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\begin{document}  

% The rest
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\begin{titlepage}

\begin{center}
 \begin{small}
 \begin{tabular}{llrr}
 Submitted to & & &
% \epsfig{file=H1logo_col.epsi,width=1.5cm}  \epsfig{file=zeus_logo.eps,width=1.1cm}
\\[.2em]
 \hline
 \multicolumn{4}{l}{{\bf
                 23rd International Symposium on Lepton-Photon Interactions at High Energy,
LP2007},} \\
 \multicolumn{4}{l}{August 13-18,~2007,~Daegu, Republic of Korea.} \\
\hline
   \multicolumn{4}{l}{\footnotesize {\it Electronic Access:
     www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\multicolumn{4}{r}{H1prelim-07-171}\\[.2em]
\multicolumn{4}{r}{August 2007}\\[.2em]

 \end{tabular}
 \end{small}
 \end{center}


%\begin{flushleft}

%DESY 05-110 \hfill ISSN 0418-9833 \\
%July 2005
%\end{flushleft}

\vspace{2cm}

\begin{center}
\begin{Large}
  
   {\bf {\boldmath {Measurement of $F_2^{c\bar{c}}$ and 
 $F_2^{b\bar{b}}$
     \\ using the H1 Vertex Detector at HERA}}}

%Measurement of F_2^ccbar and F_2^bbbar using the H1
%Vertex Detector at HERA

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
  \noindent 
The inclusive charm and beauty cross sections are measured
in $e^-p$ collisions at HERA in the kinematic region 
of photon virtuality
$12 \le Q^2 \le 650~{\rm GeV}^2$ 
and Bjorken scaling variable $0.0002 \le x \le 0.032$. 
The data were collected with the H1 detector in 2006
corresponding to an integrated luminosity of $54 ~{\rm pb^{-1}}$. The charm and
beauty fractions are determined using a method based on the impact
parameter, in the transverse plane, of tracks to the primary vertex,
as measured by the H1 vertex detector. The measurements are compared with
previous data and NLO predictions.
\end{abstract}

\vspace{1.5cm}

%\begin{center}
%To be submitted to {\em Eur. Phys. J.} {\bf C}
%\end{center}

\end{titlepage}


\newpage


\section{Introduction}
In this paper measurements of the charm ($c$) and beauty ($b$) contributions to the
inclusive proton structure function $F_2$ are made in
Deep Inelastic Scattering (DIS) at HERA, using information from the H1
vertex detector, for values of the negative square of the four
momentum of the exchanged boson 
$12 \le Q^2 \le 650$~${\rm GeV}^2$, and of Bjorken $x$, $0.000197 \le x \le 0.032$. 
The analysis is based on a sample of $e^-p$ neutral current
scattering events corresponding to an integrated luminosity of $54$
${\rm pb}^{-1}$, taken in the year 2006, at an $ep$ centre of
mass energy $\sqrt{s} = 319~{\rm GeV}$, with a proton beam energy of
$920~{\rm GeV}$.
%The analysis is performed on data taken during 2006 when HERA collided
%electrons with protons and corresponds to an integrated luminosity of 
%$54 ~{\rm pb^{-1}$. 
The analysis method employed is similar to that used
by H1 in measurements of HERA-I data \cite{Aktas:2004az,Aktas:2005iw}. 



%In this high $Q^2$ region a fraction of
%$\sim 18 \%$ ($\sim 3 \%$) of DIS events contain $c$ ($b$) quarks. 
%It was found that perturbative QCD (pQCD) calculations at next-to-leading
%order (NLO) gave a good description of the data.  od,
%to extend the measurements to the range of lower $Q^2$, 

Events containing heavy quarks are distinguished from those containing
only light quarks by reconstructing the displacement of tracks from
the primary vertex, using precise spatial information from the H1
vertex detector.  The long lifetimes of $c$ and $b$ flavoured hadrons
lead to larger displacements than for light quark events. The charm
structure function $F_2^{c\bar{c}}$ and the beauty structure function
$F_2^{b\bar{b}}$ are obtained from the measured $c$ and $b$ cross
sections after small corrections for the longitudinal structure
functions $F_L^{c\bar{c}}$ and $F_L^{b\bar{b}}$. 



\section{Monte Carlo Simulation}

Monte Carlo simulations are used to correct for the effects of the
finite detector resolution, acceptance and efficiency.  The Monte
Carlo program RAPGAP\cite{Jung:1993gf} is
used to generate DIS events for the processes $ep \rightarrow
eb\bar{b}X$, $ep
\rightarrow ec\bar{c}X$ and $ep \rightarrow eqX$ where $q$ is a light
quark of flavour $u$, $d$ or $s$.  The Monte Carlo program
CASCADE\cite{cascade} is also used to produce $b$ and $c$ events.
RAPGAP combines $\cal{O}$($\alpha_s$) matrix elements with higher
order QCD effects modelled by the emission of parton showers. The
heavy flavour event samples are generated according to the massive
photon gluon fusion (PGF) matrix element with the mass of the $c$ and
$b$ quarks set to $m_c=1.5~{\rm GeV}$ and $m_b=4.75~{\rm GeV}$,
respectively.  The DIS cross section is calculated using the leading
order (LO) 3-flavour parton distribution functions (PDFs) from
\cite{Martin:2006qz}. CASCADE is an implementation of the CCFM\cite{ccfm2}
evolution equation and uses off shell  matrix elements convoluted with
$k_t$ unintegrated proton parton distributions.


The partonic system for all generated events is fragmented according
 to the LUND string model implemented within the PYTHIA
 program\cite{Sjostrand:2001yu}.  The HERACLES
 program\cite{Kwiatkowski:1990es} calculates single photon radiative
 emissions off the lepton line, virtual and electroweak corrections.
% The Monte Carlo program PHOJET\cite{Engel:1995yd} is used to simulate
% the background contribution from photoproduction ($\gamma p
% \rightarrow X$).

The samples of events generated for the $uds$, $c$, and $b$ processes
are passed through a detailed simulation of the detector response
based on the GEANT3 program\cite{Brun:1978fy}, and through the same
reconstruction software as is used for the data. We use all $b$ and
$c$ event statistics from both RAPGAP and CASCADE to compare with and
correct the data.
%A total of $50$
%million $uds$ events, $9$ million $c$ events and $ 1$ million $b$
%events were simulated to evaluate the cross sections, corresponding to
%luminosities of $90$~${\rm pb}^{-1}$, $160$~${\rm pb}^{-1}$ and
%$980$~${\rm pb}^{-1}$, respectively.



\section{H1 Detector}

Only a short description of the H1 detector is given here; a full
description may be found in\cite{Abt:1997xv}. A right handed
coordinate system is employed at H1 that has its $z$-axis pointing in
the proton beam, or forward, direction and $x$ ($y$) pointing in
the horizontal (vertical) direction.


Charged particles are measured in the central tracking detector (CTD).
This device consists of two cylindrical drift chambers interspersed
with $z$-chambers to improve the $z$-coordinate reconstruction and
multi--wire proportional chambers mainly used for triggering. The CTD
is situated in a uniform $1.15\,{\rm T}$ magnetic field, enabling
momentum measurement of charged particles over the polar angular
range\footnote{\noindent{ The angular coverage of each detector
component is given for the interaction vertex in its nominal
position.}}  $20^\circ< \theta<160^\circ$.

