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\@writefile{toc}{\contentsline {section}{\numberline {7}Results}{12}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {7.2}Jet Cross Sections in the Breit Frame}{14}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {7.3}Comparison with Muon Tagging Measurements }{14}}
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\bibcite{ZEUSmuonslab}{8}
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\bibcite{Martin:2006qz}{16}
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\bibcite{ALEPH-steering}{20}
\bibcite{Kwiatkowski:1990es}{21}
\bibcite{Brun:1978fy}{22}
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\bibcite{VFNS1part2}{28}
\bibcite{cteqvfns}{29}
\bibcite{VFNS2}{30}
\bibcite{NNLO}{31}
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\bibcite{Gladilin:1999pj}{46}
\bibcite{Aktas:2004ka}{47}
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\newlabel{RF1}{{8}{20}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces The fit parameters $\rho _l$, $\rho _c$ and $\rho _b$ along with their errors, the $\chi ^2$ per degree of freedom and the correlation coefficients. The first row lists the results of the fit used to evaluate the integrated cross sections (bin 1). The remaining rows lists the fits used to evaluate the differential cross sections for jets in the laboratory frame (bins 2--17 and 28--30) and those requiring at least one jet in the Breit frame (bins 18--27).}}{20}}
\newlabel{tab:rhotable}{{1}{20}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces  The cross sections for events with $c$ and $b$ jets for the kinematic range $Q^2>6\nobreakspace  {}{\rm  GeV}^2$, $0.07<y<0.625$, $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$ and $-1.0<\eta ^{\rm  jet}<1.5$. The measured data cross sections are shown with their statistical and systematic uncertainties. The data are compared with the predictions from the Monte Carlos RAPGAP and CASCADE and with NLO QCD, calculated using HVQDIS. The NLO QCD predictions are shown for three sets of parton distribution functions and two choices of renormalisation and factorisation scales. The errors are obtained by changing the scales by factors of $0.5$ and $2$, by varying the quark masses and using a different model for the fragmentation of the quarks.}}{21}}
\newlabel{tab:sigtheory}{{2}{21}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces The measured charm and beauty cross sections for those events in which the highest $E_T^{\rm  jet}$ jet is a charm or beauty jet. Integrated cross sections in each bin are shown. The first two rows (bin 1) are the integrated charm and beauty cross sections for the measured phase space respectively. The differential cross sections may be formed from the remaining rows by dividing by the corresponding bin width. The remaining rows list the cross sections for jets in the laboratory frame (bins 2--17 and 28--30) and those requiring at least one jet in the Breit frame (bins 18--27). The data is corrected to the hadron level. The table also shows the statistical ($\delta _{\rm  stat}$) and systematic error ($\delta _{\rm  sys}$), together with the hadronic correction $C_{\rm  had}$ that is applied to the NLO theory to compare with the data.}}{22}}
\newlabel{tab:sig}{{3}{22}}
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\@writefile{lot}{\contentsline {table}{\numberline {4}{\ignorespaces  The contributions to the total systematic error. The bin numbering scheme follows that used in table\nobreakspace  {}3\hbox {}. The first column lists the uncorrelated systematic error. The next $10$ columns represent a $+ 1 \sigma $ shift for the correlated systematic error contributions from: track impact parameter resolution; track efficiency; $c$ fragmentation; $b$ fragmentation; light quark contribution; struck quark angle $\phi _{\rm  quark}$; hadronic energy scale; photoproduction background; electron energy scale; electron theta; reweighting the jet transverse momentum distribution $P^{\rm  jet}_T$ and pseudorapidity $\eta ^{\rm  jet}$ distribution for $c$ and $b$ events; the $c$ hadron branching fractions and multiplicities; and the $b$ quark decay multiplicity. Only those uncertainties where there is an effect of $>1\%$ in any bin are listed separately; the remaining uncertainties are included in the uncorrelated error. There is an additional contribution to the systematic error due to the uncertainty on the luminosity of $4\%$.}}{23}}
\newlabel{tab:sys}{{4}{23}}
\citation{H1muons}
\citation{ZEUSmuonslab}
\citation{H1muons}
\citation{ZEUSmuonslab}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The significance distribution $S_1$ (a), $S_2$ (b) and the output of the neural network (NN Output) (c) for tracks of the highest transverse energy jet in the event. Included in the figure is the expectation from the Monte Carlo simulation for $uds$, $c$ and $b$ events. The contributions from the various quark flavours in the Monte Carlo simulation are shown after applying the scale factors $\rho _l$, $\rho _c$ and $\rho _b$, as described in the text. The background (BG) contribution from a photoproduction Monte Carlo simulation is also shown.}}{24}}
\newlabel{fig:s1s2nn}{{1}{24}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces The subtracted distributions of $S_1$ (a), $S_2$ (b) and the neural network output (c) for the highest transverse energy jet in the event. Included in the figure is the result from the fit to the data of the Monte Carlo simulation distributions of the $uds$, $c$ and $b$ quark flavours to obtain the scale factors $\rho _l$, $\rho _c$ and $\rho _b$, as described in the text. The background (BG) contribution from a photoproduction Monte Carlo simulation is also shown.}}{25}}
