%================================================================ % latex file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ %================================================================ % % Paper *** D mesons in DIS *** % *************************** % % % C.Grab, ETHZ % together with W.Erdmann and J.Gassner % based on thesis of J.Gassner % Referees: Elsen and Behnke % % History: % v0.0 : 9.10.03 0th draft, based on the Amsterdam conf. contrib. % v0.1 : 26.11.03 first draft, updated figures. % based on discussions with referees 19.11.03 % sent to ref. on 26.11. % v0.2 : 28.11.03 Updates, to be submitted to the HQ-PWG % v0.3 : 23.12.03 Preparatory version for distribution to H1 in mid-Jan. % v1.0 : 11.1.04 First distribution to H1 % v1.1 : 5.3.04 Updates of v1.0 for second round % v1.2 : 23.4.04 Updates of v1.1 for after v11 % v1.3 : 4.5.04 Updates after discussions with EE + OB + WE + JG % v1.3.1: 12.5.04 Mods on Introduction and chapter 3 (EE) % v1.3.2: 14.5.04 Mods : merge EE-comments + OB comments % v1.3.3: 17.5.04 iteration with Wolfram und Johannes % v1.3.3e: 18.5.04 small changes from EE % v1.3.4: 24.5.04 move eq.3 + small changes in Fig. by Johannes % v1.4.1 : 25.5.04 Updates after tel.conference with EE + OB + WE + JG % v1.4.2 : 26.5.04 Include comments of Wolfram % v1.4.3 : 05.6.04 Mods after referee report for second circulation % v1.4.4 : 05.6.04 Olaf's take % v1.4.5 : 05.6.04 and Eckhard again % V1.5 : 07.6.04 Christoph, incorporate Eckhard's comment % Jo, wolfram need to see this before it becomes 2.0 % v1.5.1: 9.6.04 Continued to incorporate all comments of the collaboration % v1.5.2: 9.6.04 After discussions with EE, re-read, only minor corrections. % v1.5.3: 10.6.04 caption style changed % V2.0 : 11.6.04 v1.5.3 = declared v2.0 % v2.1 : 7.7.04 Implemented Paul N. comments on style and English. % included comments by Gayler, Guillermo and Katerina. % and Wolframs rephrased paragraph 2.3 % v2.2 ... v2.5 : Wolfram, Olaf, Eckhard worked on the draft.... % % V2.5 : 4.8.04 Wolfram, Olaf, Eckhard worked on the draft.... % % V2.6 : 3.8.04 EE rephrased in section 3. % V2.7 : 5.8.04 CG added Olafs comments, and merged with EE rephrased vsn.2.6 % % V3.0 : 11.8.04 CG implemented all comments from public-reading( 9.8.04) % Moved all figs, tables to end of paper, according to Paul Newman. % Checked author list according to Web-page. % Proof-read by Wolfram. % V3.1 : 12.8.04 CG implemented comments from Paul, and Eckhard % % % \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} \usepackage{color} \usepackage{lineno} \usepackage{rotating} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm 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\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$^{-1}$}}} \newcommand{\unit}[1]{\ {\rm#1}} % % Some useful tex commands % \newcommand{\ye}{$y$} \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.} %% Special abbrev. for the DDIS-paper % \newcommand{\Dstar}{\particle{D^{*}}} \newcommand{\Dstarplus}{\particle{D^{*+}}} \newcommand{\Dsubs}{\particle{D_s}} \newcommand{\Dsubsplus}{\particle{D^{+}_s}} \newcommand{\Dzero}{\particle{D^{0}}} \newcommand{\Dplus}{\particle{D}^+} \newcommand{\BR}{{\cal B}} % \newcommand{\GeV}{\mathrm{GeV}} \newcommand{\mev}{\mathrm{MeV}} \newcommand{\dst}{$D^{*+}$} \newcommand{\dc}{$D^+$} \newcommand{\dn}{$D^0$} \newcommand{\ds}{$D^+_s$} \newcommand{\dstdec}{$D^{*+} \rightarrow D^0 \pi^+_s \rightarrow (K^- \pi^+) \pi^+_s$} \newcommand{\dcdec}{$D^+ \rightarrow K^- \pi^+ \pi^+$} \newcommand{\dndec}{$D^0 \rightarrow K^- \pi^+$} \newcommand{\dsdec}{$D^+_s \rightarrow \phi \pi^+ \rightarrow (K^+ K^-) \pi^+$} % \newcommand{\particle}[1]{#1} \newcommand{\cbar}{\particle{\bar{c}}} \newcommand{\bbar}{\particle{\bar{b}}} \newcommand{\ccbar}{c\cbar} \newcommand{\bbbar}{b\bbar} \newcommand{\pb}{\rm pb} \newcommand{\icaption}[1]{\caption{\it #1}} % \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=/h1/www/images/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 5-0166} &\\ & Parallel Session & {\bf 5} &\\ \hline & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \end{tabular} \end{small} \end{center} \vspace*{2cm} \begin{center} \Large {\bf Inclusive Production of {\boldmath $D^+, D^0, D_s^+$} and {\boldmath $D^{*+}$} Mesons \\ in Deep Inelastic Scattering at HERA} \vspace*{1cm} {\Large H1 Collaboration} \end{center} \begin{abstract} \noindent Inclusive production cross sections are measured in deep inelastic scattering at HERA for meson states composed of a charm quark and a light antiquark or the charge conjugate. %the charmed mesons $D=c\bar{q}$, where $q$ is any of the light quarks %$u, d$ and $s$. The measurements cover the kinematic region of photon virtuality $2 < Q^2 < 100 \ \gev^2$, inelasticity $0.05 < y < 0.7$, $D$ meson transverse momenta $p_t(D) \ge 2.5 \ \gev$ and pseudorapidity $|\eta(D)| \le 1.5$. % The identification of the $D$-meson decays and the reduction of the combinatorial background profit from the reconstruction of displaced secondary vertices by means of the H1 silicon vertex detector. % The production of charmed mesons containing the light quarks $u,d$ and $s$ is found to be compatible with a description in which the hard scattering is followed by a factorisable and universal hadronisation process. \end{abstract} \end{titlepage} \pagestyle{plain} \newpage \section{Introduction} \noindent The production of heavy quarks in deep inelastic positron-proton interactions at HERA proceeds % at centre-of-mass-energies of $\sqrt{s}=319\;$GeV$ almost exclusively via photon-gluon fusion, where a photon coupling to the incoming positron interacts with a gluon in the proton to form a charm-anticharm pair (figure~\ref{fig:bgf}). % Measurements of differential charm production cross sections ~\cite{Aid:1996hj,Adloff:1998vb,Adloff:2001zj, Breitweg:1999ad,Chekanov:2003rb} are well reproduced by a description based on perturbative QCD (pQCD). % In this framework cross sections d$\sigma$ for $D$ mesons (bound $c\bar{q}$ states of charm quarks with light antiquarks) can be computed\cite{Ellis:1988sb,Smith:1991pw,Laenen:1992zk,Frixione:1993dg, Frixione:1994nb,Frixione:nn}\ by convoluting the parton level hard scattering cross section d$\hat{\sigma}$ with a fragmentation function $D_D^{(c)}(z)$: \begin{eqnarray} % {\rm d}\sigma(ep \to e' D X) & = & % \int {\rm d}z \ \ D_D^{(c)}(z) % \cdot {\rm d}\hat{\sigma}(ep \to e' c X')(p/z)\ \ \ \ . \label{eq:f1} {\rm d}\sigma(p) & = & \int {\rm d}z \ \ D_D^{(c)}(z) \cdot {\rm d}\hat{\sigma}(p/z)\ \ \ \ . \label{eq:f1} \end{eqnarray} % \noindent The cross section d$\hat{\sigma}$ here describes the hard scattering process $(ep \to e' c X')$ and the perturbative evolution from the $c$-quark production scale down to a scale of order of the heavy quark mass $m_c$\cite{Nason:1999zj}. %(within the DGLAP formalism\cite{}) The non-perturbative part of the hadronisation, $D_D^{(c)}(z)$, accounts for the transition of an on-shell quark $c$ of momentum $p/z$ into a hadron $D$ carrying a fraction $z$ of the quark momentum. % %% ------------------- This factorisation ansatz can be shown to hold in the asymptotic limit of large production scales~\cite{collins}. It assumes that the non-perturbative component $D_D^{(c)}(z)$ is independent both of the hard scattering process, e.g. $ee-, ep-$ or $ pp-$scattering, and of the scale at which the charm quark is produced. % and of the type of charm meson $D$ produced. These properties are collectively referred to as ``universality''\cite{Frixione:nn,Mele:1990cw,Nason:1993xx,Nason:1999zj}. It has been argued %by Nason {\it et al.