The CTD tracks are linked to hits in the vertex detector (central
silicon tracker CST)\cite{cst} to provide precise spatial track
reconstruction. The CST consists of two layers of double-sided silicon
strip detectors surrounding the beam pipe, covering an angular range
of $30^\circ< \theta<150^\circ$ for tracks passing through both
layers.   The information on the $z$-coordinate of the CST tracks
is not used in the analysis presented in this paper. For CTD tracks
with CST hits in both layers the transverse distance of closest
approach (DCA) to the nominal vertex in $x$--$y$ can be measured with
a resolution of $33\;\mu\mbox{m} \oplus 90 \;\mu\mbox{m} /p_T
[\mbox{GeV}]$, where the first term represents the intrinsic
resolution (including alignment uncertainty) and the second term is
the contribution from multiple scattering in the beam pipe and the
CST; $p_T$ is the transverse momentum of the track.


The track detectors are surrounded in the forward and central
directions ($4^\circ<\theta<155^\circ$) by a fine grained liquid argon
calorimeter (LAr) and in the backward region
($153^\circ<\theta<178^\circ$) by a lead--scintillating fibre
calorimeter (SPACAL)\cite{Nicholls:1996di} with electromagnetic and
hadronic sections. These calorimeters provide energy and angular
reconstruction for final state particles from the hadronic system and
are also used in this analysis to measure and identify the scattered
electron.  
%A planar drift chamber (BDC~\cite{Adloff:2000qk}),
%positioned in front of the SPACAL ($151^\circ<\theta<178^\circ$),
%measures the angle of the scattered electron and allows suppression of
%photoproduction background, where particles from the hadronic final
%state fake a electron signal.

Electromagnetic calorimeters situated downstream in the electron beam
direction allow detection of photons and electrons scattered at very
low $Q^2$. The luminosity is measured from the rate of photons
produced in the Bethe-Heitler process $ep\rightarrow ep\gamma$.



\section{Experimental Method}

\subsection{Event and Track Selection}

The events are selected by requiring a compact electromagnetic cluster
in either the LAr or SPACAL calorimeters.  The $z$ position of the interaction
vertex, reconstructed by one or more charged tracks in the tracking
detectors, must be within $\pm 20~{\rm cm}$ of the centre of the
detector to match the acceptance of the CST.  Photoproduction events
are suppressed by requiring $\sum_{i} (E_i - p_{z,i}) >35~{\rm GeV}$.
Here, $E_i$ and $p_{z,i}$ denote the energy and longitudinal momentum
components of a particle and the sum is over all final state particles
including the scattered electron and the hadronic final state
(HFS). The HFS particles are reconstructed using a combination of
tracks and calorimeter deposits in an energy flow algorithm that
avoids double counting. The event kinematics, $Q^2$ and the
inelasticity variable $y$, are reconstructed with the `$e\Sigma$'
method\cite{Bassler:1994uq}, which uses the scattered electron and the
HFS.  The Bjorken scaling variable $x$ is obtained from $x =
Q^2/sy$. In order to have good acceptance in the SPACAL and to ensure that the
HFS has a significant transverse momentum, events are selected in the
range $6.3 < Q^2 < 1585 \ {\rm GeV^2}$. The analysis is restricted to
$0.07<y<0.625$ to ensure that the direction of the quark which is struck
by the photon is mostly in the CST angular range and to reduce
photoproduction background.  
%A further cut of
%$y<0.63$ is imposed for events with $Q^2 < 18$~${\rm GeV}^2$ to reduce
%photoproduction background.

%The triggers used in the analysis require a SPACAL energy deposit in
%association with a loose track requirement. Although these triggers
%are almost $100\%$ efficient, not all events could be recorded, due to
%the large rate for low $Q^2$ events. A fraction of events is rejected at
%the first trigger level (L1) and final trigger level (L4).  The Monte
%Carlo events are assigned weights to account for the events rejected
%at L1 while the data events are assigned weights to account for the
%events rejected at L4.  The weights are largest for those events with
%an electron at low radius and low energy.
% The overall effect of the trigger is a reduction of the effective
% luminosity by a factor of about $10$ for the lowest $Q^2$ bin and
% $1.4$ for the highest. After applying the event weights and the
% inclusive selection detailed above, the total number of events is
% about $1.5$ million. The background from photoproduction events is
% estimated from the PHOJET Monte Carlo simulation. In most of the $y$
% range this background is negligible and does not exceed $9\%$ in
% any $x$-$Q^2$ bin used in this analysis.


%The primary event vertex in $r$--$\phi$ is reconstructed from all
%tracks (with or without CST hits) and the position and spread of the
%beam interaction region \cite{Aktas:2004az}.  
The position of the beam interaction region, calculated at regular
time intervals using information from tracks with CST hits, is used
as the position of the primary event vertex in $r$--$\phi$.
% is reconstructed from all
%tracks (with or without CST hits) and the position and spread of the
%beam interaction region \cite{Aktas:2004az}.  
The impact parameter of
a track, which is the transverse distance of closest approach (DCA) of
the track to the primary vertex point, is only determined for those
tracks which are measured in the CTD and have at least one CST hit
linked (referred to as CST tracks). Only CST tracks with a transverse
momentum $>0.5~{\rm GeV}$ are included in the DCA and related
distributions that are used to separate the different quark
flavours. 
%In the kinematic range of this measurement, the fraction of
%$c$ ($b$) events that have at least one charged track within the
%angular range of the CST, with transverse momentum $>0.5~{\rm GeV}$ and
%originating from the decay of a heavy flavoured hadron, is expected to
%be $82\%$ ($96\%$), as determined from the Monte Carlo simulation. The
%efficiency to obtain a CST track from a CTD track is $76\%$, within
%the angular range of the CST.

In order to determine a signed impact parameter ($\delta$) for a
track, the azimuthal angle of the struck quark $\phi_{\rm quark}$ must
be determined for each event. To do this, jets with a minimum $p_T$ of
$1.5 \ {\rm GeV}$, in the angular range $15^\circ < \theta < 155^{\rm
o}$, are reconstructed using the invariant $k_T$ algorithm\cite{KTJET}
in the laboratory frame using all reconstructed HFS particles. The
angle $\phi_{\rm quark}$ is defined as the $\phi$ of the jet with the
highest transverse momentum or, if there is no jet reconstructed in
the event, as $180^\circ-\phi_{\rm elec}$, where $\phi_{\rm elec}$ is
the azimuthal angle of the electron in degrees.  The direction
defined in the transverse plane by $\phi_{\rm quark}$ and the primary
vertex is called the quark axis.
Approximately $95\%$ ($99\%$) of $c$ ($b$) events have $\phi_{\rm quark}$
reconstructed from a jet, as determined from the Monte Carlo simulation.

%The difference between the reconstructed to the true $\phi_{\rm
%quark}$ (defined as the azimuthal angle of the quark with highest
%transverse momentum) is estimated from the Monte Carlo simulation to
%have a resolution of about $5^\circ$ for events with a reconstructed
%jet.
% and $35^\circ$ for the rest. 
%The resolution of $\phi_{\rm quark}$
%is checked with events containing a reconstructed $D^*$
%meson. Figure~\ref{fig:deltaphi} shows the difference between the
%reconstructed $D^*$ azimuthal angle and $\phi_{\rm quark}$ for events
%with and without a reconstructed jet. Both distributions are well
%described by the Monte Carlo simulation.

