%=====================================================% % TeX File for the Paper:- % % % % {\bf High Transverse Momentum 2-Jet and 3-Jet % % Measurements in Photoproduction} % % % %=====================================================% \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \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} %\textheight25cm \textwidth16.0cm \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 % This alternative topmargin shifts the 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\newcommand{\ptmia}{\ensuremath{P_{T}^{MI}~}} \newcommand{\lqcd}{\ensuremath{\Lambda_{QCD}~}} \newcommand{\lqcdiv}{\ensuremath{\Lambda_{QCD}^{[4]}~}} \newcommand{\lqcdv}{\ensuremath{\Lambda_{QCD}^{[5]}~}} \newcommand{\alps}{\ensuremath{\alpha_s}~} \newcommand{\si}{\ensuremath{\sigma}} \newcommand{\g}{\ensuremath{\gamma}} \newcommand{\hc}{\ensuremath{H^{c}_{i}~}} \newcommand{\ptmin}{\ensuremath{P_{T}^{min}~}} \newcommand{\msbar}{\ensuremath{\overline{MS}~}} \newcommand{\gev}{\ensuremath{\rm{GeV}} } \newcommand{\gevns}{\ensuremath{\rm{GeV}}} \newcommand{\mev}{\ensuremath{\rm{MeV}} } \newcommand{\mevns}{\ensuremath{\rm{MeV}}} \newcommand{\rcone}{\mbox{$R_0$}~} % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} A} \def\NPB{{\em Nucl. Phys.} B} \def\PLB{{\em Phys. Lett.} B} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} D} \def\ZPC{{\em Z. Phys.} C} % % % % %===============================title page=============================% % % \begin{titlepage} % EXTERNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \noindent Submitted to the 30th International Conference on High-Energy Physics ICHEP2000, \\ Osaka, Japan, July 2000 % INTERNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\begin{flushleft} %% DESY-??-??? \hfill ISSN ????????\\ % \noindent %Date: \today %Version: OSAKA write-up \\ %Editors: P. Bate, S. Caron, A. Mehta \\ %Referees: S. Schmitt, S. Maxfield \\ %%Comments by Thursday 24/6/99 12:00 %\end{flushleft} \vspace{2cm} \begin{center} \begin{Large} {\bf Measurements of 2-Jet and 3-Jet Cross Sections at High Transverse Momentum in Photoproduction} \vspace{1cm} H1 Collaboration \end{Large} \end{center} \vspace{1cm} \begin{abstract} \noindent Single differential 2-jet and 3-jet cross sections as a function of jet transverse momentum and invariant mass are measured in photoproduction using the H1 detector at HERA. The data sample comprises all available $e^+p$ data collected from 1994-97. Jets are found using the longitudinal boost-invariant \kt algorithm run in the laboratory frame with a minimum transverse momentum of the highest transverse momentum jet of greater than $25~\gev$. When the cross sections for two and three jet production are compared with QCD predictions, no significant deviations from expectation are found. \end{abstract} \vfill % EXTERNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \noindent \begin{flushleft} %\begin{tabular}{ll} {\bf Abstract: 977/978 } \\ {\bf Parallel session: 3,11 } \\ {\bf Plenary talk: 11,7b } %\\[0.2cm] %{\bf Electronic Access:} & % http://www-h1.desy.de/publications/H1\_sci\_results.shtml \\ %\end{tabular} \end{flushleft} % INTERNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{titlepage} % % % %============================authors=========================================== % % % %%\noindent %%\begin{flushleft} %% \input h1auts %%\end{flushleft} % % %%\begin{flushleft} %%\noindent %%\input h1inst %%\end{flushleft} % % % % % %============================The Paper======================= % % % % % \newpage %------------------------------------------------------------------ \section{Introduction and Motivation} % At HERA high transverse momentum jets are preferentially produced in photoproduction where the photon virtuality, $\qsq \approx 0~\gevsq$. In this paper single differential photoproduction 2-jet and 3-jet $ep$ cross sections in jet transverse momentum \ptj up to $\sim 75\gev$ and invariant mass up to $\sim 180 \gev$ are presented. These jet cross sections are sensitive