COMP/CSA06DOC/muonalignment.tex

\subsubsection{Muon alignment}
A similar example was run for the Muon system alignment. The goal of this analysis was to demonstrate the possibility of performing the
Muon System standalone alignment with tracks at a remote Tier-2 (Spanish T2, in
this case). The exercise
was foreseen to prove the data and workflow, but also the performance of the
algorithms was tested. The exercise was split in several subtasks:
\begin{itemize}
\item{Data import to T2 and prompt analysis}
\item{Re-reconstruction: remote access to geometry DB}
\item{Extraction of alignment constants and production of re-aligned geometry file}
\item{Re-Reconstruction with re-aligned geometry}
\end{itemize}

The basic sample for this exercise was a 2 Million event Z, decaying to muon
pairs. The full RECO sample was imported for the different versions as they were made available
(4.4 TB for the last version)
although many of the tasks could be performed onto the AlCaReco produced at CERN-T0 (as described in Section~\ref{calibtool}) with a much smaller size of about 20 GB for the same 2 Million events. Other samples and formats were also used for checks,
like 0.5 Million
W decays to muons (AOD), ttbar (semileptonic and di-leptonic decays) or minimum
bias. As soon as the sample was fully transferred, prompt analysis was performed
using 90 CPU in which these jobs were priorized. The jobs, submitted with the standard CRAB tools,
consisted in running
over the whole sample to check data quality producing basic distributions 
derived from standalone muon and global track quantities
(transverse momentum and invariant mass, for dimuon case). The latency was dominated by
the different steps in the data transfer. For the AlCaReco sample, results
were available within the next day of the sample availability at T0.

Re-reconstruction of the samples was performed locally at the T2, starting from the DIGI, in the RECO
sample. Two different tests were done. 
On the first case, a distorted geometry Database is read from the T0. The one defined in the
so-called ShortTerm Scenario,  mimicking the misalignment conditions at the very
beginning of data taking was used. The access was made with Frontier through the local SQUID cache. 
The obtained invariant mass in each case is shown for the Global (using tracker and muon hits)
and Standalone Muon (muon hits only) reconstruction in Figure~\ref{fig:muscenario}. A clear widening of the
distribution is observed due to the wrong situation of the muon chambers. The effect is less evident for
the Global reconstruction, because the momentum resolution for these energies largely depends on the Tracker, which is assumed
perfectly aligned in this case.
Alternatively, the re-reconstruction was tested using a local DB, previously created off-line, which 
was supplied during the job submission, together with other input files.
No significant delay was found due to the remote access to DB.

\begin{figure}[!htb]
\begin{center}
    \includegraphics[width=0.45\textwidth,clip=]{figs/GBInvM_ideal_shortTerm.pdf}
    \includegraphics[width=0.45\textwidth,clip=]{figs/SAInvM_ideal_shortTerm.pdf}
\caption{\label{fig:muscenario} Reconstructed mass for Z$\to\mu\mu$ sample with
Global or Standalone Muons for ideal or ShortTerm geometry.}
\end{center}
\end{figure}

A simplified version of the Muon alignment with tracks algorithm was applied to the
sample (AlCaReco). It is based in the so-called Blobel
method~\cite{blobel}\cite{alitrak}, which provides a relatively simple procedure to simultaneously fit track parameters 
and alignment
constants. The method is 
in principle iterative, but for this application the problem is nearly linear and only one step is
needed. This has the advantage that is enough to provide track fit residuals and local coordinates of the hit, when the fit is 
performed ignoring the alignment constants. No refit or iterations are needed, nor access to the geometry and, hence, it is very fast and can be run in a standalone mode if necessary. For this exercise only the barrel muon chambers
are aligned in the more relevant d.o.f. displacement along the r$\varphi$ direction. The resultant linear system has 240 unknowns,
which is small enough to handle the problem with standard methods. However, the alignment with tracks problems without additional
constrains leads to a singular matrix, which cannot be inverted. The method proposed here, looks for the degrees of freedom
corresponding to the singularity
characterized as eigenvectors of eigenvalue 0 and store them. They correspond to invariants of the problem, that cannot be resolved
without the introduction of additional constrains.
For this exercise they were ad-hoc fixed to zero, although in a
real case external constrain will be included (mechanical references, hardware alignment or other physic constrains). 

