Adding the description of real data (Marian)

diff --git a/TPC/doc/calib/clusterParam/clusterParam.tex b/TPC/doc/calib/clusterParam/clusterParam.tex
index 125b2ad933d2b70d86cffc531151e66e88f1992b..a3071e511ad5af01770956b4992a7af09c05703d 100644 (file)
--- a/TPC/doc/calib/clusterParam/clusterParam.tex
+++ b/TPC/doc/calib/clusterParam/clusterParam.tex
@@ -647,4 +647,89 @@ several pad-rows are needed. This information is available only
 during tracking procedure.\r
 \r
 \r
+\r
+\subsection{Space point resolution parameterization}\r
+\r
+The space point resolution is the function of many parameters but for the ALICE TPC the dominant one are the diffusion, track inclination angle and deposited charge.\r
+The space point resolution was extracted from the data in bins of these variables.\r
+\r
+In the first approximation the angular part and diffusion part are independent. The\r
+paramaterization is obtained fitting parameters $p_{0}$,$p_L$ and $p_A$\r
+\begin{eqnarray}\\r
+     \sigma^2_{{\rm{COG}}} \approx p^2_0+p^2_{L}L_{\rm{Drift}}+p^2_{A}\tan^2\alpha\r
+         \label{eqResCOG0}  \r
+     \nonumber\\\r
+     p^2_L \approx  \frac{\sigma^2_DG_{\rm{g}}}{N_{\rm{ch}}}\r
+     \nonumber\\\r
+     p^2_A \approx \frac{L_{\rm{pad}}^2G_{\rm{Lfactor}}}{N_{\rm{chprim}}} \r
+\end{eqnarray}\r
+\r
+\r
+\r
+\begin{table}\r
+\caption{Resolution parameterization}\r
+\begin{tabular}{|l|l|l|l|} \hline\r
+Pad size               & 0.75x0.4 $cm^2$       & 1.0x0.6$cm^2$ & 1.5x0.6$cm^2$  \\  \hline\r
+$p_{0y}$                & 0.026  cm            & 0.031  cm     & 0.023 cm       \\  \hline\r
+$p_{0z}$                & 0.032  cm            & 0.032  cm     & 0.028 cm       \\  \hline\r
+$p_{Ly}\sqrt{L_{pad}}$  & 0.0051                & 0.0060        & 0.0059         \\  \hline \r
+$p_{Lz}\sqrt{L_{pad}}$  & 0.0056                & 0.0056        & 0.0059         \\  \hline \r
+$p_{Ay}/\sqrt{L_{pad}}$ & 0.13 $cm^{1/2}$      & 0.15 $cm^{1/2}$          & 0.15 $cm^{1/2}$           \\  \hline \r
+$p_{Az}/\sqrt{L_{pad}}$ & 0.15 $cm^{1/2}$               & 0.16 $cm^{1/2}$          & 0.17 $cm^{1/2}$         \\  \hline \r
+\r
+\end{tabular}\r
+\label{table:PointResolFitParam}\r
+\end{table}\r
+\r
+\r
+\begin{eqnarray}\\r
+     N_{\rm{ch}} \approx {L_{\rm{pad}}} \nonumber \\\r
+     N_{\rm{chprim}} \approx {L_{\rm{pad}}} \nonumber \\       \r
+     \nonumber\\\r
+     p_L \approx \frac{1}{\sqrt{L_{\rm{pad}}}}\r
+     \nonumber\\\r
+     p_A \approx \sqrt{L_{\rm{pad}}}\r
+\label{eq:ResolScaling}        \r
+\end{eqnarray}\r
+\r
+\r
+The TPC space resolution is scaling with the number of contributed electrons \r
+$N_{\rm{chprim}}$ and ${N_{\rm{ch}}}$, therefore is scaling with pad length.\r
+In ALICE TPC three different pad gemetries are used. \r
+The space point resolution was fitted for separatelly for each geometry. The fitted parameters $p_0$ $p_L$ and $p_A$ are shown in the table \ref{table:PointResolFitParam} rescaled with the pad length.\r
+\r
+\r
+\r
+The agreement between  previously mentioned fit and the data is on thel level of the\r
+$\approx10-20\%$. In previous formula we assumed that all of the electrons created in ionization are contibuting to the measured signal. Because of the threshold effect the\r
+part of the signal is cut-off. The fraction of the signal bellow threshold is proportional to the response function witdth and is incresing with drift length and inclination angle. The following correction function are used: \r
+\begin{eqnarray}\\r
+     \nonumber\\\r
+     p_L \approx p_{L0}p_{LC}=p_{L0}(1+p_{L1}L_{\rm{Drift}}+p_{L2}\tan^2\alpha)\r
+     \nonumber\\\r
+     p_A \approx p_{A0}p_{AC}=p_{A0}(1+p_{A1}L_{\rm{Drift}}+p_{A2}\tan^2\alpha)\r
+\end{eqnarray}\r
+\r
+The measured reolution in Y and Z direction and corresponding fits are shown on picure \ref{figPointResolYDRTAN} and \ref{figPointResolZDRTAN}. The agrement with the data is on the level of about 2\%.\r
+\r
+\r
+\begin{figure}\r
+  \centering\epsfig{figure=picClusterResol/YResol_Pad0.eps,width=0.7\linewidth}\r
+  \centering\epsfig{figure=picClusterResol/YResol_Pad1.eps,width=0.7\linewidth}\r
+  \centering\epsfig{figure=picClusterResol/YResol_Pad2.eps,width=0.7\linewidth}\r
+  \caption{Space point resolution in Y direcition as function of the drift length and the inlination angle.}\r
+  \label{figPointResolYDRTAN}\r
+\end{figure}\r
+\r
+\begin{figure}\r
+  \centering\epsfig{figure=picClusterResol/ZResol_Pad0.eps,width=0.7\linewidth}\r
+  \centering\epsfig{figure=picClusterResol/ZResol_Pad1.eps,width=0.7\linewidth}\r
+  \centering\epsfig{figure=picClusterResol/ZResol_Pad2.eps,width=0.7\linewidth}\r
+  \caption{Space point resolution in Z direcition as function of the drift length and the inlination angle.}\r
+  \label{figPointResolZDRTAN}\r
+\end{figure}\r
+\r
+\r
+\r
+\r
 \end{document}\r