} \cite{Nason:1999zj,n-mellin} that the assumptions of universality may not hold and that in fact different production processes may be sensitive to different aspects of fragmentation. % Conventionally the shape of $D_D^{(c)}(z)$ is taken to be identical for all primary produced $D$-mesons, and its normalisation accounts for the abundance of the respective meson $D$. % A well-known parametrisation of this shape is the Peterson function\cite{Peterson:1982ak} with a suitably chosen normalisation factor $n_D$ %%%CG \begin{eqnarray} D_D^{(c)}(z) & = & \frac{n_D}{ z [ 1-1/z-\epsilon_{c}/(1-z)]^2}\ \ \ \ . \label{eq:f3} \end{eqnarray} % \noindent The so-called ``Peterson parameter'' $\epsilon_{c}$ measures the hardness of the hadronisation. In practice, it is extracted from charm spectra measured predominantly at $e^+e^-$ colliders\cite{Nason:1999zj}. % \noindent In this paper the universality ansatz is explored in deep inelastic $ep$-scattering at HERA. % For this purpose production cross sections are measured for the charmed meson state $D^+, D^0, D_s^+$ and $D^{*+}$, containing the light quarks $u, d$ and $s$. % The final state requirements differ only in the light quark content or the spin of the charmed meson. % For light quark fragmentation the occurrence of different quark flavours in the fragmentation process can be described by isospin relations and probabilistic quark selection factors. % While corresponding charm quark fragmentation results are available from other scattering processes\cite{Nason:1999zj,Albrecht:1991ss,Akers:1994jc,Buskulic:1995gp} it is interesting to verify whether the relations established for light quarks can be extended to mesons containing heavy quarks produced in $ep$ scattering at HERA. In this analysis the signals of $D$ mesons are enhanced with respect to background processes by exploiting their lifetimes. % The displaced secondary decay vertices of the $D$-mesons are reconstructed from the daughter particle tracks, which are measured with high precision in the H1 central silicon tracker. A common detection method can thus be applied to all four charmed meson states. % % %_________________________________________________________________________________ \section{Experimental Aspects and Data Analysis} %_________________________________________________________________________________ The data were collected in 1999 and 2000 with the H1 detector at HERA and correspond to an integrated luminosity of $47.8 \pm 0.7~\pb^{-1} $ of $e^+p$ interactions at a centre of mass energy $\sqrt{s} = 319~\GeV$. The analysis covers the kinematic region of photon virtuality $2 < Q^2 < 100 \ \gev^2$, inelasticity $0.05 < y < 0.7$ and $D$ meson transverse momentum and pseudorapidity\footnote{In the following, the coordinate system used has its origin at the nominal $e^+p$ interaction point and its $z$-axis in the outgoing proton direction. Polar angles, $\theta$, are measured with respect to the $z$ direction. The pseudorapidity is defined as $\eta = - \ln \tan(\theta /2)$.} $p_t(D) \ge 2.5 \ \gev$ and $|\eta(D)| \le 1.5$. % The charmed mesons are detected through their decay products in the decay channels\footnote{The charge conjugate states are always implicitly included.} \dcdec, \dndec, \dsdec\ and $D^{*+}(2010) \rightarrow D^0 \pi^+ \rightarrow (K^- \pi^+) \pi^+$. \subsection{Detector and Simulation } The H1 detector and its trigger capabilities are described in detail elsewhere~\cite{Abt:1996hi}. Charged particles are measured by a set of central tracking devices including two cylindrical jet drift chambers (CJC) \cite{Burger:eb,Abt:1994dn}, mounted concentrically around the beam-line inside a homogeneous magnetic field of 1.15~T. They provide particle charge and transverse momentum measurements in the polar angle range $20^{\circ}<\theta<160^{\circ}$. Further drift chambers provide accurate measurements of the $z$-coordinates. These central tracking devices are complemented by the central silicon tracker (CST)~\cite{Pitzl:2000wz}, which consists of two cylindrical layers of silicon strip detectors with active lengths of $35.6$~cm surrounding the beam pipe at radii of $57.5$~mm and $97 $~mm from the beam axis. % The double-sided strip detectors measure $r$-$\phi$ and $z$ coordinates with resolutions of 12~$\mu$m and 25~$\mu$m, respectively. Average hit efficiencies are 97 (92)\% for $r$-$\phi$ ($z$) strips. In this analysis the measurements of the $z$-coordinates are not used for the secondary vertex determination. % When extrapolated to the interaction region, the coordinate perpendicular to a track in the transverse plane has a resolution of $ 33\;\mu\mbox{m} \oplus 90 \;\mu\mbox{m} /p_t [\mbox{GeV}]$ for tracks with CST hits in both layers. % The first term represents the intrinsic resolution and includes the uncertainty on the CST alignment. The second term accounts for the contribution from multiple scattering. One double layer of cylindrical multi-wire proportional chambers (MWPC\cite{Muller:jk}) with pad readout for triggering purposes is positioned between the CST and the CJC, and another between the two jet chambers. The backward region of H1 is equipped with a lead/scintillating fibre ``Spaghetti'' Calorimeter (SpaCal)~\cite{Appuhn:1996na}, which is optimized for the detection of the scattered positron in the DIS kinematic range considered here. It consists of an electromagnetic and a more coarsely segmented hadronic section. An eight-layer drift chamber (BDC~\cite{bdc}), mounted in front of the SpaCal, is used to reject neutral particle background. The $ep$ luminosity is determined by measuring the QED bremsstrahlung $(ep \to ep\gamma)$ event rate by tagging the photon in a photon detector located at $z = -103$\ m. % text taken from DESY 03-038 THE NC+CC analysis flagship paper Corrections for detector effects are evaluated using detailed Monte Carlo simulations. Charm and beauty electroproduction events are generated according to Leading Order (LO) QCD matrix elements with the AROMA 2.2~\cite{Ingelman:1996mv} program and are combined with parton showering in the JETSET\cite{Sjostrand:1993yb} program. The beauty cross section is enhanced by a factor 4.3 in accordance with the measurement of ~\cite{h1-bxsec-dis}. % The hadronisation step proceeds according to the Lund string model for light quarks and the Peterson model for heavy quarks. The simulation is adjusted to reproduce the world average results on the relative abundances of charmed mesons~ \cite{Gladilin:1999pj}. % The generated events are then processed by the H1 detector simulation program and are subjected to the same reconstruction and analysis chain as the real data. %_________________________________________________________________________________ \subsection{Selection of DIS Events} The analysis is based on events which contain a scattered positron detected in the SpaCal backward calorimeter. % Scattered positrons are identified as clusters in the SpaCal with energies $E_{e^{\prime}}>8$ GeV, with cluster radii less than 3.5~cm, consistent with an electromagnetic energy deposition. The cluster centres must be spatially associated with a charged track candidate in the BDC within the polar angular region $153^{\circ}<\theta<177.8^{\circ}$. % The events are triggered by the identification of a SpaCal cluster in coincidence with a central charged track signal from the MWPC and central drift chamber triggers. \noindent At fixed $\sqrt{s}$ the kinematics of the scattering process are determined by two of the Lorentz invariant variables $Q^2$, $y$ and the Bjorken scaling variable $x$. These variables are reconstructed using the scattered positron according to \begin{equation} Q^2 = 4 E_e E_{e^{\prime}} \cos ^2 \left( \frac{\theta_{e^{\prime}}}{2} \right) , {\rm \quad } y = 1 - \frac{E_{e^{\prime}}}{E_e} \sin ^2 \left( \frac{\theta_{e^{\prime}}}{2} \right), \;\; \quad x = \frac{Q^2}{ys}, \label{eq:kine} \end{equation} with $E_e$ and $E_{e^{\prime}}$ denoting the energies of the incoming and scattered positron, respectively, and $\theta_{e^{\prime}}$ the polar angle of the scattered positron. %_________________________________________________________________________________ \subsection{Decay Vertex Reconstruction} The lifetimes of between 0.4 and 1 ps of the $D$ mesons lead to a spatial separation between their production vertex, assumed to be the point of the primary $ep$ interaction, and the decay vertex, referred to as the secondary vertex. This separation is expressed here in terms of the radial decay length $l$ and its error $\sigma_l$. The decay length measures the distance between these two vertices in the $r$-$\phi$ plane, which is typically a few hundred $\mu$m. The significance $S_l = l/\sigma_l$ is a powerful discriminator to identify long-lived hadrons\cite{Gassner:2002ji}. %from background events, which originate predominantly % from random tracks from the primary vertex. Tracks are first reconstructed in the CJC and are then extrapolated into the CST, where the closest hit from strips measuring $r$-$\phi$ in each layer is associated with each track if it lies within $5\sigma$ of the extrapolated CJC track. Then the tracks are refitted using the additional information of the CST hits. Two or three such CST-improved tracks are used to form a $D$ meson candidate by fitting them to a common secondary vertex in the $r$-$\phi$ plane, while all other tracks in the event, CST-improved or not, are used for the determination of the primary vertex. For the primary vertex fit an iterative procedure is adopted. The track with the largest contribution to the $\chi^2$ is removed and the fit is repeated until the $\chi^2$ contribution of each track assigned to the primary vertex is less than three. The precisely known position and profile of the elliptical interaction region in the $r$-$\phi$ plane (``beam spot'') enter the primary vertex fit as an additional measurement of the vertex coordinates with uncertainties given by the width of the interaction region. The position of the beam spot is determined run-wise or for a large number of events inside a run by averaging the reconstructed $ep$ interaction points. The profile of the beam spot is assumed to be Gaussian and stable throughout the data-taking period. Its width is determined from a sample of events where the primary vertex is accurately measured from high momentum central tracks, which are largely unaffected by multiple scattering. % Widths of $145\ \mu$m and $25\ \mu$m are found for the horizontal and vertical directions, respectively. %% ------------------- % The uncertainty of the primary vertex determination varies from event to event with an average $69\ \mu$m in the horizontal direction. The uncertainty in the vertical direction is essentially given by the $25\ \mu$m vertical width of the beam spot.