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\begin{document} % The rest \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.)} \newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)} \newcommand{\fiipom}{\tilde F_2^D} \newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)} \newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)} \newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)} \newcommand{\pomflux}{f_{\pom / p}} \newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand {\gapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}} \newcommand {\lapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}} \def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle >$}\,} 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\newcommand{\trpp}{p_{\perp}^2} \newcommand{\alp}{\alpha_s} \newcommand{\alps}{\alpha_s} \newcommand{\sqrts}{$\sqrt{s}$} \newcommand{\LO}{$O(\alpha_s^0)$} \newcommand{\Oa}{$O(\alpha_s)$} \newcommand{\Oaa}{$O(\alpha_s^2)$} \newcommand{\PT}{p_{\perp}} \newcommand{\JPSI}{J/\psi} \newcommand{\sh}{\hat{s}} %\newcommand{\th}{\hat{t}} \newcommand{\uh}{\hat{u}} \newcommand{\MP}{m_{J/\psi}} %\newcommand{\PO}{\mbox{l}\!\mbox{P}} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\ttbs}{\char'134} \newcommand{\xpomlo}{3\times10^{-4}} \newcommand{\xpomup}{0.05} \newcommand{\dgr}{^\circ} \newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}} \newcommand{\gev}{\,\mbox{GeV}} \newcommand{\WBoson}{\mbox{$W$}} \newcommand{\fbarn}{\,\mbox{{\rm fb}}} \newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\et}{\ensuremath{E_t^*} } \newcommand{\rap}{\ensuremath{\eta^*} } \newcommand{\gp}{\ensuremath{\gamma^*}p } \newcommand{\dsiget}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}E_t^*} } \newcommand{\dsigrap}{\ensuremath{{\rm d}\sigma_{ep}/{\rm d}\eta^*} } % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2} (#3) #4} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} {\bf A}} \def\NPB{{\em Nucl. Phys.} {\bf B}} \def\PLB{{\em Phys. Lett.} {\bf B}} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} {\bf D}} \def\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \begin{center} \begin{small} %\begin{tabular}{llrr} % Submitted to & & & % \epsfig{file=H1logo_bw_small.epsi,width=1.5cm} \\[.2em] \hline % \multicolumn{4}{l}{{\bf Europhysics Conference % on High Energy Physics, EPS2007}, % July 19-25,~2007,~Manchester} \\ % Abstract: & {\bf xx-xxx} & & \\ % Parallel Session & {\bf x} & & \\ \hline % \multicolumn{4}{l}{\footnotesize {\it Electronic Access: % www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.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 $0.070.5~{\rm GeV}$ 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. 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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}