From 549a0be343f6c09189ca27854bd974269e71f30c Mon Sep 17 00:00:00 2001 From: hdalsgaa Date: Thu, 12 Apr 2012 13:28:48 +0000 Subject: [PATCH] Updated text and figures from HHD thesis --- PWGLF/FORWARD/doc/doc.tex | 99 ++++++++++++++++++++++- PWGLF/FORWARD/doc/results_PbPbdndeta.pdf | Bin 0 -> 49025 bytes PWGLF/FORWARD/doc/results_ppdndeta.pdf | Bin 0 -> 28948 bytes 3 files changed, 95 insertions(+), 4 deletions(-) create mode 100644 PWGLF/FORWARD/doc/results_PbPbdndeta.pdf create mode 100644 PWGLF/FORWARD/doc/results_ppdndeta.pdf diff --git a/PWGLF/FORWARD/doc/doc.tex b/PWGLF/FORWARD/doc/doc.tex index ca5e07522c0..6337472c207 100644 --- a/PWGLF/FORWARD/doc/doc.tex +++ b/PWGLF/FORWARD/doc/doc.tex @@ -45,6 +45,7 @@ \newcommand{\NA}{\N{\text{A}}{}} \newcommand{\Ngood}{{\ensuremath N_{\text{good}}}} \newcommand{\GeV}[1]{\unit[#1]{\AlwaysText{GeV}}} +\newcommand{\TeV}[1]{\unit[#1]{\AlwaysText{TeV}}} \newcommand{\cm}[1]{\unit[#1]{\AlwaysText{cm}}} \newcommand{\secref}[1]{Section~\ref{#1}} \newcommand{\figref}[1]{Figure~\ref{#1}} @@ -186,7 +187,7 @@ Each of these steps will be detailed in the following. \label{sec:sub:event_inspection} The first thing to do, is to inspect the event for triggers. A number -of trigger bits, like \INEL{}, \INELONE{}, \NSD{}, and so on is then +of trigger bits, like \INEL{} (Minimum Bias for Pb+Pb), \INELONE{}, \NSD{}, and so on is then propagated to the \AOD{} output. Just after the sharing filter (described below) but before any further @@ -194,6 +195,12 @@ processing, the vertex information is queried. If there is no vertex information, or if the vertex $z$ coordinate is outside the pre--defined range, then no further processing of that event takes place. +\subsubsection{Displaced Vertices} +\label{sec:sub:sub:dispvtx} + +The analysis can be set up to run on the `displaced vertices' that +occur during LHC Pb+Pb running. Details on the displaced vertices, and +their selection can be found in the VZERO analysis note \cite{maxime}. \subsection{Sharing filter} \label{sec:sub:sharing_filter} @@ -376,7 +383,7 @@ corrected\footnote{The sharing correction can be disabled, in which and calculates the inclusive (primary + secondary) charged particle density in pre--defined $\etaphi$ bins. -\subsubsection{Inclusive number of charged particles} +\subsubsection{Inclusive number of charged particles: Energy Fits} \label{sec:sub:sub:eloss_fits} The number charged particles in a strip $\mult[,t]$ is calculated @@ -420,6 +427,50 @@ The fit procedure is stopped when one for $j+1$ \end{itemize} $N_{max}$ is then set to $j$. Examples of the result of these fits are given in \figref{fig:eloss_fits} in Appendix~\ref{app:eloss_fits}. +\subsubsection{Inclusive number of charged particles: Poisson Approach} +\label{sec:sub:sub:poisson} +Another approach to the calculation of the number of charged particles +is using Poisson statistics. +Assume that in a region of the FMD % where +$\mult$ +%is azimuthally uniform in $\eta$ intervals it +is +distributed according to a Poisson distribution. This means that the +probability of $\mult=n$ becomes: +\begin{equation} +P(n) = \frac{\mu^n e^{-\mu}}{n!} \label{eq:PoissonDef} +\end{equation} +In particular the measured occupancy, $\mu_{meas}$, is the probability +of any number of hits, thus using \eqref{eq:PoissonDef} : +\begin{equation} +\mu_{meas} = 1 - P(0) = 1 - e^{-\mu } +%\Rightarrow \mu = \ln +%(1 - \mu_{meas})^{-1} \label{eq:PoissonDef2} +\end{equation} +which implies: +\begin{equation} +\mu = \ln +(1 - \mu_{meas})^{-1} \label{eq:PoissonDef2} +\end{equation} +The mean number of particles in a hit strip becomes: +\begin{eqnarray} +C &=& \frac{\sum_{n>0} n P(n>0)}{\sum_{n>0} P(n>0)} \nonumber \\ + &=& \frac{e^{-\mu}}{1-e^{-\mu}} \mu \sum \frac{\mu^n}{n!