% and not significantly improved by tracks In the fit for the secondary vertex the momentum of the $D$ meson candidate is constrained to be parallel (or anti-parallel) to the vector connecting the primary and secondary vertices. This provides a powerful constraint to reject random track combinations. The primary vertex position and its error are used as external measurements in the fit. The uncertainty on the decay length is dominated by the resolution of the secondary vertex reconstruction. % $D$ meson decay candidates are selected by applying requirements on the following variables: the minimal transverse momentum $p_t$ of daughter tracks, a signed impact parameter\footnote{The impact parameter $d$ is the distance of closest approach of a track to the primary vertex. It is positive if the angle between the momentum vector of the $D$ meson candidate and the vector pointing from the primary vertex to the point of closest approach is less than $90^\circ$.} $d$ of significance $S_d = d/\sigma_d$ for at least two tracks, the secondary vertex fit probability ${\cal P}_{\it VF}$, the error on the decay length measurement $\sigma_l$ and the vertex separation significance $S_l = l/\sigma_l$. The detailed cuts, chosen to optimise the signal significance, are listed in table~\ref{tab:selection}. At most one missing CST hit is allowed for each $D$ meson candidate. The CST geometry confines the $D$ mesons to lie in a polar angular range of typically $25^\circ < \theta < 155 ^\circ$. % % %% -------------------------------------------------------------- % To test the understanding of the CST, its response to data has been compared with simulations for a sample of ``tagged'' $\Dzero$ mesons (figure~\ref{fig:eff-sl}a). These $\Dzero$ mesons originate from a \dstdec\ decay chain and are selected by a cut about the nominal value of $\Delta m = m(K \pi \pi_s) - m(K \pi)$ corresponding to a window of three times the resolution. In this channel a good signal purity can be achieved without a lifetime cut, thus allowing a determination of the efficiency of the CST reconstruction. Figure~\ref{fig:eff-sl}b shows the measured decay length significance distribution $S_l$ of tagged $D^0$ candidates, together with its fitted decomposition into a signal and a background contribution. The functional form of the signal distribution is taken from the simulation, whereas the background shape is extracted from the %250-MeV$/c^2$-wide sideband regions on both sides of the nominal \dn\ mass in the $m(K\pi)$ spectrum of the data, as indicated in figure~\ref{fig:eff-sl}a. % In the fit of the $S_l$ distribution only the normalisations of the signal and of the background are left as free parameters. The $\chi^2/{\it ndf} = 34/32$ indicates that the MC simulation describes the signal shape very well. Furthermore, the number of $\Dzero$ candidates extracted by means of the $S_l$ fit is found to be fully consistent with the number determined from the fit shown in figure~\ref{fig:eff-sl}a) to the invariant mass distribution $m(K\pi)$. To illustrate the purity that can be reached, the invariant mass distributions for $\Dplus \to K^+ \pi^- \pi^+$ candidate events are compared before and after a stringent cut $S_l>8$ in figure~\ref{fig:phenix}. The signal-to-background ratio improves by a factor 50 while 20\% of the signal is retained. For the cross section measurements described below a less stringent cut $S_l>5$ is chosen to increase the efficiency, albeit with a reduced purity. %__________________________________________________________________________ \subsection{Signal Determination} The reconstruction of $D$ mesons uses all CST-improved charged particle tracks. % in the central H1 detector $(20^{\circ} < \theta < 160^{\circ})$. No explicit particle identification is applied, and each track is assumed to be either a kaon or a pion as appropriate. The tracks of suitable charge are required to pass the transverse momentum criteria specified in table~\ref{tab:selection}. They are then fitted to a common secondary vertex, which must also fulfil the requirements listed in table~\ref{tab:selection}. % The number of signal events is then determined for each $D$ meson individually by fitting the invariant mass distributions of the candidate combinations with a Gaussian to describe the signal and an appropriate background shape. The signal mass and width are left free in the fit. % The invariant mass distributions used to extract the final number of signal events after all the vertexing cuts are shown in figure~\ref{fig:dall-cst}. The specific choices for the fits are the following: %% -------------------------------------------------------------- a) \dcdec : the 3-particle invariant mass distribution $m(K \pi \pi)$ is fitted using a Gaussian for the signal and a linear function describing the background shape (figure~\ref{fig:dall-cst}a). % Wrong sign combinations are not relevant in this mode. %% -------------------------------------------------------------- b) \dndec: the 2-particle invariant mass distribution $m(K \pi)$~(figure~\ref{fig:dall-cst}b) is fitted using a Gaussian for the signal, an exponentially falling function to describe the combinatorial background and a contribution from wrong-charge combinations. The latter contribution arises since with no particle identification applied, each \dndec\ decay also enters the distribution as a $\bar{D^0} \to K^+ \pi^-$ candidate. The contribution of this wrong-charge assignment is modelled by a broad Gaussian with the mean position, the width and the normalisation relative to the correct-charge Gaussian determined from the simulation and subsequently kept fixed in the fit. %% -------------------------------------------------------------- c) \dsdec: because the $\Dsubs$ decays via the intermediate vector meson resonance $\phi$, it has a restricted 3-body phase space, allowing criteria to be applied to suppress the combinatorial background. In particular, the 2-particle combination $m(K^+ K^-)$ is required to lie within a $\pm 2 \sigma$ window ($\pm$11~MeV) around the nominal $\phi$ mass. %(i.e.\ within 11 MeV/$c^2$ of 1020 MeV/$c^2$). The distribution in the cosine of the angle $\theta^*$ (helicity angle), defined as the angle between the $K$-momentum vector and the $\Dsubs$ flight direction, transformed into the $\phi$ rest frame, follows a $\cos ^2 \theta^*$ shape. A value of $| \cos \theta^* | > 0.4$ is required. The 3-particle invariant mass distribution $m(K K \pi)$, fitted using a Gaussian for the signal and an exponential background function, is shown in figure~\ref{fig:dall-cst}c. %% -------------------------------------------------------------- d) \dstdec : the $\Delta m$-tagging technique is applied \cite{Feldman:1977ir}. % those $K^-\pi^+$ pairs with an invariant mass % consistent with the $D^0$ mass within $\pm 80$ MeV$/c^2$ % are combined with a third track - hypothetically assumed to be a pion % (``$\pi^+_{slow}$'') - of charge opposite in sign to that of the % kaon candidate. For all candidate combinations lying within a 3 sigma window ($\pm$ 3.6 MeV) of the nominal value of $\Delta m = m(K \pi \pi_s) - m(K \pi)$, the invariant mass distribution $m(K \pi)$ is fitted using a Gaussian for the signal and an exponential function describing the background shape. The Figure \ref{fig:dall-cst}d shows this $m(K \pi)$ distribution after the cut on $\Delta m$. % The number of signal events extracted this way is found to be % compatible with the other procedure, where % the $\Delta m$ distribution is fitted, after a cut on the % $m(K^-\pi^+)$ around the nominal $D^0$-mass. % $\Dzero$ mesons from this identified \dstdec chain are referred to as % tagged $\Dzero$s. %% -------------------------------------------------------------- The fitted $D$ meson mass values are all found to be compatible within errors with the world average values\cite{PDG2000}, and the widths are in agreement with the expected detector resolutions. For the $D$ meson differential distributions the data sample is divided into bins and the number of signal events is extracted in each bin separately. The position and width of the Gaussian describing the signal are fixed to the values found in the inclusive sample. If left free both positions and widths are found to be stable. % and the remaining