%================================================================ % 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} \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{\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{\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{\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{\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}, #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} \noindent %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% For conference papers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% coment the header and fill the right conference %%%%% {\it {\large version of \today}} \\[.3em] \begin{center} %%% you may want to use this line for working versions \begin{small} \begin{tabular}{llrr} {\bf H1prelim-08-032} Submitted to & & & \epsfig{file=/h1/iww/ipublications/H1PublicationTemplates/H1logo_bw_small.epsi ,width=1.5cm} \\[.2em] \hline \multicolumn{4}{l}{{\bf XVI International Workshop on Deep-Inelastic Scattering, DIS2008}, April 7-11,~2008,~London} \\ % Abstract: & {\bf } & & \\ Parallel Session & {\bf Hadronic Final States and QCD} & & \\ \hline \multicolumn{4}{l}{\footnotesize {\it Electronic Access:https://www-h1.desy.de/publications/H1preliminary.short\_list.html %www-h1.desy.de/h1/www/publications/conf/conf\_list.html }} \\[.2em] \end{tabular} \end{small} \end{center} %Write-up for H1prelim\_08\_032 \\ %\today %\rm \vspace*{2cm} \begin{center} \begin{Large} {\boldmath \bf Measurement of Inclusive Jet Production Deep-Inelastic $ep$ Scattering at low $Q^2$ } \vspace{2cm} %Artem Baghdasaryan, Armen Bunyatyan H1 Collaboration \end{Large} \end{center} \vspace{2cm} \begin{abstract} \noindent Jet production is studied in deep-inelastic positron-proton scattering over a range of four momentum transfer squared $57.5~GeV$, $156\deg<\theta_e<175\deg$, respectively. Jets are identified with the inclusive $k_t$ algorithm in Breit frame. The minimum $E_T$ is required to be above 5 GeV in that frame. To ensure that jets are fully contained in the calorimeter, the pseudorapidity of jets in the laboratory frame is required to be $-1<\eta^{Lab}<2.5$. %For dijet and three-jet % cross sections an additional cut on the total invariant mass of the % jet system, $M_{jj}>25~\GeV$, is applied. The final data sample contains 175,000 events with at least one jet satisfying the selection criteria. % Out of these 53800 events have at least 2 jets, % 5650 events at least 3 jets and 456 events have 4 or more jets. % % (11786 with $M_{jj}>25~\GeV$), 5650 at least 3 jets (4614 % with $M_{jj}>25~\GeV$), and 456 events have 4 and more jets. %-------------------------------------------------------------------- \section{Monte Carlo Models and Correction procedure} For the the calculation of correction factors due to detector effects, initial state radiation and hadronization RAPGAP3.1 and DJANGOh1.4 Monte Carlo generators are used. The CTEQ6D and CTEQ6L parametrizations of the parton distribution functions in the proton are used in RAPGAP and DJANGOh, respectively. The data distributions are corrected for effects of limited detector acceptance and resolution and for higher order QED effects using bin-to-bin corrections. The bin sizes were chosen to ensure the sufficient statistics and sufficiently high stability and purity in each bin. The correction factor for each distribution are defined as the ratio of cross section at hadron level for Monte Carlo sample which is generated without QED corrections to that at detector level with QED corrections included. The correction factor is taken as the average of the values from DJANGO and RAPGAP, respectively. The difference between the of corrections from the two Monte Carlo programs is on the average less than 5\% and is included in the systematic erros. For comparison with NLO calculations the hadronization corrections are calculated as the ratios of cross sections on the parton level to that on the hadron level. Again, the