\chapter{Analysis Method}
	\label{chapter_analysis_method}
\section{Comparison of {\MC} and Data}
	In order to measure the cross sections in a manner independent of the specific characteristics of the detector, the data were corrected to the hadron level using leading-order {\MC}.  Before this was done, it was ensured that the detector-level distributions for the most important observables matched well between data and {\MC}.  The agreement was examined both within the phase space used for the analysis, and in regions slightly outside the selection cuts.
\subsection{Reweighting Procedure}
	The generated distributions of $\zvtx$ and $Q^2$ are input parameters to the {\MC}s.  The $\zvtx$ distribution was determined from a selection of ZEUS NC events in the same data taking period, and the $Q^2$ distribution has been determined from several measurements.  In order to improve the agreement between data and {\MC}, these input distributions were effectively altered by filling {\MC} histograms with weights differing slightly from 1, as functions of $\zvtx$ and $Q^2$.  {\MC} events were assigned per-event weights given by $w = w_{z}\times w_{Q^2}\times w_{track}$ for all detector-level quantities, and $w = w_{z}\times w_{Q^2}$ for all hadron- and parton-level quantities.  The terms, $w_{z}$ and $w_{Q^2}$ refer to independent weights for the generated values of $z_{vtx}$ and $Q^2$ respectively. The variable $w_{track}$ refers to a weight which accounts for a tracking veto which was not included in the {\MC} detector description at the time of generation.  These factors are described in detail in Appendix~\ref{chapter_reweghting_factors}.

\subsection{Detector-level Comparisons}
	\label{section_det_level_comparisons}
	In figures \ref{figure_kinematic_control_e_ARD} (a)--(f), the comparison between data and ARIADNE 4.08 ~\cite{cpc:71:15} kinematic distributions is shown for $e^{-}p$ inclusive jet samples.  Equivalent comparisons for  $e^{+}p$ are included in appendix~\ref{chapter_mc_data_comparison}.  It can be observed that all presented quantities shown are in good agreement, both inside and outside of the selection criteria. In figures \ref{figure_jets_control1_e_ARD} and \ref{figure_jets_control2_e_ARD}, detector-level jet quantities are shown.  From ~\ref{figure_jets_control1_e_ARD}(a), it can be observed that data events have significantly more jets per event than the {\MC}, which is expected because higher order terms not included in the LO {\MC} are responsible for multi-jet production.  The shape of the $\etjet$ and $\rapjet$ distributions for jets with highest, second- and third-highest $\etjet$ are all in good agreement, however, so it is still acceptable to use the {\MC} samples to correct event and jet variables.
\begin{figure}[htbp]
	\begin{center}
		\includegraphics[draft=false, width=.9\textwidth]
			{\thesisplotdir/kinematic_control_plot_e_inclusive_ARIADNE}

	\end{center}
		\caption[Detector-Level Kinematic Variable Comparison between $e^{-}p$ Data and ARIADNE]{
			\fixspacing{Comparison between detector level kinematic quantities of $e^{-}p$ data and CC DIS ARIADNE.  Filled histograms and closed points represent data and MC events which were selected for the inclusive-jet sample.  Stars and empty histograms represent data and MC events which fall outside the kinematic selection, but were only rejected by the selection cut indicated by the dashed line.  The selection cut on $Q^2>200$ is applied, but not shown.  The {\MC} has been area-normalized to the data for each  plot shown.}
		}
	\label{figure_kinematic_control_e_ARD}
\end{figure}
\begin{figure}[htbp]
	\begin{center}
		\includegraphics[draft=false, width=.9\textwidth]
			{\thesisplotdir/jets_control_plot_1_e_inclusive_ARIADNE}

