%================================================================ % LaTeX file with preferred layout for the contributed papers to % the ICHEP Conference 98 in Vancouver % process with: latex hep98.tex % dvips -D600 hep98 %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} % \usepackage{lineno} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm %===============================title page============================= % Some useful tex commands % \newcommand{\GeV}{\rm GeV} \newcommand{\TeV}{\rm TeV} \newcommand{\pb}{\rm pb} \newcommand{\cm}{\rm cm} \newcommand{\hdick}{\noalign{\hrule height1.4pt}} \newcommand{\xgobs}{$x_{\gamma}^{obs}\,$} \newcommand{\xgobsm}{x_{\gamma}^{obs}} \newcommand{\bbb}{b\bar{b}} \newcommand{\ccb}{c\bar{c}} \newcommand{\ra}{\rightarrow} \begin{document} \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 XXII International Symposium on Lepton-Photon Interactions at High Energy}, June~30,~2005,~Uppsala} \\ & Abstract: & {\bf 405} &\\ & Sessions: & {\bf Flavor physics} and {\bf QCD and hadron structure} &\\ \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 Measurement of Charm and Beauty Photoproduction \\ at HERA \\ Using Inclusive Lifetime Tagging } \vspace*{1cm} {\Large H1 Collaboration} \end{center} % \linenumbers \begin{abstract} \noindent A measurement of the charm and beauty photoproduction cross sections at the $ep$ collider HERA is presented. The data were collected in the years 1999 and 2000 and correspond to an integrated luminosity of 57.7pb$^{-1}$. Events are selected with two or more jets with large transverse momenta, $p_t^{jet_{1(2)}}>11(8)$ GeV, in the central rapidity range, $-0.88<\eta^{jet}<1.3$. The lifetime signature of $c$ and $b$-flavoured hadrons is exploited to determine the fractions of events in the sample containing charm or beauty. Differential cross sections as a function of the jet transverse momentum, the rapidity and \xgobs are measured in the photoproduction region \mbox{$Q^2<1$ GeV$^2$}, with inelasticity $0.15110$ GeV$^2$~\cite{Aktas:2004az}. The charm and beauty cross sections are determined using a fit to the lifetime signature of charged particles in jets. This inclusive method yields measurements of differential cross sections that extend to larger values of transverse momenta than in previous HERA analyses in which leptons from beauty quark decays were used to measure beauty cross sections~\cite{Adloff:1999nr,Breitweg:2000nz, Chekanov:2003,Chekanov:2004,Aktas:2005zc,Aktas:2005bt}. % Events with two jets in the final state are selected to measure the photoproduction dijet charm or beauty cross section $$ \sigma(e^+p \rightarrow e^+ (c\bar{c}~{\rm or}~b\bar{b}) X \rightarrow e^+ + jj + X'). $$ % The cross sections are measured differentially as functions of the transverse momentum and pseudo-rapidity of the leading jet and of \xgobs, defined as the fraction of the $(E-p_z$) of the hadronic system that is carried by the two highest $p_T$ jets: %. $$ \xgobsm = \frac{ (E-p_z)_{jet_1} +(E-p_z)_{jet_2}}{(E-p_z)_h}. $$ In LO QCD, \xgobs is the fraction of the photon's energy that enters the hard interaction. %The measurements are compared to predictions of pQCD. % \section{Detector Description} \label{sec:det} The H1 detector is described in detail in~\cite{Abt:1997xv}. Charged particles emerging from the interaction region are measured by the central tracking detector (CTD) in the pseudo-rapidity range $-1.74 < \eta < 1.74$\footnote{The pseudo-rapidity $\eta$ of an object with polar angle $\theta$ is given by $\eta = -\ln \; \tan (\theta/2)$, where $\theta$ is measured with respect to the $z$-axis given by the proton beam direction.}. The CTD consists of two large cylindrical central jet drift chambers (CJCs), two $z$-chambers and two multi-wire proportional chambers arranged concentrically around the beam-line within a solenoidal magnetic field of 1.15 T. The CTD provides triggering information based on track segments in the $r$-$\phi$ plane from the CJC and the $z$-position of the vertex from the multi-wire proportional chambers. The CJC tracks are linked with hits in the Central Silicon Tracking detector (CST)~\cite{cst}, which consists of two cylindrical layers of silicon strip sensors, surrounding the beam pipe at radii of $R=57.5$ mm and $R=97 $ mm from the beam axis. % %With an effective length of 358 mm the CST covers %a large part of the $ep$ interaction region %and has a polar angle acceptance of $30^0 <\theta< 150^0$ %for the outer layer. % These double-sided sensors, with readout strip pitches of 50 $\mu$m and 88 $\mu$m, provide resolutions of 12 $\mu$m in $r$-$\phi$ and 25 $\mu$m in $z$. Average hit efficiencies are 97 (92)\% in $r$-$\phi$ ($z$). % For the measurement of the