From 0a89eed18b698ff7eb4b2a0d9dde9dd0733d320d Mon Sep 17 00:00:00 2001 From: cholm Date: Wed, 12 Jan 2011 13:46:00 +0000 Subject: [PATCH] Updates --- PWG2/FORWARD/doc/doc.tex | 70 ++++++++++++++++++++++++++-------------- 1 file changed, 45 insertions(+), 25 deletions(-) diff --git a/PWG2/FORWARD/doc/doc.tex b/PWG2/FORWARD/doc/doc.tex index 9d900471796..66d3299ab82 100644 --- a/PWG2/FORWARD/doc/doc.tex +++ b/PWG2/FORWARD/doc/doc.tex @@ -332,26 +332,38 @@ charged particles in a given by a simple threshold: \end{array}\right.\quad, \end{align} where $t$ is the strip identifier, $\Delta_t$ is the scaled energy -deposition in that strip, and 'low cut' is a predefined cut. For high -flux events, the number charged particles in a strip is calculated -using multiple Landau distributions fitted to the energy loss spectrum -at a given $\eta$ value. +deposition in that strip, and 'low cut' is a predefined +cut\footnote{This low--flux mode is perhaps deprecated.}. + +For high flux events, the number charged particles in a strip is +calculated using multiple Landau distributions fitted to the energy +loss spectrum at a given $\eta$ value. \begin{align} - \Delta_{2,mp} &= 2 \Delta_{mp}+ 2 w \log(2)\nonumber\\ - \Delta_{3,mp} &= 3 \Delta_{mp}+ 3 w \log(2)\nonumber\\ - N_{ch,t} &= \frac{\landau{\Delta_t,\Delta_{mp},w}+ - 2\,\alpha\,\landau{\Delta_t,\Delta_{2,mp},2w} + - 3\,\beta\,\landau{\Delta_t,\Delta_{3,mp},3w}}{% - \landau{\Delta_t,\Delta_{mp},w}+ - \alpha\,\landau{\Delta_t,\Delta_{2,mp},2w} + - \beta\,\landau{\Delta_t,\Delta_{3,mp},3w}}\quad, + \Delta_{i,mp} &= i (\Delta_{1,mp}+ \xi_1 \log(i))\nonumber\\ + \xi_i &= i\xi_1\nonumber\\ + \sigma_i &= \sqrt{i}\sigma_1\nonumber\\ + N_{ch,t} &= \frac{\sum_i^{N_{max}} + i\,a_i\,F(\Delta_t;\Delta_{i,mp},\xi_i,\sigma_i)}{ + \sum_i^{N_{max}}\,a_i\,F(\Delta_t;\Delta_{i,mp},\xi_i,\sigma_i)}\quad, \end{align} -where $\landau{x,\psi,W}$ is the evaluation of the Landau distribution -with most probable value $\psi$ and width $W$ at $x$, $w$ is the width -of the first MIP peak, $\Delta_{mp}$ the most probable value of -the first MIP peak, and $\alpha$ and -$\beta$ are the relative strength of the second and third MIP peak in -the fitted energy loss spectrum. +where $F(x;\Delta_{mp},\xi,\sigma)$ is the evaluation of the Landau +distribution $f_L$ with most probable value $\Delta_{mp}$ and width +$\xi$, folded with a Gaussian distribution with spread $\sigma$ +\cite{nim:b1:16,phyrev:a28:615}. +$$ +F(x;\Delta_{mp},\xi,\sigma) = \frac{1}{\sigma \sqrt{2 \pi}} +\int_{-\infty}^{+\infty} d\Delta' f_{L}(x;\Delta',\xi) +\exp{-\frac{(\Delta_{mp}-\Delta')^2}{2\sigma^2}} +$$ +$\Delta_{1,mp}$, $\xi_1$, and $\sigma_1$ are the parameters for the +first MIP peak, $a_1=1$, and $a_i$ is the relative weight of the +$i^{\text{th}}$ MIP peak. The parameters $\Delta_{1,mp}, \xi_1, +\sigma_1, a_2, \ldots a_{N_{max}}$ are obtained by fitting +$$ +\sum_{i=1}^{j} F(x;\Delta_{i,mp},\xi_{i},\sigma_i) +$$ +for increasing $j$ to the energy loss spectra in separate $\eta$ +bins. \subsubsection{Acceptance and double-hit corrections} @@ -377,7 +389,9 @@ hits a strip. However, for low--flux events, it is not possible to reconstruct the 3\textsuperscript{rd} nor even the 2\textsuperscript{nd} MIP peak in the energy loss spectrum. Therefore, the strip signal needs to be corrected to the average -number of particle impinging on a strip at a given $\eta$. +number of particle impinging on a strip at a given $\eta$\footnote{As + before, this low--flux mode is deprecated and this correction is not + applied}. \begin{align} d_{t,r}(\eta) &= \left\{ \begin{array}{cl} \langle @@ -536,8 +550,9 @@ three corrections %% for MC events - from AliFMDAnalysisTaskSharing - number of not %% empty mc events per vertex bin %% - This is a one dimension histogram in $\eta$, generated from running - the full analysis on simulated data. +This is a one dimension histogram in $\eta$, generated from running +the full analysis on simulated data\footnote{With improved energy loss + fits, this correction is redundant and not used} . \begin{align} \label{eq:sharing_corr} m_v(\eta) &= @@ -773,7 +788,6 @@ void Analyse() { gSystem->Load("libANALYSIS.so"); // Load analysis libraries gSystem->Load("libANALYSISalice.so"); // General ALICE stuff - gSystem->Load("libPWG2forward.so"); // Older HHD code gSystem->Load("libPWG2forward2.so"); // New code TH2D* sum = 0; // Summed hist @@ -784,16 +798,17 @@ void Analyse() int nWithVertex= 0; // # of ev. w/vertex int nAvailable = tree->GetEntries(); // How many entries float vzLow = -10; // Lower ip cut - float vzHigh = 10; // Upper ip cut + float vzHigh = +10; // Upper ip cut int mask = AliAODForwardMult::kInel;// Trigger mask - tree->SetBranchAddress("forward", &forward); // Set the address + tree->SetBranchAddress("Forward", &forward); // Set the address for (int i = 0; i < nAvailable; i++) { // Read the i'th event tree->GetEntry(i); // Create sum histogram on first event - to match binning to input - if (!sum) sum = static_cast(mult->Clone("d2ndetadphi")); + if (!sum) + sum = static_cast(mult->GetHistogram()->Clone("d2ndetadphi")); // Other trigger/event requirements could be defined if (!mult->IsTriggerBits(mask)) continue; @@ -821,4 +836,9 @@ void Analyse() dndeta->Draw(); } \end{lstlisting} + +\begin{thebibliography}{99} +\bibitem{nim:b1:16} Nucl.Instrum.Meth.B1:16 +\bibitem{phyrev:a28:615} Phys.Rev.A28:615 +\end{thebibliography} \end{document} -- 2.43.5