	\end{center}
		\caption[Detector-Level Jet Variable Comparison between $e^{-}p$ Data and ARIADNE 1/2]{
			\fixspacing{Comparison between detector level jet quantities of $e^{-}p$ data and CC DIS ARIADNE.  All events shown appear with all inclusive-jet selection cuts applied, but no correction to jet variables has been applied.  Within these plots, a jet is defined as any $k_T$ cluster object with $\etjet$ greater than $5~\GeV$ and $-1<\rapjet<2.5$.}
		}
	\label{figure_jets_control1_e_ARD}
\end{figure}
\begin{figure}[htbp]
	\begin{center}
		\includegraphics[draft=false, width=.9\textwidth]
			{\thesisplotdir/jets_control_plot_2_e_inclusive_ARIADNE}

	\end{center}
		\caption[Detector-Level Jet Variable Comparison between $e^{-}p$ Data and ARIADNE 2/2]{
			\fixspacing{Comparison between detector level jet quantities of $e^{-}p$ data and ARIADNE.  All details as in figure \ref{figure_jets_control1_e_ARD}.}
		}
	\label{figure_jets_control2_e_ARD}
\end{figure}
\section{Correction Procedures Applied to Data Events}
\subsection{Inactive Material Corrections}
	\label{section_dead_material}
	As particles left the interaction region, they passed through the MVD, HERA beampipe, and support materials before entering the active region of the CTD.  Particles then passed through the solenoid and more support structures  before reaching the CAL.  This means that particles would transfer some of their energy to materials without readout before being measured, and their immediately reconstructed quantities would not reflect the state shortly after the $ep$ interaction.  In order to estimate and correct these effects, samples of {\MC} with detector simulation were generated, which are described in chapter~\ref{chapter_event_simulation}.   By comparing parton-level values of generated events and the reconstructed values from the detector simulation, estimations of energy loss or reconstruction bias were performed.  Profile histograms were created for parton and reconstructed values in $\ptmiss$, and $y$, and the resultant values of these histograms showed the average reconstructed value for a certain generated value.  Linear fits to these histograms then yielded correction factors.  These corrections changed the reconstructed values on the order of 10\%, and are presented in detail in appendix~\ref{chapter_corrections}.
 
	These correction factors were then applied to data events, and {\MC} events at the detector level to produce values which are referred to here as at the {corrected-detector level}, which means detector values corrected for dead material.  These values were then used to produce distributions, which in turn were used to produce the cross sections presented in chapter~\ref{chapter_results}.  Correction factors were first applied to $\ptmiss$ and $y$, and then these values were used as described in equation~\ref{equation_jaquet_blondel} to produce corrected values of $Q^2$ and $x$.  

	In figures~\ref{mc_pt_resolution_plot_e_ARIADNE} and~\ref{mc_y_resolution_plot_e_ARIADNE}, the bias and resolution of $\ptmiss$ and $y$, respectively, are presented. MC samples presented here are from $e^-p$ ARIADNE samples described in section~\ref{chapter_event_simulation}.  The central line indicates the mean reconstructed values for each variable, before and after corrections were applied.  Error bands indicate the 1-$\sigma$ limits as taken from Gaussian fits along the vertical axis.  
\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\centerline{\includegraphics[draft=false,
		width=1.\textwidth]{\thesisplotdir/mc_pt_resolution_plot_e_ARIADNE}}}
	\end{picture}
	\caption[Reconstruction of $\ptmiss$]{ Comparison between hadron- and detector-level $\ptmiss$ for $e^-p$ CC DIS ARIADNE.  Central lines indicate the mean reconstructed value, while the outer lines and shaded regions indicate $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $\ptmiss$.}
	\label{mc_pt_resolution_plot_e_ARIADNE}
\vfill
\end{figure}