If the angle between the quark axis and
the line joining the primary vertex to the point of DCA is less than
$90^\circ$, $\delta$ is defined as positive, and is defined as 
negative otherwise. Tracks with
azimuthal angle outside $\pm 90^\circ$ of $\phi_{\rm quark}$ are
rejected. The $\delta$ distribution, shown in figure~\ref{fig:dca}, is
seen to be asymmetric with positive values in excess of negative
values indicating the presence of long lived particles. It is found to
be well described by the Monte Carlo simulation.
Tracks with $|\delta|>0.1~{\rm cm}$ are rejected from the analysis
to suppress light quark events containing long lived strange particles.


\subsection{Quark Flavour Separation}
\label{quarkflavourseparation}

The method used in \cite{Aktas:2004az} to distinguish between the $c$,
$b$ and light quark flavours is used in the present analysis.  The
quantities $S_1$ and $S_2$ are defined as the significance
($\delta/\sigma(\delta)$) of the track with the highest and second
highest absolute significance, respectively, where $\sigma(\delta)$ is
the error on $\delta$.  Distributions of $S_1$ for events with only 1
reconstructed CST track and $S_2$ for events with $\ge2$ reconstructed
CST tracks are made.  Events in which $S_1$ and $S_2$ have opposite
signs are excluded from the $S_2$
distribution. Figure~\ref{fig:s1s2} shows the significance
distributions.  The simulation gives a reasonable description of the
data.

In order to reduce the uncertainty due to the resolution of $\delta$
and the light quark normalisation, the contents of the negative bins
in the significance distributions are subtracted from the contents of
the corresponding positive bins. The subtracted distributions are
shown in figure~\ref{fig:s1s2negsub}. It can be seen that the
resulting distributions are dominated by $c$ quark events, with a $b$
fraction increasing with significance. The light quarks contribute a
small fraction for all values of significance.

The fractions of $c$, $b$ and light quarks of the data are extracted
in each $x$--$Q^2$ interval using a least squares simultaneous fit to
the subtracted $S_1$ and $S_2$  distributions (as in
figure~\ref{fig:s1s2negsub}) and the total number of inclusive
events before any CST track selection. The $c$, $b$ and $uds$ Monte
Carlo simulation samples are used as templates.  The Monte Carlo $c$,
$b$ and $uds$ contributions in each $x$--$Q^2$ interval are scaled by
factors $P_c$, $P_b$ and $P_l$, respectively, to give the best fit to
the observed subtracted $S_1$ and $S_2$ and total
distributions. Only the statistical errors of the data and Monte Carlo
simulation are considered in the fit.  The fit to the subtracted
significance distributions mainly constrains $P_c$ and $P_b$, whereas
the overall normalisation constrains $P_l$.

The results of the fit to the complete data sample are shown in
figure~\ref{fig:s1s2negsub}. The fit gives a good description of all
the significance distributions, with a $\chi^2/ n.d.f$ of $26.2/31$.
Values of $P_c= 0.97 \pm 0.02$, $P_b= 0.86 \pm 0.08$ and $P_l= 1.062 \pm 0.005$ are 
obtained.  
The $c$ and $b$ scale factors are found to be
anti-correlated with an overall correlation coefficient of $-0.72$.
Acceptable $\chi^2$ values are also found for the
fits to the samples in the separate $x$--$Q^2$ intervals.  
%Since the same event may enter the $S_1$, $S_2$ and $S_3$ distributions, it was
%checked using a high statistics Monte Carlo simulation that
%this has negligible effect on the results of the fits with the present
%data statistics. 


The results of the fit in each $x$--$Q^2$ interval are converted to a
measurement of the `reduced $c$ cross section'
defined from
the differential cross section as
\begin{equation}
\tilde{\sigma}^{c\bar{c}} (x, Q^2) = \frac{{\rm d}^2\sigma^{c\bar{c}} }{{\rm d} x\,{\rm d} Q^2}  \frac {x Q^4 } {2 \pi \alpha^2 (1+ (1-y)^2)},
\end{equation}

\noindent using:
\begin{equation}
\tilde{\sigma}^{c\bar{c}} (x, Q^2) = 
\tilde{\sigma} (x, Q^2) \frac{P_c N^{\rm MC gen}_c}{P_c N^{\rm MC gen}_c+P_b N^{\rm MC gen}_b+P_l N^{\rm MC gen}_l}  
\delta_{\rm BCC},
\end{equation}
where $\tilde{\sigma} (x, Q^2)$ is the measured inclusive reduced
cross section from 
H1(\cite{Adloff:2000qk} for $Q^2 \le 60 \ {\rm GeV^2}$, otherwise\cite{H19900NCCC}) 
and $N^{\rm MC gen}_c$,
$N^{\rm MC gen}_b$ and $N^{\rm MC gen}_l$ are the number of $c$, $b$ and
light quark events generated from the Monte Carlo in each bin. A bin
centre correction $\delta_{\rm BCC}$ is applied using a NLO QCD
expectation for $\tilde{\sigma}^{c\bar{c}}$ to convert the bin
averaged measurement into a measurement at a given $x$--$Q^2$ point.
The NLO QCD expectation is calculated from the results of a fit
similar to that performed in~\cite{Adloff:1999ah} but using the FFNS
scheme to generate heavy flavours. A small correction ($\le 2.6\%$) 
for the beam energy difference is
applied, using the NLO QCD expectation, 
to the measurement of
$\tilde{\sigma} (x, Q^2)$ with $Q^2 \le 60 \ {\rm GeV^2}$ 
which was performed at a lower centre of
mass energy of $301~{\rm GeV}$ than the data presented here.  The
cross section is defined so as to include a correction for pure QED
radiative effects. Events that contain $c$ hadrons via the decay of
$b$ hadrons are not included in the definition of the $c$ cross
section. The differential $b$ cross section is evaluated in the same
manner.






\section{Results}
\label{results}
The measurements, shown as a function of $x$ for fixed values of
$Q^2$, of $\tilde{\sigma}^{c\bar{c}}$ are shown in
figure~\ref{fig:f2cc} and of $\tilde{\sigma}^{b\bar{b}}$ in
figure~\ref{fig:f2bb}. Also shown in these figures are the HERA I data
extracted using the displaced track method. All data show good
agreement for both $\tilde{\sigma}^{c\bar{c}}$ and
$\tilde{\sigma}^{b\bar{b}}$ for all measured $x$ and $Q^2$ values. We
therefore average the results using the method of~\cite{Glazov:2005rn}.
In this method the correlation  between the systematic errors of the
data points are taken into account. The averaged measurements are also shown
in figures figure~\ref{fig:f2cc} and \ref{fig:f2bb}.

The measurement of $\tilde{\sigma}^{c\bar{c}}$ are compared in
figure~\ref{fig:f2ccav} with those extracted from $D^*$ meson
measurements by H1~\cite{H1Dstar} and ZEUS~\cite{ZEUSDstar}, obtained
using a NLO program~\cite{Harris:1997zq} based on DGLAP evolution to
extrapolate the measurements outside the visible $D^*$ range.  The
measurements for $\tilde{\sigma}^{c\bar{c}}$ from the present
analysis, the HERA I data and the $D^*$ extraction methods are in good
agreement.

