%================================================================ % LaTeX file with prefered layout for H1 paper drafts % use: dvips -D600 file-name %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \usepackage{cite} \usepackage{setspace} %\usepackage{./mcite} %%%%%%%%%%%% Comment the next two lines to remove the line numbering %\usepackage[]{lineno} %\linenumbers %%%%%%%%%%%% Comment the next two lines to remove the line numbering \usepackage{multirow} \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============================= \begin{document} % The rest \newcommand{\pom}{{I\!\!P}} \newcommand{\reg}{{I\!\!R}} \def\gsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle >$}\,} \def\lsim{\,\lower.25ex\hbox{$\scriptstyle\sim$}\kern-1.30ex% \raise 0.55ex\hbox{$\scriptstyle <$}\,} \newcommand{\trm}{m_{\perp}} \newcommand{\trp}{p_{\perp}} \newcommand{\trmm}{m_{\perp}^2} \newcommand{\trpp}{p_{\perp}^2} \newcommand{\alps}{\alpha_s} \newcommand{\sqrts}{$\sqrt{s}$} \newcommand{\LO}{$O(\alpha_s^0)$} \newcommand{\Oa}{$O(\alpha_s)$} \newcommand{\Oaa}{$O(\alpha_s^2)$} \newcommand{\Oo}{$O(1)$} \newcommand{\pperp}{T} \newcommand{\PT}{p_{\perp}} \newcommand{\pt}{p_{_{T}}} \newcommand{\JPSI}{J/\psi} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\dgr}{^\circ} \newcommand{\gev}{\,\mbox{GeV}} \newcommand{\GeV}{\rm GeV} \newcommand{\GeVS}{\rm GeV^2} \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^2} } \newcommand{\xp}{x_p} \newcommand{\xpi}{x_\pi} \newcommand{\xg}{x_\gamma} \newcommand{\xgj}{x_\gamma^{jet}} \newcommand{\xpj}{x_p^{jet}} \newcommand{\xpij}{x_\pi^{jet}} \renewcommand{\deg}{^\circ} \newcommand{\qsq}{\ensuremath{Q^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^*} } \newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}} \newcommand{\Ptav}{\left\langle P_T \right\rangle} \newcommand{\lt}{<} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2}, #4 (#3)} \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\PR{{\em Phys. Rev.} } \def\ZPC{{\em Z. Phys.} {\bf C}} \def\ZP{{\em Z. Phys.} } \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\EJA{{\em Eur. Phys. J.} {\bf A}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \begin{flushleft} {\tt DESY 09-162 \hfill ISSN 0418-9833} \\ {\tt February 2010} \\ \end{flushleft} %\it %\noindent %Version 2.0 \\ %Editors: Artem Baghdasaryan (artyom$@$mail.desy.de) \\ %\hspace*{14mm} Armen Bunyatyan (bunar$@$mail.desy.de) \\ %\hspace*{14mm} Maxime Gouzevitch (gouzevit$@$mail.desy.de) \\ %Referees: Leif J\"onsson (leif.jonsson$@$hep.lu.se)\\ %\hspace*{16mm} Steve Maxfield (sjm$@$hep.ph.liv.ac.uk)\\ %% (\today) \\ %%\vspace{2cm} %\rm %\noindent %Comments by Friday, 16 June 2009 % Final Reading Wednesday, 7 October 2009 \vspace*{50mm} \begin{center} \begin{Large} {\boldmath \bf Jet Production in $ep$ Collisions at Low $Q^2$ and\\ Determination of $\alpha_s$ } \vspace*{10mm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent The production of jets is studied in deep-inelastic $e^{+}p$ scattering at low negative four momentum transfer squared $55~\GeV$. The 2-jet cross section is also presented as a function of $\xi = x_{\rm Bj} (1+ M^2_{12} / Q^2 )$, which in LO corresponds to the momentum fraction of the proton carried by the interacting parton (see Figs.\ref{diagrams}(b) and \ref{diagrams}(c)). % % for the photon % virtualities $55~\GeV$. % The variable $x_{\rm Bj}$ denotes the Bjorken scaling variable and $M_{12}$ the invariant mass of the two jets of highest $P_T$. The data correspond to higher integrated luminosity and a higher centre-of-mass energy than in the previous H1 analyses at low $Q^2$ \cite{Adloff:2000tq,Adloff:2002ew}. The larger data set together with improved understanding of the hadronic energy measurement significantly reduces the total uncertainty of the cross section measurements. The results are compared with perturbative QCD predictions at next-to-leading order (NLO) corrected for hadronisation effects, and $\alpha_s$ is extracted from a fit of the predictions to the data. These measurements allow the running of the strong coupling to be tested down to the limits of the perturbative calculation. Together with the high $Q^2$ measurements~\cite{Aaron:2009vs} the data test the running of $\alpha_s$ in the range of renormalisation scale $\mu_r$ between about $6$ and $70$~GeV. % Differential inclusive jet cross sections are measured as a functions % of $Q^2$ and $E_T^{jet}$, % dijet and three-jet production cross sections are measured as functions % of $Q^2$, transverse energy of the leading jet $E_{T,lead}$, % the average transverse jet energy $\hat{E_T^{jet}}$, \begin{figure}[h] \epsfig{file=d09-162f1a.eps,width=45mm} \hspace*{8mm}\epsfig{file=d09-162f1b.eps,width=45mm} \hspace*{8mm}\epsfig{file=d09-162f1c.eps,width=45mm} \label{diagrams} \caption{\label{fig:feynborn} Deep-inelastic lepton-proton scattering at different orders in $\alps$: (a) Born contribution $\mathcal{O}(1)$ and $\mathcal{O}(\alpha_s)$ processes (b) QCD Compton scattering and (c) boson-gluon fusion.