impact parameter, tracks are used with two hits in the CST $r$-$\phi$-layers. For these tracks the measurement of the transverse distance of closest approach has a resolution of $\sigma_{DCA} \approx 33\;\mu\mbox{m} \oplus 90 \;\mu\mbox{m} /p_T [\mbox{GeV}]$. % % See plot for this resolution vs pt % in ~obehnke/hd/bphan/paw/dcapres.ps % (from bbbar mc with % cutting on 50 cm cjc tracklength and requiring two cst hits % The first term represents the intrinsic resolution and includes the uncertainty of the CST alignment, the second gives the contribution from multiple scattering in the beam pipe. % The energies of final state particles are determined using CTD track information and measurements of the energy deposited in the liquid argon (LAr) calorimeter, which surrounds the tracking chambers and covers the range $-1.5 < \eta < 3.4$. The backward region ($-4.0 < \eta < -1.4$) is covered by a lead--scintillating fibre calorimeter (SPACAL~\cite{Nicholls:1996di}) with electromagnetic and hadronic sections. The calorimeters are surrounded by the iron return yoke of the solenoidal magnet. \section{Data Selection and Monte Carlo Samples} \label{sec:sel} The data used in this analysis were recorded in 1999 and 2000 and correspond to an integrated luminosity of $57.7\,$pb$^{-1}$. % The events were triggered by a combination of signals from the calorimeter, the central drift chambers and the multi-wire proportional chambers. % Photoproduction events are selected by requiring that there be no high energy electromagnetic cluster anywhere in the calorimeter. This restricts the range of negative four-momentum transfer squared to $Q^2<1$ GeV$^2$. Background from remaining DIS events in which the scattered electron simulates a jet, is removed by requiring that the transverse jet size $R$ $>0.02$ and $m^{jet}/p_t^{jet} > 0.1$ where $m^{jet}$ is the reconstructed mass, calculated from the jet daughter particles, and $p_t^{jet}$ the transverse momentum of the jet. The inelasticity $y$ is calculated using the Jacquet-Blondel method~\cite{JB}, and the measurement is made in the range \mbox{0.15 $11(8)$ GeV}. % Monte Carlo event samples for the processes $ep\ra e\bbb X$, $ep\ra e\ccb X$ and light quark production are generated using the PYTHIA program~\cite{PYTHIA} which is based on leading order QCD and uses parton showers to simulate higher order effects. % PYTHIA simulates direct and resolved photon processes and also includes excitation processes, in which one heavy quark ($c$ or $b$) originates from the resolved photon or the proton. % PYTHIA is run in an inclusive mode and generates all the above processes using massless matrix elements. % The CTEQ5L~\cite{cteq5l} parton densities are used % hep-ph/9903282 for the proton and those of GRVG-LO~\cite{grvg} % M.~Gluck, E.~Reya and A.~Vogt, Phys. Rev. D46, 1973 (1992) for the photon. For the fragmentation of charm and beauty quarks, the Peterson function~\cite{peterson} is used. % %The detector resolutions of the Monte Carlo simulations %are tuned to accurately describe those of the data. %The measured cross sections are compared with predictions from %PYTHIA and also from the Monte Carlo generator %program CASCADE~\cite{Jung:2000hk} %which implements the CCFM~\cite{ccfm} evolution equation %using off-shell matrix elements convoluted %with $k_t$-unintegrated parton distributions in the proton. \section{NLO QCD Calculation} \label{sec:nlo} Calculations in perturbative QCD are performed to next-to-leading order using the program FMNR by Frixione {\it et al.}\,~\cite{Frixione:1994dv} which implements the cross section calculation in a fixed order massive scheme, i.e.\, charm and beauty quarks are generated exclusively in the hard process via boson--gluon fusion diagrams, assuming the proton and photon to contain only light quarks. % The calculations are performed in the DIS scheme using values of 1.5 (4.75) GeV for the $c$ ($b$)-quark mass, respectively. The renormalisation scales are set to the transverse masses $m_t=\sqrt{m_q^2 + p_{t,q\bar{q}}^2}$, where $p_{t,q\bar{q}}^2$ is the average of the squared transverse momenta of the quark and anti-quark. For beauty, the factorisation scale $\mu_f$ is set to $m_t$ while for charm $\mu_f=\sqrt{4(m_c^2 + p_{t,c\bar{c}}^2)}$. The CTEQ5D parton distribution functions~\cite{cteq5l} are used for the distribution of partons in the proton. For the resolved photon processes, which contribute less than 10\% to the total cross sections, the GRV-G HO distributions~\cite{grvg} are used. % FMNR provides parton level event distributions, i.e.