The  $\tilde{\sigma}^{c\bar{c}}$ data are compared with two predictions
from NLO QCD based on the variable flavour number scheme (VFNS) from
MRST\cite{Martin:2004dh} and CTEQ\cite{cteqvfns}, and with predictions
based on CCFM\cite{ccfm2} parton evolution.  The predictions provide a
reasonable description of the present data.


The $\tilde{\sigma}^{b\bar{b}}$ data are compared in
figure~\ref{fig:f2bbav} as a function of $x$ for fixed values of $Q^2$
with the two VFNS NLO QCD predictions and the CCFM prediction.  The
difference between the two VFNS NLO QCD calculations, which reaches a
factor $2$ at the lowest $Q^2$ and $x$, arises from the different
treatments of threshold effects by MRST and CTEQ.  The data are
compared with ZEUS data\cite{zeusf2b} in
figure~\ref{fig:f2bbavh1zeus}. The ZEUS cross sections are derived
from events with a jet and a muon, and Monte Carlo models used to
extrapolate over unseen phase space. The ZEUS data are somewhat higher
than the H1 measurements.
%Within the current experimental errors
%these differences cannot be resolved. 


The structure function $F_2^{c\bar{c}}$ is evaluated from the reduced cross section

\begin{equation}
\tilde{\sigma}^{c\bar{c}} =   F_2^{c\bar{c}}   - \frac{y^2 }{1+ (1-y)^2}  F_L^{c\bar{c}},
\label{eq:sigcc}
\end{equation}
where the longitudinal structure function $F_L^{c\bar{c}}$ is
estimated from the same NLO QCD expectation as used for the bin centre
correction.  The structure function $F_2^{b\bar{b}}$ is evaluated in
the same manner.





The measurements $F_2^{c\bar{c}}$ and $F_2^{b\bar{b}}$ are shown as a
function of $Q^2$ in figure~\ref{fig:f2ccq2} and
figure~\ref{fig:f2bbq2}. The $F_2^{b\bar{b}}$ values are compared with
the ZEUS measurements in figure~\ref{fig:f2bbq2h1zeus}.
%The measurements of $F_2^{c\bar{c}}$ and
%$F_2^{b\bar{b}}$ show positive scaling violations which increase with
%decreasing $x$.  
The data are compared with the VFNS QCD predictions
from MRST and CTEQ at NLO and a recent calculation at NNLO\cite{NNLO}. 
%The charm data are more precise than the spread in predictions of the QCD calculations.


%The measurements are also presented in
%figure~\ref{fig:frac} in the form of the fractional contribution to
%the total $ep$ cross section
%\begin{equation}
%f^{c\bar{c}} =  \frac{{\rm d}^2 \sigma^{c\bar{c}}} {{\rm d} x\, {\rm d} Q^2}
%/
%\frac{
%{\rm d}^2 \sigma}{ {\rm d} x\, {\rm d} Q^2
%}.
%\end{equation}
%The $b$ fraction $f^{b\bar{b}}$ is defined in the same manner.  
%In the present kinematic range the value of 
%$f^{c\bar{c}}$ is around $24\%$ on average and 
%increases slightly with increasing $Q^2$ and decreasing $x$.
%The value of $f^{b\bar{b}}$ increases rapidly with
%$Q^2$ from $0.4\%$ at $Q^2 = 12 \ {\rm GeV^2}$ to $1.5\%$ at 
%$Q^2 = 60 \ {\rm GeV^2}$. 
%The NLO QCD predictions of MRST shown in figure~\ref{fig:frac} are found to
%describe the data reasonably well.

%Table~\ref{tab:sig} gives a summary of the results including the breakdown of
%the systematic errors.


\section{Conclusion}

The differential charm and beauty cross sections in Deep Inelastic
Scattering are measured for a wide range of $Q^2$ and Bjorken $x$
using the impact parameters of tracks from decays of long lived $c$
and $b$ hadrons as reconstructed from the vertex detector, using a
part of the HERA II data.  The cross sections and derived structure
functions $F_2^{c\bar{c}}$ and $F_2^{b\bar{b}}$ are found to agree
with previous measurements and be described by by predictions of
perturbative QCD. A combination of the HERA I data with the HERA II
data has been performed resulting  in a more precise measurement.


 
%In this kinematic range the charm cross section contributes on average $24\%$
%of the inclusive $ep$ cross section, and the beauty fraction increases
%from $0.4\%$ at $Q^2 = 12 \ {\rm GeV^2}$ to $1.5\%$ at $Q^2 = 60 \
%{\rm GeV^2}$.  
% to be reasonably well described


%\section*{Acknowledgements}

%We are grateful to the HERA machine group whose outstanding efforts
%have made this experiment possible.  We thank the engineers and
%technicians for their work in constructing and maintaining the H1
%detector, our funding agencies for financial support, the DESY
%technical staff for continual assistance and the DESY directorate for
%support and for the hospitality which they extend to the non-DESY
%members of the collaboration.  We are grateful to S.~Kretzer,
%R.~S.~Thorne and W.~K.~Tung for providing us with their calculations
%and for productive discussions.





 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{thebibliography}{99}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\cite{Aktas:2004az}
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  %``Measurement of F2(c anti-c) and F2(b anti-b) at high Q**2 using the H1
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\ifpdf
\href{http://arXiv.org/ps/hep-ex/0411046}{[hep-ex/0411046].}
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[hep-ex/0411046].
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%%CITATION = HEP-EX 0411046;%%

\bibitem{Aktas:2005iw}
  A.~Aktas {\it et al.}  [H1 Collaboration],
  %``Measurement of F2(c anti-c) and F2(b anti-b) at low Q**2 and x using  the
  %H1 vertex detector at HERA,''
  Eur.\ Phys.\ J.\  C {\bf 45} (2006) 23
  [arXiv:hep-ex/0507081].
  %%CITATION = EPHJA,C45,23;%%


%%% RAPGAP MC
\bibitem{Jung:1993gf}
H.~Jung,
%``Hard diffractive scattering in high-energy e p collisions and the Monte Carlo
%generation RAPGAP,''
Comput.\ Phys.\ Commun.\  {\bf 86} (1995) 147;\\
%%CITATION = CPHCB,86,147;%%
\ifpdf
(see also 
\href{http://www.desy.de/~jung/rapgap/}
{http://www.desy.de/$\sim$jung/rapgap/}).
\else
(see also http://www.desy.de/$\sim$jung/rapgap/).
\fi

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

%\cite{Jung:2000hk}
\bibitem{cascade}
  H.~Jung and G.~P.~Salam,
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\ifpdf
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\else
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  %%CITATION = HEP-PH 0012143;%%


\bibitem{ccfm2}
M.~Ciafaloni,
%%``Coherence Effects In Initial Jets At Small Q**2 / S,''
Nucl.\ Phys.\ B {\bf 296} (1988) 49;
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S.~Catani, F.~Fiorani and G.~Marchesini,
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S.~Catani, F.~Fiorani and G.~Marchesini,
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G.~Marchesini,
%%``QCD coherence in the structure function and associated distributions at
%%small x,''
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\ifpdf
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[hep-ph/9412327].
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%%CITATION = HEP-PH 9412327;%%




%%% fixed flavour
\bibitem{Martin:2006qz}
  A.~D.~Martin, W.~J.~Stirling and R.~S.~Thorne,
  %``MRST partons generated in a fixed-flavour scheme,''
  Phys.\ Lett.\  B {\bf 636} (2006) 259
  [arXiv:hep-ph/0603143].
  %%CITATION = PHLTA,B636,259;%%


