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\begin{document}

\newcommand{\pom}{{I\!\!P}}
\newcommand{\reg}{{I\!\!R}}
\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.)}
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\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}{$\stackrel {\textstyle>}{\sim}$}}
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   {\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{$\scriptstyle <$}\,}
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\newcommand{\dsf}{\mbox{$F_2^{D(3)}$}}
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\newcommand{\dsfvb}{\mbox{$F_2^{D(3)}(\beta,Q^2,x)$}}
\newcommand{\dsfpom}{$F_2^{I\!\!P}$}
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\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}}
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\newcommand{\sqrts}{$\sqrt{s}$}
\newcommand{\LO}{\mathcal{O}(\alpha_s^0)}
\newcommand{\Oa}{\mathcal{O}(\alpha_s)}
\newcommand{\Oaa}{O(\alpha_s^2)}
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\newcommand{\JPSI}{J/\psi}
\newcommand{\sh}{\hat{s}}
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\newcommand{\uh}{\hat{u}}
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%\newcommand{\PO}{\mbox{l}\!\mbox{P}}
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% Journal macro
\def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4}
\def\NCA{\em Nuovo Cimento}
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\def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}}
\def\NPB{{\em Nucl. Phys.}   {\bf B}}
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\def\PRD{{\em Phys. Rev.}    {\bf D}}
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\newcommand{\BJKLW}{BLJK1,Bartels_qqga,BLJK2}
\def\rapgap{{\sc Rapgap}}


%\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em]
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline
Submitted to & & &
\epsfig{file=eps/H1logo_bw_small.epsi,width=2.cm} 
\\[.2em] \hline
\multicolumn{4}{l}{{\bf
                32nd International Conference
                on High Energy Physics, ICHEP04},
                August~16,~2004,~Beijing} \\
                 & Abstract:        & {\bf  6-0178}    &\\
                 & Parallel Session & {\bf 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
% & \multicolumn{3}{r}{\footnotesize {\it
%    draft version v4}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
{\bf Diffractive {\boldmath $\dstar$} Meson Production in
Deep-Inelastic Scattering at HERA }

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

\begin{abstract}
A new measurement is presented of
$\dstar$ meson production 
in diffractive deep-inelastic scattering at HERA.
%
The data were collected in the years 1999 and 2000
and correspond to an integrated luminosity of 42.6$\;\mbox{pb}^{-1}$.
%
Cross sections are measured for the process
$ep \rightarrow eXY$
%
where the system $X$
contains at least one $\dstar$ meson and is separated
by a large rapidity gap from a low mass proton remnant system $Y$.
%
The cross section is given in the deep-inelastic kinematic region of 
$2< Q^2 < 100 \ {\rm GeV^2}$ with inelasticity $0.05 < y < 0.7$.
%
The diffractive kinematic region is defined by
$\xpom < 0.04$, $M_Y < 1.6  \ {\rm GeV}$ and $|t| < 1 \ {\rm GeV^2}$.
%
The $\dstar$ mesons are restricted to the range $\ptlab > 2 \ {\rm GeV}$ and
$|\etalab | < 1.5$.
%
%
The cross section is presented differentially 
as a function of various kinematic variables.
%
%hannes FPSchilling
%The data are compared with several QCD-based calculations.
The data are compared with NLO QCD calculations using the recent
H1 diffractive PDF's as well as with a model of 2-gluon exchange.
%hannes
\end{abstract}
\end{titlepage}

%---------------------------------------------------------------------------------------------------
\section{Introduction}
\label{section:introduction}
%---------------------------------------------------------------------------------------------------

This paper presents a measurement of 
diffractive $\dstar$ production in deep inelastic scattering at HERA.
%
This process is illustrated in Fig.~\ref{kinefig}. 
It is characterized by two distinct hadronic systems $X$ and $Y$ which are separated by a large rapidity gap.
%
The system $X$ contains at least one $\dstar$ meson, whereas $Y$ consists of the elastically scattered proton 
or a low mass diffractive state.
%
As a hard scale is already provided by the charm quark mass, 
diffractive charm production is 
interesting to test different 
perturbative QCD approaches to diffraction.
%
\par
There are essentially two different ways theoretically to describe hard 
diffractive processes: 
the collinear factorization
approach using diffractive parton densities \cite{Collins_pom}, 
defined in analogy to the inclusive parton densities of the proton, and the
$\kt$-factorization approach with 2-gluon exchanges using un-integrated 
gluon densities~\cite{BLJK2}. 
%
Whereas the former approach makes no a priori statement about the nature of the 
diffractive mechanism, the latter describes diffraction 
as the exchange of a colorless two (or more) gluon state. 
%
\par
In the collinear factorization approach diffractive parton densities are applied, 
which are obtained from next-to-leading order (NLO) QCD fits 
%hannes FPSchilling comment
to the reduced diffractive cross section ~\cite{H1_F2D3_prel}. 
%hannes
Charm production proceeds dominantly via the Boson Gluon Fusion process (BGF)\/, 
as depicted in Fig.~\ref{kinefig}. 
%hannes FPSchilling comment
According to the factorization theorem~\cite{Collins_pom}, the hard scattering matrix elements are
the same as for inclusive heavy flavor production.
%hannes
%
Thus diffractive charm production is directely sensitive to the diffractive gluon
density, which is only indirectly constrained in inclusive measurements of diffraction
via scaling violations.
%
For color compensation the system $X$ (see Fig.~\ref{kinefig})
contains a diffractive remnant in addition to the $c\bar{c}$ pair.
\par 
In the perturbative 2-gluon approach, the non-diffractive un-integrated gluon densities in the proton
are combined to a colorless 2-gluon state.
%
This state can couple directly to the
%hannes $c\bar{c}$ pair ($\gamma^* p \to c\bar{c} \;p$), leaving no diffractive remnant or to a $c\bar{c} g$  system 
%hannes ($\gamma^* p \to c \bar{c} g\; p$). 
$c\bar{c}$ pair ($\gamma^* p \to c\bar{c} \;p$) or to a $c\bar{c} g$  system 
($\gamma^* p \to c \bar{c} g\; p$). 
%
In the latter case, the gluon may have
significant transverse momentum, in contrast 
to the remnant in the collinear factorisation approach.
%
%Although the partonic final state looks 
%similar to the case of collinear factorization, the difference
%is, that the gluon is not part of the diffractive remnant, but of the hard scattering process, with a
%significant transverse momentum.
\par
%
\begin{figure}[h]
\centering \epsfig{file=eps/dstar.production.eps,width=0.6\linewidth}
\caption{ \em The process under study in this article is $ep \rightarrow
eXY \rightarrow e(\dstar X')Y$.
The electron ($e$) couples to a photon ($\gamma^{\star}$) which interacts with
the proton ($p$) via a color singlet exchange, producing two distinct
final state hadronic systems $X$ and $Y$.  The systems $X$ and $Y$ are
separated by the largest gap in rapidity between the final state hadrons.}
\label{kinefig}
\end{figure}

