelastic $ep$ scattering 
%and on the charm contribution to the proton structure $F^{c}_2$ 
from the 1996 and 1997
H1 data have been presented. The measured visible cross section is found to 
be larger than predicted by the NLO HVQDIS program using the GRV-HO 98
parton densities in the proton and a Peterson fragmentation function with 
transverse momentum smearing.
From the results on the single and double 
differential cross sections the phase space region in the $D^{*+}$ meson 
production dynamics responsible for this difference is singled out to the 
forward pseudorapidity and small $p_t$ region. 
The predictions of the CCFM based CASCADE program are in better agreement
with the data than those from HVQDIS.
%generally agree better with data.
 
By extrapolating the visible $D^{*+}$ meson production cross section to full
phase space in $p_t(D^{*+})$ and $\eta(D^{*+})$,
the charm contribution to the proton structure $F^{c}_2$ has been 
extracted in the framework of NLO DGLAP and of CCFM QCD. 
Compared to the previous H1 study, the kinematic range has been extended down 
to $Q^2=1.5~\gev^2$.  The data exhibit large
scaling violations as well as a steep rise of $F^{c}_2$ towards small $x$.
This rise tends to be steeper than expected from the NLO DGLAP 
evolution while it agrees well with the CCFM based calculations.

%The differential inclusive $D^{*+}$ cross sections
%are found to be in reasonable agreement with the NLO expectation, both in shape
%and absolute value. The kinematic range of the measurement of $F^{c}_2$
%could be extended down to $Q^2=2.5$~GeV$^2$. Good agreement is observed with
%respect to our previous measurement as well as with the extraction of 
%$F^{c}_2$ from the NLO QCD fit to the H1 inclusive $F_2$ data.
\begin{thebibliography}{References}
\bibitem{h1f2c} C. Adloff \etal~(H1 Collaboration), Z. Phys. C72(1996)593.
\bibitem{zeusf2c} J. Breitweg \etal~ (ZEUS Collaboration), 
Phys. Lett. B407(1997) 402; Euro. Phys. J. C12 (2000) 1.
\bibitem{emc} J. J. Aubert \etal~ (EMC Collaboration), 
Nucl. Phys. B213 (1983) 31.
\bibitem{h1gluon} C. Adloff \etal~(H1 Collaboration), 
Nucl. Phys. B545 (1999) 21.
\bibitem{riemersma} E. Laenen \etal, Nucl.\ Phys.\ {B392} (1993) 162, 229;
                 E. Laenen \etal, Phys.\ Lett.\  {B291} (1992) 325;
 S. Riemersma, J. Smith, and W.L. van Neerven: Phys. Lett. B347
        (1995) 143.
\bibitem{harris} B.W. Harris and J. Smith, Nucl. Phys. B452 (1995) 109, 
Phys. Lett. B353(1995)535.
\bibitem{hvqdis} B.W. Harris and J. Smith, Phys. Rev. D57 (1998) 2806.
%\bibitem{acot} M.A.G. Aivazis  \etal~, Phys. Rev. D50 (1994) 3102.
%\bibitem{collins} J.C. Collins, Phys. Rev. D58 (1998) 094002.
%\bibitem{mrst} A.D. Martin \etal~, Euro. Phys. J. C4 (1998) 463.
%\bibitem{kretzer} S. Kretzer and I. Schienbein, Phys. Rev. D59 (1999) 54004.
\bibitem{peterson} C. Peterson \etal, Phys. Rev. D27(1983)105.
\bibitem{ccfm} M. Ciafaloni, Nucl. Phys. B296 (1988) 49;
S. Catani, F. Fiorani and G. Marchesini, Phys. Lett. B234 (1990) 339; 
Nucl. Phys. B336 (1990) 18; G. Marchesini, Nucl. Phys. B445 (1995) 45.