%%% pythia 6.2
%\cite{Sjostrand:2001yu}
\bibitem{Sjostrand:2001yu}
  T.~Sjostrand, L.~Lonnblad and S.~Mrenna,
  %``PYTHIA 6.2: Physics and manual,''
  arXiv:hep-ph/0108264.
  %%CITATION = HEP-PH/0108264;%%

%%% Heracles
\bibitem{Kwiatkowski:1990es}
A.~Kwiatkowski, H.~Spiesberger and H.~J.~M\"{o}hring,
%``Heracles: An Event Generator For E P Interactions At Hera Energies Including
%Radiative Processes: Version 1.0,''
Comput.\ Phys.\ Commun.\  {\bf 69} (1992) 155.
%%CITATION = CPHCB,69,155;%%

%%% GEANT
\bibitem{Brun:1978fy}
R.~Brun, R.~Hagelberg, M.~Hansroul and J.~C.~Lassalle,
%``Geant: Simulation Program For Particle Physics Experiments. User Guide And
%Reference Manual,''
CERN-DD-78-2-REV.
%\href{http://www.slac.stanford.edu/spires/find/hep/www?r=cern-dd-78-2-rev}{SPIRES entry}









\bibitem{Abt:1997xv}
I.~Abt {\it et al.}  [H1 Collaboration],
%``The Tracking, calorimeter and muon detectors of the H1 experiment at HERA ,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310 and 348.
%CITATION = NUIMA,A386,348;%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bibitem{cst}
% CST paper
D.~Pitzl {\it et al.},
%``The H1 silicon vertex detector,''
Nucl.\ Instrum.\ Meth.\ A {\bf 454}  (2000) 334
\ifpdf
\href{http://arXiv.org/ps/hep-ex/0002044}{[hep-ex/0002044].}
\else
[hep-ex/0002044].
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%%CITATION = HEP-EX 0002044;%%

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

\bibitem{Nicholls:1996di}
T.~Nicholls {\it et al.}  [H1 SPACAL Group],
%``Performance of an electromagnetic lead / scintillating 
%fiber calorimeter for the H1 detector,''
Nucl.\ Instrum.\ Meth.\ A {\bf 374} (1996) 149.
%%CITATION = NUIMA,A374,149;%%


%\cite{Bassler:1994uq}
\bibitem{Bassler:1994uq}
  U.~Bassler and G.~Bernardi,
  %``On the kinematic reconstruction of deep inelastic scattering at HERA: The
  %Sigma method,''
  Nucl.\ Instrum.\ Meth.\ A {\bf 361} (1995) 197
\ifpdf
\href{http://arXiv.org/ps/hep-ex/9412004}{[hep-ex/9412004].}
\else
  [hep-ex/9412004];
\fi
%%CITATION = HEP-EX 9412004;%%


%\cite{Ellis:tq}
\bibitem{KTJET}
S.~D.~Ellis and D.~E.~Soper,
%``Successive Combination Jet Algorithm For Hadron Collisions,''
Phys.\ Rev.\ D {\bf 48} (1993) 3160
\ifpdf
\href{http://arXiv.org/ps/hep-ph/9305266}{[hep-ph/9305266].}
\else
[hep-ph/9305266];
\fi
%%CITATION = HEP-PH 9305266;%%

S.~Catani, Y.~L.~Dokshitzer, M.~H.~Seymour and B.~R.~Webber,
%``Longitudinally invariant K(t) clustering algorithms for hadron hadron
%collisions,''
Nucl.\ Phys.\ B {\bf 406} (1993) 187.
%%CITATION = NUPHA,B406,187;%%


%% 99/00 low Q2 for F2 points
%\cite{Adloff:2000qk}
\bibitem{Adloff:2000qk}
  C.~Adloff {\it et al.}  [H1 Collaboration],
  %``Deep-inelastic inclusive e p scattering at low x and a determination of
  %alpha(s),''
  Eur.\ Phys.\ J.\ C {\bf 21} (2001) 33
\ifpdf
\href{http://arXiv.org/ps/hep-ex/0012053}{[hep-ex/0012053].}
\else
  [hep-ex/0012053].
\fi
%%CITATION = HEP-EX 0012053;%%


%%% high Q2 results for F2
\bibitem{H19900NCCC}
C.~Adloff {\it et al.}
\ifpdf \href{http://www-h1.desy.de/publications/H1publication.short_list.html}{[H1 Collaboration],}
\else [H1 Collaboration],
\fi
Eur.\ Phys.\ J {\bf C 30} (2003) 1
\ifpdf
\href{http://arXiv.org/ps/hep-ex/0304003}{[hep-ex/0304003.}
\else
[hep-ex/0304003].
\fi




%%% fit of which we use a FFNS version                             
\bibitem{Adloff:1999ah}
  C.~Adloff {\it et al.}  [H1 Collaboration],
  %``Measurement of neutral and charged current cross-sections in positron
  %proton collisions at large momentum transfer,''
  Eur.\ Phys.\ J.\ C {\bf 13} (2000) 609
\ifpdf
\href{http://arXiv.org/ps/hep-ex/9908059}{[hep-ex/9908059].}
\else
  [hep-ex/9908059].
\fi
%%CITATION = HEP-EX 9908059;%%

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



%\cite{Glazov:2005rn}
\bibitem{Glazov:2005rn}
  A.~Glazov,
  %``Averaging of DIS cross section data,''
  AIP Conf.\ Proc.\  {\bf 792} (2005) 237.
  %%CITATION = APCPC,792,237;%%


%%%%%%%%%%%%%%%%%%%%%% OTHER MEASUREMENTS
%\cite{Adloff:1996xq}
%\bibitem{H1ZEUSDstar}
%C.~Adloff {\it et al.}  [H1 Collaboration],
%%``Inclusive D0 and D*+- production in neutral current deep inelastic  e p
%%scattering at HERA,''
%Z.\ Phys.\ C {\bf 72} (1996) 593
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/9607012}{[hep-ex/9607012].}
%\else
%[hep-ex/9607012];
%\fi
%%%CITATION = HEP-EX 9607012;%%

%%\cite{Breitweg:1997mj}
%J.~Breitweg {\it et al.}  [ZEUS Collaboration],
%%``D* production in deep inelastic scattering at HERA,''
%Phys.\ Lett.\ B {\bf 407} (1997) 402
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/9706009}{[hep-ex/9706009].}
%\else
%[hep-ex/9706009];
%\fi
%%%CITATION = HEP-EX 9706009;%%


%%\cite{Adloff:1998vb}
%C.~Adloff {\it et al.}  [H1 Collaboration],
%%``Measurement of D* meson cross sections at HERA and determination of the
%%gluon density in the proton using NLO QCD,''
%Nucl.\ Phys.\ B {\bf 545} (1999) 21
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/9812023}{[hep-ex/9812023].}
%\else
%[hep-ex/9812023];
%\fi
%%%CITATION = HEP-EX 9812023;%%

%%\cite{Breitweg:1999ad}
%J.~Breitweg {\it et al.}  [ZEUS Collaboration],
% %``Measurement of D*+- production and the charm contribution to F2 in  deep
%%inelastic scattering at HERA,''
%Eur.\ Phys.\ J.\ C {\bf 12} (2000) 35
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/9908012}{[hep-ex/9908012].}
%\else
%[hep-ex/9908012].
%\fi
%%%CITATION = HEP-EX 9908012;%%