\newlabel{fig:s1s2nnnegsub}{{2}{25}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  The differential cross sections for the highest transverse energy charm jet in the laboratory frame as a function of $E_T^{\rm  jet}$, $\eta ^{\rm  jet}$, $Q^2$ and the number of laboratory frame jets in the event $N^{\rm  jet}$. The measurements are made for the kinematic range $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$, $-1<\eta ^{\rm  jet}<1.5$, $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from the Monte Carlo models RAPGAP and CASCADE. The normalised theory to data ratio $R^{\rm  norm}$ is also shown. The inner error bars on the data points at $R^{\rm  norm} = 1$ display the relative statistical errors, and the outer error bars show the relative statistical and systematic uncertainties added in quadrature. }}{26}}
\newlabel{fig:xscmc}{{3}{26}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  The differential cross sections for the highest transverse energy charm jet in the laboratory frame as a function of $E_T^{\rm  jet}$, $\eta ^{\rm  jet}$, $Q^2$ and the number of laboratory frame jets in the event $N^{\rm  jet}$. The measurements are made for the kinematic range $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$, $-1<\eta ^{\rm  jet}<1.5$, $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from NLO QCD where the bands indicate the theoretical uncertainties.}}{27}}
\newlabel{fig:xscnlo}{{4}{27}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  The differential cross sections for the highest transverse energy beauty jet in the laboratory frame as a function of $E_T^{\rm  jet}$, $\eta ^{\rm  jet}$, $Q^2$ and the number of laboratory frame jets in the event $N^{\rm  jet}$. The measurements are made for the kinematic range $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$, $-1<\eta ^{\rm  jet}<1.5$, $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from the Monte Carlo models RAPGAP and CASCADE. The normalised theory to data ratio $R^{\rm  norm}$ is also shown. The inner error bars on the data points at $R^{\rm  norm} = 1$ display the relative statistical errors, and the outer error bars show the relative statistical and systematic uncertainties added in quadrature. }}{28}}
\newlabel{fig:xsbmc}{{5}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  The differential cross sections for the highest transverse energy beauty jet in the laboratory frame as a function of $E_T^{\rm  jet}$, $\eta ^{\rm  jet}$, $Q^2$ and the number of laboratory frame jets in the event $N^{\rm  jet}$. The measurements are made for the kinematic range $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$, $-1<\eta ^{\rm  jet}<1.5$, $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from NLO QCD where the bands indicate the theoretical uncertainties.}}{29}}
\newlabel{fig:xsbnlo}{{6}{29}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces  The differential cross sections ${\rm  d}\sigma /{\rm  d}E_T^{* {\rm  jet}}$ and ${\rm  d}\sigma /{\rm  d}Q^2$ for events with a jet in the Breit frame, where the jet with the highest transverse energy in the laboratory frame satisfying $E_T^{\rm  jet}>1.5\nobreakspace  {}{\rm  GeV}$ and $-1<\eta ^{\rm  jet}<1.5$ is a charm jet. The measurements are made for the kinematic range $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from the Monte Carlo models RAPGAP and CASCADE (upper plots) and the NLO QCD calculation (lower plots), where the bands indicate the theoretical uncertainties. For the upper plots the normalised theory to data ratio $R^{\rm  norm}$ is also shown. The inner error bars on the data points at $R^{\rm  norm} = 1$ display the relative statistical errors, and the outer error bars show the relative statistical and systematic uncertainties added in quadrature. }}{30}}
\newlabel{fig:xscbreit}{{7}{30}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces  The differential cross sections ${\rm  d}\sigma /{\rm  d}E_T^{* {\rm  jet}}$ and ${\rm  d}\sigma /{\rm  d}Q^2$ for events with a jet in the Breit frame, where the jet with the highest transverse energy in the laboratory frame satisfying $E_T^{\rm  jet}>1.5\nobreakspace  {}{\rm  GeV}$ and $-1<\eta ^{\rm  jet}<1.5$ is a beauty jet. The measurements are made for the kinematic range $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the predictions from the Monte Carlo models RAPGAP and CASCADE (upper plots) and the NLO QCD calculation (lower plots), where the bands indicate the theoretical uncertainties. For the upper plots the normalised theory to data ratio $R^{\rm  norm}$ is also shown. The inner error bars on the data points at $R^{\rm  norm} = 1$ display the relative statistical errors, and the outer error bars show the relative statistical and systematic uncertainties added in quadrature. }}{31}}
\newlabel{fig:xsbbreit}{{8}{31}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces The upper plots show the differential cross section ${\rm  d}\sigma /{\rm  d}Q^2$ for events with a jet in the Breit frame with $E_T^{* {\rm  jet}}>6\nobreakspace  {}{\rm  GeV}$, where the jet with the highest transverse energy in the laboratory frame satisfying $E_T^{\rm  jet}>1.5\nobreakspace  {}{\rm  GeV}$ and $-1<\eta ^{\rm  jet}<1.5$ is a beauty jet. The lower plots show the differential cross section ${\rm  d}\sigma /{\rm  d}Q^2$ for events with a beauty jet in the laboratory frame with $E_T^{\rm  jet}>6\nobreakspace  {}{\rm  GeV}$ and $-1<\eta ^{\rm  jet}<1.5$. The present measurements are made for the kinematic range $Q^2>6\nobreakspace  {}{\rm  GeV}^2$ and $0.07 < y <0.625$. The inner error bars show the statistical error, the outer error bars represent the statistical and systematic errors added in quadrature. The data are compared with the measurements obtained using muon tagging from H1\nobreakspace  {}\cite  {H1muons} (upper plots) and ZEUS\nobreakspace  {}\cite  {ZEUSmuonslab} (lower plots) extrapolated to the present phase space and shifted in $Q^2$ for visual clarity. For the muon data the outer error bars show the statistical, systematic and extrapolation uncertainties added in quadrature. The data are also compared with the predictions from the Monte Carlo models RAPGAP and CASCADE (left) and the NLO QCD calculation (right), where the bands indicate the theoretical uncertainties. }}{32}}
\newlabel{fig:xsq2breith1zeus}{{9}{32}}