%\bibitem{bfkl} E. Kuraev, L. Lipatov and V. Fadin, 
%Sov. Phys. JETP 44 (1976) 443; Sov. Phys. JETP 45 (1977) 199;
%Y. Balitskii and L. Lipatov, Sov. J. Nucl. Phys. 28 (1978) 822.
\bibitem{f2cccfm} J. Kwieci\'nski, A.D. Martin and P.L. Sutton, 
Phys. Rev. D53 (1996) 6094; Z. Phys. C71 (1996) 585.
\bibitem{cascade} H. Jung, Proc. 7th DIS Workshop, 
Nucl. Phys. B (Proc. Suppl.) 79 (1999) 429;hep-ph/9905554.
\bibitem{hannes} H. Jung, Proc. Workshop on Monte Carlo Generators for HERA 
Physics, 1999, DESY-PROC-1999-02, p.75; hep-ph/9908497;
H. Jung and G. Salam, to be published. 
%\bibitem{ccfmmc} H. Jung and G. Salam, in preparation.
\bibitem{uigd} S.P. Baranov, H. Jung and N.P. Zotov,
 Proc. Workshop on Monte Carlo Generators for HERA 
Physics, 1999, DESY-PROC-1999-02, p.484. 
\bibitem{h1f296} S. Aid \etal, Nucl. Phys. B470 (1996) 3.
%\bibitem{smallx} G. Marchesini and B. Webber, Nucl. Phys. B349 (1991) 617;
%Nucl. Phys. B349 (1991) 617; Nucl. Phys. B386 (1992) 215.
\bibitem{h1det} I. Abt \etal~ (H1 Collaboration), Nucl. Instr. Meth. A386 
(1997) 310 and 348.
\bibitem{spacal} R.D. Appuhn \etal~(H1 SpaCal group), Nucl. Inst. Meth.
A386 (1997) 397.
\bibitem{bdc} H1 Collaboration, Technical proposal for the upgrade of the 
backward region of the H1 detector, DESY internal report PRC-93/02.
\bibitem{cjc} J. B\"urger \etal (H1 Collaboration), Nucl. Inst. Meth.
A279 (1989) 217.
\bibitem{dcrphi} T. Wollf \etal, Nucl. Inst. Meth. A323 (1992) 537.
\bibitem{mwpc} K. M\"uller \etal, Nucl. Inst. Meth. A312 (1992) 457.
\bibitem{aroma} G. Ingelman, J. Rathsman and G.A. Schuler, Comp. Phys. Comm. 101(1997)135.
\bibitem{grvlo} M. Gl\"uck, E. Reya and A. Vogt, Z. Phys. C67(1995)433.
\bibitem{lundf} B. Anderson, G. Gustafson, and B. S\"oderberg, 
Z. Phys. C20 (1983) 317; M.G. Bowler, Z. Phys. C11 (1981) 169;
D.A. Morris, Nucl. Phys. B313 (1989) 634.
\bibitem{jetset} T. Sj\"ostrand, Comp. Phys. Comm. 82 (1994) 74.
\bibitem{herwig} G. Marchesini \etal, Comp. Phys. Comm. 67 (1992) 465.
\bibitem{rapgap} H. Jung, Comp. Phys. Comm. 86 (1995) 147.
\bibitem{herakles} A. Kwiatkowski, H. Spiesberger and H.J. M\"ohring,
Proc. of the 1991 Workshop on Physics at HERA, DESY, Hamburg, 
Vol. 3 (1992) 1294; Z. Phys. C 50 (1991) 165.
\bibitem{geant} R. Brun \etal, CERN DD/EE/84-1 (1987).
\bibitem{h1f2} C. Adloff et al. (H1 Collaboration), Nucl. Phys. B497(1997)3..
\bibitem{feldmann} G. Feldmann \etal, Phys. Rev. Lett. 38 (1977) 1313.