primarily to the dynamics of the hard partonic scatter, allowing the validity of Quantum Chromodynamics (QCD) to be tested up to the highest transverse momenta and masses available at HERA. The understanding of QCD jet production is essential if the sensitivity to hadronic decays of massive particles is to be exploited. A data sample requiring at least two hard jets of which one must have transverse momentum greater than $25~\gev$ is defined. A subsample, requiring a third hard jet, is then constructed. From these samples differential 2-jet and 3-jet $ep$ cross sections in jet transverse momentum and jet invariant mass are evaluated. The paper is organized as follows. In section \ref{det} the H1 detector is presented while Section \ref{models} reviews the theoretical models. The jet algorithm used and the phase space considered in the analysis are defined in section \ref{jets}. Section \ref{analysis} details the analysis method. A discussion of the cross section measurements is presented in section \ref{results}. The final section provides a summary of the results and their interpretation. A full description of the analysis may be found in \cite{pb_thesis}. \section{The H1 Detector} \label{det} % The H1 detector is described in detail in~\cite{h1det}. Only those components relevant to the analysis are described here. The Liquid Argon (LAC )~\cite{Lar} and SpaCal~\cite{SpaCal} calorimeters are used to trigger events, reconstruct the hadronic energy of the final state and anti-tag positrons. The central tracking detector (CTD) is used to reconstruct the interaction vertex and to supplement the measurement of hadronic energy flow. A coordinate system in which the nominal interaction point is at the origin and the incident proton beam defines the $+z$ direction is used. The LAC covers the polar angle range $4^\circ < \theta < 154^\circ$ with full azimuthal acceptance. It consists of an electromagnetic section and a hadronic section. The total depth varies between 4.5 and 8 hadronic interaction lengths. The angular region \mbox{$153^\circ < \theta < 177.8^\circ$} is covered by the SpaCal, a lead/scintillating-fibre calorimeter. It also contains an electromagnetic and a hadronic section. The hadronic energy scale of the LAC is known to $4\%$ and of the SpaCal to $7\%$. The CTD consists of two concentric cylindrical drift chambers, coaxial with the beam-line, with a polar angle coverage of $15^\circ < \theta < 165^\circ$. The entire CTD is immersed in a 1.15 T magnetic field. The luminosity determination is based on measurement of the $ep \rightarrow ep \gamma$ Bethe-Heitler process, where the positron and photon are detected in crystal Cherenkov calorimeters located downstream of the interaction point. \section{Theoretical Models and Simulations} \label{models} In this paper QCD-inspired Monte Carlo event generators are used to unfold the data and, along with next to leading order (NLO) QCD calculations, are compared to the corrected data cross sections. A brief description of the generators and calculations used for these purposes are described below. To simulate the direct and resolved QCD photoproduction of jets the PYTHIA 5.7~\cite{pythia} and HERWIG 5.9~\cite{herwig} event generators are used. Both programs contain the Born level QCD hard scattering matrix elements, regulated by a minimum cutoff, \ptmin. Leading logarithmic parton showers simulate higher order QCD radiation. GRV-LO~\cite{Gluck:1992jc} parton distribution functions (PDFs) for the proton and photon are applied. The Lund String model is used by PYTHIA to hadronize the outgoing partons, while HERWIG uses the Cluster Hadronization approach. Multiple interactions between the proton and resolved photon are dealt with in PYTHIA by extending the perturbative parton-parton scattering below \pthat, the transverse momentum of the main partonic scatter, to a new limit, \ptmia. In HERWIG (in order to model the multiple interactions), 20$\%$ of events were simulated with the proton and resolved photon remnants interacting, producing soft particles. Table \ref{param_table} summarizes the major parameters used in these two event generators. The EPVEC~\cite{epvec} program is used to model the contribution to the cross sections arising from real $W$ production. A full detector simulation~\cite{geant} is applied to all Monte Carlo events. \begin{table} \input{param_table.tex} \caption{Description of event generators used to simulate photoproduction processes.