differences are included in the systematic errors. %% -------------------------------------------------------------- \subsection{Acceptance and Efficiency Determination} \label{simulation} The Monte Carlo simulation of charm and beauty production is used to determine the detector acceptance and the efficiency of the reconstruction and selection cuts. % % v1.0 , and again in v1.3 The detector efficiencies are determined to be around $60\%$ for events within the combined geometric and kinematic acceptances, which vary between $36\%$ and $62\%$ for the different mesons. % %the detector efficiencies %are determined to be 58$\%$, 68$\%$, 57$\%$ and 60$\%$ for events within the %acceptances of 36$\%$, 44$\%$, 49$\%$ and 62$\%$ (including %the geometrical and kinematical acceptance requirements). %pure vertexing=lifetime efficiencies The lifetime tagging efficiencies are found to be 19$\%$, 11$\%$, 21$\%$ and 39$\%$, for $\Dplus$, $\Dzero$, $\Dsubsplus$ and $\Dstarplus$, respectively. %--------------- Migrations due to the limited detector resolution are small for the chosen bin sizes in the differential distributions and are corrected by means of Monte Carlo simulation. % ------------------------------------------------------------ \subsection{Cross Section Determination and Systematic Errors} The visible cross section $\sigma_{\it vis}$ is defined for the sum of the observed number of $D$ mesons, $N_D$, for both particle and antiparticle meson states according to the formula \begin{equation} \sigma_{vis}(ep \rightarrow e' D X) = \frac{N_{D} + N_{\bar{D}}} { {\cal L} \cdot \epsilon \cdot (1 + \delta_{rad}) }\qquad , \label{eq:sigman} \end{equation} where $\cal{L}$ denotes the integrated luminosity and $\epsilon$ the total efficiency including all acceptances and branching ratios, which are taken from \cite{PDG2000}. The radiative corrections $\delta_{rad}$ correct the measured cross sections to the Born level and are calculated using the program HECTOR\cite{Arbuzov:1995id}. They amount to $\delta_{rad} = 2.6 \%$ on average and vary between $-4\%$ and $+9\%$ over the kinematic range considered. %% -------------------------------------------------------------- % here are the systematic errors. The systematic errors on $\sigma_{\it vis}$, summarised in table~\ref{tab:syserr}, are dominated by the uncertainty on the CJC tracking efficiency (conservatively estimated to $^{+5}_{-1}\% $ per track in this analysis). A $10 \% $ uncertainty is assigned to the lifetime cut efficiency to account for a possible inaccuracy in the description of the resolution function in the simulation. This number is estimated by variations of the $S_l$-cut and covers the differences between data and simulation~\cite{Gassner:2002ji}. % The CST efficiency uncertainty is $1\%$ per hit. The systematic error on the signal extraction is determined by variation of the background shapes in the fits. Backgrounds to the signals from other charm decays are estimated from Monte Carlo simulations to be at most $3\%$ and are also included in the systematic errors. % The dependence of the simulated acceptances and efficiencies on parameter choices made for the simulation (charm mass, parton density distributions, fragmentation parameters and QCD scales, cf. section~\ref{sec:th}) is found to be less than $\pm 2\% $ in all cases and is included in the systematic error. The uncertainty on the absolute SpaCal electromagnetic energy scale contributes a maximal change in $\sigma_{\it vis}$ of $^{+4}_{-9}\%$. The error due to initial state radiation (ISR) corrections is estimated to be $\pm 2.6\% $, the average size of the correction itself. The results obtained when reconstructing the kinematic variables using the scattered positron have been checked with the $\Sigma$-method, which combines the hadronic final state and the positron measurement\cite{Bassler:1994uq} and are found to be in good agreement. The electron detection, the tracking and the vertexing errors are to a large extent common between the different mesons and result in correlated systematic errors of about 15\%. The $\Dsubs$ meson suffers from a particularly large ($24.7\%$) uncertainty due to the poorly known branching fraction to $\phi \pi$. \subsection{Theoretical predictions and uncertainties} \label{sec:th} % The measured cross sections are compared with LO QCD predictions based on the AROMA 2.2~\cite{Ingelman:1996mv} program, which incorporates the universality ansatz. The predictions include the contributions from decays of excited charmed hadrons. % For the nominal predictions the program is run using the GRV-98 proton structure function parametrisation\cite{Gluck:1998xa}, a charm quark mass of $m_c=1.5$ GeV and Peterson fragmentation with $\epsilon_c = 0.078$. The contributions of decays of beauty hadrons is simulated using a quark mass of $m_b=4.75$ GeV and $\epsilon_b = 0.0069$. It is scaled %by a factor 4.3 to reproduce the result of \cite{h1-bxsec-dis}. The renormalisation and factorisation scales are both set to $\mu = \sqrt{Q^2+ m_t^2(q) + m_t^2({\bar q})}$, where $m_t(q) = \sqrt{p_t^2 + m_q^2}$ is the ``transverse'' mass of the quark $q$. % The prediction uncertainties are estimated by simultanously changing the renormalisation and factorisation scales by a factor of two or 0.5, varying $m_c$ between 1.4 GeV and 1.6 GeV, and changing $\epsilon_c$ to $0.048$. The contributions are added in quadrature. They are dominated by the quark mass and fragmentation parameter variations (for details see \cite{Gassner:2002ji}). %Order of uncertainty is $\sim$ 10\% % For the $\Dstar$ meson production cross section the AROMA prediction is also compared with a next to leading order (NLO) calculation in the DGLAP scheme \cite{ref:DGLAP} using the HVQDIS program \cite{Harris:1997zq}. % The GRV98-HO parton densities of the proton\cite{Gluck:1998xa} are used, supplemented by a Peterson fragmentation parametrisation with $\epsilon_c = 0.035$ and $\epsilon_b = 0.0033$ as in \cite{Nason:1999zj,Nason:1998ug}. % The renormalisation and factorisation scales are both set to $\mu = \sqrt{Q^2+ 4 m_q^2}$ with the same quark mass values as are used for the AROMA simulation. %and the quark masses are set to $m_c = 1.5$ GeV and $m_b = 4.75$ GeV. % The uncertainties on the NLO prediction are estimated analogously to the LO case. They are dominated by variations of the renormalisation and factorisation scales and by changing the mass $m_c$ between 1.3 GeV and 1.7 GeV ~\cite{Frixione:nn}. % see the ref. on page 1146, which states: % HVQDIS favours a mass of 1.5 +- 0.2 % also Frixione+Nason in hep-ph/0201281 use 1.3 to 1.7 % % use $\epsilon_c$ to $0.045$ and ifferent PDF functions % - CTEQ4F3 - CTEQ5F3 - GRV98 - % do not contribute significantly. Added in quadrature, the total uncertainties are of approximately $15 \% $. % %% -------------------------------------------------------------- \section{Results} %_________________________________________________________________________________ % %First, the inclusive production cross section measurements of the %four $D$ mesons are presented, followed by %measurements of the differential cross sections. %Based on the inclusive cross section values, fragmentation factors are extracted. %They are then used to determine various ratios sensitive to different %aspects of fragmentation. These ratios are compared with previous %measurements. \subsection{Differential Production Cross Sections} Differential production cross sections are determined for all four $D$ mesons individually and are tabulated in tables~\ref{tab:dplus}-\ref{tab:dstar}. As an example the results for the \dc\ meson are shown in figure~\ref{fig:dc-xsec} as a function of the kinematic variables $p_t(D^+)$, $\eta(D^+)$, $Q^2$ and $y$. For all mesons the cross sections fall rapidly with $Q^2$ and $p_{t}(D)$, as expected from the hard scattering. % The distributions are well reproduced by the LO AROMA simulation, which is overlaid in figure~\ref{fig:dc-xsec}. The estimated beauty contributions are shown separately as dashed lines. The shaded bands indicate the uncertainties on the predictions. The differential distributions for the remaining $D^0, D_S$ and $D^*$ mesons are equally well described by the LO QCD simulation~\cite{Gassner:2002ji}. %The cross sections are tabulated in tables~\ref{tab:dstar}-\ref{tab:dsubs}. %The values are bin averaged, no bin-center correction has been applied. For a direct comparison of the differential cross sections extracted for the four different $D$ mesons, the differential cross sections have been scaled with the inverse fragmentation factors derived further below (cf. table~\ref{tab:ffrag}) and are shown in figure~\ref{fig:all-xsec} as a function of $p_t(D)$, $\eta(D)$ and $Q^2$. Within the present experimental accuracy the normalised cross sections are compatible with one another. %_________________________________________________________________________________ \subsection{Inclusive Production Cross Sections} The inclusive electroproduction cross sections are determined in the visible kinematic range of $2 \le Q^2 \le 100~\gev^2$, \ $0.05 \le y \le 0.7$, \ $p_t(D) \ge 2.5~\GeV$ and \ $|\eta(D)| \le 1.5$. The measured values for the four $D$ mesons are summarised in table~\ref{tab:xsection}. % The $\Dstar$ meson results are consistent with earlier measurements at HERA\cite{Adloff:1998vb, Adloff:2001wr, Adloff:2001zj, Breitweg:1999ad, Chekanov:2003rb} once the differences in kinematic regions are taken into account. % For the $\Dstar$ meson the visible production cross section has also been calculated in the next to leading order (NLO) DGLAP scheme\cite{ref:DGLAP} with the HVQDIS program \cite{Harris:1997zq} (see section~\ref{sec:th}). % The NLO prediction yields a value of $\sigma_{\it vis} = 2.76\pm 0.41$~nb for the $\Dstar$, which is in good agreement with the LO AROMA value of $2.61\pm 0.31$~nb. %albeit with an appropriately different set of fragmentation %parameters\cite{Nason:1999zj}. % %%%Note: the NLO value is HVQDIS (c + 2.15*b); not 4.3 * b which is for LO). % % -- old comparison paragraph: %In order to compare the measurements with previous results\footnote{All %earlier results have been obtained at $\sqrt{s}=300\,$GeV. %A correction for the $\sqrt{s}$ of this analysis raises the referred cross sections % by typically 5\%.}, $\sigma(ep \to e \Dstar X)$ has also been %determined in the kinematic range of %the earlier H1 publication \cite{Adloff:1998vb}, where a %lower $p_t(\Dstar)$ cut of $1.5$~GeV$/c$ was used. The present analysis %yields in that range a value of %$\sigma_{\it vis} = 5.28$~nb, %which agrees within errors with the published H1 value %of $(5.75 \pm 0.35 \pm 0.79)$~nb and also with the %QCD predictions of 5.53~nb at LO and of 5.77~nb at NLO. %% %The present result is also consistent within one standard deviation %with the H1 measurement~\cite{Adloff:2001wr}. %%%% published =$4.17 \pm 0.9$~nb ; present ana = $3.82\pm 0.23$~nb; LO=3.86~nb). %When extrapolated into the significantly different kinematical region %of ref.\cite{Adloff:2001zj} ($1 < Q^2 < 100 \ \gev^2$ and %$p_t(D^*)\ > 1.5 \gev /c $) the cross section is %lower than the value found in \cite{Adloff:2001zj}. %The difference amounts to about 3 $\sigma$ of the statistical errors %of the two independent event samples when no uncertainty is %attributed to the extrapolation procedure. %However, the large systematic errors of the track reconstruction %is to a large extent uncorrelated between the two different data %taking periods. %The difference in the observed visible cross sections can thus be %accomodated within the total error. % Note for explanation: % Zeus values are in agreement with LO and NLO % Note, that the ZEUS experiment founds that their $D^*$ % cross section measurement $8.31 \pm0.31 $ nb % is well described by the NLO prediction of 8.44 nb, % in a very similar kinematical region. % ZEUS D* EPJ C12(00)1 & % $ pt = [\ 1.5,\,15.\ ]$ & $ Q^2 = [\ 1,\,600\ ]$ % $y [.02,.7]$ % ZEUS result = $8.31 \pm0.31 ^{+0.30}_{-0.50} $ nb % HVQDIS NLO prediction = 8.44 nb %%%%%%%%% -- end comparison with previous pubs %% -------------------------------------------------------------------- \subsection{Fragmentation Factors and Ratios} % In the absence of decays of excited intermediate charm states, the relative abundance of the various charmed hadrons is given by the primary production rate, which is directly proportional to $n_D$, the normalisation of the fragmentation functions (equation~\ref{eq:f3}). However, the experimentally determined fragmentation factors $f^{}(c\rightarrow D)$ include all possible decay chains that result in that particular $D$ meson, in addition to the direct production. % Thus, the measured pseudoscalar $D^+$, $D^0$ and $D_s$ mesons contain a large fraction of mesons produced in $D^*_{(s)}$ decays. The fragmentation factors $f^{}(c\rightarrow D)$ are deduced from a comparison of the measured cross sections $\sigma_{vis}$ with the LO expectation $\sigma_{vis}^{MC}$ after correcting for the beauty contribution to which an uncertainty of 50\% is attributed. Explicitly, the following relationship is used: \begin{eqnarray} \displaystyle f^{}(c\rightarrow D) = \frac{\displaystyle \sigma_{\it vis}(ep \rightarrow e'DX) - \sigma^{\it MC}_{\it vis} (ep \rightarrow e' b\bar{b}X' \rightarrow e'DX)} % { \displaystyle \sigma^{\it MC}_{\it vis} (ep \rightarrow c\bar{c} \rightarrow e'DX)} \cdot \displaystyle f_{\rm wa}(c \rightarrow D). \end{eqnarray} The resulting values for $f(c\rightarrow D)$ are listed in table~\ref{tab:ffrag}. For comparison, the world average values $f_{\rm wa}(c\rightarrow D)$ are also shown. The measurements $f(c\rightarrow D)$ agree well within errors with the world average values $f_{\rm wa}(c\rightarrow D)$. Constraints can be explicitly imposed on the measurements to improve the experimental accuracy. The constraint %(equation~\ref{eq:constraintsone}) \begin{eqnarray} 1 & = & f(c \to D^+) + f(c \to {D^0}) + f(c \to D_s) + f(c \to \Lambda_c, \Xi_c, \Omega_c) \label{eq:constraintsone} \end{eqnarray} introduces contributions of fragmentation to charmed baryons, which are not determined in this analysis. World average values~\cite{PDG2000} are taken instead, yielding a %the contributions from $\Lambda_c, \Xi_c$ and $\Omega_c$ baryons sum up to a total of $f(c \to \Lambda_c, \Xi_c, \Omega_c) = 8.64 \pm 2.50\% $. The constraint% (equation~\ref{eq:constraintstwo}) \begin{eqnarray} f(c \to D^+) & = & f(c \to {D^0}) - 2 \cdot f(c \to D^{*+}) \cdot \BR(D^{*+} \to D^0 \pi) \label{eq:constraintstwo} \end{eqnarray} is derived by assuming isospin symmetry independently in both the vector and pseudoscalar sectors ($n_{D^{*+}} = n_{D^{*0}}$\ and $n_{D^{+}} = n_{D^{0}}$). The branching fraction $\BR(D^{*+} \to D^0 \pi)$ is taken as $67.6 \pm 0.5~\%$~\cite{PDG2000}. The $D^{*0}$ mesons, which are not explicitly reconstructed in this analysis, are assumed to decay entirely into final states containing a $D^0$ meson~\cite{PDG2000}. The results of a fit for the fragmentation factors using the constraints of equation~\ref{eq:constraintsone} and equation~\ref{eq:constraintstwo} are listed separately in table~\ref{tab:ffrag} as $f_{\rm constraint}(c \to D)$. The fit takes the correlations of the uncertainties between the different mesons into account. In comparison with the unconstrained results the errors are reduced and the value $f(c\to D^0)$ moves closer to the world average, whereas the other factors do not change significantly. %_________________________________________________________________________________ Ratios of fragmentation factors are useful to characterise distinct aspects of fragmentation, such as the proportions of light quark flavours $u,d$ and $s$ created in the fragmentation process and the formation of different angular momentum states. Such quantities have been measured in light quark fragmentation and charm fragmentation in $e^+e^-$ annihilation~\cite{Nason:1999zj,Albrecht:1991ss,Akers:1994jc,Buskulic:1995gp}. It is important to verify their applicability for deep inelastic scattering. Various ratios are extracted from the $D$ meson fragmentation factors obtained without the constraints of equations~\ref{eq:constraintsone} and ~\ref{eq:constraintstwo}. The common experimental uncertainties largely cancel in this procedure. Expressed both in terms of the normalisation factors for primary $D$ mesons produced, $n_D$, and in terms of the experimentally accessible fragmentation factors $ f(c \rightarrow D)$, the ratios considered are: %For clarity, the numbers for primary produced vector mesons %($D^{*+},D^{*0},D^{*+}_s $) and for primary produced pseudoscalar mesons %($ D^+, D^0, D^+_{s} $ ) are spelled out explicitly \setlength{\jot}{1.5mm} \begin{eqnarray} P_V^{d} = & \frac{n_{D^{*+}}} {n_{D^{*+}}+n_{D^+}} & = \frac{f(c \rightarrow D^{*+})} {f(c\rightarrow D^+) +f(c\rightarrow D^{*+})\cdot {\it \BR}(D^{*+}\rightarrow D^0\pi^+)}; \label{eq:pvd} \\ % P_V^{u+d} = & \frac{2 \cdot n_{D^{*+}}}{n_{D^{*+}}+n_{D^+}+n_{D^{*0}}+n_{D^0}} & = \qquad \qquad \frac{2\cdot f(c \rightarrow D^{*+})}{f(c\rightarrow D^+) +f(c\rightarrow D^0)}; \label{eq:pvud}\\ % R_{u/d} = & \frac{n_{D^{*0}}+n_{D^0}} {n_{D^{*+}}+n_{D^+}} & = \frac{ f(c\rightarrow D^0) -f(c\rightarrow D^{*+})\cdot {\it \BR}(D^{*+}\rightarrow D^0\pi^+)} { f(c\rightarrow D^+) +f(c\rightarrow D^{*+})\cdot {\it \BR}(D^{*+}\rightarrow D^0\pi^+)}; \label{eq:rud}\\ % \gamma_s = & \frac{2 \cdot (n_{D^{*+}_{s}}+n_{D^+_{s}})}{n_{D^{*+}}+n_{D^+}+n_{D^{*0}}+n_{D^0}} & = \qquad \qquad \frac{ 2\cdot f(c \rightarrow D_s^+)}{ f(c\rightarrow D^+) +f(c\rightarrow D^0)}. \label{eq:gammas} \end{eqnarray} %------------------------------------- \noindent The fragmentation characteristics derived according to equations~\ref{eq:pvd}-\ref{eq:gammas} are