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44\title{Definitions of TPC related track properties}
45\author{}
46
47\begin{document}
48\begin{minipage}[20]{400pt}
49\pagestyle{empty}
50\begin{center}
51ALICE Internal Note \\ ALICE-INT-2011-XXX
52%\put(125,60){\includegraphics[width=0.2\textwidth]{../godlo.eps}}
53\maketitle
54\begin{abstract}
55This document is supposed to help users in the analysis of ALICE TPC data.
56\end{abstract}
57\end{center}
58\end{minipage}
59
60\setcounter{page}{1}
61
62\section{Definitions}
63
64\subsection{Clusters}
65
66 \begin{description}
67
68 \item[TPC cluster.] A charged particle traversing the TPC induces a signal on a given pad-row. If the charge in a search window of 5 pads in wire direction and 5 bins in time direction exceeds a certain threshold and fulfills all necessary quality criteria, it is called a cluster. Therefore the maximum number of clusters per track is 159 which corresponds to the number of pad rows in a given TPC sector. Curling track parts are reconstructed as separate tracks.
69
70\medskip
71 {\it Number of TPC clusters:} $n_{cl}$ / {\tt AliESDtrack::GetTPCNcls() }
72\medskip
73
74 The number of clusters assigned to a track is related to the track length in the sense that low $p_{t}$-tracks which do not reach the outer wall of the TPC have less clusters assigned. However, the relation is not straightforward, because the pad length in the TPC is increasing with radial distance to the center.
75
76
77\begin{figure}[htbp]
78\begin{center}
80\caption{A charged particle in one TPC sector. In this case, the track crosses all 159 pad rows (63 in the inner read-out chamber and 96 in the outer read-out chamber).}
82\end{center}
83\end{figure}
84
85
86 \item[Findable clusters.] The number of findable clusters is the number of geometrically possible clusters which can be assigned to a track. It takes into account dead zones due to chamber boundaries or the limited $\eta$-acceptance. For the time being, clusters on dead front-end cards are counted as findable.
87
88\medskip
89 {\it Number of findable TPC clusters:} $n_{find}$ / {\tt AliESDtrack::GetTPCNclsF() }
90\medskip
91
92 \item[Non-findable clusters.] If a track crosses the boundary between two chambers or leaves the $\eta$-acceptance, the clusters in this area are declared as non-finable.
93
94 \item[Missing cluster / cluster below threshold.] Findable clusters can be missing, because their charge is below threshold (e.g. due to baseline shifts etc.). They can be identified by looking into the neighboring pad-rows, e.g. if there is no reconstructed cluster on pad row $i$, but clusters are found on the pad rows $i-1$ and $i+1$ (or $i-r$ and $i+r$ in general). The number of clusters below threshold is called $n_{miss}$.
95
96 \item[Number of crossed rows $n_{eff}$.] The relevant quantity for the $p_{t}$-resolution of a track is the effectively sampled track length of a particle in the TPC, because the resolution scales roughly $\propto \frac{1}{\sqrt{n_{cl}}}$ (statistics) and $\propto n_{eff}^{2}$ (lever arm) where $n_{eff} = n_{cl} + n_{miss}$. The number is available via the {\it AliRoot}-Function:
97
98\medskip
99 {\it Number of crossed rows:} $n_{eff}$ / {\tt AliESDtrack::GetTPCClusterInfo(r = 2,1)}.
100\medskip
101
102 In this particular case ($r = 2$), a missing cluster is assigned if a cluster is found on one of the two neighboring pad-rows. The number of crossed rows $n_{eff}$ can also be called effective cluster track length. We can consider the following example: Imagine a charged particle enters the TPC at the inner wall with a $p_{t}$ in such a way that it would cross all pad crows in an active area, but it undergoes a catastrophic hadronic interaction in the middle of the TPC, then $n_{find} = 159$, but $n_{eff} = 80$ and (if e.g. 3\% of the clusters were below threshold) $n_{cl} = 76$.
103
104 \item[Number of clusters after first iteration.] If a track is recognized as a kink candidate, it is split into a mother and a daughter track. However, the number of assigned clusters $n_{cl}$ is the sum of the clusters assigned to the mother and the daughter. The number of clusters assigned to the mother track are still available via the number of clusters assigned during the first (inward) tracking iteration.
105
106\medskip
107 {\it Number of clusters after first iteration:} $n_{cl,iter1}$ / {\tt AliESDtrack::GetTPCNclsIter1()}.
108\medskip
109
110
111 \end{description}
112
113\subsection{Track parameters}
114
115There are two types of relevant track parameters for a TPC based data analysis: {\it global} (track parameters are updated with inner detectors, i.e. the ITS) and {\it TPC stand-alone (TPC-SA)}.