In this paper the diffractive production of $\dstar$
mesons is investigated in the deep inelastic scattering
regime, where the large photon virtuality provides a further hard scale
in addition to the charm quark mass.
% 
The measurement is performed with the H1 detector at 
HERA and is based on a three times larger sample 
than in a previous publication \cite{Adloff:2001wr},
allowing for more differential investigations.
%
The results are compared 
with predictions using both the collinear factorisation
and the 2-gluon exchange approaches.
%

The paper is organized as follows: 
The kinematics of diffractive DIS are introduced in section \ref{section:kinematics}.
In section \ref{section:experiment}, the H1 detector and the data selection, are described.
The cross section measurement and the evaluation of the systematic uncertainties are explained
in section \ref{section:xsection}.  
In section \ref{section:results} the results are presented and discussed.

%---------------------------------------------------------------------------------------------------
\section{Kinematics}
\label{section:kinematics}
%---------------------------------------------------------------------------------------------------

The process studied in this paper is shown in Fig.~\ref{kinefig}.
%
The electron couples to 
a virtual photon $\gamma^{\star}$ (with four-momentum $q$) which interacts with the
proton (with four-momentum $P$).
%
The photon and the proton dissociate into two distinct hadronic systems $X$ and $Y$, with
invariant masses $\mx$ and $\my$, respectively.
The two systems are separated by a large rapidity gap.
%
In addition to the standard DIS 
kinematic variables $Q^2$, $y$ and Bjorken $x$ the following variables are defined
%
\begin{equation}
 \label{xpomtbeta}
 \xpom = \frac{q \cdot (P - p_Y)}{q \cdot P} \ ; \qquad t = (P-p_Y)^2 \ ; \qquad
 \beta = \frac{Q^2}{2q\cdot (P-p_Y)} = \frac{x}{\xpom};
\end{equation}
%
where $p_Y$ is the four-momentum of $Y$.
%
The quantity $\xpom$ may be interpreted as the longitudinal momentum fraction of the colorless exchange,
with respect to the incoming proton.
The variable $t$ is the squared four-momentum transferred at the proton vertex. 
The variable $\beta$ can be interpreted as the fractional longitudinal momentum of the
colorless exchange carried by the struck quark.    
%
In this analysis $t$ and $\my$ are constrained to be small by the
experimental selection and are integrated over implicitly.
%
Furthermore the variable  $\zpom$ is introduced as
%
\begin{equation}
 \label{zpom}
 \zpom = \beta \cdot \left(1 + \frac{\hat{s}} {Q^2}\right)
 = \frac{Q^2 + \hat{s}}{Q^2 + M_X^2}, 
\end{equation}
%
where $\hat{s}$ denotes the invariant mass 
of the charm quark pair emerging from the hard subprocess. 
%
$\zpom$ is an estimator
for the fraction of the colour singlet exchange momentum, 
which enters the hard scattering.
%
%---------------------------------------------------------------------------------------------------
\section{Experimental aspects and data analysis}
\label{section:experiment}
%---------------------------------------------------------------------------------------------------

The data used for this analysis were taken in the years 1999 and 2000, when
%hannes FPSchilling comment
%HERA collided positrons with energy 
HERA collided positrons of energy 
%hannes
$E_e = 27.5 \ {\rm GeV}$
with protons of energy 
$E_p = 920 \ {\rm GeV}$.
%
Requiring all detectors which are essential for this analysis 
to be fully operational results in an integrated luminosity of 
$42.6$~pb$^{-1}$.

\subsection{The H1 Detector}

The H1 detector is described in detail in \cite{H1:det}.
%
Only the components most relevant for this analysis are briefly discussed in this section.
%
The coordinate system used has its origin
at the nominal $e^+p$ interaction point. Its
%hannes FPSchilling comment
%$z$-axis in the outgoing proton direction 
$z$-axis in the outgoing proton direction is
%hannes
referred to as the `forward' direction.
%
Charged particles emerging from the interaction region are measured by the central tracking
%hannes FPSchilling comment
%device (CTD) in the range of $-1.5 < \eta < 1.5$\footnote{The pseudorapidity 
detector (CTD) in the range of $-1.5 < \eta < 1.5$\footnote{The pseudorapidity 
%hannes
$\eta$ of an object detected with polar angle $\theta$ is defined as
$\eta = - \ln \ \tan (\theta / 2)$.}.  
%
The CTD comprises two large
cylindrical central jet drift chambers (CJC) 
and two $z$ chambers situated concentrically around the beam-line 
within a solenoidal magnetic field of 1.15 T. 
%
The CTD also provides triggering
information  based on track segments in the $r-\phi$ plane 
from the CJC and the position of the vertex using a double 
layer of multi-wire proportional chambers (MWPC).
%
The energies of final state particles are measured in the Liquid Argon (LAr) calorimeter,
which surrounds the tracking chambers and covers the range of $-1.5 < \eta < 3.4$. 
%
The backward region ($-4.0 < \eta < -1.4$) is covered by
a lead-scintillating fiber calorimeter (SPACAL~\cite{spacal}) with electromagnetic and
hadronic sections.  
%