This procedure was applied to the Z$\to\mu\mu$ sample reconstructed with a distorted geometry 
%(ShortTerm).
in which Barrel chambers are displaced from their nominal position alternatively by 1 mm.
The alignment constants obtained in this way are stored with MuonAlignment tools into a geometry DB, which constitutes an
approximation of the nominal geometry. 
Muon reconstruction was again performed taking as input this geometry. Figure~\ref{fig:reali} shows
the invariant mass for Standalone Reconstruction in the barrel, for each of the three geometries. It can be appreciated that the
alignment recovers almost totally the precision given by the ideal geometry.

\begin{figure}[!htb]
\begin{center}
    \includegraphics[width=0.45\textwidth,clip=]{figs/ideal_misal_corrected_SAInvM_Barrel.pdf}
%    \includegraphics[width=0.45\textwidth,clip=]{figs/muscenario2.pdf}
\caption{\label{fig:reali} Reconstructed mass for Z$\to\mu\mu$ sample with
Global or Standalone Muons for ideal (black), misaligned (red) and aligned (blue) geometry.}
\end{center}
\end{figure}


Revision:	1.3
Committed:	Sat Jan 27 11:30:41 2007 UTC (18 years, 3 months ago) by acosta
Content type:	application/x-tex
Branch:	MAIN
Changes since 1.2:	+1 -1 lines
Log Message:	more spelling, edits
#	User	Rev	Content
1	acosta	1.1	\subsubsection{Muon alignment}
2			A similar example was run for the Muon system alignment. The goal of this analysis was to demonstrate the possibility of performing the
3			Muon System standalone alignment with tracks at a remote Tier-2 (Spanish T2, in
4			this case). The exercise
5			was foreseen to prove the data and workflow, but also the performance of the
6			algorithms was tested. The exercise was split in several subtasks:
7			\begin{itemize}
8			\item{Data import to T2 and prompt analysis}
9			\item{Re-reconstruction: remote access to geometry DB}
10			\item{Extraction of alignment constants and production of re-aligned geometry file}
11			\item{Re-Reconstruction with re-aligned geometry}
12			\end{itemize}
13
14			The basic sample for this exercise was a 2 Million event Z, decaying to muon
15			pairs. The full RECO sample was imported for the different versions as they were made available
16			(4.4 TB for the last version)
17			although many of the tasks could be performed onto the AlCaReco produced at CERN-T0 (as described in Section~\ref{calibtool}) with a much smaller size of about 20 GB for the same 2 Million events. Other samples and formats were also used for checks,
18			like 0.5 Million
19			W decays to muons (AOD), ttbar (semileptonic and di-leptonic decays) or minimum
20			bias. As soon as the sample was fully transferred, prompt analysis was performed
21			using 90 CPU in which these jobs were priorized. The jobs, submitted with the standard CRAB tools,
22			consisted in running
23			over the whole sample to check data quality producing basic distributions
24			derived from standalone muon and global track quantities
25			(transverse momentum and invariant mass, for dimuon case). The latency was dominated by
26			the different steps in the data transfer. For the AlCaReco sample, results
27			were available within the next day of the sample availability at T0.
28
29			Re-reconstruction of the samples was performed locally at the T2, starting from the DIGI, in the RECO
30			sample. Two different tests were done.
31			On the first case, a distorted geometry Database is read from the T0. The one defined in the
32			so-called ShortTerm Scenario, mimicking the misalignment conditions at the very
33			beginning of data taking was used. The access was made with Frontier through the local SQUID cache.
34			The obtained invariant mass in each case is shown for the Global (using tracker and muon hits)
35			and Standalone Muon (muon hits only) reconstruction in Figure~\ref{fig:muscenario}. A clear widening of the