116
117 \begin{description}
118
119 \item[TPC-SA track parameters at the primary vertex.] They describe the track properties at the primary vertex as obtained with the TPC stand-alone. These track parameters are last updated at the inner wall of the TPC and then propagated through the material of the inner detectors to the vertex.
120
121\medskip
122 {\tt AliESDtrack::GetTPCInnerParam()}.
123\medskip
124
125
126 \item[Global track parameters at the inner TPC wall.] They describe the track properties at the inner wall of the TPC as obtained with the global tracking. These track parameters must be used for the particles identification, because the energy loss of a track inside the TPC is a function of the total momentum $p_{tot,TPC}$ inside the TPC. The global track parameters at the inner TPC wall are a good - though not perfect - approximation for this, because the energy loss inside the TPC fill gas is rather small. \footnote{N.B.: The TPC-SA track parameters at the primary vertex should never be used for pid!}
127
128\medskip
129 {\tt AliESDtrack::GetInnerParam()}.
130\medskip
131
132
133 \item[Global track parameters at the primary vertex.] These are the standard parameters of the ESD track and used in the majority of the physics analyses.
134
135
136 \item[Global track parameters at the outer TPC wall.] They are only stored in the AliESDfriends and are usually not relevant for physics analysis.
137
138 \end{description}
139
140\subsection{PID related quantities}
141
142\begin{description}
143
144 \item[Energy loss $dE/dx$.] A charged particle traversing the TPC fill gas is losing energy mainly via ionization processes. The mean energy loss $dE/dx$ per unit path length can be described with the Bethe-Bloch formula
145
146
147 \langle{dE\over dx}\rangle = {4\pi N e^{4} \over mc^{2}} {Z^{2} \over \beta^{2}} \Bigl(\ln{2mc^{2}\beta^{2}\gamma^{2} \over I} - \beta^{2} - {\delta(\beta) \over 2} \Bigr) \; .
148 \label{eq.:Bethe}
149
150
151 \item[Energy deposit.] If the energy transfer to the ionized electron exceeds a certain value, the range of the ionized electron becomes so large, that it escapes from the sampling of the charge signal of a given track. In addition to this, some of the energy loss also results only in excitation of the fill gas atoms and no electrons are released. The detectable deposited energy of a track in a given pad-row is therefore slightly different from the energy loss of the charged particle.
152
153 \item[Maximum cluster charge $Q_{max}$.] The maximum cluster charge represents the maximum value of all digits in a cluster as shown in figure \ref{figTPCpadRows}.
154
155 \item[Total cluster charge $Q_{tot}$.] The total cluster charge is given by the sum of all digits in a cluster. It corresponds to the energy deposit of a track on a given pad-row.
156
157 \item[TPC dE/dx signal $S$.] Because of the long tail towards higher energy losses in the distribution function of the cluster charge, the average energy deposit is not a good estimator as it would be for a Gaussian distribution. Therefore, the so-called truncated mean is used. The truncated mean $S$ of all cluster charges, also called the {\it TPC $dE/dx$ signal}, is defined as the average over lowest values, which correspond to a 60\%-fraction of the whole sample. The values of $S$ follow an almost perfect Gaussian distribution.
158
159\medskip
160 {\it TPC dE/dx signal $S$} / {\tt AliESDtrack::GetTPCSignal()}.
161\medskip
162
163 \item[Number of clusters used for PID $n_{pid}$.] Clusters which are located very close to the chamber boundaries or from overlapping tracks are not used for the calculation of the TPC dE/dx signal. Therefore the number of clusters used for the calculation of the dE/dx-signal can be different from the number of clusters of a track. This quantity is of important relevance for the dE/dx-resolution.
164
165 {\it Number of clusters used for pid:} $n_{pid}$ / {\tt AliESDtrack::GetTPCsignalN()}.
166
167\end{description}
168
169\section{Recommendation for TPC Cluster Selection}
170
171One of the major systematic error in the physics analysis is introduced by selection criteria on the number of clusters. Based on experience with TPC data of 2009 and 2010, it is known that TPC gain and baseline variation influence the distribution of found clusters up to 30\% level. This variation is time, energy loss, and running condition dependent and it is only partially described in the MC. However, this variation influences the TPC tracking performance only to the level of $\sqrt{1 - n_{miss}/n_{find}}$.
172
173
174Most analyses cut on the number of found TPC Clusters divided by the number of findable clusters $\varepsilon_{thr} = \frac{found clusters}{findable clusters}$. However the number of found clusters is not robust as explained below.