\,two or three outgoing partons, the heavy quark antiquark pair and possibly a gluon. Parton level jets are reconstructed using the inclusive $k_t$ jet-algorithm in the $p_t$ recombination scheme. % To allow comparisons with the data, corrections to the hadron level are determined using the PYTHIA Monte Carlo event generator. At the hadron level, jets are constructed using the inclusive $k_t$ algorithm~\cite{kt} using all generated stable particles including neutrinos. % The parton to hadron level corrections are found to be less than $5\%$ in all bins except for the region $0.7<$\xgobs$<0.85$ $(0.85<$\xgobs$<1)$ where the correction is $\sim 40\%$ $(\sim 15\%)$. The theoretical uncertainties of the NLO calculation have been estimated by variations of the renormalisation and factorisation scale parameters up and down by a factor of two (in the same direction, i.e.\,$\mu_R=\mu_f$) and the $c$ ($b$) mass between 1.3 and 1.7 (4.5 and 5) GeV. These variations, added linearly, lead to a change in the cross section predictions of 30--35\% for charm and 20--30\% for beauty. % The cross section variation when using other proton structure functions such as MRSG or MRST1 \cite{mrs} is less than 8\% in all regions of the measurement. The latter uncertainty is added to the scale uncertainties in quadrature. \section{Lifetime Tag Observables} \label{sec:impactparm} %The fraction of beauty events in the sample is determined %using the lifetime information of the tracks in the jets. The analysis is based on CTD tracks which are linked to hits in both $r$-$\phi$ layers of the CST in order to improve the precision of the track parameters. In this paper, CST-improved CTD tracks are referred to as ``CST tracks''. CST tracks are required to have a minimum transverse momentum of 500 MeV and a polar angle $30^\circ<\Theta_{track}<150^\circ$. CST tracks are associated to one of the two highest $p_t$ jets if they lie within a cone of 1 in \mbox{$\eta$-$\phi$} space centred about the jet axis. For the final sample, only those events are selected in which at least one associated CST track is found. The transverse momentum $p_t^{jet_1}$ and the pseudo-rapidity $\eta^{jet_1}$ distribution of the leading jet, i.e. that with highest $p_t$, are shown in figure~\ref{fig:ctrl:ptjet}a and b. Figure~\ref{fig:ctrl:ptjet}c shows \xgobs reconstructed from both jets. The data are compared to the Monte Carlo simulation PYTHIA (see section~\ref{sec:sel}) which gives a good description of the data. The transverse momentum and polar angle distributions of CST tracks are compared to the Monte Carlo simulation in figure~\ref{fig:ctrl:pttrk}a and b. %In figure~\ref{fig:ctrl:pttrk}c the number of %CST hits for the selected CST tracks is shown. The number of CST tracks in the two leading jets is shown in figure~\ref{fig:ctrl:pttrk}c. The simulation also gives a reasonable description of these distributions. The primary event vertex is reconstructed from all tracks (with or without CST hits) taking into account the position and spread of the beam interaction region. The transverse extensions of the beam interaction region are measured to be $145~{\rm \mu m}$ in $x$ and $25~{\rm \mu m}$ in $y$ for the data-taking period considered here. The mean position of the beam is measured as the average over many events; the resulting error on the mean position is small in comparison to the size of the beam-spot, with a typical uncertainty of $\sim 5~{\rm \mu m}$. In this analysis, the signed track impact parameter with respect to the event vertex is used to separate the different quark flavours. The signed impact parameter is defined as positive if the angle between the jet axis and the line between the vertex and distance of closest approach of the track to the vertex is less than $90^\circ$, and is defined as negative otherwise. The impact parameter distribution (figure~\ref{fig:dca}a) is seen to be asymmetric; the number of positive values exceeds the number of negative values, indicating the presence of long lived particles. The simulation gives a reasonable description of the data. The component of the simulation that arises from light quarks is almost symmetric at small distance of closest approach (DCA). The $c$ component has a moderate asymmetry and the $b$ component shows a marked asymmetry with an exponential fall-off to positive values of DCA. The asymmetry seen at $|{\rm DCA}|>0.1~{\rm cm}$ is mainly due to long lived strange particles such as $K_S^0$. In order to reduce the effects of the strange component, a cut of $|{\rm DCA}|<0.1~{\rm cm}$ is imposed. The significance~\cite{Buskulic:1993ka}, defined as the ratio of the DCA to its error, is shown in figure~\ref{fig:dca}b for all CST tracks with $|{\rm DCA}|<0.1~{\rm cm}$. Apart from the tails the simulation provides a good description of the data. The separation of charm and beauty events is further enhanced