summarised in table~\ref{tab:fratios}. The ratio $P_{V}$ measures the fraction of vector mesons produced in the fragmentation chain. This ratio has been evaluated separately for the $c\bar{d}$-quark combination (equation~\ref{eq:pvd}) and the sum of $c\bar{u}$ and $c\bar{d}$ quark combinations (equation~\ref{eq:pvud}). Isospin invariance $ f(c\rightarrow D^{*+}) = f(c\rightarrow D^{*0}) $ has been assumed for $P_V^{u+d}$ and the result agrees well with values measured at LEP~\cite{ff:aleph,ff:delphi}. The $P_V^d$ result is larger than the LEP value by around 1.5 sigma. The ratio $R_{u/d}$ of probabilities for a charm quark to hadronise together with a $u$ or $d$-quark agrees well with a value of unity, as is also the case at LEP~\cite{ff:aleph}. The suppression of $s$-quarks with respect to $u$ and $d$ quarks is measured by the factor $\gamma_{s}$. The value of $\gamma_{s}$ extracted in this analysis suggests a suppression of almost a factor 3. This observation agrees well with the suppression factor measured in the fragmentation of primary light quarks and with measurements of charm fragmentation in $e^+e^-$~\cite{ff:ado}. %_________________________________________________________________________________ \section{Conclusions} Production cross sections of the charmed mesons $\Dplus$, $\Dzero$, $\Dsubs$ and $D^{*+}$ are measured in deep inelastic $ep$ collisions at HERA. The measurements rely on the precise reconstruction of the $D$ meson production and decay vertices using the central silicon tracker of the H1 detector. % The differential production cross sections of all four $D$ mesons measured in the same kinematic region show a very similar dependence on the transverse momentum $p_t(D)$ and the pseudorapidity $\eta(D)$ of the charmed hadron, as well as on the photon virtuality $Q^2$. Based on the measured cross sections, the fragmentation factors $ f(c\rightarrow D)$ are extracted. They are found to agree with the world average values, which are dominated by measurements made in $e^+e^-$ collisions. Based on ratios of these $ f(c\rightarrow D)$ the fragmentation-sensitive parameters $P_V$, $R_{u/d}$ and $\gamma_{s}$ are determined. They are also in agreement with the world average values. The measurements of the cross sections and of the fragmentation-sensitive ratios thus support the validity of the commonly made assumptions that the charm quark production and the fragmentation processes factorise and that the non-perturbative component of the hadronisation $D_D^{(c)}(z)$ is well described by a universal fragmentation ansatz, independent of the hard scattering process and of the charm production scale. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Acknowledgements} We are grateful to the HERA machine group whose outstanding efforts have made this experiment possible. 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The hadronisation into a charmed meson $D$ is described by the fragmentation function $D_D^{(c)}(z)$ (cf. equation~\ref{eq:f3}). } \label{fig:bgf} \end{center} \end{figure} \vspace{2cm} %% -------------------------------------------------------------- % Decay length significance for tagged D0 and \begin{figure}[htb] \begin{center} \epsfig{file=eps/dstar_Sl_sig_decomp.eps,width=16cm} \icaption{ %\large a) Invariant mass distribution $m(K\pi)$ and b) signed decay length significance distribution $S_l$ measured for tagged $\Dzero$ mesons in data (solid points). Superimposed is the fitted decomposition into signal ($S$, hatched) and background ($B$, shaded) contributions (see text). The background in b) is determined from the $m(K\pi)$ sideband regions $(sb)$ as indicated in a). } \label{fig:eff-sl} \end{center} \end{figure} %% ------------------- % %% Phenix plot for D+ \begin{figure}[hhh] \begin{center} \epsfig{file=eps/dc_phoenix5.eps,width=16. cm} \icaption{ %\large Invariant mass distributions $m(K \pi \pi)$ for $D^+ \rightarrow K^- \pi^+ \pi^+$ decay candidates (a) before and (b) after a cut on the decay length significance $S_l> 8$.} %where $l$ is the radial separation distance between the meson production and its decay vertex, %and $\sigma_l$ the error of $l$. %When vertexing information measured with the CST is exploited, %the background contribution is suppressed by $\cal O$(300) and the signal to background ratio %is improved by a factor $\cal O$(50) while retaining $\cal O$(20 $\%)$ of %the signal.} \label{fig:phenix} \end{center} \end{figure} %% -------------------------------------------------------------- % %% all four signals from CST \begin{figure}[tb] \begin{center} \epsfig{file=eps/dmeson_signals.eps} % \epsfig{file=eps/dstar_vfit2dc_signal3.eps,width=7.8cm} \end{center} \icaption{ %\large Invariant mass distributions for the four $D$ meson candidate decays that are used to determine the number of signal events: a) $\Dplus \to K^- \pi^+ \pi^+$, b) $\Dzero \to K^- \pi^+$, c) $\Dsubsplus \to \phi \pi^+ \to K^+ K^- \pi^+$ and d) $\Dstarplus \to \Dzero \pi^+_s \to K^- \pi^+ \pi^+_s$ ( the invariant mass $m(K \pi)$ is shown after the $\Delta m$ cut). The curves show the fits in which the signals are described by a Gaussian and the backgrounds are parametrised as discussed in the text. } \label{fig:dall-cst} \end{figure} %% -------------------------------------------------------------- % %% Dplus DIFFERENTIAL \begin{figure}[tb] \begin{center} \epsfig{file=eps/dc_differential.eps,width=16cm} \end{center} \icaption{ %\large Differential production cross section for \dc \ as a function of %the $\Dplus$ variables a) the \dc \ transverse momentum $p_t(D^+)$, b) the pseudorapidity $\eta(D^+)$, c) the photon virtuality $Q^2$, and d) the inelasticity $y$. The symbols denote the values averaged over the bins and are plotted at the bin centres. The error bars show the statistical (inner bars) and the total (outer bars) errors, respectively. The solid lines show the LO AROMA predictions including scaled beauty contributions, shown separately as dashed lines. The shaded bands indicate the uncertainties on the predictions (see text).} \label{fig:dc-xsec} \end{figure} %_________________________________________________________________________________ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %% ALL DIFFERENTIAL \begin{figure}[htb] \begin{center} \epsfig{file=eps/all_xsections.eps} \end{center} \icaption{ %\large Visible differential production cross sections for all four $D$ mesons, divided by their respective measured fragmentation factors, are shown as a function of a) the $D$ meson transverse momentum $p_t(D)$, b) the pseudorapidity $\eta(D)$, and c) photon virtuality $Q^2$. The error bars indicate the quadratic sum of the statistical errors and the systematic errors which are not common to the different $D$ mesons. An overall common systematic error of $15\%$ is not shown. The cross sections are displayed on the horizontal axis at the position that corresponds to the average differential cross section, obtained using the AROMA simulation. } \label{fig:all-xsec} \end{figure} \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Tables %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htb] \renewcommand{\arraystretch}{1.1} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline {\bf Selection criteria} & \dc & \dn & \ds & \dst \\ \hline min $p_t(K)\ [ \mev ]\ $ & 500 & 800 & 400 & 250 \\ min $p_t(\pi)\ \ [ \mev ]\ $ & 400 & 800 & 400 & 250 \\ min $p_t(\pi_s)\ [ \mev ]\ $ & - & - & - & 140 \\ % min $|\cos(\theta^*)|\ $ & - & - & 0.4 & - \\ \hline min impact par. sig. $ S_d $ & 2.5 & 2 & 1 & -1 \\ % $\max(p_t)\ >$ & \multicolumn{4}{c|}{$800\,MeV/c$} \\ % $\theta_{\it track}\ $ & \multicolumn{4}{c|}{$[\ 20^\circ,\,160^\circ\,]$} \\ min decay length sig. $ S_l $ & 5 & 3 & 2 & 1 \\ \hline max decay length error $ \sigma_l $ & \multicolumn{4}{c|}{300~$\mu$m} \\ min fit probability ${\cal P}_{\it VF} $ & \multicolumn{4}{c|}{ 0.05} \\ \hline \end{tabular} \end{center} \icaption{ %\large Selection criteria for each of the four $D$ mesons. Listed are the minimal transverse momenta of the daughter tracks (cuts on the slow pion $\pi_s$ are only applicable for the $D^*$ meson) and the requirements on the vertexing parameters (see text). } \label{tab:selection} \end{table} % % -------------------------------------------------------------------------- \begin{table}[htb] \renewcommand{\arraystretch}{1.4} \centering \begin{tabular}{|c|c|c|c|c|} \hline {\bf Source of uncertainty} & \dc & \dn & \ds & \dst \\ %\hline \hline %Acceptance & \multicolumn{4}{c|}{$< 2.0$}\\ %\hline CJC efficiency & $^{+15.0}_{\ -3.0}$ & $^{+10.0}_{\ -2.0}$ & $^{+15.0}_{\ -3.0}$ & $^{+15.0}_{\ -3.0}$ \\ \hline %CJC resolution ($\pm10\%$) & $^{+3.0}_{-1.5}$ & $^{+0.6}_{-0.7}$ &$^{+1.8}_{-3.7}$ & $^{+2.4}_{-0.5}$ \\ %\hline CST efficiency & $\pm 5.6$ & $\pm 3.6$ & $\pm 5.4$ & $\pm 3.6$ \\ \hline %CST resolution ($\pm20\%$) & $^{+2.0}_{-1.0}$ & $^{+0.4}_{-0.1}$ & $^{+0.1}_{-3.6}$ & $^{+1.5}_{-0.2}$ \\ %\hline Lifetime tag & \multicolumn{4}{c|}{$\pm 10.0$} \\ \hline %SpaCal calibration ($\pm4\%$) & $^{+3.6}_{-7.3}$ & $^{+3.4}_{-8.1}$ & $^{+4.5}_{-7.8}$ & $^{+4.5}_{-9.0}$ \\ %\hline Signal extraction & $^{+1.7}_{-0.4}$ & $^{\ +4.9}_{-13.4}$ & $^{\ +1.4}_{-12.1}$ & $^{+3.7}_{-3.2}$ \\ \hline Branching fraction & $\pm6.7$ & $\pm2.3$ & $\pm24.7$ \ & $\pm2.3$ \\ \hline %ISR correction & \multicolumn{4}{c|}{$\pm2.6$} \\ %\hline %trigger efficiency & \multicolumn{4}{c|}{$\pm1.0$} \\ %\hline %others & \multicolumn{4}{c|}{$< 2$} \\ %\hline \hline Total systematic error & $^{+21.2}_{-16.0}$ & $^{+16.5}_{-19.9}$ & $^{+32.0}_{-31.8}$ & $^{+20.0}_{-15.2}$ \\ \hline \end{tabular} \icaption{ %\large Percentage systematic errors on the inclusive cross sections for the different $D$ mesons. Only the dominant contributions and the total error are shown. } \label{tab:syserr} \end{table} % % -------------------------------------------------------------------------- % % \begin{table}[htb] \renewcommand{\arraystretch}{1.2} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline {\bf Cross section [nb]} & \dc & \dn & \ds & \dst \\ % \hline \hline $\sigma_{\it vis}(ep \rightarrow eDX)$ & $2.16$ & $6.53$ & $1.67$ & $2.90$ \\ Stat.