} \label{param_table} \end{table} The JetViP \cite{jetvip} program, in which hard scattering matrix elements up to \Oaaa are implemented, is also used to compare QCD predictions to the data. The VEGAS~\cite{vegas} package is used to perform the integration over the allowed phase space with five iterations to ensure stability. Divergences in the real and virtual corrections are handled by JetViP using the phase-space slicing approach. In calculating NLO 2-jet cross sections, 2-loop $\alpha_s$ with 5 flavours is used in the \msbar scheme and GRV-HO~\cite{Gluck:1992jc} PDFs chosen for the proton and photon, whilst for the (LO) 3-jet cross sections, 1-loop $\alpha_s$ with 5 flavours and GRV-LO PDFs were used. In all cases, \lqcd is taken from the proton PDF. For estimating the Neutral Current Deep Inelastic Scattering (NC DIS) background, events with \qsq $>$ 4 \gevsq were generated using RAPGAP 2.3~\cite{rapgap} with CTEQ4M~\cite{cteq4m} parameterizations for the proton (a structureless photon is assumed) and parton showering. % \section{Jet Selection} \label{jets} The longitudinally boost-invariant \kt algorithm as proposed in \cite{invkt} is used in this analysis to define jets. This algorithm avoids the ambiguities that occur in cone-type algorithms~\cite{seyphen}. The algorithm is implemented using the KTCLUS~\cite{ktclus} package and run in the inclusive mode. Details of the implementation of this algorithm can be found in \cite{subjets}. The $\pt$-weighted scheme has been used throughout this analysis: \begin{equation} \etj = \sum_{i} E_{T, i} , \hskip8mm \etaj = \frac{\sum_i E_{T,i} \; \eta_i}{\sum_{i} E_{T,i}} , \hskip8mm \phij = \frac{\sum_i E_{T,i} \; \phi_i}{\sum_{i} E_{T,i}} , \label{recomb} \end{equation} where the index, $i$ runs over all final state objects. Since the jets are defined as massless, the rapidity and pseudorapidity of the jets are equivalent, as are the transverse momentum, \ptj and transverse energy, \etj. Cuts on jet transverse momentum are made such that $\ptji>25$~GeV, $\ptjii>15$~GeV and for the 3-jet sample, $\ptjiii >10$~GeV. The pseudorapidity of each jet, \etaj is restricted to $-0.5 < \etaj < 2.5$. All jets are then well contained in the LAC. Asymmetric cuts on the \ptj of the top two jets are made to avoid NLO uncertainties due to infrared-sensitive regions of phase space. The measured kinematic region is restricted to $y < 0.9$ and $\qsq < 4 \gevsq $. % \section{Cross Section Measurement Procedure} \label{analysis} \subsection{Event Selection} The data sample was collected with the H1 detector from 1994-97, when 820 \gev protons collided with 27.6 \gev positrons, resulting in a centre-of-mass energy of 300~GeV. The integrated luminosity obtained is 35.7~$\rm pb ^{-1}$. Energy deposits in the calorimeters and tracks in the CTD were combined to reconstruct the hadronic energy of events~\cite{mx_paper}. The $z$ coordinate of the event vertex, reconstructed from hit pattens in the CTD, is limited to -36 $<$ $z_{vertex}$ $<$ 34 cm. A cut on the missing transverse momentum \ptm$<$ 20 \gev is imposed to remove Charged Current and non-$ep$ events. Jet selections as described in section~\ref{jets} are applied. The measured jet energies are calibrated to their true energies using a large sample of single jet NC DIS events. In these events the jet momentum may be precisely estimated from kinematic constrains~\cite{pb_thesis}. The only significant background in the di-jet sample arises from NC DIS events. These are suppressed by removing events with a electron identified in the LAC or SpaCal with