	From figure~\ref{mc_pt_resolution_plot_e_ARIADNE}, it can be observed that $\ptmiss$ was reconstructed before corrections on average approximately 10\% below its hadron-level value, for $\ptmiss>20~\GeV$.  For $\ptmiss<20~\GeV$, the reconstructed bias in $\ptmiss$ decreases.  The corrected value of $\ptmiss$ was within a few percent for $\ptmiss>20$, but is biased above the hadron-level value for $\ptmiss<20$.  The principle $\ptmiss>11~\GeV$ cut was not applied during the production of this histogram, but the supplementary $\ptmiss>20~\GeV$ cleaning cut for forward-jet events was retained.
\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\centerline{\includegraphics[draft=false,
		width=1.\textwidth]{\thesisplotdir/mc_y_resolution_plot_e_ARIADNE}}}
	\end{picture}
	\caption[Reconstruction of $\ptmiss$ and $y$]{Comparison between generator- and detector-level $y$ for $e^-p$ CC DIS ARIADNE.  Central lines indicate the mean reconstructed value, while the outer lines and shaded regions indicate $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $y$.}
	\label{mc_y_resolution_plot_e_ARIADNE}
\vfill
\end{figure}

	From figure~\ref{mc_y_resolution_plot_e_ARIADNE}, it can be observed that the relative difference between the mean reconstructed $y$ and generated value as a function of the generated $y$ was roughly linear, with negative slope.  From the 1-standard deviation lines, it can also be seen that the resolution of $y$ deteriorates with increasing $y$.  After reconstruction, no systematic shift in $y$ can be observed below $y$ of .9, which is the boundary of the chosen phase space. No $y$ cut was applied during the production of this histogram.

\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put (0.0,-11.){\centerline{\includegraphics[draft=false,
		width=1.\textwidth]{\thesisplotdir/mc_q2_resolution_plot_e_ARIADNE}}}
	\end{picture}
	\caption[Reconstruction of $Q^2$]{\it Comparison between hadron- and detector-level $Q^2$ for $e^-p$  CC DIS ARIADNE. Central lines indicate the mean reconstructed value, while the outer lines and shaded regions indicate $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $Q^2$.}
	\label{mc_q2_resolution_plot_e_ARIADNE}
\vfill
\end{figure}
	Figure~\ref{mc_q2_resolution_plot_e_ARIADNE} shows that the reconstructed values of $Q^2$ were systematically below their hadron-level values by approximately 20\% before corrections were applied.  Near a generated $Q^2$ value of approximately $200~\GeV^2$, events were reconstructed within a few percent of the proper value.  After corrections the reconstructed $Q^2$ is within 10\% of the generated value for events with generated $Q^2>300$.  The relative difference between generated and reconstructed values is no longer constant however, with the mean reconstructed value above the generated.  No $Q^2$ cut was applied during the production of this histogram.

\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\centerline{\includegraphics[draft=false,
		width=1.\textwidth]{\thesisplotdir/mc_x_resolution_plot_e_ARIADNE}}}
	\end{picture}
	\caption[Reconstruction of $x$]{\it Comparison between hadron- and detector-level $x$ for $e^-p$ CC DIS ARIADNE. Central lines indicate the mean reconstructed value, while the outer lines and shaded regions indicate $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $x$.}
	\label{mc_x_resolution_plot_e_ARIADNE}
\vfill
\end{figure}
	Figure~\ref{mc_x_resolution_plot_e_ARIADNE} shows the trend of reconstructed values of $x$, before and after corrections.  It can be observed that before corrections, the reconstructed value was below the hadron-level value by nearly 20\% over the range (0.01, 0.2).  After corrections, the reconstructed values were typically within a few percent of their generated values.
\subsection{Jet Quantity Corrections}
\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\centerline{\includegraphics[draft=false, width=1.\textwidth]{\thesisplotdir/mc_etjet_resolution_plot_e_ARIADNE}}}
	\end{picture}
		\caption[Reconstruction of $\etjet$]{
			\fixspacing{Comparison between hadron- and detector-level $\etjet$ for $e^{-}p$ CC DIS ARIADNE. Central lines indicate the mean reconstructed value, while the outer lines and shaded regions indicate $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $\etjet$.}
		}
	\label{mc_etjet_resolution_plot_e_ARIADNE}
\vfill
\end{figure}
	Figure~\ref{mc_etjet_resolution_plot_e_ARIADNE} compares the reconstructed $\etjet$ values for all jets with $\etjet>3~\GeV$ to the hadron-level values for the same jets within the $\rapjet$ range $-1.5 < \rapjet < 2.5$.  No other jet cuts were applied.  It can be seen from the figure that the average reconstructed value for $\etjet$ is below the hadron-level value over the entire range of accessible values,and that the resolution suffers a notable degradation below approximately $15~\GeV$.  After corrections, the resolution remains unchanged, but the average value of reconstructed $\etjet$ is much closer to the hadron-level value.  The resolution for hadron-level jets is approximately 20\% in the range $5 < \etjet < 15~GeV$, and approximately 10\% for $\etjet > 15~\GeV$.