by using different significance distributions for events with different track multiplicities. The first significance $S_1$ is defined for events with exactly one CST track associated to a jet and is simply the significance of this track. The second significance $S_2$ is defined for events with two or more CST tracks associated to one of the two jets and is the significance of the track with the second highest absolute significance. Events in which the tracks with the first and second highest absolute significance in a jet have different signs are removed from the $S_2$ distribution. This latter condition removes around $50\%$ of events from the $S_2$ distribution, predominantly from the light quark event sample. % The $S_1$ and $S_2$ distributions are shown in figure~\ref{fig:s1s2}. %The distribution of $S_2$ gives a better separation power of light to %heavy quarks, since for heavy quarks %$\ge 2$ tracks are usually produced with high significance, %whereas for light quarks the chances of two tracks being produced at %large significance due to resolution effects are small. By %requiring the two most significant tracks to have the same sign %further suppresses the background contribution. Events with one %CST track are retained to improve the statistical precision of the %measurements. In order to reduce the uncertainty due to the DCA resolution and the light quark normalisation, the negative bins in the $S_1$ and $S_2$ distributions are subtracted from the positive. The subtracted distributions are shown in figure~\ref{fig:negsub}. The resulting distributions are dominated by $c$ quark events\footnote{Events that contain $c$ hadrons resulting from the decay of $b$ hadrons are included in the definition of $b$ quark events.}, with an increasing $b$ fraction towards increasing significance. The contribution from light quarks is seen to be small. \section{Determination of the Charm and Beauty Components} \label{sec:fit} The $b$, $c$ and light quark fractions in the data are extracted by simultaneously fitting the subtracted $S_1$ and $S_2$ distributions $N^{data}_{i}$ and the total number of events $N^{data}_{tot}$ with the Monte Carlo $b$, $c$ and light quark distributions used as templates in each interval of the measurement. The Monte Carlo $b$, $c$ and light quark distributions are allowed to be modified by the scale factors $P_b$, $P_c$ and $P_l$, respectively, such that the $\chi^2$ given by \begin{eqnarray} \label{chi2formula} \chi^2 &=&\sum_{i} \frac{(N_i^{\rm data}- P_b N^{\rm MC}_{bi}-P_c N^{\rm MC}_{ci}-P_l N^{\rm MC}_{li})^2} {\sigma^2 (N_i^{\rm data}) +(P_b\sigma(N^{\rm MC}_{bi}))^2 +(P_c\sigma(N^{\rm MC}_{ci}))^2 +(P_l\sigma(N^{\rm MC}_{li}))^2} \\ & + & \frac {(N^{\rm data}_{\rm tot}- P_b N^{\rm MC}_{ {\rm tot} b} -P_c N^{\rm MC}_{{\rm tot} c} -P_l N^{\rm MC}_{{\rm tot} l})^2 } {\sigma^2 (N^{\rm data}_{\rm tot}) +(P_b\sigma(N^{\rm MC}_{{\rm tot} b}))^2 +(P_c\sigma(N^{\rm MC}_{{\rm tot} c}))^2 +(P_l\sigma(N^{\rm MC}_{{\rm tot} l}))^2} \nonumber \end{eqnarray} is minimized, where $i$ runs over all bins of $S_1$ and $S_2$ with significances $< 13$. % CHECK GIVE REASON The results of the fit to the complete data sample are shown in figure~\ref{fig:negsub}. % stability The fit gives acceptable $\chi^2$ values for the total event sample and for all bins of the measurement. Consistent results are also found when different significance distributions are fitted, for example fitting the unsubtracted $S_1$ or $S_2$ distributions (either simultaneously or alone), and when the fit is repeated after the DCA cut is varied. Consistent results in all bins are also obtained when the multi-impact parameter probability observable as described below (section~\ref{sec:jetprob}) is used. %% no systematic errors chapter, summary here %%for lepton photon The total systematic error on the charm (beauty) cross section is estimated to be 14\% (21\%). The dominant contributions are the uncertainties in the description of the track resolutions and the track efficiencies, leading to errors on the cross section of up to $\sim$ 10\% each. %The uncertainty due to the trigger thresholds amounts to 5\%. Model dependent uncertainties, such as the uncertainties on the various $D$ and $B$ meson lifetimes, decay branching fractions and mean charge multiplicites are estimated to contribute 4\% and 7\% to the total systematic uncertainties for the charm and beauty cross section measurements, respectively. %\section{Systematic Errors} %\label{systematics} %The following sources of systematic uncertainty, %as listed in table~\ref{tab:sys}, %are considered by variation of the corresponding quantities in the Monte Carlo %simulation: %\begin{itemize} %\item A track efficiency uncertainty of $\pm 3.6\%$. %\item An uncertainty in the impact parameter % resolution of the tracks is estimated by % introducing an additional Gaussian smearing of 200~$\mu{\rm m}$ to % $5\%$ of the tracks and 25~$\mu{\rm m}$ to the rest. %\item A $2\%$ uncertainty on the hadronic energy scale leading % to an uncertainty of the $c$ ($b$)-cross section of 6\% (2\%). %\item A $25\%$ uncertainty on the composition of direct and resolved % processes in the MC simulation. %\item The trigger efficiency is studied by comparison % of the simulation with the data using events with the % same cuts on the jets at moderate % $Q^2>2$ GeV$^2$, in which the scattered electron triggers the % events independently of the conditions required for the triggers % under study. The uncertainty is determined to be 5\% on average. % increasing to 10\% in the smallest bin of transverse momentum. %\item The uncertainty of the jet axis reconstruction % is estimated by introducing an % additional Gaussian smearing of 2$^\circ$. %\item The uncertainty of the asymmetry of the light quark impact parameter % distribution is % estimated by repeating the fits with the light quark $S_1$ and $S_2$ % distributions (figure~\ref{fig:negsub}) set to zero. %\item The uncertainties arising from the various $D$ and $B$ meson lifetimes, % decay branching fractions and mean charge multiplicites are % estimated by varying the input values of the Monte Carlo % simulation by the errors on the % world average measurements, or by adjusting the simulation to the world % average value depending on which variation is larger. For the % branching fractions of quarks to mesons and the lifetimes of the % mesons the central values and errors on the world averages are taken % from\cite{Hagiwara:fs}. For the mean charged track multiplicities the % values and uncertainties for $c$ and $b$ quarks are taken from % MarkIII~\cite{Coffman:1991ud} and LEP/SLD~\cite{lepjetmulti} % measurements, respectively. %%%%% missing items %\item An uncertainty on the description of the heavy quark final state % in the Monte Carlo is estimated by repeating the analysis % with the CASCADE Monte Carlo yielding variations of CHECK \% and CHECK \%. %% \item An uncertainty on the fragmentation function of the heavy quarks %% used in the Monte Carlo is estimated by repeating the fits with the %% Monte Carlo templates generated using the Peterson fragmentation %% function\cite{peterson}. %\item The luminosity is known to an accuracy of 1.5\%. %\end{itemize} %The dominant contributions are the uncertainties in the description %of the track resolutions and the track efficiencies, %leading to errors on the cross section of $\sim$ 10\% each. %The uncertainty due to the trigger thresholds amounts to 5\%. %Model dependent uncertainties, such as the %uncertainties on the various $D$ and $B$ meson lifetimes, %decay branching fractions and mean charge multiplicites %are estimated to contribute 4\% and 7\% %to the total systematic uncertainties for the charm and beauty %cross section measurements, respectively. %The total systematic errors on the charm and beauty cross sections are %calculated by adding the individual uncertainties %listed in table~\ref{tab:sys} in quadrature, assuming symmetric errors. %For charm (beauty) a total systematic uncertainty of 14\% (21\%) is obtained. %increasing to 16\% (23\%) at the smallest values of transverse momentum. \section{Measurement Using a Multi-Impact Parameter \\ Probability} \label{sec:jetprob} The results are cross checked using an alternative method to separate the quark flavours also based on the use of the significance distributions of the selected tracks $S_i$. The method was employed by the ALEPH collaboration~\cite{Buskulic:1993ka}. The quantity $$ P(S_i)=\frac{1}{\sqrt{2\pi}} \int_{\chi^2}^{\infty} e^{-t^2}dt, $$ where $\chi_i^2=S_i^2$, can be interpreted as the probability that a track originates at the primary vertex. The probability for tracks with negative significance is set to unity. A multi impact parameter (MIP) probability $P_{MIP}$ is then constructed by combining the probabilities of the $N$ CST tracks within each jet: $$ P_{MIP}=\Pi \sum_{j=0}^{N-1} (- \ln \Pi)^j / j!, $$ where $j$ runs over all CST tracks and $$ \Pi=\prod_{i=1}^N P(S_i) $$ The distribution of the negative logarithm $-\log(P_{MIP})$ for both jets is shown in figure~\ref{fig:jetprob}. The contributions from events containing $b$, $c$ and $uds$ quarks are determined by a fit~\cite{Barlow:dm,rootfracfitter} to the $-\log(P_{MIP})$ distribution, using the Monte Carlo expectations for the shapes of each of these quark flavours. The fractions of $c$ and $b$-events obtained from a fit to the MIP probability, when converted into a cross section, are