energy above 5 GeV and by requiring $y<0.9$, with $y$ reconstructed using hadronic variables~\cite{yJB}. Further cuts detailed in \cite{pb_thesis} reduce the contamination from NC DIS interactions to less than $4\%$ in all bins. Kinematic and jet distributions are well described by the Monte Carlo predictions. % \subsection{Correction of the Data for Detector Effects} % The data cross sections are obtained from the measured event rates by correcting for acceptance losses and inefficiencies bin-by-bin, using the cross-section weighted sum of events generated by PYTHIA and EPVEC. The background from NC DIS processes is estimated using RAPGAP and is subtracted on a statistical basis. The bin purity, defined as the number of events generated and reconstructed in a bin divided by the number reconstructed in the bin, is greater than $35\%$ for each bin. The ratio of bin contents before and after detector simulation is close to one. Bin centre corrections, radiative corrections and hadronization corrections are not applied. \subsection{Systematic Uncertainties} The systematic error on the measurement arises from the following sources: \begin{itemize} \item A $4$ \% uncertainty on the jet energy scale including a $2$ \% uncertainty that is correlated bin to bin. The jet energy scale uncertainty results in an error of $15$--$20$ \% on the cross sections. \item The uncertainty in the acceptance correction was estimated by taking the difference between the corrections obtained from HERWIG and PYTHIA. The resulting error on the cross sections is $\sim 10$\%. \item The uncertainty in the trigger efficiency results in a error of $\sim 4$\% on the cross section. \item The uncertainty on the background from DIS events is evaluated by varying the Monte Carlo estimate by $\pm 100\%$. The resulting error on the cross sections is $\sim 1\%$. \item The uncertainty in the integrated luminosity results in an overall normalisation error of $1.5$\% on the cross section. \end{itemize} All systematic errors are added in quadrature. \section{Results} \label{results} % Cross sections for the 2-jet sample as functions of the transverse momentum of the leading jet and the average of the two leading jets are shown in figure \ref{fig:2jets}. Cross sections for the 3-jet sample as functions of the transverse momentum of the third highest jet, the invariant mass of the two leading jets $M^{12}$ and of all three jets $M^{123}$ are shown in figure \ref{fig:3jets}. In the measured ranges the cross sections fall by three orders of magnitude. The total uncertainty, evaluated by adding systematic and statistical errors in quadrature, is typically $15\%$ on the 2-jet cross sections and $20\%$ on the 3-jet cross sections. The shape of the data are well described by the implementations of PYTHIA 5.7 and HERWIG 5.9. %Both models underestimate the total cross %section, with scale factors of 1.13 (2.1) and 1.19 (4.3) being applied %to PYTHIA (HERWIG) for the 2-jet and 3-jet cross sections respectively %in figures~\ref{fig:2jets} and \ref{fig:3jets}. Hadronization corrections are studied with PYTHIA and HERWIG by comparing cross sections before and after hadronization of the outgoing partons (after parton showering). The correction is $\sim 10 \%$ or lower in all bins and is not applied to the data, nor to any of the QCD models. The cross sections are also compare to QCD calculations as implemented in the JetViP program. The calculations agree well in shape and normalisation with the data. The kinematic configuration of massive particle decay would correspond in the 3-jet sample to the case where all three jets have large transverse momenta and are well separated from each other such that invariant masses of jet pairs are large. While no significant deviation is seen in figure~\ref{fig:3jets} it is noted that the QCD prediction yields a considerable number of events also at large $\ptj$ and invariant mass in the inclusive distributions presented here. In the highest bin of the invariant mass of the top three jets, the