average of the corrections obtained from the two Monte Carlo programs is taken as the final correction factor. The hadronization correction factors agree on the level of 2\% between the two Monte Carlo simulations. %--------------------------------------------------------------------------------- \section{Systematic Uncertainties} The following sources of systematic errors are considered: \begin{itemize} \item the 2\% uncertainty on the absolute hadronic energy scale of the LAr calorimeter leads to an uncertainty of about 4--10\% on the jet cross section. This is strongly correlated between data points; \item the uncertainty of the SPACAL hadronic energy scale of 7\% contributes to less than 1\% to the cross section; \item the uncertainties on the measurements of the positron energy (2\%) and angle (1mrad) lead to 1--3\% systematic uncertainties in the cross sections; \item the uncertainty of the corrections for detector effects and initial state radiation is 2--15\%, \item luminosity is measured with the uncertainty of 1.5\%; \item finally, 1\% uncertainty is attributed to the trigger efficiencies as evaluated using independent triggers. \end{itemize} % In total, for single inclusive cross sections the total systematic error % varies from bin to bin between 8 and 19\%, being on the average about 10\%. %--------------------------------------------------------------------------- \section{Results} The results shown in figires \ref{final1}-\ref{final5} comprise inclusive jet cross sections as function of $Q^2$ and $E_T$, as well as the double differential cross sections in $Q^2$ and $E_T$. The measured cross-sections are compared with NLO QCD calculations. The NLO calculations are made using the NLOJET++ program. The calculations are performed in the $\overline{\rm MS}$ scheme for five massive quark flavours, and the parton PDF of the proton taken from the %CTEQ6.1M set \cite{cteq61m}. CTEQ6 set \cite{cteq61m}. $Q^2$ is used as factorization scale ($\mu_F$), whereas the renormalization scale ($\mu_R$) is chosen to be $\sqrt{(Q^2+E_T^2)/4}$. The error band on NLO predictions reflect the variation the scales $\mu$ by a factor of 2 up and down using the NLOJET++ \cite{nlojet} program. The NLO QCD calculations corrected for hadronization provide quite reasonable description of single inclusive jet cross sections. The measurements show strong sensitivity to the choice of the renormalisation scale. The calculations have been repeated with $\mu_R=E_T$. This scale provides worse description of the data at lower $Q^2$ and $E_T$, as shown in the figures \ref{final3} and \ref{final4}. %The results for comparison with the data are obtained using the values %provided by $fastNLO$ \cite{fastnlo} package. The fastNLO program \cite{fastnlo} was used to estimate uncertainty on NLO predictions arising from variations of factorization and renormalization scales, from the value of $\alps$ and the proton PDF. The different sources of uncertainties are shown with different error bands: \begin{itemize} \item uncertainty arising from the renormalisation and factorisation scales ($\mu_R$, $\mu_F$) are estimated by varying them by factors 2 and 0.5 separately and added the results of variation in quadrature. The contribution to uncertainty is up to 30\%. \item variation of $\alps$ between 0.116 and 0.120 gives variation of cross sections up to 5\% \item variation of 40 different eigenvectors of CTEQ6 proton PDF parameterisation gives up to 6\% incertainty \end{itemize} %The present results for single inclusive jet cross sections %are compared to the previous results from the paper \cite{H1jet2}. %% and \cite{H1jet1} respectively. %Since this measurement has been made in a %somewhat different kinematic range, our analysis has been repeated with %the cuts used in this paper. The residual difference between %the present and old results can be explained by the difference in %proton beam energy, as has been checked with NLOJET program. \section{Extraction of the strong coupling $\alpha_s$} The measured double differential inclusive jet cross sections (Fig.