} + \nonumber \\ + &=& \frac{e^{-\mu}}{1-e^{-\mu}} \mu e^{\mu} \nonumber \\ + &=& \frac{\mu}{1-e^{-\mu}} +\end{eqnarray} +%While $\mu$ can be calculated analytically for practical purposes we +With $\mu$ defined in \eqref{eq:PoissonDef2} this calculation is +carried out per event in +regions of the FMD each containing 256 strips. %Defining +%$\mu_{meas}^{region}$ to be the measured occupancy + In such a region, +$\mult$ for a hit strip ($N_{hits} \equiv 1$) in that region becomes: +\begin{equation} +\mult = N_{hits} \times C = 1 \times C = C +\end{equation} +Where C is calculated using $\mu_{meas}^{region}$. \subsubsection{Azimuthal Acceptance} @@ -724,9 +775,39 @@ $n_{i,f}=n_{i,[-3,-1]}$ and $n_{i,b}=n_{i,[1,3]}$. \section{Some results} %% \figurename{}s \ref{fig:1} to \ref{fig:3} shows some results. -Figures below show some examples. Note these are not finalised +Figures below show some examples \cite{hhd:2009}. Note these are not finalised plots. +\begin{figure}[hbp] + \centering + \includegraphics[keepaspectratio,width=\textwidth]{% + results_ppdndeta} + \caption{$\dndeta$ for pp for \INEL{} events at + $\sqrt{s}=\GeV{900}$, $\sqrt{s}=\TeV{2.76}$, and $\sqrt{s}=\TeV{7}$ + $\cm{-10}\le v_z\le\cm{10}$, rebinned by a factor 5 \cite{hhd:2009}. +% Middle panel +% shows the ratio of ALICE data to UA5, and the bottom panel shows +% the ratio of the right (positive) side to the left (negative) side +% of the forward $\dndeta$. +} + \label{fig:1} +\end{figure} +\begin{figure}[hbp] + \centering + \includegraphics[keepaspectratio,width=\textwidth]{% + results_PbPbdndeta} + \caption{$\dndeta$ for Pb+Pb for Minimum Bias events at + $\sqrt{s_{NN}}=\TeV{2.76}$ $\cm{-10}\le v_z\le\cm{10}$, rebinned by a + factor 5 in 10 centrality intervals \cite{hhd:2009}. +% Middle panel +% shows the ratio of ALICE data to UA5, and the bottom panel shows +% the ratio of the right (positive) side to the left (negative) side +% of the forward $\dndeta$. +} + \label{fig:2} +\end{figure} + +\iffalse \begin{figure}[hbp] \centering \includegraphics[keepaspectratio,width=\textwidth]{% @@ -739,7 +820,7 @@ plots. \label{fig:1} \end{figure} -\iffalse + \begin{figure}[tbp] \centering \includegraphics[keepaspectratio,width=\textwidth]{% @@ -946,6 +1027,12 @@ void Analyse(int mask=AliAODForwardMult::kInel, Multiplicity Detector --- From Design to Installation}, Ph.D.~thesis, University of Copenhagen, 2009, \url{http://www.nbi.dk/~cholm/}. +\bibitem{maxime} Guilbaud, M. \textit{et al}, \textit{Measurement of the charged-particle +multiplicity density at forward rapidity +with ALICE VZERO detector in central +Pb-Pb collision at $\sqrt{s_{NN}}=\TeV{2.76}$}, + ALICE internal note, 2012, + \url{https://aliceinfo.cern.ch/Notes/node/17/}. \bibitem{nim:b1:16} %% \bibitem{Hancock:1983ry} S.~Hancock, F.~James, J.~Movchet {\it et al.}, @@ -958,6 +1045,10 @@ void Analyse(int mask=AliAODForwardMult::kInel, Energy Straggling Of Protons And Pions In The Momentum Range 0.7-gev/c To 115-gev/c,'' Phys.\ Rev.\ \textbf{A28} (1983) 615, \url{http://cdsweb.cern.ch/record/145395/files/PhysRevA.28.615.pdf}. +\bibitem{hhd:2009} Dalsgaard, H.~H., \textit{Pseudorapidity Densities in p+p and Pb+Pb collisions at + LHC measured with the ALICE experiment}, + Ph.D.~thesis, University of Copenhagen, 2011, + \url{http://www.nbi.dk/~canute/thesis.pdf}. \end{thebibliography} \end{document} diff --git a/PWGLF/FORWARD/doc/results_PbPbdndeta.pdf b/PWGLF/FORWARD/doc/results_PbPbdndeta.pdf new file mode 100644 index 0000000000000000000000000000000000000000..700fa2303da16a6f4d17aff19dd26ff28d5e446c GIT binary patch literal 49025 zcmd3P1yq*H+O~nHfFPlON+T)p^3sSP-2wvA-7O_uiiD&f-5??j0!oK;iF8OvN+U?u zKhFzn_c_P!bMLjz`Od%gLWk#>nS18Cue)X**S;++AVdeFXGXa_G5M(*1xCzBY@uz8 za`!F@gPen<9x(&ImW`IFg#ikKw3dOMH8C^jAdABAz}Cjp$Q=9*KmHwhDQTe#`paAE zoxVi5cMnC+To;;;=}+_WTj^=pSXdEL$v$`>N35V{Wo=|(PRv5j#KFJ_qefvsya$g2 zv~2W 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