EPVEC generation of $W$ production ($ep \rightarrow eq W$, $W \rightarrow q q$) accounts for $7\%$ of the cross section prediction. % \section{Conclusions} Photoproduction of jets with high transverse momentum is investigated. Cross sections are measured for two or more jets and three or more jets as a function of transverse momentum up to $75\gev$ and as a function of invariant mass up to $180\gev$. The measured cross sections are compatible within errors with QCD predictions for photoproduction processes based on Monte Carlo event generator models and NLO QCD calculations. %The invariant mass cross sections are particularly %interesting in view of their sensitivity to massive particle decay. % \section*{Acknowledgements} % We are grateful to the HERA machine group whose outstanding efforts have made and continue to make this experiment possible. We thank the engineers and technicians for their work in constructing and now maintaining the H1 detector, our funding agencies for financial support, the DESY technical staff for continual assistance, and the DESY directorate for the hospitality which they extend to the non-DESY members of the collaboration. We wish to thank B. P\"{o}tter and M. Seymour for many helpful discussions. % the bibliography \begin{thebibliography}{99} \bibitem{pb_thesis} Paul Bate; PhD thesis, Univ. of Manchester, England : ``High Transverse Momentum 2-Jet and 3-Jet Cross Section Measurements in Photoproduction''. \bibitem{h1det} H1 Collaboration, I.\ Abt et al., Nucl. Instr. and Meth. {\bf A386} (1997) 310 and 348. \bibitem{Lar} H1 Calorimeter Group, B.\ Andrieu et al., Nucl. Instr. and Meth. {\bf A336} (1993) 460. \bibitem{SpaCal} H1 SpaCal Group, R.\ D.\ Appuhn et al., Nucl. Instr. and Meth. {\bf A386} (1997) 397. \bibitem{pythia} T. Sjostrand, CERN-TH-6488 (1992), Comput. Phys. Commun. {\bf 82} (1994) 74. % %\bibitem{Adloff:1998aw} H1 Collab., C.~Adloff et al.; %``Observation of events with an isolated high energy lepton and missing transverse momentum at HERA,'' %Eur.\ Phys.\ J.\ {\bf C5}, 575 (1998).%, hep-ex/9806009. %%CITATION = EPHJA,C5,575;%% \bibitem{herwig} G.\ Marchesini et al., Comp. Phys. Comm. {\bf 67} (1992) 465. \bibitem{Gluck:1992jc} M.~Gl\"uck, E.~Reya and A.~Vogt, Phys. Rev. {\bf D46} (1992) 1973. \bibitem{epvec} U.~Baur,~J.A.M.~Vermaseren and D.~Zeppenfeld, %\Journal{\NPB}{375}{1992}{3}. Nucl.\ Phys.\ {\bf B375} (1992) 3. \bibitem{geant} R. Brun et al., GEANT3 User's Guide, CERN-DD/EE-84-1 (1987). \bibitem{jetvip} B.~Potter, %``JetViP 1.1: Calculating one- and two-jet cross sections with virtual photons % in NLO {QCD},'' Comput.\ Phys.\ Commun.\ {\bf 119} (1999) 45.%, hep-ph/9806437. % \bibitem{vegas} G.P. Lepage, J. Comp. Phys. {\bf 27} (1978) 192. % %\bibitem{tbeam} H1 Calorimeter Group, B.\ Andrieu et al., Nucl. Instr. % and Meth. % {\bf A350} (1994) 57; \\ % H1 Calorimeter Group, B.\ Andrieu et al., Nucl. Instr. and Meth. % {\bf A336} (1993) 499. \bibitem{rapgap} H.\ Jung, Comp. Phys. Comm. {\bf 86} (1995) 147. \bibitem{cteq4m} H. L. Lai et al., Phys. Rev. {\bf D55} (1997), 1280. \bibitem{invkt} {S.D. Ellis and D.E. Soper}{,} \newblock Phys. Rev. {\bf D48} (1993) 3160. \bibitem{seyphen} {M.H. Seymour}{,} \newblock in: Les Rencontres de la Vall\'ee d'Aoste, La Thuile, France (1997) and Nucl. Phys. {\bf B513} (1998) 269. \bibitem{ktclus} {S. Catani, Yu.L. Dokshitzer, M.H. Seymour and B.R. Webber}{,} \newblock Nucl. Phys. {\bf B406} (1993) 187. \bibitem{subjets} H1 Collab., C.~Adloff et al., %``Measurement of internal jet structure in dijet production in deep-inelastic scattering at HERA,'' Nucl.\ Phys.\ {\bf B545} (1999) 3. %, hep-ex/9901010. %\bibitem{django} G. A. Schuler and H. Spiesberger, Proceedings of the % Workshop ``Physics at HERA'', vol. 3, eds. W. Buchm\"uller, G. % Ingelman, DESY (1992) 1419. %\bibitem{ariadne} L. L\"onnblad, Comp. Phys. Comm. {\bf 71} (1992) 15. %\bibitem{heracles} A. Kwiatkowski, H. Spiesberger and H.