175Instead the TPC group has introduced a new variable - the ratio of number of crossed rows to the number of findable clusters - which is almost independent on track multiplicity and $\eta$. At the end of this section a recommendation on what variables to cut on in order to achieve good $p_{t}$ resolution and fake removal is given. \newline
176
177\noindent TPC clusters can be lost due to unknown reasons or because their charge is below threshold (caused by the front-end electronics; these clusters are called missing clusters). The threshold of the cluster finder approaches the digital threshold (due to the 1pad cluster functionality). The unknown reasons summarize effects such as dead zones, missing partitions and decays.
178$\varepsilon_{thr}$ depends on the digital threshold, on multiplicity, energy loss, drift length and track angle. The later three determine simply the amplitude of the signal. \newline
179\noindent The dependence of $\varepsilon_{thr}$ on these is shown in figures \ref{fig_2dim_dep_a} and \ref{fig_2dim_dep_b} for PbPb data taken in 2010.
180 The different colors correspond to different energy loss. The lowest lying distribution corresponds to low energy loss the one overlaying all high energy loss. Multiplicity is defined by the number of contributors to the TPC vertex.
181For better visualization the plots \ref{fig_2dim_dep_a} and \ref{fig_2dim_dep_b} are projected in slices of multiplicity and $\eta$. Then for a given threshold, a limit removing the lower x\% of the distribution, the related $\varepsilon_{thr}$ is determined. The output is shown in Figures \ref{fig_1dim_dep_a} and \ref{fig_1dim_dep_b}. A clear dependence on track multiplicity and $\eta$ is seeable.
182
183\noindent In Figures \ref{fig_2dim_dep_c} and \ref{fig_2dim_dep_d} as well as \ref{fig_1dim_dep_c} and \ref{fig_1dim_dep_d} one can see the corresponding plots for the ratio of number of crossed rows to the number of findable clusters. The ratio, the newly introduced variable, is almost independent from energy loss, multiplicity and $\eta$ (z-direction). The dip in the $\eta$-plot is due to the crossing of tracks with the central cathode.
184
185
186
187\begin{figure}[htbp]
188\centering \mbox{
189 \subfigure[$\varepsilon_{thr}$ vs $\eta$]{\includegraphics[width=0.6\mylinewidth]{figures/new_ethres_vs_eta.pdf}\label{fig_2dim_dep_a}}
190 \subfigure[$\varepsilon_{thr}$ vs multiplicity]{\includegraphics[width=0.6\mylinewidth]{figures/new_ethres_vs_multi.pdf}\label{fig_2dim_dep_b}}}
191\centering \mbox{
192 \subfigure[Number of crosses rows divided by number of findable clusters vs $\eta$]{\includegraphics[width=0.6\mylinewidth]{figures/new_cros_vs_eta.pdf}\label{fig_2dim_dep_c}}
193 \subfigure[Number of crosses rows divided by number of findable clusters vs multiplicity]{\includegraphics[width=0.6\mylinewidth]{figures/new_cros_vs_multi.pdf}\label{fig_2dim_dep_d}}}
194 \caption[]{$\varepsilon_{thr}$ and number of crosses rows divided by number of findable clusters vs $\eta$ and multiplicity for PbPb data taken in 2010. Multiplicity is defined by the number of contributors to the TPC vertex. The different colors correspond to different energy loss. The lowest lying distribution corresponds to low energy loss the one overlaying all high energy loss.}
195\label{fig_2dim_dep}
196\end{figure}
197
198\begin{figure}[htbp]
199\centering \mbox{
200 \subfigure[$\varepsilon_{thr}$ vs $\eta$ for various thresholds]{\includegraphics[width=0.6\mylinewidth]{figures/ethres_vs_eta_threshold.pdf}\label{fig_1dim_dep_a}}
201 \subfigure[$\varepsilon_{thr}$ vs multiplicity for various thresholds]{\includegraphics[width=0.6\mylinewidth]{figures/ethres_vs_multi_thresholds.pdf}\label{fig_1dim_dep_b}}}
202\centering \mbox{
203 \subfigure[Number of crosses rows divided by number of findable clusters vs $\eta$ for various thresholds]{\includegraphics[width=0.6\mylinewidth]{figures/ncrossed_vs_eta_thres.pdf}\label{fig_1dim_dep_c}}
204 \subfigure[Number of crosses rows divided by number of findable clusters vs multiplicity for various thresholds]{\includegraphics[width=0.6\mylinewidth]{figures/crossedrows_vs_multi_thres.pdf}\label{fig_1dim_dep_d}}}
205 \caption[]{$\varepsilon_{thr}$ and number of crosses rows divided by number of findable clusters for a given threshold as a function of $\eta$ and multiplicity for PbPb data taken in 2010. Multiplicity is defined by the number of contributors to the TPC vertex.}
206\label{fig_1dim_dep}
207\end{figure}
208
209\subsection{Available Variables and Cut Recipes} \label{subsection_qavariables}
210Analyses with the TPC can make use of the following QA variables:
211\begin{enumerate}
212\item Number of TPC clusters
213\item Number of findable clusters
214\item Number of crossed rows
215\item Number of clusters in crossed rows
216\item Covariance matrix elements
217\item All combinations and ratios of the items above
218\end{enumerate}
219
220\noindent To achieve good $p_{t}$ resolution for high momenta a cut on the number of crossed rows and the covariance matrix elements are recommended. Cuts on ITS remove already a lot of fakes. Further improvement is reached with a minimal cut on the number of crossed rows and on the ratio of number of crossed rows to number of findable clusters. The application of the cuts depends on the type of analysis, e.g. the cuts proposed for further fake removal do not apply for V0 analysis (gamma conversion, kinks, etc.).