\ error & $\pm 0.19$ & $\pm 0.49$ & $\pm 0.41$ & $\pm 0.20$ \\ Syst.\ error & $^{+0.46}_{-0.35}$ & $^{+1.06}_{-1.30}$ & $^{+0.54}_{-0.54}$ & $^{+0.58}_{-0.44}$ \\ \hline AROMA LO prediction $ \sigma_{\it vis}$ & $2.45$ & $5.54$ & $1.15$ & $2.61$ \\ Prediction uncertainty & $\pm 0.30$ & $\pm 0.69$ & $\pm 0.30$& $\pm 0.31 $ \\ \hline Estimated beauty contribution & $10\%$ & $9\%$ & $17\%$ & $7\%$ \\ \hline \end{tabular} \end{center} \icaption{ %\large Inclusive charmed meson electroproduction cross sections for the four meson states in the visible kinematic range, defined by $2\, \le \,Q^2 \le 100\, \GeV^2,\ \ 0.05 \le y \le 0.7, \ p_t(D) \ge 2.5\,\GeV$ and $|\eta(D)| \le 1.5. $ Also given are the predictions for $D$ meson production (including the beauty contribution) based on a LO Monte Carlo simulation. } \label{tab:xsection} \end{table} % -------------------------------------------------------------------------- % \begin{table}[tbh] %\large \renewcommand{\arraystretch}{1.35} \begin{center} %\hspace*{-1.cm} \begin{tabular}{|c|c|c|c|c|} \hline {\bf Fragmentation factors} & \dc & \dn & \ds & \dst \\ \hline $ f(c \to D)$ & $0.202$ & $0.658$ & $0.156$ & $0.263$ \\ Stat.\ error & $\pm 0.020$ & $\pm 0.054$ & $\pm 0.043$ & $\pm 0.019 $ \\ Syst.\ error & $^{+0.045}_{-0.033}$ & $^{+0.117}_{-0.142}$ & $^{+0.036}_{-0.035}$ & $^{+0.056}_{-0.042}$\\ Theo.\ error & $^{+0.029}_{-0.021}$ & $^{+0.086}_{-0.048}$ & $^{+0.050}_{-0.046}$ & $^{+0.031}_{-0.022}$ \\ \hline $f_{\rm constraint}(c \to D)$ & $0.203$ & $0.560$ & $0.151$ & $0.263$ \\ Total error & $\pm 0.026$ & $\pm 0.046$ & $\pm 0.055$ & $\pm 0.032 $ \\ \hline $f_{\rm wa}(c \to D)$ & $0.232 \pm 0.018$ & $0.549 \pm 0.026$ & $0.101 \pm 0.027$ & $0.235 \pm 0.010$ \\ \hline \end{tabular} \end{center} \icaption{ % \large Fragmentation factors deduced from the measured cross sections. The small $b$~contributions are subtracted. Also listed is the result of the constrained fit $f_{\rm constraint}(c \to D)$, its error (see text), and the world average numbers, given as $f_{\rm wa}(c \to D)$. The theoretical errors include the branching ratio uncertainty and the model dependences of the acceptance determination. } \label{tab:ffrag} \end{table} % -------------------------------------------------------------------------- % \begin{table}[tbh] \renewcommand{\arraystretch}{1.1} \begin{center} \begin{tabular}{|c|cccc|ccr|} \hline {\bf Ratio} & \multicolumn{4}{c|}{{\bf this measurement}} & \multicolumn{3}{c|}{{\bf $e^+e^-$ experiments}} \\ % \hline & value & stat.error & syst.error & theo.error & value & error & ref. \\ \hline $P_V^d$ & $0.693$ & $\pm$ $0.045$ & $\pm$ $0.004$ & $\pm$ $0.009$ & $0.595$ & $\pm$ $0.045$ & \cite{ff:aleph} \\ $P_V^{u+d}$ & $0.613$ & $\pm$ $0.061$ & $\pm$ $0.033$ & $\pm$ $0.008$ & $0.620$ & $\pm$ $0.014$ & \cite{ff:delphi}\\ $R_{u/d}$ & $1.26$ & $\pm$ $0.20$ & $\pm$ $0.11$ & $\pm$ $0.04$ & $1.02$ & $\pm$ $0.12$ & \cite{ff:aleph} \\ $\gamma_s$ & $0.36$ & $\pm$ $0.10$ & $\pm$ $0.01$ & $\pm$ $0.08$ & $0.31$ & $\pm$ $0.07$ & \cite{ff:ado} \\ \hline \end{tabular} \end{center} \icaption{Fragmentation characteristics derived according to equations~\ref{eq:pvd}-\ref{eq:gammas} from the ratios of the fragmentation factors of table~\ref{tab:ffrag}. Values measured by $e^+e^-$ experiments are also quoted. The theoretical errors include the branching ratio uncertainty and the model dependences of the acceptance determination. } \label{tab:fratios} \end{table} \clearpage % \section*{} %======================================================================================= % % tables with bin wise x-sections: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % D+ decay channel: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % tables with bin wise x-sections: % \begin{center} \begin{table}[h] % \vspace*{\textheight} \vspace*{1cm} \hspace*{1.5cm} \renewcommand{\arraystretch}{1.6} \scriptsize % % bins related to D-meson kinematics \begin{tabular}[t]{|@{\quad $[$\ }c@{\ $]$\quad }|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{\small $p_t(D^+)$} & \small ${\rm d}\sigma_{vis}/{\rm d}p_t$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}\:]$} & $[\unit{nb/GeV}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline 2.5, \,\ 3.0 & \small 1.95\; & $\pm0.32\; $ & $+0.41\;$ & $-0.34\; $ & $+0.13\;$ & $-0.14\;$ \\ 3.0, \,\ 3.5 & \small 1.05\; & $\pm0.18\; $ & $+0.22\;$ & $-0.17\; $ & $+0.07\;$ & $-0.08\;$ \\ 3.5, \,\ 4.0 & \small 0.556 & $\pm0.128 $ & $+0.121$ & $-0.090$ & $+0.039$ & $-0.039$ \\ 4.0, \,\ 5.0 & \small 0.353 & $\pm0.054$ & $+0.104$ & $-0.054$ & $+0.026$ & $-0.024$ \\ 5.0, \,\ 6.0 & \small 0.063 & $\pm0.023$ & $+0.072$ & $-0.010$ & $+0.004$ & $-0.005$ \\ 6.0, 10.0 & \small 0.025 & $\pm0.005$ & $+0.005$ & $-0.004$ & $+0.002$ & $-0.002$ \\ \hline % \multicolumn{7}{c}{}\\ \hline \multicolumn{1}{|c|}{\small $\eta(D^+)$} & \small ${\rm d}\sigma_{vis}/{\rm d}\eta$ & \multicolumn{5}{c|}{errors \ $[\unit{nb}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{} & $[\unit{nb}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline -1.50, -1.00 & \small 0.84 & $\pm0.16$ & $+0.25$ & $-0.12$ & $+0.06$ & $-0.08$ \\ -1.00, -0.50 & \small 0.97 & $\pm0.15$ & $+0.20$ & $-0.14$ & $+0.07$ & $-0.07$ \\ -0.50, \ 0.00 & \small 0.66 & $\pm0.12$ & $+0.14$ & $-0.10$ & $+0.05$ & $-0.04$ \\ \ 0.00, \ 0.50 & \small 0.83 & $\pm0.13$ & $+0.18$ & $-0.13$ & $+0.06$ & $-0.06$ \\ \ 0.50, \ 1.00 & \small 0.76 & $\pm0.15$ & $+0.36$ & $-0.22$ & $+0.06$ & $-0.05$ \\ \ 1.00, \ 1.50 & \small 0.28 & $\pm0.13$ & $+0.15$ & $-0.09$ & $+0.02$ & $-0.03$ \\ \hline % \multicolumn{7}{c}{\parbox[l][8mm][c]{11cm}{}} \\ \hline \multicolumn{1}{|c|}{\small $Q^2$} & \small ${\rm d}\sigma_{vis}/{\rm d}Q^2$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}^2\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}^2\,]$} & $[\unit{nb/GeV}^2\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ % \hline \,\ 2, \ \ \ 4 & \small 0.200\; & $\pm0.038\; $ & $+0.047\; $ & $-0.033\; $ & $+0.014\; $ & $-0.015\;$ \\ \,\ 4, \ \ \ 7 & \small 0.155\; & $\pm0.025\; $ & $+0.034\; $ & $-0.025\; $ & $+0.011\;$ & $-0.011\; $ \\ \,\ 7, \,\ 12 & \small 0.095\; & $\pm0.015\; $ & $+0.021\; $ & $-0.014\; $ & $+0.008\;$ & $-0.007\; $ \\ 12, \,\ 22 & \small 0.0373 & $\pm0.0072$ & $+0.0105$ & $-0.0060$ & $+0.0025$ & $-0.0027$ \\ 22, \,\ 35 & \small 0.0153 & $\pm0.0036$ & $+0.0033$ & $-0.0026$ & $+0.0010$ & $-0.0012$ \\ 35, 100 & \small 0.0042 & $\pm0.0009$ & $+0.0009$ & $-0.0007$ & $+0.0003$ & $-0.0003$ \\ \hline % \end{tabular} % \caption[Single differential \dc\ production cross section results] \icaption{\label{tab.dc.xsec.bins} The bin-averaged single differential \dc\ production cross section measurements $\sigma_{vis}(ep\rightarrow eD^+X)$ with statistical, experimental systematic and theoretical errors. The latter include the uncertainties of the branching ratio and the model dependence of the acceptance determination.