In the direction of the outgoing protons 
several detectors are installed close to the beam pipe
which are used 
in the selection of large rapidity gap events.
%
The Forward Muon Detector (FMD) is located at $z=6.5 \ \mathrm{m}$.
%It covers the pseudorapidity range of $1.9<\eta<3.7$. 
%hannes
It can detect particles directly 
in the region $1.9<\eta<3.7$, and from larger
pseudorapidities via beam-pipe scattering.
%hannes
%
The PLUG calorimeter measures energies
in the range of $3.5<\eta <5.5$.
%
The Proton Remnant Tagger (PRT) consists of 
scintillators surrounding the beam pipe at $z=26 \ \mathrm{m}$.
%
It tags hadrons in the region of $6.0 \ \lapprox \ \eta \ \lapprox \ 7.5$.
%

\subsection {Event Selection}

The selected events were triggered by an electromagnetic energy cluster in the SPACAL,
in coincidence with a charged track signal recorded in both the MWPC and  
%hannes FPSchilling comment
% the CJC .
the CJC and a reconstructed event vertex.
%hannes
%
%hannes PaulT comment
%In the offline analysis the scattered positrons are selected as electromagnetic SPACAL clusters
In the offline analysis the scattered positron is selected as an electromagnetic SPACAL cluster
%hannes
with energy $E'_{e} > 8 $~{\rm GeV}.
%
The DIS kinematic variables $Q^2$ and $y$ 
are reconstructed from the energy and polar angle of the scattered positron.
%
The scaling variable Bjorken $x$ 
is subsequently calculated from $x=Q/ys$ where $s$
denotes the $ep$ center-of-mass energy squared.
%
The accepted kinematic range is $2<Q^2<100 ~{\rm GeV^2}$ and $0.05<y<0.7$. 
%

Diffractive events are selected by demanding 
no detector activity above noise thresholds in the forward detectors, 
i.e. the PRT, the FMD, the PLUG
and the most forward part ($\eta > 3.2$) of the LAr calorimeter.
%
%hannes FPSchilling comment
%According to Monte Carlo studies this restricts 
%the mass of the proton remnant system to $\my < 1.6 \ \rm{GeV}$ 
%and the momentum transfer to the proton to $|t| < 1 \ \rm {GeV}^2$. 
Using Monte Carlo simulations the data are then corrected to the range of 
the proton remnant system of $\my < 1.6 \ \rm{GeV}$ 
and the squared four-momentum transfer to the proton of $|t| < 1 \ \rm {GeV}^2$.
%hannes
%
The four-momentum of the photon dissociation system $X$,
which is well contained in the central detector, 
is reconstructed using information from the LAr and SPACAL calorimeters
and the CTD\cite{fscomb}.
%
The variable $\xpom$ is calculated from
\begin{equation}
\label{xpomandbeta}
  \xpom = \frac {Q^2 + M_X^2}{Q^2+ W^2}, \ 
\end{equation}
%
where $W$ is
the photon-proton center of mass energy which is given by  $W^2 = ys - Q^2$.
The kinematic range is restricted to $\xpom<0.04$,
which suppresses contributions from non-diffractive scattering and secondary reggeon
exchanges. 
%
The quantity $\beta$
is calculated from $\beta = x / \xpom$. 
%
The observable $\zpomobs$ is defined as
%
\begin{equation}
 \label{zpomdstar}
 \zpomobs =  \frac{ M_{c\bar{c}}^2 +Q^2}{\mx^2+Q^2},
\end{equation}
where $M_{c\bar{c}}^2$ is a hadron level estimate of $\hat{s}$
which is reconstructed from the scattered positron and 
the $D^{*\pm}$ meson. 
Further details are given in \cite{Adloff:2001wr}.
%