221For other types of analyses we recommend to accept only tracks with a ratio of number of crossed rows to number of findable clusters of larger than 0.83. This has the advantage of also being independent of one missing partition in the read out (see Fig. \ref{fig_pp_mc_data}). \newline
222\noindent Figure \ref{fig_pp_mc_data} shows the ratio of number of crossed rows to findable clusters for experimental data (pp LHC10d) and for the respective MC sample. The distribution for experimental data has a small peak at slightly below 0.9 and then increases in comparison to the MC distribution slower. This is due to a missing partition. Depending on the angle with which the track passes the missing partition up to all clusters are correspondingly not recorded. \newline
223\noindent Though given the anchor runs MC will not follow the time dependence due to missing partitions in data. Further discrepancies between MC and data are due to different species abundance. Thus a comparison of data to MC is only possible by keeping the upper x\% of the distributions in both MC and data.
224
225A summary of the recommended cuts can be found in Table \ref{table_cuts} \newline \newline \newline
226
227\begin{figure}[htbp]
228\begin{center}
229\includegraphics[width=0.6\textwidth]{figures/pp_mc_data.pdf}
230\caption{Number of crosses rows divided by number of findable clusters for pp data LHC10d (black) and the corrresponding MC sample (red). Shown for tracks with an energy loss of 70-79 and an event multiplicity of 30-45 contributors to the TPC vertex.}
231\label{fig_pp_mc_data}
232\end{center}
233\end{figure}
234
235\begin{table}[\htb]
236 \begin{center}
237\begin{tabular}{l||l}
238\hline
239\textbf{Goal} & \textbf{Cut} \\
240\hline \hline
241Good pt resolution & Cut on 4. + 5. for high momenta \\
242Fake removal & Minimal cut on 3. + on 3./2. \\
243MC vs real data & Keep upper x\% of distribution in MC and data
244respectively \\
245\end{tabular}
246\end{center}
247\caption[]{Recommended cuts to achieve good $p_{t}$ resolution and fake removal. The numbers are explained at the beginning of Section \ref{subsection_qavariables}.} \label{table_cuts}
248\end{table}
249
250\subsection{QA Selection based on the estimated resolution} \label{subsection_COVARvariables}
251
252The tracking performance of ALICE detector is described by covariance matrix of tracks. The actual uncertainty of the track parameters depends on many parameters:
253\begin{itemize}
254\item At high track momenta the resolution is determined mainly by track topology, detectors contributing to the measuremant (TPC only, constrained parameters, Combined tracks) and by quality of alignment and calibration.
255\item At low momenta the track uncertainty is determined by multiple scatterring and by energy loss in the material (PID dependent)
256\end{itemize}
257
258Following empirical parameterization can be used to describe the mean uncertanties of the track parameters:
259
260 \sigma_{xx}=k_{xx0}\sqrt{1+k_{xx1}/p_{t}^{k_{xx2}}}\sqrt{dEdx/dEdx_{MIP}}
261 \label{eq.:TrackResol}
262
263
264
265\begin{figure}[htbp]
266\begin{center}
267\includegraphics[width=0.8\textwidth]{figures/covarScaledTPC.eps}
268\label{fig_CovarTPC}
269\end{center}
270\caption{Normalized covariance elements and the mean uncerntainty of track parameters for the TPC only tracks at vertex}
271\end{figure}
272
273\begin{figure}[htbp]
274\begin{center}
275\includegraphics[width=0.8\textwidth]{figures/covarScaledConst.eps}
276\label{fig_CovarTPC}
277\end{center}
278\caption{Normalized covariance elements and the mean uncerntainty of track parameters for the combined constrained tracks at vertex. Several bands for the uncertainty in the angular measurement due differnt track topology (Presence if the differnt ITS layers).}
279\end{figure}
280
281
282
283
284\end{document}