\bibitem{PDG} C. Caso \etal~ (Particle Data Group),Eur. Phys. J.(1998)1
\bibitem{hector} A. Arbuzov \etal, Comp. Phys. Comm. 94 (1996) 128.
\bibitem{grv} M. Gl\"uck, E. Reya and A. Vogt, Eur. Phys. J. C5 (1998)461-470.
\bibitem{hadro} R. Barate \etal (ALEPH Collaboration), CERN-EP-99-094, 
submitted to Eur. Phys. J. C.
\bibitem{norrbin} E. Norrbin, hep-ph/9909437;
E. Norrbin and T. Sj\"ostrand, hep-ph/0005110. 
%\bibitem{h1f2} C. Adloff et al. (H1 Collaboration), Nucl. Phys. B497(1997)3.
%\bibitem{beauty}
%C. Adloff  \etal~ (H1 Collaboration), contributed paper 
%submitted to the 29th International Conference on 
%High-Energy Physics ICHEP98, \\ Vancouver, Canada, July 1998
%abstract 575.
%\bibitem{karin} K. Daum \etal, in the Proceedings of the Workshop on 
%``Future Physics at HERA'', eds. G. Ingelman, A. De Roeck, R. Klanner, Hamburg
%1995, p 89-101.
\bibitem{h1nlo2000} C. Adloff  \etal~ (H1 Collaboration), 
Contributed paper to the 30th International Conference on 
High-Energy Physics ICHEP2000, Osaka, Japan, July 2000
abstract 945
\end{thebibliography}

\newpage
\unitlength1cm
%
%-----  Scatel
%
\begin{figure*}
\unitlength1cm
\begin{picture}(17.8,7.5)
\put(0,0)
{\epsfig{file=H1prelim-00-172.fig1a.eps,width=8.6cm}}
\put(8.5,0)
{\epsfig{file=H1prelim-00-172.fig1b.eps,width=8.6cm}}
\large
\put(4.2,0.3){(a)}
\put(13.6,0.3){(b)}
\end{picture}
%    \input{gammagluon} 
%\epsfig{file=qpm.eps,width=8cm}
\caption{Distribution of (a) the polar angle and 
(b) the energy of the scattered
positron for events with identified $D^{*+}$ mesons. The data is compared 
with the absolute prediction of the AROMA Monte Carlo simulation (open
histogram). 
}
\label{scatel}
\end{figure*}
%
%-----  
%

\begin{figure}[t] 
\begin{picture}(15.,7.5)
\put(2,-0.3){\epsfig{file=H1prelim-00-172.fig2.eps,
width=10.5cm}}
\end{picture}
\caption{\label{fig1}{Distribution of the mass difference 
$\Delta{m} = m(K^- \pi^+ \pi_s^+) - m(K^- \pi^+)$ for 
DIS events with $D^*$ candidates.
The data points are obtained from the $K^- \pi^+$ mass combinations
fulfilling $|m(K^- \pi^+) - m_{D^0}| <$ 70 MeV.
The solid line represents the result of the fit described in the text.
The shaded histogram shows the background expectation from the like sign $K\pi$
pairs.
}}
\end{figure} 
\newpage
\begin{figure}[t] 
\begin{picture}(15.,19.)