\ref{final5}) have been used to extract the strong coupling $\alpha_s$. The extracted value of $\alpha_s(M_Z)$ averaged over all measured data points is $$\alpha_s(M_Z) = 0.1186 \pm 0.0014 (exp) ^{+0.0132} _{-0.0101} (theory) \pm 0.0021 (pdf),~~ \chi ^2/ndf = 20.49 / 27$$ The results of the fit are shown in Figs.\ref{final7} and Figs.\ref{final8}. Fig.\ref{final9} shows the $\alpha_s(\mu=Q)$ from this measurement together with the values obtained from high $Q^2$ region ($Q^2>150~GeV^2$) \cite{highQ2}. \section{Summary} Inclusive jet cross-sections have been measured for values of $Q^2$ between 5 and 100 $\GeV^2$ and $0.2)$ & % 0.1171 & 0.0010 & +0.0048 & -0.0036 & 0.0018 & 28.1/23 \\ % (high $Q^2$) & & & & & & \\ \hline %% % $\sigma_{3JET}/\sigma_{DIS}=f(Q^2)$ & % 0.1179 & 0.0014 & +0.0056 & -0.0034 & 0.0009 & 4.53/5 \\ % (high $Q^2$) & & & & & & \\ \hline %% \end{tabular} \caption{Values of $\alpha_S(M_Z)$ obtained from a fit of 28 measurements of double differential inclusive jet cross sections $d^2\sigma/dQ^2dE_T$ (this measurement, upper row) and from the fits to the inclusive jet, dijet and treejet normalised cross sections at high $Q^2$ ($Q^2>150~GeV^2$) \cite{highQ2}} \end{table} %*****************************************************************8 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \epsfig{file= H1prelim-08-032.fig1.eps, width=70mm,angle=270,bbllx=63pt,bblly=63pt,bburx=390pt,bbury=790pt,clip= } \caption{Inclusive jet cross sections $d\sigma/dQ^2$ and $d\sigma/dE_T$, compared with NLO predictions corrected for hadronisation. The NLO calculation use the factorization scale $\mu_F^2=Q^2$ and the renormalization scale $\mu_R^2=(Q^2+E_T^2)/4$. The error bands reflect the uncertainties on NLO predictions arising from either hadronisaton corrections and the variation of renormalisation anf factorisation scales by factors 2 and 0.5.} \label{final1} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \epsfig{file= H1prelim-08-032.fig2.eps, width=150mm,angle=270,bbllx=57pt,bblly=180pt,bburx=570pt,bbury=690pt,clip= } \caption{Inclusive jet cross sections $d\sigma/dQ^2$ and $d\sigma/dE_T$, compared with NLO predictions corrected for hadronisation. The NLO calculation use the factorization scale $\mu_F^2=Q^2$ and the renormalization scale $\mu_R^2=(Q^2+E_T^2)/4$. The error bands reflect the uncertainties on NLO predictions arising from either hadronisaton corrections and the variation of renormalisation anf factorisation scales by factors 2 and 0.5, or variation of $\alps$ from 0.116 to 0.120, or PDF uncertainties calculated from variation of 40 eigenfunctions of CTEQ6.1 proton PDF.} \label{final2} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file= H1prelim-08-032.fig3.eps, width=80mm,angle=270,bbllx=64pt,bblly=64pt,bburx=390pt,bbury=790pt,clip= } \caption{Inclusive jet cross sections $d\sigma/dQ^2$, compared with NLO predictions corrected for hadronisation using two different choices of renormalisation scale $\mu_R^2=(Q^2+E_T^2)/4$ or $E_T^2$.} \label{final3} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file= H1prelim-08-032.fig4.eps, width=80mm,angle=270,bbllx=64pt,bblly=64pt,bburx=390pt,bbury=790pt,clip= } \caption{Inclusive jet cross sections $d\sigma/dE_T$, compared with NLO predictions corrected for hadronisation using two different choices of renormalisation scale $\mu_R^2=(Q^2+E_T^2)/4$ or $E_T^2$.