\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\includegraphics[draft=false, width=1.\textwidth]{\thesisplotdir/mc_rapjet_resolution_plot_e_ARIADNE}}
	\end{picture}
		\caption[Reconstruction of $\rapjet$]{
			\fixspacing{Comparison between hadron- and detector-level $\rapjet$ for $e^{-}p$CC DIS ARIADNE. Central lines indicate the mean reconstructed value, while the shaded region indicates $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $\rapjet$.}
		}
	\label{mc_rapjet_resolution_plot_e_ARIADNE}
\vfill
\end{figure}

	Figure~\ref{mc_rapjet_resolution_plot_e_ARIADNE} compares reconstructed $\rapjet$ values to hadron-level values of the same jets for all jets with $\etjet>3~\GeV$.  No other jet cuts were applied.  It can be seen from the figure that the average reconstructed value for $\rapjet$ is in agreement with the hadron-level value over the entire range of accessible values, with the exception of jets with $\rapjet > 2.5$, which were not considered in the final sample.  The resolution also suffers a notable degradation at $\rapjet>2.5$.  No corrections were applied to $\rapjet$ values.
		
\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,9.0)
		\put(0.0,-1.5){\includegraphics[draft=false, width=1.\textwidth]
			{\thesisplotdir/mc_phijet_resolution_plot_e_ARIADNE}}
	\end{picture}
		\caption[Reconstruction of $\phijet$]{
			\fixspacing{Comparison between hadron- and detector-level $\phijet$ for $e^{-}p$ Cc DIS ARIADNE. Central lines indicate the mean reconstructed value, while the shaded region indicates $\pm$1-standard-deviations obtained from a Gaussian fit in the reconstructed values for each value of generated $\phijet$.}
		}
	\label{mc_phijet_resolution_plot_e_ARIADNE}
\vfill
\end{figure}
	Figure~\ref{mc_phijet_resolution_plot_e_ARIADNE} compares reconstructed $\phijet$ values to hadron level values for the same jets, for all jets with $\etjet>3~\GeV$, $-1.5 < \rapjet < 2.5$.  No other jet cuts were applied.  It can be seen from the figure that the average reconstructed value for $\phijet$ is in agreement with the hadron-level value, within one or two degrees, and that the resolution is on average within 5 degrees.  No corrections were applied to $\phijet$ values.
\subsection{Transverse Energy Corrections}
	\label{section_transverse_energy_corrections}
	To understand the the uncertainty in the absolute energy scale of the jets, the differences between data and {\MC} simulation in single-jet NC DIS events was studied~\cite{Wing:2002fc}.  Because the transverse energy of the single jets and electrons is expected to be equal in these events, the reconstructed transverse energy of the electron, $E_{T,\mbox{\tiny DA}}$, provided an alternative means of estimating the transverse energy of the jets.  The ratio of jet $E_T$ to electron $E_T$, $R =<\etjet/E_{T,\mbox{\tiny DA}}>$ was therefore expected to be near one.   The double ratio of data to {\MC}, $R_{\mbox{\tiny DATA}}/R_{\mbox{\tiny MC}}-1$, vs. $\rapjet$ is presented in figure  \ref{plot_before_escale_rapjet} (a) before correction factors were applied.  In figure \ref{plot_after_escale_rapjet} (b) the same ratio is plotted after correction factors were applied to the data, showing a far better agreement between data and {\MC}.  The same ratio as a function of the hadronic system angle, $\gammah$ is presented in figures \ref{plot_before_escale_gamma} and \ref{plot_after_escale_gamma}.  These corrected ratios were then used to estimate the final uncertainty on the jet energy scale, as discussed in section~\ref{section_jet_escale_uncert}.  The correction factors are presented in detail in appendix~\ref{chapter_corrections}.
\begin{figure}[htbp]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,7.0)(.1,.1)
		\put(0.0,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0211ncol}}
		\put(7.5,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0221col}}
	\end{picture}
		\caption[Jet Transverse Energy Before And After Corrections vs. $\rapjet$]{Jet transverse energy data-MC double ratios before and after corrections vs. $\rapjet$ for $e^{-}p$ CC DIS ARIADNE.}
		