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

\bibitem{H1Dstar}
%\cite{Adloff:2001zj}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of D*+- meson production and F2(c) in deep inelastic  scattering
%at HERA,''
Phys.\ Lett.\ B {\bf 528} (2002) 199
\ifpdf
\href{http://arXiv.org/ps/hep-ex/0108039}{[hep-ex/0108039].}
\else
[hep-ex/0108039].
\fi
%%CITATION = HEP-EX 0108039;%%

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

\bibitem{ZEUSDstar}
%\cite{Chekanov:2003rb}
%\bibitem{Chekanov:2003rb}
S.~Chekanov {\it et al.}  [ZEUS Collaboration],
%``Measurement of D*+- production in deep inelastic e+- p scattering at HERA,''
Phys.\ Rev.\ D {\bf 69} (2004) 012004
\ifpdf
\href{http://arXiv.org/ps/hep-ex/0308068}{[hep-ex/0308068].}
\else
[hep-ex/0308068].
\fi
%%CITATION = HEP-EX 0308068;%%

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

%\bibitem{zeusBdis}
%S.~Chekanov {\it et al.}  [ZEUS Collaboration],
%%``Measurement of beauty production in deep inelastic scattering at HERA,''
%Phys.\ Lett.\ B {\bf 599} (2004) 173
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/0405069}{[hep-ex/0405069].}
%\else
%[hep-ex/0405069].
%\fi
%%%CITATION = HEP-EX 0405069;%%


%\bibitem{Aktas:2005zc}
%  A.~Aktas {\it et al.}  [H1 Collaboration],
%  %``Measurement of beauty production at HERA using events with muons and
%  %jets,''
%  Eur.\ Phys.\ J.\ C {\bf 41} (2005) 453
%\ifpdf
%\href{http://arXiv.org/ps/hep-ex/0502010}{[hep-ex/0502010].}
%\else
%[hep-ex/0502010].
%\fi
%%%CITATION = HEP-EX 0502010;%%


%%%%%%%%%%%%%%%%%%%%%% THEORY
\bibitem{Harris:1997zq}
 B.~W.~Harris and J.~Smith,
%``Charm quark and D*+- cross sections in deeply inelastic scattering at
%HERA,''
 Phys.\ Rev.\ D {\bf 57} (1998) 2806
\ifpdf
\href{http://arXiv.org/ps/hep-ph/9706334}{[hep-ph/9706334].}
\else
[hep-ph/9706334].
\fi
%%CITATION = HEP-PH 9706334;%%


\bibitem{Martin:2004dh}
A.~D.~Martin, R.~G.~Roberts, W.~J.~Stirling and R.~S.~Thorne,
%``Parton distributions incorporating QED contributions,''
Eur.\ Phys.\ J.\ C {\bf 39} (2005) 155
\ifpdf
\href{http://arXiv.org/ps/hep-ph/0411040}{[hep-ph/0411040].}
\else
[hep-ph/0411040].
\fi
%%CITATION = HEP-PH 0411040;%%

\bibitem{cteqvfns}
S.~Kretzer, H.~L.~Lai, F.~I.~Olness and W.~K.~Tung,
%``CTEQ6 parton distributions with heavy quark mass effects,''
Phys.\ Rev.\ D {\bf 69} (2004) 114005
\ifpdf
\href{http://arXiv.org/ps/hep-ph/0307022}{[hep-ph/0307022].}
\else
[hep-ph/0307022].
\fi
%%CITATION = HEP-PH 0307022;%%






% FFNS

%\bibitem{massive}
%%\bibitem{Laenen:1992zk}
%E.~Laenen, S.~Riemersma, J.~Smith and W.~L.~van Neerven,
%%``Complete O (alpha-s) corrections to heavy flavor structure functions in
%%electroproduction,''
%Nucl.\ Phys.\ B {\bf 392} (1993) 162;
%%CITATION = NUPHA,B392,162;%%

%%\bibitem{Laenen:1992xs}
%E.~Laenen, S.~Riemersma, J.~Smith and W.~L.~van Neerven,
%%``O(alpha-s) corrections to heavy flavor inclusive distributions in
%%electroproduction,''
%Nucl.\ Phys.\ B {\bf 392} (1993) 229.
%%%CITATION = NUPHA,B392,229;%%


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

% ACOT

%\bibitem{VFNS1}
%%\bibitem{Olness:1987ep}
%F.~I.~Olness and W.~K.~Tung,
%%``When Is A Heavy Quark Not A Parton? Charged Higgs Production And Heavy Quark
%%Mass Effects In The QCD Based Parton Model,''
%Nucl.\ Phys.\ B {\bf 308} (1988) 813;
%%%CITATION = NUPHA,B308,813;%%

%%\bibitem{Aivazis:1993kh}
%M.~A.~G.~Aivazis, F.~I.~Olness and W.~K.~Tung,
%%``Leptoproduction of heavy quarks. 1. General formalism and kinematics of
%%charged current and neutral current production processes,''
%Phys.\ Rev.\ D {\bf 50} (1994) 3085
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9312318}{[hep-ph/9312318].}
%\else
%[hep-ph/9312318];
%\fi
%%%CITATION = HEP-PH 9312318;%%

%%\bibitem{Aivazis:1993pi}
%M.~A.~G.~Aivazis, J.~C.~Collins, F.~I.~Olness and W.~K.~Tung,
%%``Leptoproduction of heavy quarks. 2. A Unified QCD formulation of charged and
%%neutral current processes from fixed target to collider energies,''
%Phys.\ Rev.\ D {\bf 50} (1994) 3102
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9312319}{[hep-ph/9312319].}
%\else
%[hep-ph/9312319];
%\fi
%%%CITATION = HEP-PH 9312319;%%

%%\bibitem{Kramer:2000hn}
%M.~Kr\"{a}mer, F.~I.~Olness and D.~E.~Soper,
%%``Treatment of heavy quarks in deeply inelastic scattering,''
%Phys.\ Rev.\ D {\bf 62} (2000) 096007
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0003035}{[hep-ph/0003035].}
%\else
%[hep-ph/0003035].
%\fi
%%CITATION = HEP-PH 0003035;%%

% MRST

%\bibitem{VFNS2}
%%\bibitem{Thorne:1997ga}
%R.~S.~Thorne and R.~G.~Roberts,
%%``An ordered analysis of heavy flavour production in deep inelastic
%%scattering,''
%Phys.\ Rev.\ D {\bf 57} (1998) 6871
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9709442}{[hep-ph/9709442].}
%\else
%[hep-ph/9709442];
%\fi
%%%CITATION = HEP-PH 9709442;%%
%
%
%%\bibitem{Thorne:1997uu}
%R.~S.~Thorne and R.~G.~Roberts,
%%``A practical procedure for evolving heavy flavour structure functions,''
%Phys.\ Lett.\ B {\bf 421} (1998) 303
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9711223}{[hep-ph/9711223].}
%\else
%[hep-ph/9711223];
%\fi
%%%CITATION = HEP-PH 9711223;%%

%%\bibitem{Thorne:2000zd}
%R.~S.~Thorne and R.~G.~Roberts,
%%``A variable number flavour scheme for charged current heavy flavour  structure
%%functions,''
%Eur.\ Phys.\ J.\ C {\bf 19} (2001) 339
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0010344}{[hep-ph/0010344].}
%\else
%[hep-ph/0010344];
%\fi
%%%CITATION = HEP-PH 0010344;%%