\subsection {\boldmath$D^*$ identification}

The $D^{*+}$ mesons are reconstructed using the decay channel
%
\begin {equation}
 D^{*+} \rightarrow D^0 \pi^+_{slow} \rightarrow (K^- \pi^+) \pi^+_{slow  } \
\;  (+ c.c.),
\end {equation}
%
which has a branching fraction of $2.57\%$~\cite{pdg2004}.
% -----------------------
% pdg 2004 numbers:
% D0 -> Kpi 3.80 
% Dstar -> D0 pi 0.677
% --> 2.5726%
% -----------------------
The decay products are detected in the CTD. 
To ensure good detection efficiency and to reduce combinatorial background, 
the tracks are required to lie within the angular range of $20^{\rm o}< \theta <160^{\rm o}$ and to have a 
transverse momentum $p_T$ relative to the beam axis of at least $120$~MeV
for the $\pi_{slow}$, $300$~MeV for the other $\pi$ and $500$~MeV for the $K$.
%
The invariant mass of the $K \pi$ combination has to be consistent with the
$D^0$ mass within $\pm 80$~MeV. Furthermore the direction of the reconstructed
$D^{*\pm}$ candidate is restricted to $|\eta(D^{*\pm})|<1.5$ and its
transverse momentum to $p_T(D^{*\pm})>2$~GeV. 
%
In Fig.~\ref{deltam} the distribution of the mass difference 
$\Delta M = M(K^{\mp}\pi^{\pm}\pi^{\pm}_{slow})-M(K^{\mp}\pi^{\pm})$ is shown for all selected events 
and all track combinations which fulfill the above requirements.
%
The number of $D^{*\pm}$ mesons is determined by fitting the $\Delta M$ spectrum
with a Gaussian distribution for the signal together with a background parameterized 
as $a(\Delta M - m_{\pi})^b (1- c\, (\Delta M)^2)$, where $m_{\pi}$ is the mass of the charged pion.
%
The resulting number of identified $D^{*\pm}$ mesons is $140 \pm 16$.
%
\begin{figure}[h]
\begin{center}
\mbox{\epsfig{figure=eps/dstar.yield.eps,angle=0,width=1.0\textwidth}}
\end{center}
\caption{ \em  Distribution of the mass difference
$\Delta M=M(K^{\mp} \pi^{\pm} \pi_{slow}^{\pm})-M(K^{\mp}\pi^{\pm})$. The fitted curve is of the form
$a(\Delta M - m_{\pi})^b (1- c\, (\Delta M)^2 )
+$ Gaussian function for the signal.}
\label{deltam}
\end{figure}
%

%---------------------------------------------------------------------------------------------------
\section{Cross Section determination and systematic errors}
\label{section:xsection}
%---------------------------------------------------------------------------------------------------

The differential cross sections are obtained from 
fits to the $\Delta M$ distributions performed
separately in each kinematic bin.
%
The fits yield numbers of detected $\dstar$ mesons,
which are translated into $\dstar$ cross sections
by dividing by the branching ratio of the selected $\dstar$
decay channel and the integrated luminosity.
%
Further corrections are applied
for detector efficiencies, acceptances and migrations
due to the finite resolution of the H1 detector.
%
These corrections are 
calculated by running the H1 detector simulation program on a sample of
$D^{*\pm}$ events produced by the diffractive Monte Carlo generator 
\rapgap ~\cite{RAPGAP,RAPGAP208} using diffractive parton densities. 
%
The \rapgap\ program is used to model events which
contain an elastically scattered proton ($M_Y=m_p$) in the kinematic range $x_{\pom}<0.1$.
%
Migrations from $\xpom > 0.1$ or from large values of $M_Y$ ($M_Y>5 \ \rm\ GeV$)
%hannes FPSchilling comment
%are modeled by using the \rapgap\ program in the inclusive mode.
are modeled by using the \rapgap\ program in its non-diffractive mode.
%hannes
%
This contribution is of the order of $1\%$ of the selected sample of events.
%
An additional correction of $10\%$
% \pm 10\%$ 
is applied to account
for the net smearing across the $\my=1.6 \ \rm GeV$ boundary.
%
Since only elastically scattered protons are simulated in
\rapgap\ , this correction is evaluated using the proton dissociation
simulation in the DIFFVM~\cite{DIFFVM,DIFFVM2} generator\footnote{For the
correction, it is assumed that the
ratio of diffractive proton elastic to diffractive proton
dissociative interactions is $1:1$.}.
%

The following sources of systematic uncertainties and the resulting influence
%hannes
%on the relative error of the cross section measurement have been studied:
on the cross section measurement have been studied:
%hannes
%
\begin {itemize}
\item The uncertainty on the trigger efficiency is taken from a comparison of 
the efficiency determined from data using a monitor trigger sample and 
the result of a Monte Carlo simulation and is estimated to be $\pm 3\%$.
%
\item Varying the reconstructed energy and polar angle of the scattered 
electron within 
%hannes PaulT commnents
%the resolution of the SpaCal results in a $\pm3 \%$ error.
the estimated uncertainties on the resolution and energy scale of the SPACAL
results in an uncertainty of $\pm3 \%$.
%hannes
%
\item The track reconstruction efficiency and uncertainties related to
the signal extraction from the fit to the $\Delta M$ distribution have been 
determined by analyzing an inclusive $D^*$ sample 
%{\bf check reference}
and are estimated to be $^{+11\%}_{-6\%}$ and $\pm 3\%$, respectively.
%
\item The uncertainty in the hadronic energy scale of the
liquid argon calorimeter is taken into account
%hannes by varying in the Monte Carlo simulation 
by varying (in the Monte Carlo simulation)  
the energies of the reconstructed hadronic final state
by 4\%.
%
This affects the $M_X$ reconstruction and
leads to changes of the cross section of $\pm 4\%$.
%
% Olaf: not clear according to Paul N
%\item An uncertainty of $\pm3\%$ is assigned to the correction factors which 
%have been applied to account for the effect of the forward detector selection.
%
\item As an estimate of the uncertainty 
in the acceptance and migration corrections due to uncertainties 
in the physics model for 
diffractive $D^{*\pm}$ 
production, the effect of varying in the simulation the shape of various 
kinematic distributions within limits set by previous measurements have been 
studied. Reweighting the $x_{\pom}$ distribution on the generator level by 
$(1/x_{\pom})^{\pm0.05}$, the $\beta$ distribution by $(1\pm 1.5 \beta)$, the 
$M_Y$ distribution by $(1/M_Y)^{\pm 0.3}$, the $|t|$ distribution 
for elastic scattering by
$e^{\pm 2 |t|}$, the $|t|$ distribution for proton dissociation 
by $e^{\pm |t|}$ and
varying the assumed ratio of proton-dissociative to proton-elastic
cross sections from $1:2$ to $2:1$, 
results in a systematic uncertainty of
%{\bf check} 
$\pm 12\%$ on the cross section.
%
\item 
As an estimate of the uncertainty in the charm fragmentation scheme
the default parameterization of the Peterson model was changed to the
Lund string model~\cite{jetset} in the simulation, 
leading to a change in the measured cross section of $-3\%$.
%
\end {itemize}

The total systematic error for each data point has been obtained by adding all
individual contributions in quadrature. It ranges between $15\%$ and $28\%$.