	\label{plot_before_escale_rapjet}
	\label{plot_after_escale_rapjet}
\vfill
\end{figure}
\begin{figure}[htbp]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,7.0)(.1,.1)
		\put(0.0,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0212ncol}}
		\put(7.5,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0222col}}
	\end{picture}
		\caption[Jet Transverse Energy Before And After Corrections vs. $\gammah$]{Jet transverse energy data-MC double ratios before and after corrections vs. $\gammah$ for $e^{-}p$ CC DIS ARIADNE.}
		
	\label{plot_before_escale_gamma}
	\label{plot_after_escale_gamma}
\vfill
\end{figure}

	The same correction factors derived from $R_{\mbox{DATA}}/R_{\mbox{MC}}$ in the NC DIS sample were applied to data in the CC DIS samples presented here.
\section{Correction Procedures Applied to Theoretical Calculations}
\label{section_theroretical_corrections}
\subsection{QED Corrections}
	Because the {\mepjet} program does not include QED radiative effects, correction factors were applied to the born-level partonic distributions.  The correction factors are presented in the data tables located in appendix~\ref{chapter_data_tables}.  They were determined by generating samples of {\MC}  using the program {\sc Heracles}~4.6.1~\cite{cpc:69:155,*spi:www:heracles} via {\sc
  Django}~1.3~\cite{cpc:81:381,*spi:www:djangoh11}, with and without QED radiating effects.  The Fermi coupling constant was set to $G_F=1.1664\cdot 10^{-5}~\GeV^{-2}$ and the mass of the $Z$ boson was set to $M_Z=91.1876~\GeV$.
	The resulting distributions reflected jets of partons including higher order effects in $\alphaem$.
\subsection{Hadronization Corrections}
	In order to correct the distributions from the fixed-order calculations to the full hadron level, correction factors were applied individually to each bin of each histogram.  These correction factors were derived from the ratios between hadronic and partonic distributions in the {\MC} samples described in chapter~\ref{chapter_event_simulation}.  ARIADNE samples were used to determine the SM predictions, and correction samples from the LEPTO~6.5
program~\cite{cpc:101:108} were used to estimate the systematic uncertainty due to the modelling of the QCD cascade.  These correction factors are presented in the data tables located in appendix~\ref{chapter_corrections}.  The final distributions reflected jets of hadrons including higher order effects in both $\alphaem$ and $\alphas$.
\section{Estimation of Experimental Systematic Uncertainties}
\label{section_jet_escale_uncert}
The same NC DIS data and {\MC} samples described in section \ref{section_transverse_energy_corrections} were used to estimate the uncertainty of the energy scale of the jets.  In figure \ref{plot_escale_uncert_rap}(a), the double ratio $R_{\mbox{\tiny DATA}}/R_{\mbox{\tiny MC}}$ is presented, where individual points correspond to events with jets from specific bins of $\rapjet$.  The residual disagreement between data and MC in these regions gives an estimate of the absolute uncertainty in the reconstruction for jets in the CC sample.  In figure \ref{plot_escale_uncert_gamma}(b), the double ratio $R_{\mbox{\tiny DATA}}/R_{\mbox{\tiny MC}}$, where $R=P_T^{H}/E_{T,DA}$, is shown.  Here $P_T^{H}$ is the transverse momentum of the hadronic system, and points representing events from specific bins of $\gammah$.  The residual deviation from 1 here represents an estimation of the absolute energy scale uncertainty of calorimetric quantites.
\begin{figure}[htb]
\vfill
	\setlength{\unitlength}{1.0cm}
	\begin{picture} (18.0,6.5)(.1,.1)
		\put(0.0,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0211esuncol}}
		\put(6.0,6.){(a)}
		\put(7.5,0.){\includegraphics[draft=false, width=.45\textwidth]
			{\oldplotdir/cc0212esuncol}}
		\put(9.0,6.){(b)}
	\end{picture}
		\caption[$E_T$ reconstruction vs. $\rapjet$ and $\gammah$]{$E_T$ reconstruction in bins of $\rapjet$ (a) and $\gammah$ (b) vs. $E_{T,DA}$ for $e^{-}p$ NC DIS ARIADNE, where $E_{T,DA}$ is the transverse energy of the isolated electron.  The vertical axis represents the double ratio of ZEUS Data over MC for the quantites $\etjet/E_{T,DA}$(a) and $P_T^{H}/E_{T,DA}$(b), were $P_T^{H}$ is the transvese momentum of the entire hadronic system. }
		