found to agree with the result obtained by the method described above (section~\ref{sec:fit}). \section{Results} \label{sec:results} The fit results are converted to measurements of the charm and beauty cross section by determining the scale factors $P_c$ and $P_b$ from the fit according to equation~\ref{chi2formula} for the samples in each bin. In each bin of the measurement the differential cross section is obtained by multiplying the bin-averaged cross section predicted by the Monte Carlo simulation by the scale factor and dividing by the bin size. The total dijet charm photoproduction cross section in the range $Q^2<1$ GeV$^2$, $0.1511(8)$ GeV and \mbox{ $-0.88<\eta^{jet_{1,2}}<1.3$} is measured to be $$ \sigma(ep\rightarrow ec\bar{c}X \rightarrow ejjX) = 694 \pm 69 (stat.) \pm 96 (sys.) {\rm pb}. $$ For beauty, the measurement yields a cross section for the same kinematic range $$ \sigma(ep\rightarrow eb\bar{b}X \rightarrow ejjX) = 145 \pm 18 (stat.) \pm 30 (sys.) {\rm pb}. $$ %% %% total cross sections for Pythia, CASCADE, FMNR %% Figures~\ref{fig:xsec:cpt}--\ref{fig:xsec:bxgamma} show the measured differential cross sections as functions of $p_t^{jet_1}$, $\eta^{jet_1}$ and \xgobs, respectively. The data are compared with predictions from the NLO QCD calculation FMNR as well as from the Monte Carlo programs PYTHIA and CASCADE~\cite{Jung:2000hk}. The latter implements the CCFM~\cite{ccfm} evolution equation using off-shell matrix elements convoluted with $k_t$-unintegrated parton distributions in the proton. While the charm data are reasonably well described in both normalization and shape, the beauty data are found to be somewhat higher than the prediction from the NLO QCD calculation. The main difference between the beauty data and the NLO calculation appears to originate in the region of positive values of rapidity, as can be seen in figure~\ref{fig:xsec:beta}, and small values of \xgobs, where the prediction lies significantly below the data. In these regions the contribution to the cross section from events with resolved photons is particularly large. The prediction from PYTHIA for this contribution is indicated in the figures ~\ref{fig:xsec:cpt}--\ref{fig:xsec:beta} by the dashed-dotted line. PYTHIA and CASCADE give a good description of the shapes of the data distributions. However, the beauty data are generally higher in normalisation than the PYTHIA (CASCADE) prediction by a factor $\sim 1.8$ ($\sim 1.6$), respectively. \section{Conclusions} \label{sec:conclusions} A measurement of differential charm and beauty dijet photoproduction cross sections at HERA has been presented. The measurement makes use of the precise tracking information available from the H1 vertex detector. The heavy quark cross sections are determined by making use of the lifetime distributions of charm and beauty hadrons. The cross sections are measured as functions of the transverse momentum of the leading jet $d\sigma/dp_t^{jet_1}$, the rapidity of the jet $\eta^{jet_1}$ and \xgobs. While the charm cross sections are reasonably well described in both normalization and shape, the beauty cross sections are found to be higher than a calculation in perturbative QCD to next-to-leading order. The Monte Carlo generators PYTHIA and CASCADE describe the shape of the charm and beauty data. However, for beauty PYTHIA (CASCADE) fall below in normalization by a factor $\sim 1.8$ ($\sim 1.6$). \begin{thebibliography}{99} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \bibitem{Aktas:2004az} A.~Aktas {\it et al.} [H1 Collaboration], %``Measurement of F_2^ccbar and F_2^bbbar at High Q^2 using the H1 Vertex Detector at HERA,'' to appear in Eur.\ Phys.\ J.\ C., [hep-ex/0411046]. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\cite{Adloff:1999nr} \bibitem{Adloff:1999nr} C.~Adloff {\it et al.} [H1 Collaboration], %``Measurement of open beauty production at HERA,'' Phys.\ Lett.\ B {\bf 467} (1999) 156 [Erratum-ibid.\ B {\bf 518} (2001) 331] [hep-ex/9909029]. %%CITATION = HEP-EX 9909029;%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\cite{Breitweg:2000nz} \bibitem{Breitweg:2000nz} J.~Breitweg {\it et al.} [ZEUS Collaboration], %``Measurement of open beauty production in photoproduction at HERA,'' Eur.\ Phys.\ J.\ C {\bf 18} (2001) 625 [hep-ex/0011081]. %%CITATION = HEP-EX 0011081;%% %%%%%%%%%%%%%%%%%%%%%%%%%%%% \bibitem{Chekanov:2003} S.~Chekanov {\it et al.} [ZEUS Collaboration], %''Beauty photoproduction measured using decays into muons in dijet events %in ep collisions at $\sqrt(s)$=318 GeV'' DESY-03-212, submitted to Physical Review D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % ZEUS prel. 2002 partially supserseded by Chekanov:2003 \bibitem{Chekanov:2004} S. 