} \end{figure} %--------------------------------------------------------------------------------------------------- \section{Experimental Method} \label{section:experiment} %--------------------------------------------------------------------------------------------------- The data used for this analysis were recorded with H1 detector in the years 1999 and 2000, when HERA collided positrons of energy $E_e = 27.6 \ {\rm GeV}$ with protons of energy $E_p = 920 \ {\rm GeV}$ giving a centre-of-mass energy $\sqrt{s}=319~\rm GeV$. % %Requiring all detectors which are essential for this analysis %to be fully operational results in an integrated luminosity of The corresponding integrated luminosity is $43.5$~pb$^{-1}$. \subsection{The H1 detector} A detailed description of the H1 detector can be found in \cite{Abt:1997hixv,Appuhn:1997na}. Here, a brief account of the components most relevant to the present analysis is given. The origin of the H1 coordinate system is the nominal $ep$ interaction point. The direction of the proton beam defines the positive $z$-axis (forward direction). The polar angle $\theta$ is measured with respect to this direction. The pseudorapidity is defined as $\eta=-\ln\tan(\theta/2)$. In the central region \mbox{($20^\circ\!<\!\theta\!<\!160^\circ$)} the $ep$ interaction region is surrounded by a two-layered silicon strip detector~\cite{Pitzl:2000wz} and two large concentric drift chambers (CJCs), operated inside a $1.16$~T solenoidal magnetic field. The trajectories of charged particles are measured in the central tracker with a transverse momentum resolution of $\sigma(p_T)/p_T=0.006\, p_T/$GeV$\, \oplus \,$0.02~\cite{Kleinwort:2006zz}. Two additional drift chambers complement the CJCs by precisely measuring the $z$-coordinates of track segments and hence improve the determination of the polar angle. The central tracking detectors also provide triggering information based on track segments measured in the $r$-$\phi$ plane of the central jet chambers and on the $z$ position of the event vertex obtained from the double layers of two multiwire proportional chambers (MWPCs). The forward tracking detector and the backward drift chamber (BDC) measure tracks of charged particles at smaller \mbox{($7^\circ\!<\!\theta\!<\!25^\circ$)} and larger \mbox{($155^\circ\!<\!\theta\!<\!175^\circ$)} polar angle than the central tracker, respectively. A finely segmented electromagnetic and hadronic liquid argon (LAr) calorimeter~\cite{Andrieu:1993kh} surrounds the tracking chambers. It has a polar angle coverage of \mbox{$4^\circ\!<\!\theta\!<\!154^\circ$} and full azimuthal acceptance. The energy resolution is % $\sigma(E)/E=12\%/\sqrt{E/\gev}\oplus 1\%$ $\sigma(E)/E=0.12/\sqrt{E/\gev}\oplus 0.01$ for electromagnetic showers and % $\sigma(E)/E=50\%/\sqrt{E/\gev}\oplus 2\%$ $\sigma(E)/E=0.5/\sqrt{E/\gev}\oplus 0.02$ for hadrons, as measured in test beams~\cite{Andrieu:1993tz}. %~\cite{Andrieu:1994yn,Andrieu:1993tz}. A lead-scintillating fibre spaghetti calorimeter (SpaCal)~\cite{Appuhn:1997na} covers the backward region \mbox{$153^\circ\!<\!\theta\!<\!178^\circ$}. Its main purpose is the detection of scattered positrons. The energy resolution of the SpaCal for positrons is % $\sigma(E)/E=7.1\%/\sqrt{E/\gev}\oplus 1\%$. $\sigma(E)/E=0.071/\sqrt{E/\gev}\oplus 0.01$. % In the backward % region \mbox{$153^\circ\!<\!\theta\!<\!178^\circ$}, particle energies are measured % by a lead-scintillating fibre spaghetti calorimeter (SpaCal)~\cite{Appuhn:1997na}. % For positrons, the energy resolution of the SpaCal % is $\sigma(E)/E=7.1\%/\sqrt{E/\gev}\oplus 1\%$. The luminosity is measured via the Bethe-Heitler Bremsstrahlung process $ep \rightarrow ep \gamma$, the final state photon being detected in a crystal calorimeter at $z=-103$~m. %------------------------------------------------------------- \subsection{Event and jet selection } \label{sec:jetsel} The data sample of this analysis was collected using a combination of triggers which require the scattered positron to be measured in the SpaCal, at least one high transverse momentum track ($p_\pperp>800\ {\rm MeV}$) to be reconstructed in the central tracking chambers and an event vertex to be identified by the MWPCs. The trigger efficiency is close to $100\%$ for the whole analysis phase space as determined from the data using independent triggers as a reference. The selection of NC DIS events is based on the identification of the scattered positron as the most energetic compact calorimetric deposit in the SpaCal with an energy $E_e'>7.5~\rm GeV$ and a polar angle $156\deg<\theta_e'<175\deg$. The energy weighted radius of this cluster is required to be less than $4$~cm, as expected for an electromagnetic shower. The cluster must be geometrically associated with a track candidate in the BDC. % %Further, the NC DIS events are selected requiring a scattered positron %measured in the SpaCal calorimeter with an %energy $E_e'>7.5~\rm GeV$ and a polar angle $156<\theta_e'<175\deg$. The \mbox{$z$-coordinate} of the primary event vertex is required to be within $\pm 35~\rm cm$ of the nominal position of the interaction point. The remaining clusters in the calorimeters and the charged tracks are combined to reconstruct the hadronic final state, using an algorithm which avoids double counting of energy \cite{Peez:2003zd,Portheault:2005uu}. The total longitudinal energy balance, determined as the difference of the total energy $E$ and the longitudinal component of the total momentum $P_z$, calculated from all detected particles including the scattered positron, must satisfy $45 < E -P_{z} < 65~\gev$. This requirement reduces contributions of DIS events with hard initial state photon radiation. For the latter events, the undetected photons propagating in the negative $z$ direction lead to values of $E -P_{z}$ significantly lower than the expected value $2E_e=55.2\gev$. After this selection the contribution from photoproduction is negligible as estimated using Monte Carlo simulations. % Together with the scattered positron and primary event vertex selections % the cut on $E -P_{z}$ also reduces the % contributions from photoproduction (estimated using Monte Carlo simulations), % cosmic muons and beam induced background to a negligible level. The kinematic region covered by this analysis is defined by \begin{center} $55~\GeV$ & & \multirow{3}{*}{$-1.0 < \eta_{\rm Lab}^{\rm jet} < 2.5$} \\ \cline{1-3} 2-jet & $P_{T}^{\rm jet1},~P_{T}^{\rm jet2}>5~\GeV$ & \multirow{2}{*}{$M_{12}>18~\GeV$} & \\ \cline{1-2} 3-jet & $P_{T}^{\rm jet1},~P_{T}^{\rm jet2},~P_{T}^{\rm jet3}>5~\GeV$ & & \\ \hline % \end{tabular} \vspace{\baselineskip} \caption{The NC DIS and jet selection criteria.