Changeset 490 in svn for trunk/paper/CommPhysComp
- Timestamp:
- Jul 15, 2009, 8:14:23 PM (15 years ago)
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- trunk/paper/CommPhysComp
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trunk/paper/CommPhysComp/notes.tex
r483 r490 615 615 \subsection{Jet resolution} 616 616 617 The majority of interesting processes at the \textsc{lhc} contain jets in the final state. The jet resolution obtained using \textsc{Delphes} is therefore a crucial point for its validation. Even if \textsc{Delphes} contains six algorithms for jet reconstruction, we use here the jet clustering algorithm (\textsc{jetclu}) with $R=0.7$ to validate the jet collection. 618 619 This validation is based on $pp \rightarrow gg$ events produced with \textsc{MadGraph/MadEvent} and hadronised using \textsc{Pythia}~\citep{bib:mgme,bib:pythia}. The events were arranged in $14$ bins of gluon transverse momentum $\hat{p}_T$. In each $\hat{p}_T$ bin, every jet in \textsc{Delphes} is matched to the closest jet of generator-level particles, using the spatial separation between the two jet axes 617 The majority of interesting processes at the \textsc{lhc} contain jets in the final state. The jet resolution obtained using \textsc{Delphes} is therefore a crucial point for its validation, both for \textsc{cms}- and \textsc{atlas}-like detectors. 618 This validation is based on $pp \rightarrow gg$ events produced with \textsc{MadGraph/MadEvent} and hadronised using \textsc{Pythia}~\citep{bib:mgme,bib:pythia}. 619 620 For a \textsc{cms}-like detector, a similar procedure as the one explained in public results is applied here. 621 The events were arranged in $14$ bins of gluon transverse momentum $\hat{p}_T$. In each $\hat{p}_T$ bin, every jet in \textsc{Delphes} is matched to the closest jet of generator-level particles, using the spatial separation between the two jet axes 620 622 \begin{equation} 621 623 \Delta R = \sqrt{ \big(\eta^\textrm{rec} - \eta^\textrm{MC} \big)^2 + \big(\phi^\textrm{rec} - \phi^\textrm{MC} \big)^2}<0.25. 622 624 \end{equation} 623 The jets made of generator-level particles, here referred as \textit{MC jets}, are obtained by applying the same clusteringalgorithm to all particles considered as stable after hadronisation.625 The jets made of generator-level particles, here referred as \textit{MC jets}, are obtained by applying the algorithm to all particles considered as stable after hadronisation. 624 626 Jets produced by \textsc{Delphes} and satisfying the matching criterion are called hereafter \textit{reconstructed jets}. 625 626 The ratio of the transverse energies of every reconstructed jet $E_T^\textrm{rec}$ and its corresponding \textsc{mc} jet $E_T^\textrm{MC}$ is calculated in each $\hat{p}_T$ bin. 627 All jets are computed with the clustering algorithm (\textsc{jetclu}) with a cone radius $R$ of $0.7$. 628 629 The ratio of the transverse energies of every reconstructed jet $E_T^\textrm{rec}$ to its corresponding \textsc{mc} jet $E_T^\textrm{MC}$ is calculated in each $\hat{p}_T$ bin. 627 630 The $E_T^\textrm{rec}/E_T^\textrm{MC}$ histogram is fitted with a Gaussian distribution in the interval \mbox{$\pm 2$~\textsc{rms}} centred around the mean value. 