-J. M\"ohring, % Comp. Phys. Comm. {\bf 69} (1992) 155. \bibitem{mx_paper} H1 Collab., C. Adloff et al., Z. Phys. {\bf C74} (1997) 221. \bibitem{yJB} A. Blondel and F. Jacquet, Proceedings of the Study of an $ep$ Facility for Europe\\ ed. U. Amaldi, DESY 79/48 (1979) 391. \bibitem{pozo} {L.A. del Pozo}{,} \newblock PhD Thesis University of Cambridge, Cambridge, England (1993) RALT-002. %\bibitem{seyjets} M.H.~Seymour, presented at 10th Topical Workshop on % Proton-Antiproton Collider Physics, Batavia, IL, 9-13 May 1995. %, hep-ph/9506421. %``Jets in QCD,'' \end{thebibliography} \newpage % % % % % % Figures and Tables %% \begin{figure}[p] \unitlength 1cm \begin{center} %% \begin{picture}(16.0,9.0)(-3,0.) \resizebox{!}{9cm} %% {\includegraphics*[1pt,1pt][536pt,502pt]{./epsfiles/etaprof.eps}} %% \end{picture} \caption{{ The pseudorapidity jet profile, %% split into regions of \ptj and \etajns. The vertical axis %% shows the summed scalar transverse momentum, $\Delta P_T$ in %% each bin %% divided by the summed scalar transverse momentum, $\Sigma P_T$ of all hadronic final state objects.}} \label{etaprof} %\end{center} %\end{center} %\begin{center} % \begin{figure}[htb] \unitlength 1cm \begin{center} %% \begin{picture}(16.0,10.0)(-3.,0.) \resizebox{!}{9cm} %% {\includegraphics*[1pt,1pt][536pt,502pt]{./epsfiles/phiprof.eps}} %% \end{picture} \caption{{ %% The azimuthal angle jet profile, split into regions of \ptj %% and \etajns. The vertical axis shows the summed scalar %% transverse momentum, $\Delta P_T$ in each bin divided by the %% summed scalar transverse momentum, $\Sigma P_T$ of all %% hadronic final state objects.}} %% \label{phiprof} %% \end{center} %% \end{figure} %\end{center} % \begin{figure}[p] \begin{center} % \center \epsfig{file=epsfiles/anal_thesis_comb_ptl.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_ptav.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m12_2jet.eps,width=7.5cm} \center \epsfig{file=./H1prelim-00-052.fig1.eps,width=18cm} \caption{Hadronic cross sections for 2-jet production as function of the leading jet transverse momentum, $P_{T}^{Jet1}$ (left) and the average transverse momentum of the top two jets, $(P_{T}^{Jet1}+P_{T}^{Jet2})/2$ (right) . The inner error bars denotes the statistical, the outer error bars the quadratic sum of all statistical and systematic errors of the data. The predictions given by the PYTHIA 5.7 using GRV-LO structure functions for the proton and photon are shown, as are the NLO parton cross sections implemented with the JetViP numerical integration program using GRV-HO structure functions respectively.} \label{fig:2jets} \end{center} \end{figure} %%\begin{figure}[t] %% \center \epsfig{file=epsfiles/anal_thesis_comb_ptl.eps,width=7.5cm} %% \epsfig{file=epsfiles/anal_thesis_comb_ptav.eps,width=7.5cm} %% \epsfig{file=epsfiles/anal_thesis_comb_m12_2jet.eps,width=7.5cm} %% \center \epsfig{file=epsfiles/anal_am_comb_2jet.eps,width=\textwidth} %%\caption{Hadronic cross sections for 2-jet production as function of %% the leading jet transverse momentum, \ptji (top left), the average %% transverse momentum of the top two jets, \ptjav (top right) and the %% invariant mass of the two leading jets $M_{12}$ (bottom). The inner %% error bars denotes the statistical, the outer error bars the %% quadratic sum of all statistical and systematic errors of the data. %% The predictions given by the PYTHIA 5.7 and HERWIG 5.9 programs, %% using GRV LO structure functions for the proton and photon are %% shown, as are the NLO parton cross sections implemented with the %% JetViP 1.1 numerical integration program using GRV LO and HO %% structure functions respectively. The HERWIG and PYTHIA cross %% sections have been scaled to the data cross section.