	\label{plot_escale_uncert_rap}
	\label{plot_escale_uncert_gamma}
\vfill
\end{figure}
\section{Estimation of Theoretical Systematic Uncertainties}

As described in section~\ref{section_scale_dependence}, the uncertainty on the NLO QCD calculations due to terms beyond NLO was estimated by varying the renormalization scale, $\mur$, between $Q/2$ and $2Q$.  The resultant change on the cross sections was typically below $\pm 2\%$ for the inclusive-jet cross sections and below $\pm 5\%$ for the dijet cross sections. For the trijets, the$\mathcal{O}(\alphas^2)$ calculations were only LO, and the resulting uncertainty on the cross sections was $\approx \pm30\%$ for all bins. This uncertainty was far larger than all other theoretical uncertainties, so no other theoretical uncertainty source was taken into account for these cross sections.  The uncertainty of the calculations due to the value of the factorization $\muf$ was estimated by repeating the calculations with $\muf  = Q/2$ and $2Q$. The effect was negligible.

The uncertainty on the NLO QCD calculations due to the uncertainty from the proton PDFs was estimated by repeating the calculations using the 22 additional sets from the ZEUS-S~\cite{pr:d67:012007} PDF extraction, which takes into account the statistical and correlated systematic experimental uncertainties of each data set used in the determination of the proton PDFs. The resulting uncertainty in the inclusive-jet $e^- p$ ($e^+ p$) cross sections was below $\pm 2 (4)\%$, except in the regions $\etjet>80\GeV$ , $Q^2>2\times10^4$ and $\log_{10}(x)>.5$ regions where it reached $\pm 4 (10)\%$. The resulting uncertainty in the dijet $e^- p$ ($e^+ p$) cross sections was below $\pm 5 (5)\%$, except in the region $\etjetbar>50\GeV$ where it reached $\pm 7 (15)\%$.

The uncertainty on the NLO QCD calculations due to the uncertainty from $\alphas(M_Z)$ was estimated by repeating the calculations using two additional sets of ZEUS-S proton PDFs, for which different values of $\alphas(M_Z)$ were assumed in the fits. The difference between the calculations using these various sets was scaled by a factor such as to reflect the uncertainty on the current world average of $\alphas(M_Z)$~\cite{ref_bethke_as}. The resulting uncertainty in the cross sections  was below $\pm 1\%$.

The uncertainty from the modeling of the QCD cascade was estimated as the difference between the hadronization corrections obtained using {\MC} samples generated by the ARIADNE and LEPTO programs. The resulting uncertainty on the inclusive-jet and dijet cross sections was typically below $\pm1\%$.  



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