%================================================================ % 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} \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}} \newcommand{\slowpi}{\pi_{\mathit{slow}}} %\newcommand{\gevsq}{\mathrm{GeV}^2} \newcommand{\fiidiii}{F_2^{D(3)}} \newcommand{\fiidiiiarg}{\fiidiii\,(\beta,\,Q^2,\,x)} \newcommand{\n}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand{\nz}{1.30\pm 0.08 (stat.)^{+0.08}_{-0.14} (syst.)} \newcommand{\fiidiiiful}{F_2^{D(4)}\,(\beta,\,Q^2,\,x,\,t)} \newcommand{\fiipom}{\tilde F_2^D} \newcommand{\ALPHA}{1.10\pm0.03 (stat.) \pm0.04 (syst.)} \newcommand{\ALPHAZ}{1.15\pm0.04 (stat.)^{+0.04}_{-0.07} (syst.)} \newcommand{\fiipomarg}{\fiipom\,(\beta,\,Q^2)} \newcommand{\pomflux}{f_{\pom / p}} \newcommand{\nxpom}{1.19\pm 0.06 (stat.) \pm0.07 (syst.)} \newcommand {\gapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle>}{\sim}$}} \newcommand {\lapprox} {\raisebox{-0.7ex}{$\stackrel {\textstyle<}{\sim}$}} 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\newcommand{\cww}{\cos^2{\theta_W}} \newcommand{\trm}{m_{\perp}} \newcommand{\trp}{p_{\perp}} \newcommand{\trmm}{m_{\perp}^2} \newcommand{\trpp}{p_{\perp}^2} \newcommand{\alp}{\alpha_s} \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{\PT}{p_{\perp}} \newcommand{\JPSI}{J/\psi} \newcommand{\sh}{\hat{s}} %\newcommand{\th}{\hat{t}} \newcommand{\uh}{\hat{u}} \newcommand{\MP}{m_{J/\psi}} %\newcommand{\PO}{\mbox{l}\!\mbox{P}} \newcommand{\PO}{I\!\!P} \newcommand{\xbj}{x} \newcommand{\xpom}{x_{\PO}} \newcommand{\ttbs}{\char'134} \newcommand{\xpomlo}{3\times10^{-4}} \newcommand{\xpomup}{0.05} \newcommand{\dgr}{^\circ} \newcommand{\pbarnt}{\,\mbox{{\rm pb$^{-1}$}}} \newcommand{\gev}{\,\mbox{GeV}} \newcommand{\WBoson}{\mbox{$W$}} \newcommand{\fbarn}{\,\mbox{{\rm fb}}} \newcommand{\fbarnt}{\,\mbox{{\rm fb$^{-1}$}}} \newcommand{\vtab}{\rule[-1mm]{0mm}{4mm}} \newcommand{\htab}{\rule[-1mm]{0mm}{6mm}} \newcommand{\photoproduction}{$\gamma p$} \newcommand{\ptmiss}{$P_{T}^{\rm miss}$} \newcommand{\epz} {$E{\rm-}p_z$} \newcommand{\vap} { $V_{ap}/V_p$} \newcommand{\Zero} {\mbox{$Z^{\circ}$}} \newcommand{\Ftwo} {\mbox{$\tilde{F}_2$}} \newcommand{\Ftwoz} {\mbox{$\tilde{F}_{2,3}$}} \newcommand{\Fz} {\mbox{$\tilde{F}_3$}} \newcommand{\FL} {\mbox{$\tilde{F}_{_{L}}$}} \newcommand{\Wtwo} {\mbox{$W_2$}} \newcommand{\Wz} {\mbox{$W_3$}} \newcommand{\WL} {\mbox{$W_{_{L}}$}} \newcommand{\Fem} {\mbox{$F_2$}} \newcommand{\Fgam} {\mbox{$F_2^{\gamma}$}} \newcommand{\Fint} {\mbox{$F_2^{\gamma Z}$}} \newcommand{\Fwk} {\mbox{$F_2^{Z}$}} \newcommand{\Ftwos} {\mbox{$F_2^{\gamma Z, Z}$}} \newcommand{\Fzz} {\mbox{$F_3^{\gamma Z, Z}$}} \newcommand{\Fintz} {\mbox{$F_{2,3}^{\gamma Z}$}} \newcommand{\Fwkz} {\mbox{$F_{2,3}^{Z}$}} \newcommand{\Fzint} {\mbox{$F_3^{\gamma Z}$}} \newcommand{\Fzwk} {\mbox{$F_3^{Z}$}} \newcommand{\Gev} {\mbox{${\rm GeV}$}} \newcommand{\Gevv}{\mbox{${\rm GeV}^2$}} \newcommand{\QQ} {\mbox{${Q^2}$}} %\newcommand{\lapprox}{\stackrel{<}{_{\sim}}} %\newcommand{\gapprox}{\stackrel{>}{_{\sim}}} % % Some useful tex commands % \newcommand{\qsq}{\ensuremath{Q^2} } \newcommand{\gevsq}{\ensuremath{\mathrm{GeV}^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^*} } % 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} {\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\ZPC{{\em Z. Phys.} {\bf C}} \def\EJC{{\em Eur. Phys. J.} {\bf C}} \def\CPC{\em Comp. Phys. Commun.} \begin{titlepage} \noindent Submitted to the XXXth International Conference on High Energy Physics ICHEP2000, \\ Osaka, Japan, July 2000 \vspace{2cm} \begin{center} \begin{Large} {\bf A measurement of Dijet Rates in Deep Inelastic Scattering at HERA } \vspace{2cm} H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent Dijet event rates, $R_2$, have been measured for deep inelastic $ep$ scattering using data collected with the H1 detector in the years 1996-1997 corresponding to an integrated luminosity of 22~${\rm \,pb}^{-1}$. $R_2$ is shown as a function of $x_B$ and $Q^2$ in the kinematic region $10^{-4}7 {\rm \,GeV}$}, \mbox{$E_{t,jet2}>5 {\rm \,GeV}$}. The corresponding dijet rates are shown in figure \ref{fig:r2nlodir}. The dijet rates increase for decreasing $x_B$ as expected, since the available phase space increases with the invariant mass of the hadronic final state $W^{2}\approx\frac{Q^2}{x_B}$. In figure \ref{fig:r2nlodir} the NLO QCD calculations are shown for two choices of the renormalization scale, namely $\mu^{2}_r=Q^2$ and $\mu^{2}_{r}=Q^{2}+E^{2}_{t}$. The factorization scale