} \label{tab:selection} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[h] \footnotesize %\normalsize \centering \begin{tabular}{ | c l | } \hline & \\ bin number & \\ (inclusive and 2-jets) & corresponding $Q^2$ range \\[5pt] \hline & \\[-8pt] 1 & $ \rm \ \ 5 \le Q^2< ~7~\GeV^2$ \\ 2 & $ \rm \ \ 7 \le Q^2< 10~\GeV^2$ \\ 3 & $ \rm 10 \le Q^2< 15~\GeV^2$ \\ 4 & $ \rm 15 \le Q^2< 20~\GeV^2$ \\ 5 & $ \rm 20 \le Q^2< 30~\GeV^2$ \\ 6 & $ \rm 30 \le Q^2< 40~\GeV^2$ \\ 7 & $ \rm 40 \le Q^2< 100~\GeV^2$ \\[3pt] \hline & \\ bin number & \\ (3-jets and 3-jets/2-jets) & corresponding $Q^2$ range \\[5pt] \hline & \\[-8pt] I & $ \rm \ \ 5 \le Q^2 < 10~\GeV^2$ \\ II & $ \rm 10 \le Q^2 < 20~\GeV^2$ \\ III & $ \rm 20 \le Q^2 < 40~\GeV^2$ \\ IV & $ \rm 40 \le Q^2 < 100~\GeV^2$ \\[3pt] \hline & \\ bin letter & corresponding $P_T$ or $\Ptav$ range \\[5pt] \hline & \\[-8pt] a & $ \rm \ \ 5 \le P_T< 10~\GeV$ \\ b & $ \rm 10 \le P_T< 15~\GeV$ \\ c & $ \rm 15 \le P_T< 20~\GeV$ \\ d & $ \rm 20 \le P_T< 80~\GeV$ \\[3pt] \hline & \\ bin letter & corresponding $\xi$ range \\[5pt] \hline & \\[-8pt] A & $ \rm 0.004 \le \xi< 0.006~$ \\ B & $ \rm 0.006 \le \xi< 0.010~$ \\ C & $ \rm 0.010 \le \xi< 0.025~$ \\ D & $ \rm 0.025 \le \xi< 0.050~$ \\ E & $ \rm \ \ 0.05 \le \xi< 0.1~$ \\ F & $ \rm \ \ \ \ 0.1 \le \xi< 0.3$ \\[3pt] \hline \end{tabular} % \caption{Nomenclature for the bins in negative four momentum transfer squared $Q^2$, jet transverse momentum $P_T$, average transverse momentum of the two leading jets $\Ptav$ and momentum fraction $\xi$ used in the following tables.} \label{tab:bins} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize Inclusive jet cross section in bins of $Q^{2}$}\\ \multicolumn{12}{c}{\normalsize Inclusive Jet Cross Section ${\rm \frac{d\sigma_{jet}}{dQ^2}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{2}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline 1 &$633\, $&$0.7 $&$6.7 $&$4.7 $&$4.8 $&$1.7 $&$0.3 $&$0.4 $&$4.2 $&$0.88 $&$5.8$ \\ 2 &$421\, $&$0.6 $&$7.0 $&$4.9 $&$5.1 $&$2.2 $&$0.2 $&$0.4 $&$4.3 $&$0.89 $&$5.3$ \\ 3 &$250\, $&$0.6 $&$6.7 $&$4.7 $&$4.9 $&$1.4 $&$0.1 $&$0.7 $&$4.4 $&$0.89 $&$4.7$ \\ 4 &$158\, $&$0.7 $&$6.6 $&$4.6 $&$4.8 $&$1.4 $&$0.1 $&$0.7 $&$4.3 $&$0.90 $&$4.0$ \\ 5 &$96.9\, $&$0.7 $&$6.5 $&$4.5 $&$4.7 $&$1.3 $&$0.2 $&$0.5 $&$4.2 $&$0.91 $&$3.5$ \\ 6 &$59.7\, $&$0.9 $&$6.4 $&$4.4 $&$4.6 $&$1.5 $&$0.1 $&$0.5 $&$4.0 $&$0.91 $&$2.6$ \\ 7 &$21.0\, $&$0.7 $&$5.9 $&$4.1 $&$4.3 $&$1.3 $&$0.1 $&$0.6 $&$3.7 $&$0.92 $&$1.5$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 2-Jet Cross Section in Bins of $Q^{2}$}\\ \multicolumn{12}{c}{\normalsize 2-Jet Cross Section ${\rm \frac{d\sigma_{2-jet}}{dQ^2}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{2}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline 1 &$83.6\, $&$1.5 $&$6.8 $&$4.8 $&$4.8 $&$1.2 $&$0.2 $&$0.2 $&$4.4 $&$0.91 $&$2.8$ \\ 2 &$56.4\, $&$1.4 $&$8.4 $&$5.9 $&$6.0 $&$3.6 $&$0.1 $&$0.5 $&$4.5 $&$0.93 $&$2.9$ \\ 3 &$33.9\, $&$1.3 $&$7.4 $&$5.2 $&$5.2 $&$1.5 $&$0.1 $&$0.7 $&$4.7 $&$0.93 $&$1.8$ \\ 4 &$22.5\, $&$1.6 $&$7.7 $&$5.5 $&$5.4 $&$2.0 $&$0.1 $&$0.7 $&$4.8 $&$0.94 $&$1.8$ \\ 5 &$14.4\, $&$1.4 $&$7.2 $&$5.1 $&$5.1 $&$1.5 $&$0.2 $&$0.5 $&$4.6 $&$0.94 $&$2.0$ \\ 6 &$9.70\, $&$1.9 $&$7.3 $&$5.2 $&$5.1 $&$1.5 $&$0.1 $&$0.6 $&$4.6 $&$0.94 $&$1.9$ \\ 7 &$3.72\, $&$1.4 $&$7.2 $&$5.1 $&$5.1 $&$1.2 $&$0.2 $&$0.6 $&$4.7 $&$0.95 $&$1.9$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet cross section in bins of $Q^{2}$}\\ \multicolumn{12}{c}{\normalsize 3-Jet Cross Section ${\rm \frac{d\sigma_{3-jet}}{dQ^2}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{2}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%]& & [\%]\\ \hline I &$10.5\, $&$2.6 $&$10.8 $&$7.7 $&$7.5 $&$4.6 $&$0.4 $&$0.4 $&$5.6 $&$0.81 $&$6.3$ \\ II &$4.56\, $&$2.7 $&$10.6 $&$7.7 $&$7.4 $&$4.0 $&$0.7 $&$0.8 $&$5.9 $&$0.82 $&$5.5$ \\ III &$2.05\, $&$2.9 $&$10.8 $&$7.9 $&$7.5 $&$4.1 $&$0.7 $&$0.6 $&$6.0 $&$0.80 $&$7.2$ \\ IV &$0.560\, $&$3.8 $&$11.7 $&$8.6 $&$7.9 $&$4.5 $&$1.0 $&$0.6 $&$6.2 $&$0.81 $&$6.1$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::jet_Q2} Inclusive jet, 2-jet and 3-jet cross sections in NC DIS measured as a function of $Q^2$. The measurements refer to the phase-space given in table \ref{tab:selection}. In the columns 3 to 6 are shown the statistical uncertainty, the total experimental uncertainty, the total uncorrelated uncertainty including the statistical one and the total bin-to-bin correlated uncertainty calculated as the quadratic sum of the following five components: the model dependence, the electron and the hadronic energy scales, the electron polar angle and the