%
%\bibitem{Cacciari:1998it}
%M.~Cacciari, M.~Greco and P.~Nason,
%``The p(T) spectrum in heavy-flavour hadroproduction,''
%JHEP {\bf 9805} (1998) 007
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9803400}{[hep-ph/9803400].}
%\else
%[hep-ph/9803400];
%\fi
%%%CITATION = HEP-PH 9803400;%%



% referenced in cteq ringberg as VFNS
%\bibitem{Cacciari:2001td}
%M.~Cacciari, S.~Frixione and P.~Nason,
%``The p(T) spectrum in heavy-flavor photoproduction,''
%JHEP {\bf 0103} (2001) 006
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0102134}{[hep-ph/0102134].}
%\else
%[hep-ph/0102134].
%\fi
%%%CITATION = HEP-PH 0102134;%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Smith et al

%\bibitem{VFNS3}
%%Chuvakin:2000zj below references 2 O(alpha_s^2) VFNS treatments
%%\bibitem{Buza:1997nv}
%M.~Buza, Y.~Matiounine, J.~Smith and W.~L.~van Neerven,
%%``Comparison between the various descriptions for charm electroproduction  and
%%the HERA-data,''
%Phys.\ Lett.\ B {\bf 411} (1997) 211
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9707263}{[hep-ph/9707263].}
%\else
%[hep-ph/9707263];
%\fi
%%%CITATION = HEP-PH 9707263;%%
%
%%\bibitem{Chuvakin:1999nx}
%A.~Chuvakin, J.~Smith and W.~L.~van Neerven,
%%``Comparison between variable flavor number schemes for charm quark
%%electroproduction,''
%Phys.\ Rev.\ D {\bf 61} (2000) 096004
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9910250}{[hep-ph/9910250].}
%\else
%[hep-ph/9910250];
%\fi
%%%CITATION = HEP-PH 9910250;%%
%
%%\bibitem{Chuvakin:2000jm}
%A.~Chuvakin, J.~Smith and W.~L.~van Neerven,
%%``Bottom quark electroproduction in variable flavor number schemes,''
%Phys.\ Rev.\ D {\bf 62} (2000) 036004
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0002011}{[hep-ph/0002011].}
%\else
%[hep-ph/0002011].
%\fi
%%%CITATION = HEP-PH 0002011;%%


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

%%\cite{ccfm}
%\bibitem{ccfm}
%M.~Hansson and H.~Jung,
%``Status of CCFM: Un-integrated gluon densities,''
%Proceedings of 11$^{th}$ International Workshop on 
%Deep Inelastic Scattering (DIS 2003), St. Petersburg, Russia, April 2003, p 488.
%Edited by V.T. Kim and L.N. Lipatov.  
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0309009}{[hep-ph/0309009].}
%\else
%[hep-ph/0309009].
%\fi
%%%CITATION = HEP-PH 0309009;%%

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


%\cite{Jung:2001hx}
%\bibitem{Jung:2001hx}
  H.~Jung,
  %``The CCFM Monte Carlo generator CASCADE,''
  Comput.\ Phys.\ Commun.\  {\bf 143} (2002) 100
\ifpdf
\href{http://arXiv.org/ps/hep-ph/0109102}{[hep-ph/0109102].} \\
\else
  [hep-ph/0109102]; \\
\fi
  %%CITATION = HEP-PH 0109102;%%
\ifpdf
(see also 
\href{http://www.desy.de/~jung/cascade/}
{http://www.desy.de/$\sim$jung/cascade/}).
\else
(see also http://www.desy.de/$\sim$jung/cascade/).
\fi


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




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



%\bibitem{Martin:1994kn}
%A.~D.~Martin, W.~J.~Stirling and R.~G.~Roberts,
%%``Parton distributions of the proton,''
%Phys.\ Rev.\ D {\bf 50} (1994) 6734
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/9406315}{[hep-ph/9406315].}
%\else
%[hep-ph/9406315].
%\fi
%%CITATION = HEP-PH 9406315;%%




\bibitem{zeusf2b}

ZEUS Collaboration, ``Measurement of $F_2^{b\bar{b}}$ at HERA II'', contribution to 
the HEP2007 International Europhysics Conference on High Energy Physics, Manchester UK,
July 2007.

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

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

\bibitem{NNLO}
R.~Thorne,
``A Variable Flavour Number Scheme at NNLO,''
To appear in the proceedings of 13$^{th}$ International Workshop on 
Deep Inelastic Scattering (DIS 2005), Madison, Wisconsin, USA, April 2005.
\ifpdf
\href{http://arXiv.org/ps/hep-ph/0506251}{[hep-ph/0506251].}
\else
[hep-ph/0506251].
\fi


%\bibitem{Sjostrand:2000wi}
%  T.~Sj\"{o}strand {\it et al.},
%  %``High-energy-physics event generation with PYTHIA 6.1,''
%  Comput.\ Phys.\ Commun.\  {\bf 135} (2001) 238
%\ifpdf
%\href{http://arXiv.org/ps/hep-ph/0010017}{[hep-ph/0010017].}
%\else
%  [hep-ph/0010017].
%\fi
%  %%CITATION = HEP-PH 0010017;%%

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





\end{thebibliography}


\newpage


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
  \begin{center} \includegraphics[width=0.95\textwidth]{H1prelim-07-171.fig1.eps}
  \caption{The distribution of the signed impact parameter $\delta$ of
  a track to the primary vertex in the $x$--$y$ plane. Included in the
  figure is the expectation from the Monte Carlo simulation for
  light, $c$
  and $b$ quarks. The contributions from the various quark flavours
  are shown after applying the scale factors obtained from the fit to
  the subtracted significance distributions of the data (see
  section~\ref{quarkflavourseparation}).}  \label{fig:dca}
  \end{center}
\end{figure}

%\begin{figure}[h!]
%  \begin{center} \includegraphics[width=0.95\textwidth]{H1prelim-07-171.fig1.eps}
%  \caption{The distribution of the significance $\delta/\sigma(\delta)$ of
%  a track to the primary vertex in the $x$--$y$ plane. Included in the
%  figure is the expectation from the  Monte Carlo simulation for
%  light, $c$ and $b$ quarks. The contributions from the various quark flavours
%  are shown after applying the scale factors obtained from the fit to
%  the subtracted significance distributions of the data (see
%  section~\ref{quarkflavourseparation}).}  \label{fig:sig}
%  \end{center}
%\end{figure}



\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{picture}(150,75)
    \put(0,0){ \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig2a.eps}}
    \put(85,0) {  \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig2b.eps}}
%    \put(40,10){  \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig4.eps}}

    \begin{Large}
      \put(-5,60){\bfseries a)}
      \put(80,60){\bfseries b)}
%      \put(40,50){\bfseries c)}
    \end{Large}