} \label{final4} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file=H1prelim-08-032.fig5.eps, width=140mm,angle=270,bbllx=60pt,bblly=50pt,bburx=570pt,bbury=750pt,clip= } \caption{Inclusive double differential jet cross sections, compared with NLO predictions corrected for hadronisation. The error bands reflect the uncertainties on NLO predictions arising from hadronisation corrections and the variation of renormalisation and factorisation scales by factors 2 and 0.5 and the hadronisation. The NLO calculation use the factorization scale $\mu_F^2=Q^2$ and the renormalization scale $\mu_R^2=(Q^2+E_T^2)/4$} \label{final5} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file=H1prelim-08-032.fig6.eps, width=140mm,angle=270,bbllx=60pt,bblly=50pt,bburx=570pt,bbury=750pt,clip= } \caption{Inclusive double differential jet cross sections, compared with NLO predictions corrected for hadronisation. The error bands reflect the uncertainties on NLO predictions arising from hadronisation corrections and the variation of renormalisation and factorisation scales by factors 2 and 0.5 and the hadronisation. The NLO calculation use the factorization scale $\mu_F^2=Q^2$ and the renormalization scale $\mu_R^2=E_T^2$} \label{final6} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file=H1prelim-08-032.fig7.eps, width=120mm,angle=270,bbllx=80pt,bblly=20pt,bburx=570pt,bbury=770pt,clip= } \caption{Results of the fitted values of $\alpha_s(E_T)$ using the inclusive jet cross sections for seven regions of $Q^2$. The error bar denotes the total experimental uncertainty of each data point. The solid line shows the two loop solution of the renormalisation group equation evolving the $\alpha_s(M_Z)$ % from Guenter obtained from a fit of 28 measurements of double differential inclusive jet cross sections $d^2\sigma/dQ^2dE_T$ (Fig.5), with the inner % averaged from all individual fits, with the blue band denoting the correlated experimental uncertainties and the grey band denoting the theoretical uncertainties associated with the renormalisation and factorisation scales, PDF uncertainty and the hadronisation corrections.} \label{final7} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] %\hspace*{-20mm} \centering \epsfig{file=H1prelim-08-032.fig8.eps, width=75mm,angle=270,bbllx=1pt,bblly=20pt,bburx=570pt,bbury=670pt,clip= } \caption{Results of the fitted values of $\alpha_s(\mu=Q)$ averaged over all $E_T$ regions. The error bar denotes the total experimental uncertainty of each data point. The solid line shows the two loop solution of the renormalisation group equation evolving the $\alpha_s(M_Z)$ % from Guenter obtained from a fit of 28 measurements of double differential inclusive jet cross sections $d^2\sigma/dQ^2dE_T$ (Fig.5), with the inner % averaged from all individual fits, with the blue band denoting the correlated experimental uncertainties and the grey band denoting the theoretical uncertainties associated with the renormalisation and factorisation scales, PDF uncertainty and the hadronisation corrections.} \label{final8} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] %\hspace*{-20mm} \centering \epsfig{file=H1prelim-08-032.fig9.eps, width=75mm,angle=270,bbllx=1pt,bblly=20pt,bburx=570pt,bbury=670pt,clip= } \caption{Results of the fitted values of $\alpha_s(\mu=Q)$ from the low $Q^2$ measurements (red points, same as poins on Fig.8) and the high $Q^2$ measurements (black points, H1prelim-08-031). The error bar denotes the total experimental uncertainty of each data point. The solid curve shows the result of evolving $\alpha_s(M_Z)$ obtained from a fit to % averaged from the inclusive, dijet and threejet normalised cross sections at high $Q^2$ ($Q^2>150~GeV^2$), with the inner blue band denoting the correlated experimental uncertainties and the grey band denoting the theoretical uncertainties associated with the renormalisation and factorisation scales, PDF uncertainty and the hadronisation corrections.} \label{final9} \end{figure} \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] \hspace*{-20mm} \epsfig{file=H1prelim-08-032.fig7_testcolor.eps, width=120mm,angle=270,bbllx=80pt,bblly=20pt,bburx=570pt,bbury=770pt,clip= } \caption{test color} \label{final10} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h] %\hspace*{-20mm} \centering \epsfig{file=H1prelim-08-032.fig8_testcolor.eps, width=75mm,angle=270,bbllx=1pt,bblly=20pt,bburx=570pt,bbury=670pt,clip= } \caption{test color} \label{final11} \end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document}