luminosity measurement uncertainties. The contributions to correlated uncertainties are listed in columns 7 to 10. The sharing of the uncertainties between correlated and uncorrelated sources is described in detail in section \ref{sec:sys}. The hadronisation correction factors applied to the NLO predictions and their uncertainties are shown in columns 11 and 12. The bin nomenclature of column 1 is defined in table \ref{tab:bins}. } \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize Inclusive jet cross section in bins of $P_T$}\\ \multicolumn{12}{c}{\normalsize Inclusive Jet Cross Section ${\rm \frac{d\sigma_{jet}}{dP_T}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline a&$1250\, $&$0.3 $&$6.8 $&$4.7 $&$4.9 $&$2.1 $&$0.2 $&$0.4 $&$4.1 $&$0.89 $&$4.4$ \\ b&$174\, $&$0.7 $&$6.6 $&$4.5 $&$4.7 $&$2.1 $&$0.1 $&$0.5 $&$3.9 $&$0.93 $&$2.8$ \\ c&$38.3\, $&$1.5 $&$9.8 $&$6.9 $&$6.9 $&$3.4 $&$0.3 $&$0.6 $&$5.8 $&$0.95 $&$2.2$ \\ d&$1.53\, $&$2.2 $&$15.3 $&$10.9 $&$10.8 $&$8.1 $&$0.6 $&$0.8 $&$6.9 $&$0.95 $&$1.5$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 2-jet cross section in bins of $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 2-Jet Cross Section ${\rm \frac{d\sigma_{2-jet}}{d\Ptav}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline a&$120\, $&$0.8 $&$6.8 $&$4.7 $&$4.9 $&$2.1 $&$0.2 $&$0.4 $&$4.1 $&$0.92 $&$2.1$ \\ b&$72.5\, $&$0.9 $&$7.7 $&$5.4 $&$5.5 $&$2.3 $&$0.1 $&$0.5 $&$4.7 $&$0.94 $&$2.3$ \\ c&$15.5\, $&$2.0 $&$11.1 $&$7.9 $&$7.8 $&$4.9 $&$0.4 $&$0.6 $&$5.9 $&$0.95 $&$2.3$ \\ d&$0.620\, $&$3.0 $&$17.8 $&$12.7 $&$12.5 $&$9.7 $&$0.6 $&$0.8 $&$7.7 $&$0.96 $&$1.8$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet cross section in bins of $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 3-Jet Cross Section ${\rm \frac{d\sigma_{3-jet}}{d\Ptav}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline a&$11.7\, $&$2.5 $&$9.2 $&$6.6 $&$6.3 $&$2.4 $&$0.5 $&$0.5 $&$5.6 $&$0.77 $&$9.5$ \\ b&$16.1\, $&$2.1 $&$9.0 $&$6.4 $&$6.3 $&$2.5 $&$0.6 $&$0.6 $&$5.5 $&$0.81 $&$6.5$ \\ c&$4.29\, $&$3.9 $&$12.7 $&$9.4 $&$8.6 $&$5.3 $&$0.8 $&$0.7 $&$6.6 $&$0.84 $&$3.6$ \\ d&$0.192\, $&$5.6 $&$20.0 $&$14.7 $&$13.6 $&$10.6 $&$1.0 $&$0.9 $&$8.4 $&$0.87 $&$4.1$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::jet_Pt} Inclusive jet, 2-jet and 3-jet cross sections in NC DIS measured as a function of $P_T$ for inclusive jet and $\Ptav$ of the two leading jets for 2-jet and 3-jet cross sections together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}. } \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize Inclusive jet cross section in bins of $Q^{2}$ and $P_T$}\\ \multicolumn{12}{c}{\normalsize Inclusive Jet Cross Section ${\rm \frac{d^2\sigma_{jet}}{dQ^2dP_T}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{3}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline 1 a&$109\, $&$0.7 $&$7.1 $&$4.9 $&$5.1 $&$2.1 $&$0.4 $&$0.5 $&$4.3 $&$0.87 $&$6.7$ \\ 1 b&$12.9\, $&$1.8 $&$6.1 $&$4.4 $&$4.2 $&$2.7 $&$0.1 $&$0.1 $&$2.9 $&$0.91 $&$3.2$ \\ 1 c&$2.77\, $&$3.8 $&$10.1 $&$7.6 $&$6.7 $&$3.4 $&$0.2 $&$0.1 $&$5.6 $&$0.95 $&$3.4$ \\ 1 d&$0.104\, $&$6.4 $&$15.0 $&$11.4 $&$9.6 $&$6.6 $&$1.0 $&$1.0 $&$6.7 $&$0.95 $&$3.4$ \\ \hline 2 a&$72.1\, $&$0.7 $&$7.6 $&$5.3 $&$5.5 $&$2.9 $&$0.3 $&$0.4 $&$4.4 $&$0.88 $&$6.1$ \\ 2 b&$9.02\, $&$1.7 $&$6.6 $&$4.7 $&$4.6 $&$2.9 $&$0.1 $&$0.5 $&$3.3 $&$0.92 $&$2.9$ \\ 2 c&$1.93\, $&$3.4 $&$15.8 $&$11.4 $&$11.0 $&$9.4 $&$0.3 $&$0.8 $&$5.4 $&$0.95 $&$3.1$ \\ 2 d&$0.0729\, $&$5.8 $&$24.6 $&$17.8 $&$17.0 $&$15.5 $&$0.1 $&$0.6 $&$6.8 $&$0.95 $&$3.1$ \\ \hline 3 a&$42.8\, $&$0.6 $&$7.6 $&$5.3 $&$5.4 $&$2.7 $&$0.2 $&$0.6 $&$4.4 $&$0.89 $&$5.2$ \\ 3 b&$5.45\, $&$1.6 $&$7.0 $&$5.0 $&$4.9 $&$2.8 $&$0.2 $&$0.7 $&$3.7 $&$0.92 $&$2.9$ \\ 3 c&$1.12\, $&$3.3 $&$12.2 $&$8.9 $&$8.4 $&$6.0 $&$0.2 $&$0.8 $&$5.6 $&$0.95 $&$2.8$ \\ 3 d&$0.0484\, $&$5.5 $&$20.5 $&$15.0 $&$14.0 $&$12.0 $&$0.7 $&$1.0 $&$7.0 $&$0.95 $&$2.8$ \\ \hline 4 a&$26.7\, $&$0.8 $&$7.3 $&$5.1 $&$5.2 $&$2.7 $&$0.1 $&$0.6 $&$4.2 $&$0.90 $&$4.3$ \\ 4 b&$3.68\, $&$1.9 $&$7.6 $&$5.4 $&$5.3 $&$2.7 $&$0.1 $&$0.7 $&$4.2 $&$0.93 $&$2.7$ \\ 4 c&$0.783\, $&$3.9 $&$12.6 $&$9.2 $&$8.5 $&$6.1 $&$0.4 $&$0.8 $&$5.7 $&$0.94 $&$4.1$ \\ 4 d&$0.0326\, $&$6.5 $&$17.2 $&$13.0 $&$11.3 $&$8.9 $&$0.5 $&$0.8 $&$6.8 $&$0.95 $&$4.1$ \\ \hline 5 a&$16.4\, $&$0.7 $&$7.0 $&$4.8 $&$5.0 $&$2.5 $&$0.3 $&$0.5 $&$4.1 $&$0.90 $&$3.7$ \\ 5 b&$2.21\, $&$1.8 $&$7.5 $&$5.4 $&$5.3 $&$2.5 $&$0.1 $&$0.4 $&$4.4 $&$0.94 $&$3.0$ \\ 5 c&$0.508\, $&$3.5 $&$10.2 $&$7.6 $&$6.9 $&$2.8 $&$0.3 $&$0.6 $&$6.1 $&$0.95 $&$3.0$ \\ 5 d&$0.0198\, $&$5.6 $&$15.0 $&$11.2 $&$9.9 $&$7.1 $&$0.4 $&$0.6 $&$6.7 $&$0.96 $&$2.9$ \\ \hline 6 a&$9.72\, $&$1.0 $&$7.3 $&$5.1 $&$5.2 $&$3.2 $&$0.1 $&$0.6 $&$3.8 $&$0.91 $&$2.6$ \\ 6 b&$1.65\, $&$2.2 $&$8.6 $&$6.2 $&$5.9 $&$3.3 $&$0.2 $&$0.5 $&$4.6 $&$0.95 $&$2.6$ \\ 6 c&$0.383\, $&$4.5 $&$11.1 $&$8.4 $&$7.3 $&$3.7 $&$0.2 $&$0.5 $&$6.1 $&$0.96 $&$5.2$ \\ 6 d&$0.0120\, $&$7.5 $&$15.0 $&$11.8 $&$9.3 $&$5.4 $&$0.7 $&$0.6 $&$7.3 $&$0.94 $&$2.8$ \\ \hline 7 a&$3.37\, $&$0.8 $&$6.5 $&$4.5 $&$4.7 $&$2.8 $&$0.1 $&$0.7 $&$3.4 $&$0.91 $&$1.5$ \\ 7 b&$0.614\, $&$1.7 $&$9.5 $&$6.7 $&$6.7 $&$4.2 $&$0.2 $&$0.6 $&$5.0 $&$0.96 $&$1.7$ \\ 7 c&$0.146\, $&$3.3 $&$10.6 $&$7.8 $&$7.2 $&$2.8 $&$0.4 $&$0.6 $&$6.4 $&$0.94 $&$2.7$ \\ 7 d&$0.00677\, $&$5.3 $&$12.0 $&$9.2 $&$7.7 $&$2.5 $&$0.6 $&$0.6 $&$7.1 $&$0.96 $&$2.6$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::Ijet_Q2PT} Double differential inclusive jet cross sections as a function of $Q^2$ and $P_T$ together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}.} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 2-jet cross section in bins of $Q^{2}$ and $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 2-Jet Cross Section ${\rm \frac{d^2\sigma_{2-jet}}{dQ^2d\Ptav}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{3}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline 1 a&$10.1\, $&$2.0 $&$6.7 $&$4.8 $&$4.6 $&$1.9 $&$0.6 $&$0.5 $&$3.9 $&$0.91 $&$3.3$ \\ 1 b&$5.06\, $&$2.6 $&$7.6 $&$5.6 $&$5.1 $&$2.2 $&$0.1 $&$0.2 $&$4.4 $&$0.91 $&$2.8$ \\ 1 c&$1.08\, $&$5.5 $&$11.5 $&$8.9 $&$7.2 $&$4.6 $&$0.4 $&$0.2 $&$5.4 $&$0.95 $&$2.8$ \\ 1 d&$0.0435\, $&$8.3 $&$16.7 $&$13.1 $&$10.3 $&$6.3 $&$1.0 $&$0.9 $&$7.9 $&$0.96 $&$2.7$ \\ \hline 2 a&$6.55\, $&$1.8 $&$6.7 $&$4.8 $&$4.7 $&$1.7 $&$0.3 $&$0.3 $&$4.1 $&$0.91 $&$3.4$ \\ 2 b&$3.56\, $&$2.4 $&$8.2 $&$6.0 $&$5.7 $&$3.1 $&$0.1 $&$0.6 $&$4.5 $&$0.93 $&$3.0$ \\ 2 c&$0.767\, $&$5.0 $&$18.8 $&$13.7 $&$12.9 $&$11.4 $&$0.2 $&$0.8 $&$5.6 $&$0.95 $&$2.4$ \\ 2 d&$0.0289\, $&$7.8 $&$27.5 $&$20.2 $&$18.7 $&$17.1 $&$0.2 $&$0.8 $&$7.3 $&$0.94 $&$3.0$ \\ \hline 3 a&$3.78\, $&$1.8 $&$7.4 $&$5.2 $&$5.1 $&$2.1 $&$0.2 $&$0.7 $&$4.4 $&$0.92 $&$1.7$ \\ 3 b&$2.28\, $&$2.2 $&$7.9 $&$5.7 $&$5.4 $&$2.3 $&$0.2 $&$0.7 $&$4.6 $&$0.94 $&$2.8$ \\ 3 c&$0.441\, $&$4.9 $&$15.1 $&$11.2 $&$10.2 $&$7.9 $&$0.3 $&$0.7 $&$6.1 $&$0.94 $&$2.8$ \\ 3 d&$0.0201\, $&$7.3 $&$22.7 $&$16.8 $&$15.2 $&$13.1 $&$0.7 $&$1.0 $&$7.5 $&$0.96 $&$3.0$ \\ \hline 4 a&$2.45\, $&$2.3 $&$7.3 $&$5.3 $&$5.0 $&$1.8 $&$0.2 $&$0.7 $&$4.4 $&$0.94 $&$1.5$ \\ 4 b&$1.52\, $&$2.7 $&$8.1 $&$5.9 $&$5.5 $&$2.0 $&$0.1 $&$0.8 $&$4.8 $&$0.94 $&$2.2$ \\ 4 c&$0.327\, $&$5.7 $&$13.5 $&$10.3 $&$8.8 $&$6.3 $&$0.4 $&$0.9 $&$5.8 $&$0.92 $&$1.8$ \\ 4 d&$0.0135\, $&$8.7 $&$20.6 $&$15.8 $&$13.3 $&$10.8 $&$0.6 $&$0.8 $&$7.5 $&$0.97 $&$3.0$ \\ \hline 5 a&$1.64\, $&$2.0 $&$6.8 $&$4.9 $&$4.7 $&$1.8 $&$0.4 $&$0.4 $&$4.1 $&$0.93 $&$2.0$ \\ 5 b&$0.927\, $&$2.5 $&$8.1 $&$5.9 $&$5.6 $&$2.2 $&$0.1 $&$0.5 $&$4.9 $&$0.95 $&$2.2$ \\ 5 c&$0.213\, $&$5.1 $&$10.5 $&$8.2 $&$6.6 $&$2.5 $&$0.3 $&$0.6 $&$5.8 $&$0.96 $&$2.2$ \\ 5 d&$0.00763\, $&$7.8 $&$20.1 $&$15.2 $&$13.1 $&$10.3 $&$0.5 $&$0.6 $&$8.0 $&$0.96 $&$2.8$ \\ \hline 6 a&$0.968\, $&$2.7 $&$7.2 $&$5.3 $&$4.8 $&$2.3 $&$0.1 $&$0.6 $&$4.0 $&$0.93 $&$1.8$ \\ 6 b&$0.753\, $&$3.1 $&$8.8 $&$6.5 $&$5.9 $&$2.6 $&$0.2 $&$0.5 $&$5.0 $&$0.95 $&$1.9$ \\ 6 c&$0.138\, $&$6.3 $&$11.5 $&$9.2 $&$6.9 $&$2.8 $&$0.4 $&$0.5 $&$6.0 $&$0.95 $&$4.5$ \\ 6 d&$0.00521\, $&$9.9 $&$18.1 $&$14.5 $&$10.8 $&$7.0 $&$0.7 $&$0.7 $&$8.0 $&$0.97 $&$4.4$ \\ \hline 7 a&$0.379\, $&$2.1 $&$6.7 $&$4.9 $&$4.7 $&$1.7 $&$0.1 $&$0.6 $&$4.0 $&$0.94 $&$1.8$ \\ 7 b&$0.266\, $&$2.4 $&$8.2 $&$5.9 $&$5.6 $&$1.8 $&$0.4 $&$0.6 $&$5.1 $&$0.96 $&$1.8$ \\ 7 c&$0.0648\, $&$4.8 $&$11.2 $&$8.6 $&$7.3 $&$1.8 $&$0.6 $&$0.6 $&$6.8 $&$0.96 $&$2.7$ \\ 7 d&$0.00265\, $&$7.0 $&$15.7 $&$12.1 $&$10.0 $&$5.9 $&$0.5 $&$0.5 $&$7.9 $&$0.95 $&$1.8$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::Dijet_Q2PT} Double differential 2-jet cross sections as a function of $Q^2$ and $\Ptav$ of two leading jets together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}.} \end{table} %----------------------------------------------------------------------------------------------------- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 2-jet cross section in bins of $Q^{2}$ and $\xi$}\\ \multicolumn{12}{c}{\normalsize 2-Jet Cross Section ${\rm \frac{d^2\sigma_{2-jet}}{dQ^2d\xi}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{2}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline 1 A&$608\, $&$9.7 $&$35.3 $&$25.9 $&$24.1 $&$23.6 $&$1.2 $&$0.6 $&$4.3 $&$0.94 $&$10.2$ \\ 1 B&$3450\, $&$3.4 $&$10.0 $&$7.4 $&$6.7 $&$5.5 $&$0.5 $&$0.3 $&$3.5 $&$0.96 $&$7.0$ \\ 1 C&$3060\, $&$2.1 $&$7.2 $&$5.2 $&$5.0 $&$2.8 $&$0.8 $&$1.0 $&$3.6 $&$0.92 $&$3.3$ \\ 1 D&$687\, $&$3.4 $&$8.4 $&$6.4 $&$5.4 $&$2.7 $&$0.4 $&$1.4 $&$4.2 $&$0.87 $&$3.3$ \\ 1 E&$76.6\, $&$7.2 $&$15.1 $&$11.8 $&$9.4 $&$7.4 $&$0.6 $&$1.1 $&$5.4 $&$0.85 $&$3.4$ \\ 1 F&$4.40\, $&$15.8 $&$35.0 $&$27.2 $&$22.1 $&$20.7 $&$1.3 $&$0.9 $&$7.2 $&$0.92 $&$3.1$ \\ \hline 2 A&$723\, $&$9.7 $&$12.4 $&$11.1 $&$5.6 $&$4.4 $&$1.8 $&$0.8 $&$2.3 $&$0.97 $&$7.6$ \\ 2 B&$2470\, $&$3.3 $&$6.9 $&$5.3 $&$4.4 $&$2.2 $&$0.7 $&$0.6 $&$3.4 $&$0.97 $&$7.0$ \\ 2 C&$2060\, $&$1.8 $&$6.8 $&$4.9 $&$4.7 $&$2.2 $&$0.3 $&$0.4 $&$3.9 $&$0.93 $&$3.6$ \\ 2 D&$441\, $&$3.0 $&$10.0 $&$7.3 $&$6.8 $&$5.1 $&$0.3 $&$0.5 $&$4.2 $&$0.89 $&$1.7$ \\ 2 E&$50.7\, $&$6.3 $&$19.4 $&$14.4 $&$13.0 $&$11.5 $&$0.9 $&$0.5 $&$5.8 $&$0.87 $&$1.7$ \\ 2 F&$2.31\, $&$15.2 $&$42.2 $&$31.7 $&$27.9 $&$26.9 $&$1.7 $&$0.4 $&$7.2 $&$0.87 $&$2.0$ \\ \hline 3 A&$363\, $&$10.4 $&$13.6 $&$12.1 $&$6.3 $&$1.5 $&$0.6 $&$1.0 $&$5.8 $&$1.02 $&$5.2$ \\ 3 B&$1430\, $&$3.3 $&$6.9 $&$5.3 $&$4.4 $&$1.6 $&$0.9 $&$0.7 $&$3.7 $&$0.97 $&$4.5$ \\ 3 C&$1250\, $&$1.8 $&$6.7 $&$4.8 $&$4.7 $&$1.7 $&$0.2 $&$0.7 $&$4.1 $&$0.93 $&$1.9$ \\ 3 D&$261\, $&$3.0 $&$7.4 $&$5.5 $&$4.9 $&$1.2 $&$0.2 $&$0.7 $&$4.4 $&$0.90 $&$2.1$ \\ 3 E&$38.2\, $&$5.6 $&$18.6 $&$13.7 $&$12.6 $&$10.8 $&$1.4 $&$0.9 $&$6.1 $&$0.88 $&$2.1$ \\ 3 F&$1.21\, $&$16.0 $&$38.0 $&$29.2 $&$24.3 $&$23.0 $&$2.3 $&$1.2 $&$7.2 $&$0.87 $&$4.0$ \\ \hline 4 A&$231\, $&$13.9 $&$15.0 $&$14.4 $&$4.2 $&$1.8 $&$0.8 $&$0.6 $&$3.4 $&$1.09 $&$3.0$ \\ 4 B&$1020\, $&$4.0 $&$7.9 $&$6.2 $&$5.0 $&$1.6 $&$1.0 $&$0.6 $&$4.3 $&$0.97 $&$5.1$ \\ 4 C&$782\, $&$2.2 $&$6.7 $&$4.9 $&$4.6 $&$1.0 $&$0.3 $&$0.7 $&$4.1 $&$0.95 $&$1.9$ \\ 4 D&$189\, $&$3.5 $&$7.7 $&$5.9 $&$5.0 $&$1.1 $&$0.3 $&$0.8 $&$4.5 $&$0.90 $&$2.0$ \\ 4 E&$26.3\, $&$6.7 $&$17.2 $&$13.0 $&$11.2 $&$9.2 $&$1.3 $&$0.8 $&$6.0 $&$0.87 $&$1.5$ \\ 4 F&$0.946\, $&$17.4 $&$26.7 $&$22.5 $&$14.3 $&$13.0 $&$1.5 $&$0.7 $&$5.5 $&$0.90 $&$1.4$ \\ \hline 5 A&$82\, $&$14.3 $&$15.4 $&$14.8 $&$4.3 $&$2.2 $&$0.6 $&$0.5 $&$3.3 $&$1.04 $&$4.3$ \\ 5 B&$602\, $&$3.7 $&$7.0 $&$5.5 $&$4.3 $&$2.1 $&$1.1 $&$0.4 $&$3.2 $&$0.98 $&$3.8$ \\ 5 C&$523\, $&$1.9 $&$6.8 $&$4.9 $&$4.7 $&$1.6 $&$0.4 $&$0.5 $&$4.1 $&$0.95 $&$2.4$ \\ 5 D&$120\, $&$3.1 $&$7.9 $&$5.9 $&$5.2 $&$1.7 $&$0.4 $&$0.6 $&$4.6 $&$0.90 $&$1.0$ \\ 5 E&$16.6\, $&$5.9 $&$11.2 $&$8.9 $&$6.9 $&$2.9 $&$1.0 $&$0.6 $&$5.9 $&$0.87 $&$1.1$ \\ 5 F&$0.700\, $&$14.3 $&$29.5 $&$23.1 $&$18.3 $&$16.4 $&$1.9 $&$0.9 $&$7.7 $&$0.91 $&$1.7$ \\ \hline 6 A&$33.9\, $&$20.9 $&$21.6 $&$21.2 $&$4.3 $&$2.1 $&$1.7 $&$0.2 $&$2.9 $&$0.98 $&$6.8$ \\ 6 B&$431\, $&$5.0 $&$7.3 $&$6.2 $&$3.9 $&$0.9 $&$0.7 $&$0.6 $&$3.4 $&$0.99 $&$2.3$ \\ 6 C&$335\, $&$2.5 $&$7.1 $&$5.3 $&$4.8 $&$2.2 $&$0.4 $&$0.5 $&$4.0 $&$0.95 $&$2.9$ \\ 6 D&$93.8\, $&$4.0 $&$8.7 $&$6.7 $&$5.6 $&$2.2 $&$0.3 $&$0.5 $&$4.8 $&$0.91 $&$0.9$ \\ 6 E&$9.52\, $&$7.9 $&$12.6 $&$10.5 $&$7.1 $&$3.0 $&$1.5 $&$0.7 $&$6.0 $&$0.89 $&$1.0$ \\ 6 F&$0.427\, $&$18.9 $&$27.7 $&$23.7 $&$14.4 $&$12.3 $&$1.8 $&$0.5 $&$6.9 $&$0.91 $&$2.2$ \\ \hline 7 A&$4.83\, $&$44.7 $&$45.5 $&$45.1 $&$6.3 $&$4.8 $&$0.8 $&$0.8 $&$3.5 $&$1.17 $&$5.2$ \\ 7 B&$122\, $&$5.2 $&$9.6 $&$7.7 $&$5.7 $&$3.7 $&$0.9 $&$0.3 $&$4.0 $&$0.98 $&$1.9$ \\ 7 C&$131\, $&$2.0 $&$7.2 $&$5.1 $&$5.0 $&$2.9 $&$0.1 $&$0.4 $&$3.8 $&$0.96 $&$1.4$ \\ 7 D&$36.5\, $&$2.7 $&$8.8 $&$6.5 $&$5.9 $&$3.1 $&$0.6 $&$0.5 $&$4.8 $&$0.94 $&$1.4$ \\ 7 E&$5.81\, $&$4.9 $&$11.6 $&$8.9 $&$7.5 $&$3.1 $&$1.5 $&$0.4 $&$6.4 $&$0.90 $&$1.5$ \\ 7 F&$0.237\, $&$11.8 $&$22.1 $&$17.7 $&$13.2 $&$10.3 $&$2.3 $&$0.4 $&$7.8 $&$0.89 $&$2.7$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::Dijet_Q2Ksi} Double differential 2-jet cross sections as a function of $Q^2$ and $\xi$ together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}.} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet cross section in bins of $Q^{2}$ and $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 3-Jet Cross Section ${\rm \frac{d^2\sigma_{3-jet}}{dQ^2d\Ptav}}$ }\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & cross & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & section & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & $\rm [pb/GeV^{3}]$ & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline I a&$0.780\, $&$4.3 $&$10.0 $&$7.6 $&$6.5 $&$3.2 $&$0.3 $&$0.2 $&$5.4 $&$0.78 $&$11.4$ \\ I b&$0.951\, $&$3.8 $&$9.6 $&$7.2 $&$6.4 $&$3.4 $&$0.3 $&$0.4 $&$5.1 $&$0.81 $&$6.0$ \\ I c&$0.240\, $&$7.2 $&$20.4 $&$15.2 $&$13.5 $&$11.8 $&$0.7 $&$0.6 $&$6.3 $&$0.82 $&$5.8$ \\ I d&$0.0102\, $&$10.9 $&$24.3 $&$18.8 $&$15.4 $&$12.6 $&$0.8 $&$1.1 $&$8.5 $&$0.88 $&$5.5$ \\ \hline II a&$0.321\, $&$4.5 $&$10.5 $&$8.0 $&$6.8 $&$2.9 $&$0.6 $&$0.9 $&$5.8 $&$0.78 $&$8.4$ \\ II b&$0.409\, $&$3.9 $&$10.0 $&$7.5 $&$6.6 $&$3.1 $&$0.6 $&$0.8 $&$5.5 $&$0.82 $&$6.4$ \\ II c&$0.113\, $&$7.3 $&$17.3 $&$13.3 $&$11.2 $&$8.9 $&$0.8 $&$0.9 $&$6.5 $&$0.84 $&$4.8$ \\ II d&$0.00526\, $&$10.3 $&$24.4 $&$18.7 $&$15.7 $&$13.1 $&$1.1 $&$0.9 $&$8.4 $&$0.87 $&$4.7$ \\ \hline III a&$0.126\, $&$5.0 $&$10.8 $&$8.3 $&$6.8 $&$3.7 $&$0.5 $&$0.7 $&$5.5 $&$0.76 $&$10.3$ \\ III b&$0.203\, $&$4.2 $&$10.9 $&$8.2 $&$7.2 $&$3.9 $&$0.7 $&$0.6 $&$5.8 $&$0.81 $&$6.6$ \\ III c&$0.0503\, $&$7.6 $&$13.9 $&$11.1 $&$8.3 $&$4.0 $&$0.8 $&$0.5 $&$7.0 $&$0.86 $&$6.4$ \\ III d&$0.00231\, $&$10.6 $&$22.4 $&$17.5 $&$14.0 $&$11.0 $&$1.1 $&$0.7 $&$8.3 $&$0.87 $&$4.4$ \\ \hline IV a&$0.0350\, $&$6.8 $&$13.1 $&$10.4 $&$8.0 $&$5.0 $&$0.7 $&$0.5 $&$5.9 $&$0.78 $&$7.1$ \\ IV b&$0.0513\, $&$5.5 $&$13.9 $&$10.5 $&$9.1 $&$6.6 $&$1.2 $&$0.7 $&$5.9 $&$0.82 $&$7.1$ \\ IV c&$0.0167\, $&$9.7 $&$14.9 $&$12.5 $&$8.1 $&$3.0 $&$1.3 $&$0.8 $&$7.2 $&$0.85 $&$5.3$ \\ IV d&$0.000750\, $&$14.1 $&$20.6 $&$17.6 $&$10.6 $&$7.0 $&$1.4 $&$0.7 $&$7.7 $&$0.85 $&$5.3$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::Trijet_Q2PT} Double differential 3-jet cross sections as a function of $Q^2$ and $\Ptav$ of two leading jets together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}.} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[htp] \centering \tiny \sf \renewcommand{\arraystretch}{1.50} \begin{tabular}{|c || r || r | r | r | r || r | r | r | r || r | r|} \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet to 2-jet cross sections ratio in bins of $Q^2$}\\ \multicolumn{12}{c}{\normalsize 3-Jet to 2-Jet Cross Sections Ratio ${\rm \frac{d\sigma_{3-jet}}{dQ^2}/\frac{d\sigma_{2-jet}}{dQ^2}}$}\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & 3-jet/2-jet & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & ratio & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline I &$0.156\, $&$2.4 $&$6.8 $&$5.0 $&$4.6 $&$4.2 $&$0.6 $&$0.3 $&$1.2 $&$0.88 $&$4.7$ \\ II &$0.162\, $&$2.5 $&$6.1 $&$4.6 $&$4.1 $&$3.6 $&$0.7 $&$0.1 $&$1.2 $&$0.88 $&$5.1$ \\ III &$0.170\, $&$2.4 $&$5.1 $&$3.8 $&$3.4 $&$2.6 $&$0.8 $&$0.1 $&$1.4 $&$0.85 $&$6.9$ \\ IV &$0.151\, $&$3.7 $&$8.0 $&$6.2 $&$5.1 $&$4.6 $&$0.8 $&$0.1 $&$1.5 $&$0.85 $&$6.8$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet to 2-jet Cross-sections Ratio in bins of $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 3-Jet to 2-Jet Cross Sections Ratio ${\rm \frac{d\sigma_{3-jet}}{d\Ptav}/\frac{d\sigma_{2-jet}}{d\Ptav}}$}\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & 3-jet/2-jet & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & ratio & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline a&$0.0982\, $&$2.4 $&$4.1 $&$3.1 $&$2.6 $&$1.2 $&$0.7 $&$0.1 $&$1.5 $&$0.84 $&$8.5$ \\ b&$0.222\, $&$1.9 $&$3.2 $&$2.4 $&$2.1 $&$1.2 $&$0.4 $&$0.1 $&$0.7 $&$0.86 $&$5.2$ \\ c&$0.276\, $&$3.5 $&$4.8 $&$4.1 $&$2.5 $&$1.9 $&$0.4 $&$0.1 $&$0.7 $&$0.89 $&$3.0$ \\ d&$0.310\, $&$5.1 $&$6.8 $&$5.9 $&$3.3 $&$2.9 $&$0.4 $&$0.1 $&$0.7 $&$0.91 $&$2.9$ \\ \hline \multicolumn{12}{c}{ } \\ % \multicolumn{12}{c}{\normalsize 3-jet to 2-jet Cross-sections Ratio in bins of $Q^2$ and $\Ptav$}\\ \multicolumn{12}{c}{\normalsize 3-Jet to 2-Jet Cross Sections Ratio ${\rm \frac{d^2\sigma_{3-jet}}{dQ^2d\Ptav}/\frac{d^2\sigma_{2-jet}}{dQ^2d\Ptav}}$}\\ \multicolumn{12}{c}{ } \\ \hline & & & & total & total & \multicolumn{4}{|c||}{\underline{\hspace*{0.1cm}single contributions to correlated uncertainty\hspace*{0.1cm}} } & hadronisation & hadronisation\\ bin & 3-jet/2-jet & statistical & total & uncorrelated & correlated & model & electron & electron & hadronic & correction & correction \\ & ratio & uncert. & uncert. & uncertainty & uncert. & uncert.& energy scale & polar angle& energy scale & factor & uncertainty \\ & & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & [\%] & & [\%]\\ \hline I a&$0.0980\, $&$4.1 $&$6.7 $&$5.5 $&$3.9 $&$3.2 $&$0.7 $&$0.2 $&$1.4 $&$0.85 $&$10.2$ \\ I b&$0.228\, $&$3.5 $&$6.6 $&$5.2 $&$4.1 $&$3.7 $&$0.3 $&$0.2 $&$0.7 $&$0.87 $&$5.0$ \\ I c&$0.267\, $&$6.3 $&$12.0 $&$9.5 $&$7.4 $&$7.2 $&$0.3 $&$0.1 $&$0.8 $&$0.87 $&$5.1$ \\ I d&$0.294\, $&$10.2 $&$12.4 $&$11.3 $&$5.2 $&$4.8 $&$0.2 $&$0.3 $&$0.9 $&$0.93 $&$5.3$ \\ \hline II a&$0.103\, $&$4.4 $&$6.6 $&$5.5 $&$3.6 $&$2.8 $&$0.8 $&$0.2 $&$1.4 $&$0.84 $&$9.2$ \\ II b&$0.215\, $&$3.7 $&$5.7 $&$4.7 $&$3.3 $&$2.8 $&$0.4 $&$0.1 $&$0.8 $&$0.88 $&$6.0$ \\ II c&$0.293\, $&$6.9 $&$9.7 $&$8.4 $&$5.0 $&$4.7 $&$0.4 $&$0.1 $&$0.5 $&$0.90 $&$4.3$ \\ II d&$0.312\, $&$9.2 $&$12.0 $&$10.7 $&$5.5 $&$5.2 $&$0.5 $&$0.2 $&$0.9 $&$0.91 $&$7.6$ \\ \hline III a&$0.0966\, $&$4.6 $&$7.2 $&$6.0 $&$4.1 $&$3.4 $&$0.9 $&$0.2 $&$1.4 $&$0.81 $&$11.0$ \\ III b&$0.243\, $&$3.2 $&$4.9 $&$4.0 $&$2.8 $&$2.2 $&$0.6 $&$0.1 $&$0.9 $&$0.85 $&$6.9$ \\ III c&$0.287\, $&$6.9 $&$9.8 $&$8.4 $&$5.1 $&$4.7 $&$0.4 $&$0.1 $&$1.1 $&$0.90 $&$8.4$ \\ III d&$0.359\, $&$9.4 $&$14.0 $&$11.9 $&$7.4 $&$7.2 $&$0.5 $&$0.1 $&$0.4 $&$0.90 $&$8.5$ \\ \hline IV a&$0.0922\, $&$6.7 $&$10.9 $&$9.0 $&$6.2 $&$5.6 $&$0.6 $&$0.2 $&$2.0 $&$0.83 $&$8.8$ \\ IV b&$0.193\, $&$5.5 $&$11.0 $&$8.6 $&$6.8 $&$6.5 $&$0.8 $&$0.1 $&$0.8 $&$0.85 $&$8.8$ \\ IV c&$0.257\, $&$9.0 $&$13.3 $&$11.3 $&$6.9 $&$6.7 $&$0.7 $&$0.2 $&$0.4 $&$0.89 $&$6.6$ \\ IV d&$0.282\, $&$14.1 $&$16.1 $&$15.1 $&$5.6 $&$5.3 $&$0.9 $&$0.2 $&$0.2 $&$0.90 $&$6.3$ \\ \hline \end{tabular} \normalfont \vspace{\baselineskip} \caption{\label{tab::Ratio_Q2Pt} Ratio of 3-jet to 2-jet cross sections as a function of $Q^2$ and $\Ptav$ together with their relative errors and hadronisation correction factors. Other details are given in the caption to table \ref{tab::jet_Q2}. The bin nomenclature is defined in table \ref{tab:bins}.} \end{table} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{table}[h] \normalsize % \large \centering \renewcommand{\arraystretch}{1.80} {\large Determination of $\alpha_s$ from jets} \\[3pt] \begin{tabular}{| l | c | c | c| c | c |} \hline % \multirow{3}{*}{Measurement} & \multirow{3}{*}{$\alpha_S(M_Z)$} & \multicolumn{3}{|c|}{Uncertainty} & \multirow{3}{*}{$\chi^2/\rm ndf$} \\ \cline{3-5} & & experimental & theory & PDF & \\ \hline $\sigma_{\rm jet}\left(Q^2,P_T\right)$ & $0.1180$ & $0.0018$ & $^{+0.0122}_{-0.0090}$ & $0.0022$ & $17.5/21$ \\ \hline $\sigma_{\textnormal{2-jet}}\left(Q^2,\left\langle P_T \right\rangle \right)$ & $0.1155$ & $0.0018$ & $^{+0.0121}_{-0.0090}$ & $0.0025$ & $14.3/23$ \\ \hline $\sigma_{\textnormal{3-jet}}\left(Q^2, \left\langle P_T \right\rangle \right)$ & $0.1170$ & $0.0017$ & $^{+0.0090}_{-0.0072}$ & 0.$0014$ & $11.0/15$ \\ \hline \hline $\sigma_{\rm jet},~\sigma_{\textnormal{2-jet}},~\sigma_{\textnormal{3-jet}}$ & $0.1160$ & $0.0014$ & $^{+0.0093}_{-0.0077}$ & $0.0016$ & $50.6/61$ \\ \hline $\sigma_{\textnormal{3-jet}}/\sigma_{\textnormal{2-jet}}$ & $0.1215$ & $0.0032$ & $^{+0.0066}_{-0.0058}$ & $0.0013$ & $11.9/13$ \\ \hline \end{tabular} \vspace{\baselineskip} \caption{\label{tab::Fits} Values of $\alpha_s (M_Z)$ obtained from fits to the individual inclusive jet, 2-jet and 3-jet double differential cross sections and from a simultaneous fit to all of them and to the ratio of 3-jet to 2-jet cross sections. Fitted values are given with experimental, theoretical and PDF errors, the normalised $\chi^2$/ndf of the fit is also shown.