 \end{picture}
 \caption{The
  significance $\delta /\sigma(\delta)$ distribution (a) of the
  highest absolute significance track ($S_1$) for 1 track events
	 and (b) of the track with
  the second highest absolute significance ($S_2$).
  Included in the figure is the expectation from the Monte
  Carlo simulation for light, $c$ and $b$ quarks. The contributions from the various
  quark flavours are shown after applying the scale factors obtained
  from the fit to the subtracted significance distributions of the
  data.}
  \label{fig:s1s2}
\end{figure}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]

  \begin{picture}(150,75)
    \put(0,0){ \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig3a.eps}}
    \put(85,0) {  \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig3b.eps}}
%    \put(40,10){  \includegraphics[width=0.5\textwidth]{H1prelim-07-171.fig7.eps}}

      \begin{Large}
%        \put(-0.27,0.97){\bfseries \boldmath H1 Diffractive \dstar \, in DIS ($\xpom<0.01$)}
        \put(-5,60){\bfseries a)}
        \put(80,60){\bfseries b)}
%        \put(30,50){\bfseries c)}
     \end{Large}
 \end{picture}

 \caption{The subtracted
  significance distributions of (a) $S_1$ for 1 track events and (b) $S_2$.
  Included in the figure is
  the result from the fit to the data of the Monte Carlo distributions
of the various quark flavours.}
  \label{fig:s1s2negsub}

\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.89\textwidth]{H1prelim-07-171.fig4.eps} \caption{The
  measured reduced cross section $\tilde{\sigma}^{c\bar{c}}$ shown as
  a function of $x$ for 5 different $Q^2$ values.  The inner error
  bars show the statistical error, the outer error bars represent the
  statistical and systematic errors added in quadrature. The measurements
  are compared with those from HERA I,  and the HERA I and II averaged
  data are also shown.
 % The
 % measurements of $\tilde{\sigma}^{c\bar{c}}$ from H1 at high values
 % of $Q^2$\cite{Aktas:2004az}, 
%  The measurements obtained from $D^*$
 % mesons from H1 and ZEUS\cite{H1Dstar,ZEUSDstar} and  predictions
 % of QCD are also shown.
}  
\label{fig:f2cc} \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.89\textwidth]{H1prelim-07-171.fig5.eps}
  \caption{The measured reduced cross section
  $\tilde{\sigma}^{b\bar{b}}$ shown as a function of $x$ for 5
  different $Q^2$ values.  The inner error bars show the statistical
  error, the outer error bars represent the statistical and systematic
  errors added in quadrature.  The measurements are compared with
  those from HERA I, and the HERA I and HERA II averaged data
  are also shown.}

 % The
 % measurements of $\tilde{\sigma}^{b\bar{b}}$ from H1 at high values
 % of $Q^2$\cite{Aktas:2004az} and  
%  The predictions of QCD are also
%  shown.
  
\label{fig:f2bb} \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.89\textwidth]{H1prelim-07-171.fig6.eps} \caption{The
  measured HERA I and II averaged reduced cross section
  $\tilde{\sigma}^{c\bar{c}}$ shown as a function of $x$ for 5
  different $Q^2$ values.  The inner error bars show the statistical
  error, the outer error bars represent the statistical and systematic
  errors added in quadrature.   The measurements  obtained
  from $D^*$ mesons from H1 and ZEUS\cite{H1Dstar,ZEUSDstar} and 
  predictions of QCD are also shown.}  \label{fig:f2ccav} \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.89\textwidth]{H1prelim-07-171.fig7.eps} \caption{The
  measured HERA I and II averaged reduced cross section
  $\tilde{\sigma}^{b\bar{b}}$ shown as a function of $x$ for 5
  different $Q^2$ values.  The inner error bars show the statistical
  error, the outer error bars represent the statistical and systematic
  errors added in quadrature.  The predictions of QCD are also shown.}
  \label{fig:f2bbav} \end{center}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.89\textwidth]{H1prelim-07-171.fig8.eps} \caption{The
  measured HERA I and II averaged reduced cross section
  $\tilde{\sigma}^{b\bar{b}}$ shown as a function of $x$ for 5
  different $Q^2$ values.  The inner error bars show the statistical
  error, the outer error bars represent the statistical and systematic
  errors added in quadrature.  The preliminary data from ZEUS and the
predictions of QCD are also shown.}
  \label{fig:f2bbavh1zeus} \end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.85\textwidth]{H1prelim-07-171.fig9.eps}
  \caption{The measured HERA I and II averaged $F_2^{c\bar{c}}$ shown
  as a function of $Q^2$ for various $x$ values.  The inner error bars
  show the statistical error, the outer error bars represent the
  statistical and systematic errors added in quadrature.  
  The measurements  obtained
  from $D^*$ mesons from H1 and ZEUS\cite{H1Dstar,ZEUSDstar} and 
  predictions of QCD are also shown.}  \label{fig:f2ccq2} \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.9\textwidth]{H1prelim-07-171.fig10.eps}
  \caption{The measured HERA I and II averaged $F_2^{b\bar{b}}$ shown
  as a function of $Q^2$ for various $x$ values.  The inner error bars
  show the statistical error, the outer error bars represent the
  statistical and systematic errors added in quadrature. The
  predictions of QCD are also shown.}  

\label{fig:f2bbq2} 

\end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
  \begin{center}
  \includegraphics[width=0.9\textwidth]{H1prelim-07-171.fig11.eps}
  \caption{The measured HERA I and II averaged $F_2^{b\bar{b}}$ shown
  as a function of $Q^2$ for various $x$ values.  The inner error bars
  show the statistical error, the outer error bars represent the
  statistical and systematic errors added in quadrature. The
  preliminary data from ZEUS and predictions of QCD are also shown.}  

\label{fig:f2bbq2h1zeus} 

\end{center}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}[htb]
%  \begin{center} \includegraphics[width=0.9\textwidth]{fig9} \caption{The
%  contributions to the total cross section $f^{c\bar{c}}$ and
%  $f^{b\bar{b}}$ shown as a function of $Q^2$ for 6 different $x$
%  values. The inner error bars show the statistical error, the outer
%  error bars represent the statistical and systematic errors added in
%  quadrature.  
%  A prediction of NLO QCD is also shown.}
%  \label{fig:frac} \end{center}
%\end{figure}



%\begin{sidewaystable}
%\footnotesize
%\include{sig}
%\normalsize
%    \caption{ The measured reduced NC cross section ($\tilde{\sigma}^{q\bar{q}}$)
%    for charm ($c$) and beauty ($b$) quarks, shown with the
%    correlation coefficients ($C_{cb}$), the statistical error
%    ($\delta_{\rm stat}$), the systematic error
%    ($\delta_{\rm sys}$), the total error
%    ($\delta_{\rm tot}$) and the uncorrelated
%    systematic error ($\delta_{\rm unc}$).  The next
%    $8$ columns represent a $+ 1 \sigma$ shift for the correlated
%    systematic error contributions from: track impact parameter
%    resolution, track efficiency, $D$ multiplicity, $B$ multiplicity,
%    fragmentation, QCD model, light quark contribution and quark axis
%    $\phi_{\rm quark}$.  The $-1 \sigma$ errors are taken as
%    the negative of the upward errors.  The errors are correlated
%    between charm and beauty but uncorrelated to inclusive data, apart
%    from a normalisation uncertainty of $1.5\%$ which is $100\%$
%    correlated. The table also shows the values for $F_2^{c\bar{c}}$
%    and $F_2^{b\bar{b}}$ obtained from the measured cross sections
%    using the NLO QCD fit to correct for the contributions from
%    $F_L^{c\bar{c}}$ and $F_L^{b\bar{b}}$. The quoted relative errors
%    apply also to $F_2^{c\bar{c}}$ and $F_2^{b\bar{b}}$.}
%\label{tab:sig}
%\end{sidewaystable}


\end{document}