%---------------------------------------------------------------------------------------------------
\section {Results}
\label {section:results}
%---------------------------------------------------------------------------------------------------

The visible cross section for the kinematic region $\,2<Q^2<100$~GeV$^2$, $0.05<y<0.7$,
$x_{\pom}<0.04$, $M_Y<1.6$~GeV, $|t|<1$~GeV$^2$, 
$\ptlab > 2 \ {\rm GeV}$ and $|\etalab | < 1.5$ is measured to be
%
\begin {equation}
 \sigma (ep \rightarrow (D^{*\pm}X')Y) = 333 \pm 38 (stat.) \pm 57 (syst.)\ {\rm pb}.
\end {equation}
%
%hannes Paul T comments
%This is in broad agreement with the value of 
This is in agreement with the value of 
%hannes
$246 \pm 54 (stat.) \pm 56 (syst.) \ {\rm pb}$
which was found for the same kinematic range 
in the previous H1 measurement \cite{Adloff:2001wr}. 
%\par
It is also interesting to compare the measurement to the published measurement of
the ZEUS collaboration~\cite{ZEUS-diffcharm04},
which is quoted in a slightly different phase space, 
which mainly originates from a lower cut 
in $p_T(D^{*\pm})$.
%
Using the \rapgap\ Monte Carlo generator~\cite{RAPGAP,RAPGAP208}
to rescale the ZEUS measurement to the kinematic range of 
this paper (correction factor of  $C=0.58$ with an additional 10 \% correction for 
the different $M_Y$ ranges), results in a cross section value of
%
%\begin {equation}
%\sigma (ep \rightarrow (D^{*\pm}X)Y) = 
$305 \pm 25 (stat.)^{+20}_{-34}  (syst.)\ {\rm pb}$,
%\end {equation}
%
which is in good agreement with the measurement quoted above.
%\par

The cross section for the kinematic region, as defined above, but for $x_{\pom}<0.01$ is
measured to be
%
\begin {equation}
\sigma (ep \rightarrow (D^{*\pm}X')Y) = 131 \pm 24 (stat.) \pm 24 (syst.) \ {\rm pb}.
\end {equation}