} \end{table} %\setcounter{table}{0} %\end{center} \newpage %%%%%%%%%%%% ARTEMPLOTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f2.eps,width=160mm} \caption{Inclusive jet cross sections $d\sigma_{jet}/dQ^2$ (a) and $d\sigma_{jet}/dP_T$ (b), 2-jet cross sections $d\sigma_{2-jet}/dQ^2$ (c) and $d\sigma_{2-jet}/d\Ptav$ (d) and 3-jet cross sections $d\sigma_{3-jet}/dQ^2$ (e) and $d\sigma_{3-jet}/d\Ptav$ (f), compared with NLO QCD predictions corrected for hadronisation. The error bars show the total experimental uncertainty, defined as the quadratic sum of the statistical and systematic uncertainties. The points are shown at the average values of $Q^2$, $P_T$ or $\Ptav$ within each bin. The NLO QCD predictions are shown together with the theory uncertainties associated with the scale uncertainties and the hadronisation (grey band). } \label{incljets} \end{figure} \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f3.eps,width=160mm} \caption{Double differential inclusive jet cross sections as a function of $Q^2$ and $P_T$, compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{incljets-double} \end{figure} %***************************************************************** \begin{figure}[ht] \centering \epsfig{file=d09-162f4.eps,width=160mm} \caption{Double differential 2-jet cross sections as a function of $Q^2$ and $\Ptav$, compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{dsdQ2dEtprime} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f5.eps,width=160mm} \caption{Double differential 2-jet cross section, as a function of $Q^2$ and $\xi$, compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{dsdQ2dksi} \end{figure} %***************************************************************** \begin{figure}[ht] \centering \epsfig{file=d09-162f6.eps,width=160mm} \caption{Double differential 3-jet cross sections as a function of $Q^2$ and $\Ptav$, compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{dsdQ2dEtprime3jets} \end{figure} \vfill %%%%%%%%%%%%%%%RATIOS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f7.eps,width=160mm} \caption{Ratios of 3-jet to 2-jet cross sections as a function of $Q^2$ (a) and $\Ptav$ integrated over the full $Q^2$ range (b) compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{ratios32} \end{figure} %%%%%%%%%%%%%%%RATIOS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f8.eps,width=160mm} \caption{Ratios of 3-jet to 2-jet cross sections as a function of $\Ptav$ in four different $Q^2$ ranges compared with NLO QCD predictions corrected for hadronisation. Other details are given in the caption to Fig.~\ref{incljets}. } \label{ratios322} \end{figure} %%%%%%%%%%%%%%%MAXIMPLOTS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \epsfig{file=d09-162f9.eps,width=140mm} \caption{Values of $\alpha_s(M_{Z})$ determined using the inclusive jet cross sections measured in $22$ bins in $Q^2$ and $P_T$ with the $k$-factor below $2.5$. The error bars denote the total experimental uncertainty of each data point. The solid line shows the two loop solution of the renormalisation group equation, $\alpha_s(M_Z)$, obtained from a simultaneous fit of all $22$ measurements of the inclusive jet cross sections. The inner band denotes the experimental uncertainty and the outer band denotes the squared sum of the PDF uncertainty and the theoretical uncertainties associated with the renormalisation and factorisation scales and the model dependence of the hadronisation corrections. } \label{fig:alphas1} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f10a.eps,width=75mm} \epsfig{file=d09-162f10b.eps,width=75mm} \epsfig{file=d09-162f10c.eps,width=75mm} \caption{Values of $\alpha_s(\mu_r=\sqrt{(Q^2 + P_{T\protect\raisebox{0pt}[0pt][0pt]{,\,}\text{obs}}^{2})/2})$ extracted from inclusive jet cross section (a), 2-jet cross section (b) and 3-jet cross section (c). In each case, the solid lines show the two loop solution of the renormalisation group equation obtained by evolving the corresponding fitted value of $\alpha_s(M_Z)$, as summarized in table \ref{tab::Fits}, data rows 1-3. Other details are given in the caption to Fig.~\ref{fig:alphas1}. } \label{fig:alphas2} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f11a.eps,width=75mm} \epsfig{file=d09-162f11b.eps,width=75mm} \caption{Values of $\alpha_s(\mu_r=\sqrt{(Q^2 + P_{T\protect\raisebox{0pt}[0pt][0pt]{,\,} \text{obs}}^{2})/2})$ obtained by a simultaneous fit of all jet cross sections in each $Q^2$ bin (a) and of the ratio of 3-jet cross section to 2-jet cross section (b). The solid lines show the two loop solution of the renormalisation group equation obtained by evolving the $\alpha_s$ obtained from these measurements. For (a) the value of $\alpha_s$ is extracted from a simultaneous fit of $62$ measurements of inclusive jet, 2-jet and 3-jet double differential cross sections in bins of $Q^2$ and $P_T$ ($\Ptav$ for 2-jets and 3-jets) with $k$-factor below $2.5$, see table \ref{tab::Fits}, 4th data row. For (b), $\alpha_s$ is extracted from $14$ measurements of the 3-jet cross section normalised to 2-jet cross section, using only data points with $k$-factor below $2.5$ for both the 3-jet and 2-jet cross sections, see table \ref{tab::Fits}, 5th data row. Other details are given in the caption to Fig.~\ref{fig:alphas1}. } \vspace*{-68mm} \hspace*{-34mm}\bf (a) \hspace*{70mm} (b) \vspace*{40mm} \label{fig:alphas3} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[ht] \centering \epsfig{file=d09-162f12.eps,width=140mm} \caption{Values of $\alpha_s(\mu_r=\sqrt{(Q^2 + P_{T\protect\raisebox{0pt}[0pt][0pt]{,\,} \text{obs}}^{2})/2})$ obtained by a simultaneous fit of all jet cross sections in each $Q^2$ bin of this analysis (squares) together with the fit in different bins at high $Q^2$ (circles) \cite{Aaron:2009vs}. The solid line shows the two loop solution of the renormalisation group equation obtained by evolving the $\alpha_s(M_Z)$ extracted from jets at high $Q^2$. Other details are given in the caption to Fig.~\ref{fig:alphas1}. } \label{fig:alphas4} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}