628 631 The resolution in each $\hat{p}_T$ bin is obtained by the fit mean $\langle x \rangle$ and variance $\sigma^2(x)$: 629 632 \begin{equation} 630 633 %\frac{\sigma(R_{jet})}{\langle R_{jet} \rangle }= 631 \frac{\sigma \Big (\frac{E_T^ {rec}}{E_T^{MC}} \Big)_\textrm{fit}}{ \Big \langle \frac{E_T^{rec}}{E_T^{MC}} \Big \rangle_\textrm{fit}}~634 \frac{\sigma \Big (\frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big)_\textrm{fit}}{ \Big \langle \frac{E_T^\textrm{rec}}{E_T^\textrm{MC}} \Big \rangle_\textrm{fit}}~ 632 635 \Big( \hat{p}_T(i) \Big)\textrm{, for all }i. 633 636 \end{equation} … … 637 640 %\includegraphics[width=\columnwidth]{resolutionJet} 638 641 \includegraphics[width=\columnwidth]{fig8} 639 \caption{Resolution of the transverse energy of reconstructed jets $E_T^\textrm{rec}$ as a function of the transverse energy of the closest jet of generator-level particles $E_T^\textrm{MC}$ . The maximum separation between the reconstructed and \textsc{mc} jets is $\Delta R= 0.25$. Pink line is the fit result for comparison to the \textsc{cms} resolution~\citep{bib:cmsjetresolution}, in blue.}640 \label{fig:jetresol }642 \caption{Resolution of the transverse energy of reconstructed jets $E_T^\textrm{rec}$ as a function of the transverse energy of the closest jet of generator-level particles $E_T^\textrm{MC}$, in a \textsc{cms}-like detector. The jets events are reconstructed with the \textsc{jetclu} clustering algorithm with a cone radius of $0.7$. The maximum separation between the reconstructed and \textsc{mc}-jets is $\Delta R= 0.25$. Dotted line is the fit result for comparison to the \textsc{cms} resolution~\citep{bib:cmsjetresolution}, in blue. The $pp \rightarrow gg$ dijet events have been generated with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.} 643 \label{fig:jetresolcms} 641 644 \end{center} 642 645 \end{figure} 643 644 The resulting jet resolution as a function of $E_T^\textrm{MC}$ is shown in Fig.~\ref{fig:jetresol }.646 647 The resulting jet resolution as a function of $E_T^\textrm{MC}$ is shown in Fig.~\ref{fig:jetresolcms}. 645 648 This distribution is fitted with a function of the following form: 646 649 \begin{equation} 647 650 \frac{a}{E_T^\textrm{MC}}\oplus \frac{b}{\sqrt{E_T^\textrm{MC}}}\oplus c, 651 \label{eq:fitresolution} 648 652 \end{equation} 649 653 where $a$, $b$ and $c$ are the fit parameters. 650 654 It is then compared to the resolution published by the \textsc{cms} collaboration~\citep{bib:cmsjetresolution}. The resolution curves from \textsc{Delphes} and \textsc{cms} are in good agreement. 655 656 Similarly, the jet resolution is evaluated for an \textsc{atlas}-like detector. The $pp \rightarrow gg$ events are here arranged in $8$ adjacent bins in $p_T$. A $k_T$ reconstruction algorithm with $R=0.6$ is chosen and the maximal matching distance between the \textsc{mc}-jets and the reconstructed jets is set to $\Delta R=0.2$. The relative energy resolution is evaluated in each bin by: 657 \begin{equation} 658 \frac{\sigma(E)}{E} = \sqrt{~~ \Bigg \langle ~\Bigg( \frac{E^\textrm{rec} - E^\textrm{MC}}{E^\textrm{rec}} \Bigg)^2 ~ \Bigg \rangle ~ - ~ \Bigg \langle \frac{E^\textrm{rec} - E^\textrm{MC}}{ E^\textrm{rec} } \Bigg \rangle^2}. 659 \end{equation} 660 661 Figure~\ref{fig:jetresolatlas} shows a good agreement between the resolution obtained with \textsc{Delphes}, the result of the fit with Equation~\ref{eq:fitresolution} and the corresponding curve provided by the \textsc{atlas} collaboration~\citep{bib:ATLASresolution}. 662 663 \begin{figure}[!h] 664 \begin{center} 665 \includegraphics[width=\columnwidth]{fig8b} 666 \caption{Relative energy resolution of reconstructed jets as a function of the energy of the closest jet of generator-level particles $E^\textrm{MC}$, in an \textsc{atlas}-like detector. The jets are reconstructed with the $k_T$ algorithm with a radius $R=0.6$. The maximal matching distance between \textsc{mc}- and reconstructed jets is $\Delta R=0.2$. Only central jets are considered ($|\eta|<0.5$). Dotted line is the fit result for comparison to the \textsc{atlas} resolution~\citep{bib:ATLASresolution}, in blue. The $pp \rightarrow gg$ di-jet events have been generated with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.} 667 \label{fig:jetresolatlas} 668 \end{center} 669 \end{figure} 670 651 671 652 672 \subsection{MET resolution} … … 663 683 The distribution of the difference between $E_x^\textrm{miss}$ in \textsc{Delphes} and at generator-level is fitted with a Gaussian function in each $(\Sigma E_T)$ bin. The fit \textsc{rms} gives the \textsc{met} resolution in each bin. 664 684 The resulting value is plotted in Fig.~\ref{fig:resolETmis} as a function of the total visible transverse 665 energy .685 energy, for \textsc{cms}- and \textsc{atlas}-like detectors. 666 686 667 687 \begin{figure}[!h] … … 670 690 \includegraphics[width=\columnwidth]{fig9} 671 691 \includegraphics[width=\columnwidth]{fig9b} 672 \caption{$\sigma(E^\textrm{mis}_{x})$ as a function on the scalar sum of all towers ($\Sigma E_T$) for $pp \rightarrow gg$ events, for a \textsc{cms}-like detector (top) and an \textsc{atlas}-like detector (bottom), for di jet events produced with MadGraph/MadEvent and hadronised with Pythia.}692 \caption{$\sigma(E^\textrm{mis}_{x})$ as a function on the scalar sum of all towers ($\Sigma E_T$) for $pp \rightarrow gg$ events, for a \textsc{cms}-like detector (top) and an \textsc{atlas}-like detector (bottom), for di-jet events produced with \textsc{MadGraph/MadEvent} and hadronised with \textsc{Pythia}.} 673 693 \label{fig:resolETmis} 674 694 \end{center} … … 681 701 where the $\alpha$ parameter depends on the resolution of the calorimeters. 682 702 683 The \textsc{met} resolution expected for the \textsc{cms} detector for similar events is $\sigma_x = (0.6-0.7) ~ \sqrt{E_T} ~ \mathrm{GeV}^{1/2}$ with no pile-up\footnote{\textit{Pile-up} events are extra simultaneous $pp$ collision occurring at high-luminosity in the same bunch crossing.}~\citep{bib:cmsjetresolution}, which compares very well with the $\alpha = 0.63$ obtained with \textsc{Delphes}. Similarly, for an \textsc{atlas}-like detector, a value of $0.5 6$ is obtained by \textsc{Delphes} for the $\alpha$ parameter, while the experiment expects it in the range $[0.53~ ;~0.57]$~\citep{bib:ATLASresolution}.703 The \textsc{met} resolution expected for the \textsc{cms} detector for similar events is $\sigma_x = (0.6-0.7) ~ \sqrt{E_T} ~ \mathrm{GeV}^{1/2}$ with no pile-up\footnote{\textit{Pile-up} events are extra simultaneous $pp$ collision occurring at high-luminosity in the same bunch crossing.}~\citep{bib:cmsjetresolution}, which compares very well with the $\alpha = 0.63$ obtained with \textsc{Delphes}. Similarly, for an \textsc{atlas}-like detector, a value of $0.53$ is obtained by \textsc{Delphes} for the $\alpha$ parameter, while the experiment expects it in the range $[0.53~ ;~0.57]$~\citep{bib:ATLASresolution}. 684 704 685 705 \subsection{\texorpdfstring{$\tau$}{\texttau}-jet efficiency}
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