\subsection{Comparisons with calculations}
%
\renewcommand{\arraystretch}{1.3}
\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c||c|} \hline\hline 
\multicolumn{2}{|c||}{ $x_{\pom} < 0.04$  } & cross section \\ \hline
 \multicolumn{2}{|c||} {H1 Data} &
{$333 \pm 38 \ {\rm (stat.)} \pm 54 \ {\rm (syst.)} \ {\rm pb}$} \\ 
\hline
\multicolumn{2}{|c||} {collinear factorization - diffractive pdfs} &
\\\hline
H1 2002 prel~\protect\cite{H1_F2D3_prel} & NLO\protect\cite{hvqdis,hvqdiff}  & $ 241 
\pm^{66}_{39} \ {\rm pb}
$ \\\hline
H1 2002 prel~\protect\cite{H1_F2D3_prel} & ME+PS\protect\cite{RAPGAP,RAPGAP208}   & 
$ 224 \ {\rm pb}$\\
\hline
\hline 
\multicolumn{2}{|c||}{$x_{\pom} < 0.01$}   &  \\  
\hline
 \multicolumn{2}{|c||} {H1 Data} &
{$131 \pm 24 \ {\rm (stat.)} \pm 24 \ {\rm (syst.)} \ {\rm pb}$} \\ \hline
\multicolumn{2}{|c||} {collinear factorization - diffractive pdfs} &
 \\\hline
H1 2002 prel~\protect\cite{H1_F2D3_prel} & NLO\protect\cite{hvqdis,hvqdiff}  & $ 76 \pm^{17}_{10} \ {\rm pb} $ \\\hline
H1 2002 prel~\protect\cite{H1_F2D3_prel} & ME+PS\protect\cite{RAPGAP,RAPGAP208}   & $ 76 \ {\rm pb} $ \\
\hline 
\multicolumn{2}{|c||} {$\kt$ - factorization - two gluon} & \\\hline
CCFM set 1~\protect\cite{jung-dis03}    &BJKLW\protect\cite{\BJKLW} ($p_T>1.5 \ {\rm GeV}$)   & $139 \ {\rm pb}$ \\
\hline
\end{tabular}
\end{center}
\caption{\em 
Predictions of different calculations
for the total diffractive $\dstar $ cross section 
in the kinematic regions $x_{\pom} < 0.04\;$ 
and $x_{\pom} < 0.01\,$ 
compared with the measured cross sections.}
\label{table:model}
\end{table}
%
In Tabel~\ref{table:model} the total visible 
cross section is compared with predictions 
from different theoretical models.
%
For all calculations
the charm mass was set to $m_c = 1.5 \ {\rm GeV}$, $\Lambda_{QCD}$ was chosen to be 
to $0.20 \ {\rm GeV}$ and 
the number of active quark flavors in the % first order 
expression for 
$\alpha_s$ was taken to be $N_f = 4$.
The data are compared with two calculations based on the collinear factorization approach, 
using the parton distributions obtained from the LO (NLO) DGLAP
analysis of the reduced diffractive cross section from H1 \cite{H1_F2D3_prel}: 
%
\vspace{-3mm}
\begin{itemize}
\item
A next-to-leading order (NLO) calculation using a diffractive version of
the program HVQDIS~\cite{hvqdis,hvqdiff} with the NLO diffractive parton densities.
%
For this calculation the renormalization and factorisation scales 
were set to $\mu_f^2 = \mu_r^2 = Q^2 + 4 m_c^2$.
%
The Peterson fragmentation function was used with $\epsilon = 0.078$.
%
The uncertainties on the NLO calculation correspond to a
variation of the renormalization 
scale (preserving  $\mu_f = \mu_r$)
by factors of $1/4$ and $4$, 
%(shown as the inner band in the differential distributions), 
a variation of the charm mass within $m_c = 1.35 ... 1.65 \ {\rm GeV}$ 
and a variation of the $\epsilon$ parameter between $0.035$ and $0.1$. 
%(shown as the outer band in the differential distributions).
%
These variations are performed separately and the uncertainties are
added in quadrature.
%
%\par
\item
A calculation based on 
${\cal O}(\alpha_s)$ matrix elements and the LO diffractive parton densities,
supplemented with initial and final state parton showers
as implemented in the Monte Carlo event generator
\rapgap~\cite{RAPGAP,RAPGAP208}. 
%hannes
%{\bf check parameters ???}
The $D^*$ meson was
fragmented according to the Lund string model~\cite{jetset}. 
The
renormalization scale and the factorization scale
were set to $\mu_f^2 = \mu_r^2 = Q^2 + p_{T}^{2} + 4 m_c^2$. The LO version
of the diffractive parton densities were used~\protect\cite{H1_F2D3_prel}. For the numbers
presented here, no variation of scales, the charm-quark mass or the fragmentation 
parameters was performed.
%hannes
\end{itemize}
%
%As indicated in Table~\ref{table:model}
The calculated cross sections for the two models 
are given in Tab.~\ref{table:model} and are found to be lower
than the data in both regions $\xpom <0.04$ and
$\xpom<0.01$.
%hannes Paul T comment
However, the predictions are still consistent with the data within the estimated experimental 
and theoretical uncertainties.
The agreement between data and the NLO calculation 
%hannes
%in all differential shapes is suggestive
%f the validity of the hard scattering factorization implemented in
%the calculation. 
supports the validity of the hard scattering factorization 
%(at least at the present level of precision) 
which is applied in the calculations. 
%hannes
%two calculations result in lower cross sections than the one observed,
%but still  
%
%hannes
%Taking into account the different phase space of the measurement 
%($\my < 1.6 \, {\rm GeV}$ and $|t|<1 \, {\rm GeV^{2}}$),  the agreement 
%appears still to be reasonable.
%hannes
\par
%hannes following Paul T comment
For $x_{\pom}< 0.01$ the data are also compared to 
a prediction from the perturbative 2-gluon approach 
'BJKLW'~\cite{\BJKLW} 
using the un-integrated gluon density~\cite{jung-dis03} obtained from the 
inclusive structure function $F_2$ evolved by the CCFM evolution equations.
%hannes following Paul T comment
These calculations in the perturbative 2-gluon approach are applicable only in the region of small
$x_{\pom}$, where contributions from quark exchange can be neglected.
%hannes
%
% 
As this calculation is valid only in the perturbative region, 
a cut on the transverse momentum of the gluon needs to be applied
for the process $c\bar{c}g$, 
which is also shown in Tab.~\ref{table:model}.
%
Using a cut of $p_T > 1.5 \, {\rm GeV}$ the visible cross section in the range
$x_{\pom}<0.01$ is well reproduced.
%
%hannes PaulT comment
Varying the cut to $p_T > 2 \, {\rm GeV}$ leads to a $\sim7 \%$ variation of the cross section. 
%hannes
%(see Table~\ref{table:model}).
%
%The observation of a large gluon transverse momentum
%close to the rapidity gap would be in contradiction to the collinear
%factorization approach, since in this region only small $\pt$ diffractive
%remnants are expected.  

\subsection{Differential cross sections}

\paragraph{Measurements for \boldmath$\xpom<0.04$:}
%
In Figs.~\ref{fig:betaxpomzpom} and \ref{fig:q2ptgpeta} 
cross sections differential in various 
variables are shown
and compared to the NLO calculation~\cite{hvqdis,hvqdiff} in the collinear approach
(for details see previous section).
%, 
%which was detailed in the previous section.
%
The cross sections represent average values over the intervals shown in the figures.
%
In Fig.~\ref{fig:betaxpomzpom} the cross section is shown 
as a function of the variables
%the diffractive kinematic variables
$\xpom\,$, $\beta\,$ and $\zpomobs\,$.
%hannes Paul T comment
%which are characteristic for the kinematics of the diffractive exchange.
%hannes
%which characterize the longitudinal momentum flow from the
%proton through the diffractive exchange to the quark struck
%by the photon.
%
Figure~\ref{fig:q2ptgpeta} shows the cross section as a function of
the event kinematic variables $Q^2\,$ and 
$y\,$ and as a function of the $\dstar$ transverse momentum 
$p_{T}\,$ and rapidity
$\eta$. 
%of the $D^{*}$. 
%
As can be seen from Figs.~\ref{fig:betaxpomzpom} and \ref{fig:q2ptgpeta}, 
the differential 
cross sections are reproduced by the NLO calculation 
within the uncertainties in all quantities shown. 
%
In Fig.~\ref{fig:xpomNLORG} the cross section in $\xpom$ is shown again together 
with the predictions from the NLO calculation and  
from the LO calculation as implemented in \rapgap\ ~\cite{RAPGAP,RAPGAP208}
(for details see previous section).
%A calculation based on leading order 
%${\cal O}(\alpha_s)$ matrix elements 
%supplemented with initial and final state parton shower~\cite{RAPGAP,RAPGAP208}.
%hadron level MC 
%event generator \rapgap\ supplemented with initial and final state parton showers.
%
%hannes Paul T comments
%As can be seen the predictions from \rapgap\ are in nice agreement with the full NLO
As can be seen from Fig.~\ref{fig:xpomNLORG} the predictions from \rapgap\ are in 
agreement with the full NLO calculations. 
%
In Fig.~\ref{fig:ptZEUS} the cross section is shown as a function of $p_{T}$ and compared 
to the measurement of ZEUS~\cite{ZEUS-diffcharm04}. 
%
The ZEUS data points were rescaled to the kinematic range of 
this paper, using the \rapgap\ Monte Carlo generator~\cite{RAPGAP,RAPGAP208} 
and applying an additional 10 \% correction for the different $M_Y$ range.
%
Both measurements are in good agreement.
\vspace{-5mm}