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\\ %%CITATION = NUPHA,B296,49;%% S.~Catani, F.~Fiorani and G.~Marchesini,\\ %``QCD Coherence In Initial State Radiation,'' Phys.\ Lett.\ B {\bf 234} (1990) 339, %%CITATION = PHLTA,B234,339;%% %\cite{Catani:1989sg} %S.~Catani, F.~Fiorani and G.~Marchesini, %``Small X Behavior Of Initial State Radiation In Perturbative QCD,'' Nucl.\ Phys.\ B {\bf 336} (1990) 18;\\ %%CITATION = NUPHA,B336,18;%% G.~Marchesini, %``QCD coherence in the structure function and associated distributions at small x,'' Nucl.\ Phys.\ B {\bf 445} (1995) 49. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %K.~Abe {\it et al.} {\sf check hier noch mehr} %\bibitem{jetset} %T.~Sj\"ostrand, %``High-energy physics event generation with PYTHIA 5.7 and JETSET 7.4,'' %Comput.\ Phys.\ Commun.\ {\bf 82} (1994) 74. %%CITATION = CPHCB,82,74;% \clearpage \end{thebibliography} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{table}[p] % \begin{center} % \begin{tabular}{|l|l||c|c|} % \hline % systematic & uncertainty & error & error\\ % & & Beauty /$\%$ & Charm /$\%$ \\ % \hline \hline % Track resolution&$\oplus 25 \mu m \; \oplus 200 \mu m$ &$-10 $ &$+7$ \\ % CST track efficiency & $-3.6 \%$ &$ +11 $ & $-1$\\ % Strangeness cut & $|dca|<1.5 mm$ & $ +2 $ & $-1$\\ % s asymmetry &$100 \%$ &$ +6$ & $+3$\\ % Direct $\Leftrightarrow$ Resolved & Resolved $-25\%$ &$ +9$ &$+7$ \\ % \hline % Fragmentation & Lund / Peterson &$ 4$ & $3$\\ % B hadron multiplicities & &$ 2$ & $0.4$\\ % D hadron multiplicities & &$ 5$ & $1.5$\\ % Fragmentation fraction &PDG &$ 3$ & $1$\\ % Lifetimes &PDG &$0.5$ & $0.2$ \\ % \hline % E (Jet) & $2\%$ &$ 2 $ &$6$ \\ % Jet axis & $2^{\circ}$ gaussian smearing &$ 2 $ &$3$ \\ % Trigger & &$ 5$ & $5$\\ % Lumi & &$ 1.5$ & $1.5$\\ % \hline \hline % {\bf total} & &$ \pm 21$ & $ \pm 14$\\ % \hline % \end{tabular} % \end{center} %\caption{Table of systematic uncertainties. %The total systematic error is calculated by adding the %individual uncertainties in quadrature, assuming symmetric %uncertainties (see section~\ref{systematics}).} %\label{tab:sys} %\end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[p] \unitlength1cm \begin{picture}(8,21) \put(2.5,14.){\epsfig{file=H1prelim-04-173.fig1a.eps,width=10cm}} \put(2.5,7. ){\epsfig{file=H1prelim-04-173.fig1b.eps,width=10cm}} \put(2.5,0. ){\epsfig{file=H1prelim-04-173.fig1c.eps,width=10cm}} \put(4.5,20.2){\large a)} \put(11.5,13.2){\large b)} \put(11.5,6.2){\large c)} \end{picture} \caption{Distributions of the two leading jets in the final sample. a) $p_t^{jet_1}$, b) $\eta^{jet_1}$, c) \xgobs. The data (points) are compared with the PYTHIA simulation after applying the scale factors obtained from the fit to the subtracted significance distributions.} \label{fig:ctrl:ptjet} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,21) \put(2.5,14.){\epsfig{file=H1prelim-04-173.fig2a.eps,width=10cm}} \put(2.5,7. ){\epsfig{file=H1prelim-04-173.fig2b.eps,width=10cm}} \put(2.5,0. ){\epsfig{file=H1prelim-04-173.fig2c.eps,width=10cm}} \put(4.5,20.2){\large a)} \put(4.5,13.2){\large b)} \put(4.5,6.2){\large c)} \end{picture} \caption{Distributions of the CST tracks passing the track selection requirements. a) $p_t$, b) $\theta$, c) number of CST tracks. The data (points) are compared with the PYTHIA simulation after applying the scale factors obtained from the fit to the subtracted significance distributions.} \label{fig:ctrl:pttrk} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,21) \put(.5,10.){\epsfig{file=H1prelim-04-173.fig3a.eps,width=14cm}} \put(.5,0. ){\epsfig{file=H1prelim-04-173.fig3b.eps,width=14cm}} \put(13.2,18.8){\large a)} \put(13.2,8.8){\large b)} \end{picture} \caption{a) Distribution of the signed impact parameter of the selected CST tracks. b) Signed significance distribution after selection of tracks with impact parameter $|DCA| < 0.1$ cm. The data (points) are compared with the PYTHIA simulation after applying the scale factors obtained from the fit to the subtracted significance distributions.} \label{fig:dca} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,21) \put(.5,10.){\epsfig{file=H1prelim-04-173.fig4a.eps,width=14cm}} \put(.5,0.){\epsfig{file=H1prelim-04-173.fig4b.eps,width=14cm}} \put(13.2,18.8){\large a)} \put(13.2,8.8){\large b)} \end{picture} \caption{Significance distributions using the $b$, $c$ and $uds$-fractions from the fit to the subtracted significance distributions of the data. a) $S_1$ of CST tracks in jets with exactly one CST track, b) $S_2$ of CST tracks with the second highest significance in jets with two or more CST tracks.