is set to $\mu^{2}_f=Q^2$ and the CTEQ4M\,\cite{cte} parton densities are used for the proton. The calculations have been corrected for hadronization effects which lower the prediction by approximately 10\%. The theoretical predictions describe the data for $\mu^{2}_r=Q^2$ with scale uncertainties up to 30\%, if $\mu^{2}_r$ is varied by a factor of two. If $\mu^{2}_r=Q^2+E^{2}_t$ (where $E_{t}=(E_{t,jet1}+E_{t,jet2})/2$ ) is chosen, the NLO QCD calculations describe the data for large $x_B$ and $Q^2$ only and clearly lie below the data for low $x_B$ and low $Q^2$. In this case, however, the scale uncertainties are considerably smaller. The calculations leave room for introducing additional contributions to jet production, for example processes where the virtual photon becomes resolved and acts as a source of partons. \subsection{Contributions from a virtual photon structure?} In order to investigate a possible resolved contribution of the photon to dijet production, the data are compared to NLO QCD calculations using the program JETVIP\,\cite{bp}. For these studies the renormalization and factorization scale are set to $\mu^{2}_r=\mu^{2}_f=Q^2+E^{2}_t$ and the SAS-1D\cite{sas} parton densities for the virtual photon are used. As shown in figure \ref{fig:r2jv} the full calculation including all resolved and direct contributions leads to a better agreement with the data than a JETVIP calculation which only considers a point-like photon. \subsection{Dependence of $R_2$ on the transverse energy of the jets} %%%To study the dijet rate as a function of the %%%transverse energy of the jets the cut on $E_{t,jet1}>(5+\Delta) {\rm \,GeV}$ is %%%varied by introducing the parameter $\Delta\in[0,7~{\rm\,GeV}]$ which %%%can be interpreted as the threshold difference between the transverse %%%energy of the hardest jet and the minimum value of the transverse %%%energy as required in the jet selection. To study the dependence of the dijet rate on the transverse energy of the jets, $R_2$ is measured as a function of the parameter $\Delta$ where the highest $E_{t,jet}$ satisfies $E_{t,jet1} > (5+\Delta )$~GeV . Note that as $\Delta \rightarrow 0$ the cuts on the jets become symmetric and the NLO calculations become infrared sensitive. The measured $R_2$ as a function of $\Delta$ is presented in figure \ref{fig:r2del} for two bins in $Q^2$ and $x_B$. At large $x_B$ and large $Q^2$ and $\Delta\geq1$~GeV, when staying away from the infrared sensitive region of the calculation, the NLO QCD calculations using DISENT describe the data well for both choices of $\mu^{2}_{r}$ . In the low $x_B$,$Q^2$ regime the predictions only describe the data when choosing $\mu^{2}_{r}=Q^2$. For $\mu^{2}_{r}=Q^2+E^{2}_{t}$ a reasonable agreement between the prediction and the measurement is only observed for $\Delta=7$~GeV which is equivalent to the requirement of large transverse energies of the jets. Finally, the NLO calculations show a turnover for $\Delta$ below about $1$~GeV whereas the data continue to increase towards $\Delta=0$ showing the need for resummed calculations. The two bins shown in figure~\ref{fig:r2del} are part of a detailed scan of the phase space which is presented in figure \ref{fig:r2com}. It is evident that for fixed $Q^2$ and decreasing $x_B$ the NLO description fails to describe the data for $\mu^{2}_{r}=Q^2+E^{2}_{t}$ and that $\mu^{2}_{r}=Q^2$ is favored by the data. \section{Summary} A measurement of the dijet rate $R_2$ in the phase space region $10^{-4}(5+\Delta)$~GeV for the jet with the largest transverse energy. The data are compared to NLO predictions for two choices of the renormalization scale $\mu^{2}_{r}$. The NLO predictions have been corrected for hadronization effects. The innermost band indicates the the error from the hadronization corrections and the full error band includes the scale uncertainty added in quadrature. \label{fig:r2del} } \end{center} \end{figure} \begin{figure} %%\rule{5cm}{0.2mm}\hfill\rule{5cm}{0.2mm} %%%\vskip 2.5cm %%%\rule{5cm}{0.2mm}\hfill\rule{5cm}{0.2mm} \begin{center} %%%\psfig{figure=stamp.test.eps,width=18cm} \psfig{figure=H1prelim-00-031.fig4.eps,height=21cm} \caption{Dijet rate $R_2$ as a function of $\Delta$ in various regions of $Q^2$ and $x_B$. The two bins shown in figure~\ref{fig:r2del} are included in this figure. The innermost band indicates the the error from the hadronization corrections and the full error band includes the scale uncertainty added in quadrature. \label{fig:r2com} } \end{center} \end{figure} \end{document}