\paragraph{Measurements for \boldmath$\xpom<0.01$:}
%
In Fig.~\ref{fig:xpomlt0.01} the differential cross sections for the
region \mbox{$x_{\pom}<0.01$} are shown and compared both to the NLO calculation~\cite{hvqdis,hvqdiff} and to the
prediction from the perturbative 2-gluon calculation of {\it BJKLW}~\cite{\BJKLW}. 
%
The NLO calculation falls below the data in all differential
bins, but still agrees within errors.
%
The perturbative 2-gluon calculation of {\it BJKLW} 
uses an un-integrated gluon density, which is taken from inclusive measurements~\cite{jung-dis03}.
%
No extra free parameter or assumption for the diffractive mechanism is introduced
except for the choice of the cut-off at $\,p_{T}>1.5 \, {\rm GeV}$ for the gluon in the
$c\bar{c} g$ process.
With this cut-off inclusive jet data are described well~\cite{Aktas:2003ja}.
%
As can be seen in Fig.~\ref{fig:xpomlt0.01} also the diffractive $\dstar$ measurement is 
described well in all differential bins.
% 
%---------------------------------------------------------------------------------------------------
\section{Conclusion}
\label {section:conclusion}
%---------------------------------------------------------------------------------------------------

A new measurement of diffractive open charm production in DIS at HERA
has been presented using an integrated luminosity of 42.6$\;\mbox{pb}^{-1}$ corresponding to a
data sample 
three times larger 
than in a previous publication~\cite{Adloff:2001wr}.
%
The total $\dstar$ production cross section in the kinematic range of 
$2 < Q^2 < 100 ~{\rm GeV^2}$,
$0.05 < y < 0.7$,
$\xpom < 0.04$,
$M_Y < 1.6 ~{\rm GeV}$,
$|t| < 1 ~{\rm GeV^2}$,
$\ptlab > 2 \ {\rm GeV}$ and
$|\etalab|< 1.5$
is measured to be $ 333 \pm 38 \ {\rm (stat.)} \pm 54 \ {\rm (syst.)} \ {\rm pb}$.
%
This measurement is in agreement with previous measurements of H1~\cite{Adloff:2001wr}
and ZEUS~\cite{ZEUS-diffcharm04}.
%
When restricting the measurement to the range $\xpom < 0.01$ the 
cross section reduces to $131 \pm 24 (stat.) \pm 24 (syst.) \ {\rm pb}$.
%
The cross section has been measured differentially
as a function of various kinematic variables.
%of $ \xpom\,$,
%$\beta\,$, $\zpomobs\,$,
%$Q^2\,$, $y\,$,
%$\ptg,$  and $\etala\,$.
%
%hannes
Different QCD calculations 
%hannes 
are compared with the measurement.
%
Calculations based on 
H1 diffractive parton densities, 
extracted from
fits to $\fiidiii$ in
the collinear factorization approach and 
performed in leading and next-to-leading order pQCD,
are below the data but still agree within the errors.
%
They describe the observed shapes of the differential
cross sections well.
%
%hannes
The agreement supports the validity of the hard scattering
%hannes
factorization, whereby 
diffractive parton densities determined from inclusive
diffractive processes are universal and can be applied to
predict exclusive processes such as charm production or diffractive 
dijet 
production~\cite{h1_diff_dijets,h1_diff_dijets_eps03,h1_diff_dijets_ichep04}, 
which 
probe the gluonic content of the parton densities.
%
In the restricted kinematic region of $\xpom<0.01$ the data are 
also compared to the predictions of a calculation based on 
the perturbative 2-gluon approach using an un-integrated gluon density,
%
with which good agreement of the calculation is observed in both the measured 
inclusive cross section and in all differential cross sections.
%$~\cite{jung-dis03}
%{\it BJKLW}~\cite{\BJKLW} 
% obtained from a CCFM evolution to the 
%inclusive structure function $F_2$.
%
\clearpage 
\bibliographystyle{mysty} 
\raggedright 
\bibliography{ref}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\begin{figure}
  \setlength{\unitlength}{1cm}
  \begin{picture}(14.,16.)
    \put( 6.8, 13.7){\large a)}
    \put(14.8, 13.0){\large b)}
    \put( 6.8,  6.5){\large c)}
    \epsfig{file=eps/dstar.nlo.std.c.eps,width=1.\linewidth}
  \end{picture}
\caption{\em
Differential cross sections for $D^*$
meson production in diffractive DIS, shown as a function of 
a) $\,z_\pom$, an estimator for the longitudinal momentum fraction of the diffractive exchange
entering the hard process, 
b) $\,x_\pom$, the longitudinal proton momentum fraction taken by the diffractive exchange and 
c) $\,\beta$, an estimator for the longitudinal momentum fraction of the diffractive exchange 
carried by the struck quark.
%
All cross sections represent the average value over the corresponding bin.
%
The data are shown as points with error bars (inner: statistical, outer: total).
%
They are compared with a  
next-to-leading order QCD calculation
as implemented in a diffractive version of the program HVQDIS~\cite{hvqdis,hvqdiff},
using the NLO diffractive parton distributions from \cite{H1_F2D3_prel}.  
%
The nominal predictions are shown as the central lines of the error bands.
%
The inner error band represents the renormalization scale uncertainty,