\put(5.3,18.7){{\bf \Large H1 preliminary}\normalsize}
\put(0,12){\epsfig{file=H1prelim-00-172.fig3a.eps,
width=8.cm}}
\put(0,12){\epsfig{file=H1prelim-00-172.fig3a.frame.eps,
width=8.cm}}
\put(7,12){\epsfig{file=H1prelim-00-172.fig3b.eps,
width=8.cm}}
\put(7,12){\epsfig{file=H1prelim-00-172.fig3b.frame.eps,
width=8.cm}}
\put(0,5.75){\epsfig{file=H1prelim-00-172.fig3c.eps,
width=8.cm}}
\put(0,5.75){\epsfig{file=H1prelim-00-172.fig3c.frame.eps,
width=8.cm}}
\put(7,5.75){\epsfig{file=H1prelim-00-172.fig3d.eps,
width=8.cm}}
\put(7,5.75){\epsfig{file=H1prelim-00-172.fig3d.frame.eps,
width=8.cm}}
\put(0,-.5){\epsfig{file=H1prelim-00-172.fig3e.eps,
width=8.cm}}
\put(0,-.5){\epsfig{file=H1prelim-00-172.fig3e.frame.eps,
width=8.cm}}
\put(7,-.5){\epsfig{file=H1prelim-00-172.fig3f.eps,
width=8.cm}}
\put(7,-.5){\epsfig{file=H1prelim-00-172.fig3f.frame.eps,
width=8.cm}}
\end{picture}
\caption{\label{fig2}{Single
differential inclusive cross section $\sigma(ep \rightarrow eD^{*+} X)$
versus $W$, $x_{Bj}$, $Q^2$ and $p_{T \ D^*}$, $\eta_{D^*}$, $z_{D^*}$.
The inner and outer error bars correspond to the 
statistical and the total errors.  
The expectation of the NLO DGLAP calculation using HVQDIS is indicated by the
lower shaded band. The upper and lower bounds correspond to ($m_c=1.3~\gev$,
$\epsilon=0.035$) and ($m_c=1.5~\gev$, $\epsilon=0.10$), respectively.
The upper shaded band is the expectation of the CCFM calculations based on the
CASCADE program. The upper and lower bounds correspond to $m_c=1.3~\gev$ and
$m_c=1.5~\gev$, respectively, with a fragmentation parameter of 
$\epsilon=0.078$.
}}
\end{figure}  
\newpage
\begin{figure}[t] 
\begin{picture}(15.,21)
\put(6,19.8){{\bf \Large H1 preliminary}\normalsize}
%\put(-0,16.5){\epsfig{file=double_etaq2.ps,angle=-90.0,width=17.cm}}
%\put(-1,9){\epsfig{file=q2eta_cross_vis3_67.eps,width=18.cm}}
%\put(-1,9){\epsfig{file=q2eta_cross_box.eps,width=18.cm}}
\put(-1,9){\epsfig{file=H1prelim-00-172.fig4a.eps,width=18.cm}}
\put(-1,9){\epsfig{file=H1prelim-00-172.fig4a.frame.eps,width=18.cm}}
\put(2.1,19){$-1.5<\eta<-0.5$}
\put(6.5,19){$-0.5<\eta<0.5$}
\put(11.2,19){$0.5<\eta<1.5$}
\put(1.3,-.2){\epsfig{file=H1prelim-00-172.fig4b.eps,width=18.cm}}
\put(1.3,-.2){\epsfig{file=H1prelim-00-172.fig4b.frame.eps,width=18.cm}}
\put(4.7,9.8){$1.5<p_t<4.0$}
\put(9.1,9.8){$4.0<p_t<10.0$}
\end{picture}
\normalsize
\caption{\label{fig4}{Double differential inclusive cross section 
${\rm d}^2\sigma/{\rm d}\eta{\rm d}Q^2$ and
${\rm d}^2\sigma/{\rm d}p_t{\rm d}Q^2$ in bins of $\eta$ and $p_t$.
(See figure \ref{fig2} for details)
%The inner and outer thin error bars correspond to the 
%statistical and the total error, respectively. 
%The expectation of the NLO DGLAP calculation using HVQDIS is indicated by the
%lower shaded band. The upper and lower bounds correspond to ($m_c=1.3~\gev$,
%$\epsilon=0.035$) and ($m_c=1.5~\gev$, $\epsilon=0.10$), respectively.
%The upper shaded band is the expectation of the CCFM calculations based on the
%CASCADE program. The upper and lower bounds correspond to $m_c=1.3~\gev$ and
%$m_c=1.5~\gev$, respectively, with a fragmentation parameter of 
%$\epsilon=0.078$.