} \label{fig:s1s2} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,21) \put(.5,10.){\epsfig{file=H1prelim-04-173.fig5a.eps,width=14cm}} \put(.5,0.){\epsfig{file=H1prelim-04-173.fig5b.eps,width=14cm}} \put(4.2,18.8){\large a)} \put(4.2,8.8){\large b)} \end{picture} \caption{a) Distribution $S_1$ of the subtracted signed significance for the 1-track sample. b) Distribution $S_2$ of the subtracted signed significance for the 2- or more track sample. The data (points) are well described by the PYTHIA simulation (solid line). The decomposition of the simulation into $b$ (shaded histogram), $c$ (dotted line), $uds$ (triangles) is taken from the fit as described in section~\ref{sec:fit}.} \label{fig:negsub} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(.5,0.){\epsfig{file=H1prelim-04-173.fig6.eps,width=14cm}} \end{picture} \caption{Distribution of the negative logarithm of the multi impact parameter probability. The decomposition of the simulation into $b$ (shaded histogram), $c$ (dotted line), $uds$ (dashed line) is taken from the fit as described in section~\ref{sec:jetprob}.} \label{fig:jetprob} \end{figure} \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(.5,0.){\epsfig{file=H1prelim-04-173.fig7.eps,width=14cm}} \end{picture} \caption{Differential charm cross section $d\sigma/dp_t^{jet_1} (ep\rightarrow ec\bar{c}X \rightarrow ejj X)$ as a function of the transverse momentum $p_t^{jet_1}$ of the leading jet. The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The contribution in PYTHIA from processes in which the photon is resolved is shown separately (dashed-dotted line). The solid line indicates the prediction from a NLO QCD calculation and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:cpt} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(.5,0.){\epsfig{file=H1prelim-04-173.fig8.eps,width=14cm}} \end{picture} \caption{Differential beauty cross section $d\sigma/dp_t^{jet_1} (ep\rightarrow eb\bar{b}X \rightarrow ejj X)$ as a function of the transverse momentum $p_t^{jet_1}$ of the leading jet. The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The contribution in PYTHIA from processes in which the photon is resolved is shown separately (dashed-dotted line). The solid line indicates the prediction from a NLO QCD calculation and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:bpt} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(.5,0.){\epsfig{file=H1prelim-04-173.fig9.eps,width=14cm}} \end{picture} \caption{Differential charm cross section $d\sigma/d\eta^{jet_1} (ep\rightarrow ec\bar{c}X \rightarrow ejj X)$ as a function of the rapidity $\eta^{jet_1}$ of the leading jet. The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The contribution in PYTHIA from processes in which the photon is resolved is shown separately (dashed-dotted line). The solid line indicates the prediction from a NLO QCD calculation and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:ceta} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(.5,0.){\epsfig{file=H1prelim-04-173.fig10.eps,width=14cm}} \end{picture} \caption{Differential beauty cross section $d\sigma/d\eta^{jet_1} (ep\rightarrow eb\bar{b}X \rightarrow ejj X)$ as a function of the rapidity $\eta^{jet_1}$ of the leading jet. The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The contribution in PYTHIA from processes in which the photon is resolved is shown separately (dashed-dotted line). The solid line indicates the prediction from a NLO QCD calculation and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:beta} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(0.5,0.){\epsfig{file=H1prelim-04-173.fig11.eps,width=14cm}} \end{picture} \caption{Differential charm cross section $d\sigma/d\xgobsm (ep\rightarrow ec\bar{c}X \rightarrow ejj X)$ as a function of \xgobs . The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The prediction from a NLO QCD calculation is shown before (dashed-dotted line) and after (solid line) hadronisation corrections, and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:cxgamma} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[htb] \unitlength1cm \begin{picture}(8,10) \put(0.5,0.){\epsfig{file=H1prelim-04-173.fig12.eps,width=14cm}} \end{picture} \caption{Differential beauty cross section $d\sigma/d\xgobsm (ep\rightarrow eb\bar{b}X \rightarrow ejj X)$ as a function of \xgobs . The inner error bars indicate the statistical uncertainty and the outer error bars show the statistical and systematic error added in quadrature. Also shown is the prediction from CASCADE (dotted line) and PYTHIA (dashed line). The prediction from a NLO QCD calculation is shown before (dashed-dotted line) and after (solid line) hadronisation corrections, and the shaded band describes the scale uncertainty of the calculation.} \label{fig:xsec:bxgamma} \end{figure} \end{document}