} % \label{tab:dplus} \end{table} \end{center} \clearpage % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % D0 decay channel: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % tables with bin wise x-sections: % \begin{center} \begin{table}[th] % \vspace*{\textheight} \vspace*{1cm} \hspace*{1.5cm} \renewcommand{\arraystretch}{1.6} \scriptsize % % bins related to D-meson kinematics \begin{tabular}[t]{|@{\quad $[$\ }c@{\ $]$\quad }|c|c|c|c|c|c|} %CG \multicolumn{7}{c}{\parbox[l][8mm][c]{11cm}{\normalsize %CG $\sigma_{vis}_{vis}(ep\rightarrow eD^0X)$: single differential results}} \\ \hline \multicolumn{1}{|c|}{\small $p_t(D^0)$} & \small ${\rm d}\sigma_{vis}/{\rm d}p_t$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}\,]$} & $[\unit{nb/GeV}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline 2.5, \,\ 3.0 & \small 5.29\; & $\pm0.72\;$ & $+1.11\;$ & $-0.89\;$ & $+0.13\;$ & $-0.18\;$ \\ 3.0, \,\ 3.5 & \small 3.04\; & $\pm0.41\;$ & $+0.50\;$ & $-0.78\;$ & $+0.13\;$ & $-0.08\;$ \\ 3.5, \,\ 4.0 & \small 2.29\; & $\pm0.34\;$ & $+0.81\;$ & $-0.62\;$ & $+0.09\;$ & $-0.06\;$ \\ 4.0, \,\ 5.0 & \small 1.13\; & $\pm0.15\;$ & $+0.19\;$ & $-0.21\;$ & $+0.03\;$ & $-0.04\;$ \\ 5.0, \,\ 6.0 & \small 0.516 & $\pm0.120$ & $+0.139$ & $-0.129$ & $+0.018$ & $-0.015$ \\ 6.0, 10.0 & \small 0.056 & $\pm0.018$ & $+0.016$ & $-0.021$ & $+0.002$ & $-0.003$ \\ \hline % \multicolumn{7}{c}{}\\ \hline \multicolumn{1}{|c|}{\small $\eta(D^0)$} & \small ${\rm d}\sigma_{vis}/{\rm d}\eta$ & \multicolumn{5}{c|}{errors \ $[\unit{nb}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{} & $[\unit{nb}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline -1.50, -1.00 & \small 1.85 & $\pm0.38$ & $+0.34$ & $-0.46$ & $+0.09$ & $-0.05$ \\ -1.00, -0.50 & \small 1.74 & $\pm0.30$ & $+0.28$ & $-0.28$ & $+0.04$ & $-0.07$ \\ -0.50, \ 0.00 & \small 2.43 & $\pm0.34$ & $+0.42$ & $-0.36$ & $+0.06$ & $-0.11$ \\ \ 0.00, \ 0.50 & \small 2.88 & $\pm0.39$ & $+0.53$ & $-0.87$ & $+0.10$ & $-0.07$ \\ \ 0.50, \ 1.00 & \small 2.67 & $\pm0.37$ & $+0.52$ & $-0.87$ & $+0.10$ & $-0.07$ \\ \ 1.00, \ 1.50 & \small 1.91 & $\pm0.41$ & $+0.70$ & $-0.77$ & $+0.07$ & $-0.08$ \\ \hline % \multicolumn{7}{c}{\parbox[l][8mm][c]{11cm}{}} \\ \hline \multicolumn{1}{|c|}{\small $Q^2$} & \small ${\rm d}\sigma_{vis}/{\rm d}Q^2$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}^2\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}^2\,]$} & $[\unit{nb/GeV}^2\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ % \hline \,\ 2, \ \ \ 4 & \small 0.662\; & $\pm0.099\;$ & $+0.113\;$ & $-0.161\;$ & $+0.024\;$ & $-0.019\;$ \\ \,\ 4, \ \ \ 7 & \small 0.386\; & $\pm0.058\;$ & $+0.079\;$ & $-0.088\;$ & $+0.020\;$ & $-0.010\;$ \\ \,\ 7, \,\ 12 & \small 0.267\; & $\pm0.043\;$ & $+0.066\;$ & $-0.057\;$ & $+0.008\;$ & $-0.007\;$ \\ 12, \,\ 22 & \small 0.102\; & $\pm0.018\;$ & $+0.021\;$ & $-0.023\;$ & $+0.003\;$ & $-0.003\;$ \\ 22, \,\ 35 & \small 0.0474 & $\pm0.0113$ & $+0.0096$ & $-0.0107$ & $+0.0013$ & $-0.0013$ \\ 35, 100 & \small 0.0186 & $\pm0.0027$ & $+0.0032$ & $-0.0038$ & $+0.0005$ & $-0.0007$ \\ \hline % \end{tabular} % \caption[Single differential \dn\ production cross section results] \icaption{\label{tab.dn.xsec.bins} The bin-averaged single differential \dn\ production cross section measurements $\sigma_{vis}(ep\rightarrow eD^0X)$ with statistical, experimental systematic and theoretical errors. The latter include the uncertainties of the branching ratio and the model dependence of the acceptance determination.} \label{tab:dzero} \end{table} \end{center} \clearpage % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Ds decay channel: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % table with bin wise x-sections: % \begin{center} \begin{table}[th] % \vspace*{\textheight} \vspace*{1cm} \hspace*{1.5cm} \renewcommand{\arraystretch}{1.6} \scriptsize % % bins related to D-meson kinematics \begin{tabular}[t]{|@{\quad $[$\ }c@{\ $]$\quad }|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{\small $p_t(D_s^+)$} & \small ${\rm d}\sigma_{vis}/{\rm d}p_t$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}\,]$} & $[\unit{nb/GeV}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline 2.5, \,\ 3.5 & \small 1.09\; & $\pm0.33\;$ & $+0.22\;$ & $-0.27\;$ & $+0.27\;$ & $-0.27\;$ \\ 3.5, \,\ 4.0 & \small 0.44\; & $\pm0.20\;$ & $+0.16\;$ & $-0.09\;$ & $+0.11\;$ & $-0.11\;$ \\ 4.0, 10.0 & \small 0.071 & $\pm0.021$ & $+0.016$ & $-0.012$ & $+0.018$ & $-0.018$ \\ \hline % \multicolumn{7}{c}{}\\ \hline \multicolumn{1}{|c|}{\small $\eta(D_s^+)$} & \small ${\rm d}\sigma_{vis}/{\rm d}\eta$ & \multicolumn{5}{c|}{errors \ $[\unit{nb}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{} & $[\unit{nb}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline -1.50, -0.50 & \small 0.59 & $\pm0.19$ & $+0.12$ & $-0.10$ & $+0.15$ & $-0.15$ \\ -0.50, \ 0.75 & \small 0.50 & $\pm0.17$ & $+0.10$ & $-0.12$ & $+0.12$ & $-0.12$ \\ \ 0.75, \ 1.50 & \small 0.81 & $\pm0.25$ & $+0.43$ & $-0.29$ & $+0.20$ & $-0.21$ \\ \hline % \multicolumn{7}{c}{\parbox[l][8mm][c]{11cm}{}} \\ \hline \multicolumn{1}{|c|}{\small $Q^2$} & \small ${\rm d}\sigma_{vis}/{\rm d}Q^2$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}^2\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}^2\,]$} & $[\unit{nb/GeV}^2\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline \,\ 2, \ \ \ 6 & \small 0.172\; & $\pm0.044\;$ & $+0.048\;$ & $-0.038\;$ & $+0.043\;$ & $-0.043\;$ \\ \,\ 6, \,\ 16 & \small 0.053\; & $\pm0.017\;$ & $+0.012\;$ & $-0.012\;$ & $+0.013\;$ & $-0.013\;$ \\ 16, 100 & \small 0.0065 & $\pm0.0028$ & $+0.0014$ & $-0.0013$ & $+0.0016$ & $-0.0016$ \\ \hline % \end{tabular} % \caption[Single differential \ds\ production cross section results] \icaption{\label{tab.ds.xsec.bins} The bin-averaged single differential \ds\ production cross section measurements $\sigma_{vis}(ep\rightarrow eD_s^+X)$ with statistical, experimental systematic and theoretical errors. The latter include the uncertainties of the branching ratio and the model dependence of the acceptance determination.} % \label{tab:dsubs} \end{table} \end{center} \clearpage % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % D* decay channel: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \begin{center} \begin{table}[ht] % \vspace*{\textheight} \hspace*{1.5cm} \renewcommand{\arraystretch}{1.6} \scriptsize % % bins related to D-meson kinematics \begin{tabular}[t]{|@{\quad $[$\ }c@{\ $]$\quad }|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{\small $p_t(D^{*+})$} & \small ${\rm d}\sigma_{vis}/{\rm d}p_t$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}\,]$} & $[\unit{nb/GeV}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline 2.5, \,\ 3.0 & \small 2.31\; & $\pm0.28\;$ & $+0.50\;$ & $-0.40\;$ & $+0.07\;$ & $-0.06\;$ \\ 3.0, \,\ 3.5 & \small 1.15\; & $\pm0.16\;$ & $+0.23\;$ & $-0.19\;$ & $+0.03\;$ & $-0.04\;$ \\ 3.5, \,\ 4.0 & \small 1.03\; & $\pm0.13\;$ & $+0.21\;$ & $-0.16\;$ & $+0.03\;$ & $-0.03\;$ \\ 4.0, \,\ 5.0 & \small 0.344 & $\pm0.055$ & $+0.085$ & $-0.055$ & $+0.011$ & $-0.009$ \\ 5.0, \,\ 6.0 & \small 0.224 & $\pm0.041$ & $+0.048$ & $-0.037$ & $+0.006$ & $-0.009$ \\ 6.0, 10.0 & \small 0.027 & $\pm0.007$ & $+0.015$ & $-0.004$ & $+0.001$ & $-0.001$ \\ \hline % \multicolumn{7}{c}{}\\ \hline \multicolumn{1}{|c|}{\small $\eta(D^{*+})$} & \small ${\rm d}\sigma_{vis}/{\rm d}\eta$ & \multicolumn{5}{c|}{errors \ $[\unit{nb}\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{} & $[\unit{nb}\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ \hline -1.50, -1.00 & \small 0.62 & $\pm0.13$ & $+0.14$ & $-0.09$ & $+0.02$ & $-0.02$ \\ -1.00, -0.50 & \small 1.10 & $\pm0.13$ & $+0.23$ & $-0.14$ & $+0.03$ & $-0.03$ \\ -0.50, \ 0.00 & \small 1.20 & $\pm0.14$ & $+0.24$ & $-0.15$ & $+0.03$ & $-0.03$ \\ \ 0.00, \ 0.50 & \small 1.15 & $\pm0.16$ & $+0.22$ & $-0.20$ & $+0.03$ & $-0.04$ \\ \ 0.50, \ 1.00 & \small 0.99 & $\pm0.15$ & $+0.23$ & $-0.31$ & $+0.03$ & $-0.02$ \\ \ 1.00, \ 1.50 & \small 0.65 & $\pm0.16$ & $+0.32$ & $-0.25$ & $+0.03$ & $-0.02$ \\ \hline % \multicolumn{7}{c}{\parbox[l][8mm][c]{11cm}{}} \\ \hline \multicolumn{1}{|c|}{\small $Q^2$} & \small ${\rm d}\sigma_{vis}/{\rm d}Q^2$ & \multicolumn{5}{c|}{errors \ $[\unit{nb/GeV}^2\ ]$} \\ \cline{3-7} \multicolumn{1}{|c|}{$[\unit{GeV}^2\,]$} & $[\unit{nb/GeV}^2\ ]$ & statistical & \multicolumn{2}{c|}{experimental} & \multicolumn{2}{c|}{theoretical} \\ % \hline \,\ 2, \ \ \ 4 & \small 0.359\; & $\pm0.043\;$ & $+0.079\;$ & $-0.062\;$ & $+0.014\;$ & $-0.009\;$ \\ \,\ 4, \ \ \ 7 & \small 0.193\; & $\pm0.027\;$ & $+0.045\;$ & $-0.036\;$ & $+0.005\;$ & $-0.006\;$ \\ \,\ 7, \,\ 12 & \small 0.107\; & $\pm0.014\;$ & $+0.021\;$ & $-0.015\;$ & $+0.003\;$ & $-0.004\;$ \\ 12, \,\ 22 & \small 0.0486 & $\pm0.0068$ & $+0.0109$ & $-0.0084$ & $+0.0014$ & $-0.0013$ \\ 22, \,\ 35 & \small 0.0180 & $\pm0.0038$ & $+0.0036$ & $-0.0026$ & $+0.0005$ & $-0.0007$ \\ 35, 100 & \small 0.0064 & $\pm0.0010$ & $+0.0013$ & $-0.0009$ & $+0.0002$ & $-0.0002$ \\ \hline \end{tabular} % \caption[Single differential \dst\ production cross section results (CST)] \icaption{\label{tab.dstar.cst.xsec.bins} The bin-averaged single differential \dst\ production cross section measurements $\sigma_{vis}(ep\rightarrow eD^{*+}X)$ with statistical, experimental systematic and theoretical errors. The latter include the uncertainties of the branching ratio and the model dependence of the acceptance determination. The \dst\ tagged \dn\ signals used for the measurement fulfill life time tagging requirements. } \label{tab:dstar} \end{table} \end{center} \clearpage % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%