}}
\end{figure}  
\newpage
\begin{figure}[t] 
\begin{picture}(15.,21)
\put(6,21.8){{\bf \Large H1 preliminary}\normalsize}
\put(-0,12){\epsfig{file=H1prelim-00-172.fig5a.eps,width=16.cm}}
\put(-0,12){\epsfig{file=H1prelim-00-172.fig5a.frame.eps,width=16.cm}}
\put(2.8,21){$1.5<p_t<2.5$}
\put(6.8,21){$2.5<p_t<4.0$}
\put(10.5,21){$4.0<p_t<10.0$}
\put(-0,5.){\epsfig{file=H1prelim-00-172.fig5b.eps,width=16.cm}}
\put(-0,5.){\epsfig{file=H1prelim-00-172.fig5b.frame.eps,width=16.cm}}
\put(2.8,14.){$1.5<p_t<2.5$}
\put(6.8,14.){$2.5<p_t<4.0$}
\put(10.4,14.){$4.0<p_t<10.0$}
\put(-0,-2.){\epsfig{file=H1prelim-00-172.fig5c.eps,width=16.cm}}
\put(-0,-2.){\epsfig{file=H1prelim-00-172.fig5c.frame.eps,width=16.cm}}

\put(2.8,7.){$0.0<z_D<0.25$}
\put(6.8,7.){$0.25<z_D<0.5$}
\put(10.4,7.){$0.5<z_D<1.0$}
\end{picture}
\normalsize
\caption{\label{fig5}{Double differential inclusive cross section 
${\rm d}^2\sigma/{\rm d}p_t{\rm d}\eta$,
${\rm d}^2\sigma/{\rm d}p_t{\rm d}z_D$ in bins of $p_t$ and
${\rm d}^2\sigma/{\rm d}\eta{\rm d}z_D$ in bins of $\eta$.
(See figure \ref{fig2} for details)
%The inner and outer thin error bars correspond to the 
%statistical and the total error, respectively. 
%The expectation of the NLO DGLAP calculation using HVQDIS is indicated by the
%lower shaded band. The upper and lower bounds correspond to ($m_c=1.3~\gev$,
%$\epsilon=0.035$) and ($m_c=1.5~\gev$, $\epsilon=0.10$), respectively.
%The upper shaded band is the expectation of the CCFM calculations based on the
%CASCADE program. The upper and lower bounds correspond to $m_c=1.3~\gev$ and
%$m_c=1.5~\gev$, respectively, with a fragmentation parameter of 
%$\epsilon=0.078$.
}}
\end{figure}  
\newpage
\begin{figure}[t] 
\begin{picture}(15.,17.)
\put(-1,0){\epsfig{file=H1prelim-00-172.fig6.eps,
width=18cm}}
\end{picture}
\caption{\label{fig6}{The charm contribution to the proton structure function 
$F_2^c$ as derived from the inclusive $D^{*+}$ meson analysis in the framework
of DGLAP NLO for $m_c=1.4~\gev$. The error bars refer to the statistical 
(inner) and the total error (outer), respectively.
The shaded band represents the predictions of $F_2^c$ 
from the H1 NLO DGLAP fit
to the $F_2$ measurements ranging from $m_c=1.3~\gev$ to $m_c=1.5~\gev$.}}
\end{figure}  
\newpage
\begin{figure}[t] 
\begin{picture}(15.,17.)
\put(-1,0){\epsfig{file=H1prelim-00-172.fig7.eps,
width=18cm}}
\end{picture}
\caption{\label{fig7}{The charm contribution to the proton structure function 
$F_2^c$ as derived from the inclusive $D^{*+}$ meson  in the framework of
CCFM.The error bars refer to the statistical 
(inner) and the total error (outer), respectively. 
The shaded bands represent the CCFM predictions of $F_2^c$ using a charm quark
mass in the range from $m_c=1.3~\gev$ to $m_c=1.5~\gev$. 