} %%\label{fig:2jets} %%\end{figure} %\begin{figure}[p] % \center % \epsfig{file=epsfiles/anal_thesis_comb_pt3.eps,width=17cm} % %\caption{Hadronic cross sections for 3-jet production as function of % the jet transverse momentum of the third highest jet. The inner error bars denotes the statistical, the outer % error bars the quadratic sum of all statistical and systematic % errors of the data. The predictions given by the PYTHIA 5.7 and % HERWIG 5.9 programs, using GRV LO structure functions for the proton % and photon are shown, as is the LO parton cross sections implemented % with the JetViP 1.1 numerical integration program using GRV LO % structure functions. The HERWIG and PYTHIA cross sections have been % scaled to the data cross section.} %\label{fig:3jet_masses_pt3} %\end{figure} %%\begin{figure}[p] % \center % \epsfig{file=epsfiles/anal_thesis_comb_m12_3jet.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m13.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m23.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m123.eps,width=7.5cm} % \vspace{-3cm} \center % \epsfig{file=epsfiles/anal_am_comb_3jet.eps,width=\textwidth} %\caption{Hadronic cross sections for 3-jet production s function of % the jet transverse momentum of the third highest jet \ptjiii (top % left); as function of the invariant mass of the two leading jets % $M_{12}$ (top right), the first and third jet $M_{13}$ (middle % left), the second and third jet $M_{23}$ (middle right) and all % three jets $M_{123}$ (lower left). The inner error bars denotes the % statistical, the outer error bars the quadratic sum of all % statistical and systematic errors of the data. The predictions given % by the PYTHIA 5.7 and HERWIG 5.9 programs, using GRV LO structure % functions for the proton and photon are shown, as is the LO parton % cross sections implemented with the JetViP 1.1 numerical integration % program using GRV LO structure functions. The HERWIG and PYTHIA % cross sections have been scaled to the data cross section.} %\label{fig:3jets} %\end{figure} \begin{figure}[p] %\vspace{-2cm} \begin{center} % \center % \epsfig{file=epsfiles/anal_thesis_comb_m12_3jet.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m13.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m23.eps,width=7.5cm} % \epsfig{file=epsfiles/anal_thesis_comb_m123.eps,width=7.5cm} \vspace{-3cm} \center \epsfig{file=./H1prelim-00-052.fig2.eps,width=18cm} \caption{Hadronic cross sections for 3-jet production as function of the jet transverse momentum of the third highest jet $P_{T}^{Jet3}$ (top left); as function of the invariant mass of the two leading jets $M^{12}$ (top right) and as function of all three jets $M^{123}$ (lower left). The inner error bars denotes the statistical, the outer error bars the quadratic sum of all statistical and systematic errors of the data. The predictions given by the PYTHIA 5.7, using GRV-LO structure functions for the proton and photon are shown, as is the LO parton cross sections implemented with the JetViP numerical integration program using GRV-LO structure functions.} \label{fig:3jets} \end{center} \end{figure} % \begin{picture}(15.,11) \put(-1.0,0){\psfig{ % figure=./psfiles/ktconenewest.ps,height=15cm,bburx=548,bbury=637,bbllx=7,bblly=160,clip=}} % \put(1.6,10.){\bf\Large{{$a)$}}} % \put(9.9,10.){\bf\Large{{$b)$}}} % \put(1.6,2.6){\bf\Large{{$c)$}}} % \put(9.9,2.6){\bf\Large{{$d)$}}} \end{picture} \caption{{\it The % Hadron Level cross sections for a) the leading jet \pt, b) the % third jet \pt, c) the 2-jet invariant mass of the highest two \pt jets and % d) the 3-jet invariant mass of the highest three \pt jets. The % superscripts `$2-JET$' and `$3-JET$' are used for cross sections % where two and three jets are required respectively. Error bars % are not shown.}} \label{cl_cone_fig} \end{center} \end{figure} %\end{center} % % % %\begin{table} %\begin{center} %\input{table_two.tex} %\end{center} %\caption{The triple-differential dijet cross-section %\triple for $0.1 < y < 0.7$ in ranges of $Q^2$, $\etbarsq$ and $\xgjets$. The cross-section in pb %is given together with the statistical, positive systematic and negative %systematic errors. %The table shows measurements for %$Q^2\leq 8.0~{\rm GeV}^2$. The higher $Q^2$ region is given in %table~\ref{Tab2b}.} %\label{Tab2a} %\end{table} % \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: