\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}}
\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
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}
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
\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}
\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]{%
\label{fig:1}
\end{figure}
-\iffalse
+
\begin{figure}[tbp]
\centering
\includegraphics[keepaspectratio,width=\textwidth]{%
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.},
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}
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