}}
\end{figure}  
\newpage
\begin{figure}[t] 
\begin{picture}(15.,21.)
\put(-0.5,2){\epsfig{file=H1prelim-00-172.fig8.eps,
width=16cm}}
%\put(3,10){\white\rule{0.8cm}{1cm}\black}
%\put(3,8.9){\white\rule{10cm}{1.3cm}\black}
%\put(2,-0.25){\epsfig{file=ccfm_scale.eps,width=12cm}}
\end{picture}
\caption{\label{fig8}{The charm contribution to the proton structure function 
$F_2^c$ as derived from the inclusive $D^{*+}$ meson 
as a function of $Q^2$ for different bins in $x$.
 The error bars refer to the statistical 
(inner) and the total error (outer), respectively.
The shaded bands represent the predictions of the NLO DGLAP evolution 
based on the parton densities in the proton obtained by the NLO fit to the 
inclusive $F_2$.}}
\end{figure}  


\end{document}

\newpage
\begin{table}
%\centering
\begin{tabular}{lrr}\hline\noalign{\smallskip}
Experiment&&$D^{*+}$\cr
Systematic Errors&\cr
\noalign{\smallskip}\hline\noalign{\smallskip}
Trigger&&$\pm$~0.02\cr\noalign{\smallskip}
Tracker efficiency&$+$0.075&$-$0.034
\cr\noalign{\smallskip}
Background shape&&$\pm$~0.05\cr\noalign{\smallskip}
Mass resolution&$+$0.04&$-$0.025\cr\noalign{\smallskip}
dE/dx measurement&&$\pm$~0.03\cr\noalign{\smallskip}
$p_t(\pi_{slow})$-cut&$+$0.025&$-$0.00\cr\noalign{\smallskip}
%$\Sigma$ vs. electron method&&\cr
%for 
%Event kinematics&$+$0.01&$-$0.00\cr\noalign{\smallskip}
$E_e$, $\Theta_e$ resolution&$+$0.015&$-$0.03
\cr\noalign{\smallskip}
Luminosity&&$\pm$~0.015\cr
$\gamma p$ contribution&&$<$0.004\cr\noalign{\smallskip}
Radiative corrections&&\cr
Event kinematics&$+$0.04&$-$0.02\cr\noalign{\smallskip}
Reflections&&$\pm$~0.015\cr\noalign{\smallskip}
Branching ratio&&$\pm$~0.04\cr
\noalign{\smallskip}\hline 
\noalign{\smallskip}
Total $ep\rightarrow eD^{*+}X$
&$+$0.12&$-$0.10\cr\noalign{\smallskip}
\hline\noalign{\smallskip}
\end{tabular}
\caption{Summary of the relative experimental systematic uncertainties of the
inclusive $D^{*+}$ cross section.}
\label{expsys}
\end{table}


\begin{table}
%\centering
\begin{tabular}{lrr}\hline\noalign{\smallskip}
Model Uncertainties&&$D^{*+}$\cr
\noalign{\smallskip}\hline\noalign{\smallskip}
Fragmentation
function&$+$0.035&$-$0.025\cr\noalign{\smallskip}
Charm quark mass&$+$0.07&$-$0.02\cr\noalign{\smallskip}
Scale $\mu^2=Q^2+4m_c^2$&&$-$0.015\cr\noalign{\smallskip}
QED radiation&&$-$0.025\cr\noalign{\smallskip}
\noalign{\smallskip}
\hline 
\noalign{\smallskip}
total $ep\rightarrow eD^{*+}X$&$+$0.08&$-$0.04
\cr\noalign{\smallskip}\hline
\noalign{\smallskip}
\hline\noalign{\smallskip}
\end{tabular}
\caption{Summary of the relative model dependent uncertainties of the
 inclusive $D$ meson cross sections.}
\label{modelsys}
\end{table}