36			distribution is observed due to the wrong situation of the muon chambers. The effect is less evident for
37			the Global reconstruction, because the momentum resolution for these energies largely depends on the Tracker, which is assumed
38			perfectly aligned in this case.
39			Alternatively, the re-reconstruction was tested using a local DB, previously created off-line, which
40			was supplied during the job submission, together with other input files.
41			No significant delay was found due to the remote access to DB.
42
43			\begin{figure}[!htb]
44			\begin{center}
45			\includegraphics[width=0.45\textwidth,clip=]{figs/GBInvM_ideal_shortTerm.pdf}
46			\includegraphics[width=0.45\textwidth,clip=]{figs/SAInvM_ideal_shortTerm.pdf}
47			\caption{\label{fig:muscenario} Reconstructed mass for Z$\to\mu\mu$ sample with
48			Global or Standalone Muons for ideal or ShortTerm geometry.}
49			\end{center}
50			\end{figure}
51
52			A simplified version of the Muon alignment with tracks algorithm was applied to the
53			sample (AlCaReco). It is based in the so-called Blobel
54			method~\cite{blobel}\cite{alitrak}, which provides a relatively simple procedure to simultaneously fit track parameters
55			and alignment
56			constants. The method is
57			in principle iterative, but for this application the problem is nearly linear and only one step is
58			needed. This has the advantage that is enough to provide track fit residuals and local coordinates of the hit, when the fit is
59			performed ignoring the alignment constants. No refit or iterations are needed, nor access to the geometry and, hence, it is very fast and can be run in a standalone mode if necessary. For this exercise only the barrel muon chambers
60			are aligned in the more relevant d.o.f. displacement along the r$\varphi$ direction. The resultant linear system has 240 unknowns,
61			which is small enough to handle the problem with standard methods. However, the alignment with tracks problems without additional
62			constrains leads to a singular matrix, which cannot be inverted. The method proposed here, looks for the degrees of freedom
63			corresponding to the singularity
64	acosta	1.3	characterized as eigenvectors of eigenvalue 0 and store them. They correspond to invariants of the problem, that cannot be resolved
65	acosta	1.1	without the introduction of additional constrains.
66			For this exercise they were ad-hoc fixed to zero, although in a
67			real case external constrain will be included (mechanical references, hardware alignment or other physic constrains).
68
69			This procedure was applied to the Z$\to\mu\mu$ sample reconstructed with a distorted geometry
70			%(ShortTerm).
71	acosta	1.2	in which Barrel chambers are displaced from their nominal position alternatively by 1 mm.
72	acosta	1.1	The alignment constants obtained in this way are stored with MuonAlignment tools into a geometry DB, which constitutes an
73			approximation of the nominal geometry.
74			Muon reconstruction was again performed taking as input this geometry. Figure~\ref{fig:reali} shows
75	acosta	1.2	the invariant mass for Standalone Reconstruction in the barrel, for each of the three geometries. It can be appreciated that the
76			alignment recovers almost totally the precision given by the ideal geometry.
77	acosta	1.1
78			\begin{figure}[!htb]
79			\begin{center}
80	acosta	1.2	\includegraphics[width=0.45\textwidth,clip=]{figs/ideal_misal_corrected_SAInvM_Barrel.pdf}
81	acosta	1.1	% \includegraphics[width=0.45\textwidth,clip=]{figs/muscenario2.pdf}
82			\caption{\label{fig:reali} Reconstructed mass for Z$\to\mu\mu$ sample with
83	acosta	1.2	Global or Standalone Muons for ideal (black), misaligned (red) and aligned (blue) geometry.}
84	acosta	1.1	\end{center}
85			\end{figure}
86
87