while the outer error band shows the total uncertainty, which includes
variations of the charm mass in the range $m_c=1.35 \ldots 1.65 \rm\
GeV$ and of the parameter of the Peterson fragmentation function
$\epsilon=0.035 \ldots 0.100$, added in quadrature.
}
\label{fig:betaxpomzpom}
\end{figure}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\begin{figure}
  \setlength{\unitlength}{1cm}
  \begin{picture}(14.,16.)
    \put( 6.8, 13.7){\large a)}
    \put(14.8, 13.0){\large b)}
    \put( 6.8,  6.5){\large c)}
    \put(14.8,  6.5){\large d)}
    \epsfig{file=eps/dstar.nlo.std.b.eps,width=1.\linewidth}
  \end{picture}
\caption{\em 
Differential cross sections for $D^*$ meson production in diffractive DIS,
shown as a function of 
a) the photon virtuality $Q^2$,
b) the inelasticity $y$,
c) the transverse momentum $p_{T, D^*}$ and 
d) the pseudorapitdy $\eta_{D^*}$
of the $\dstar$ meson.
%
All cross sections represent the average value over the corresponding bin.
%
The data are shown as points with error bars (inner: statistical, outer: total).
%
They are compared with a  
next-to-leading order QCD calculation~\cite{hvqdis,hvqdiff},
using the NLO diffractive parton distributions from~\cite{H1_F2D3_prel}.  
The nominal predictions are shown as the central lines of the error bands.
%
For details see Fig.~\protect\ref{fig:betaxpomzpom}.
}
\label{fig:q2ptgpeta}
\end{figure}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\begin{figure}
\center{\epsfig{file=eps/dstar.nlo.rapgap.eps,width=.8\linewidth}}
%
\caption{ \em
Differential cross sections for $D^*$
meson production in diffractive DIS, shown as a function of $\xpom$,  
the longitudinal proton momentum fraction taken by the diffractive
exchange. 
%
All cross sections represent the average value over the corresponding bin.
%
The data are shown as points with error bars (inner: statistical, outer: total).
%
They are compared with a  
next-to-leading order QCD calculation~\cite{hvqdis,hvqdiff},
using the NLO diffractive parton distributions from~\cite{H1_F2D3_prel}.
For details see Fig.~\protect\ref{fig:betaxpomzpom}.
%
Also shown are predictions obtained with 
the LO hadron level Monte Carlo event generator \rapgap\ 
(dot-dashed curve).
%
}
\label{fig:xpomNLORG}
\end{figure}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\begin{figure}
\center{\epsfig{file=eps/dstar.nlo.pt.zeus.eps,width=0.8\linewidth}}
\caption{\em
Differential cross section for $D^*$ meson production in diffractive DIS, 
shown as a function of the transverse momentum $p_{T,D^*}$.
%
All cross sections represent the average value over the corresponding bin.
%
The data are shown as points with error bars (inner: statistical, outer: total).
%
They are compared with a  
next-to-leading order QCD calculation~\cite{hvqdis,hvqdiff},
using the NLO diffractive parton distributions from~\cite{H1_F2D3_prel}.
For details see Fig.~\protect\ref{fig:betaxpomzpom}.
%
Also shown is the measurement from ZEUS~\cite{ZEUS-diffcharm04},
rescaled to the phase space region investigated here. 
For this comparison the binning has been changed.
The data points of the ZEUS measurement are slightly displaced for visibility.
%
}
\label{fig:ptZEUS}
\end{figure}
%\vfill
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\begin{figure}
  \setlength{\unitlength}{1cm}
  \begin{picture}(14.,16.)
    \put( 6.8, 13.0){\large a)}
    \put(14.8, 13.7){\large b)}
    \put( 6.8,  6.5){\large c)}
    \put(14.8,  6.5){\large d)}
    \epsfig{file=eps/dstar.nlo.2g.eps,width=1.\linewidth}
  \end{picture}
\caption{\em
Differential cross sections for $D^*$ meson production in diffractive DIS, 
in the restricted kinematic region $\xpom<0.01$, shown as a function of 
a) $\,z_\pom$, an estimator for the longitudinal momentum fraction of the diffractive exchange
entering the hard process, 
b) $\,x_\pom$, the longitudinal proton momentum fraction taken by the diffractive exchange,
c) the transverse momentum $p_{T, D^*}$ and 
d) the pseudorapitdy $\eta_{D^*}$ of the $\dstar$ meson.
%
All cross sections represent the average value over the corresponding bin.
%
The data are shown as points with error bars (inner: statistical, outer: total).
%
They are compared with a  
next-to-leading order QCD calculation~\cite{hvqdis,hvqdiff},
using the NLO diffractive parton distributions from~\cite{H1_F2D3_prel}.  
The nominal predictions are shown as the central lines of the error bands.
%
For details see Fig.~\protect\ref{fig:betaxpomzpom}.
% 
Also shown is a prediction from the perturbative 2-gluon approach of {\it BJKLW}~\cite{\BJKLW} 
using the un-integrated gluon density obtained from a fit assuming CCFM evolution to the 
inclusive structure function $F_2$~\cite{jung-dis03} with a cut of $p_{T}>1.5 \, {\rm GeV}$ 
for the gluon in the
$c\bar{c} g$ process 
(dot-dashed curve).
}
\label{fig:xpomlt0.01}
\end{figure}

\end{document}


