Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection December 11, 2006
Track Selection
for T-Alignment studiesLouis Nicolas
EPFL
Monday SeminarDecember 11, 2006; LPHE
T-station alignment frameworkEffects of misalignmentsSolving the alignment problemTrack selection and monitoring tool for the T-station alignmentSome variables and resultsConclusion
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 2/23 December 11, 2006
LHCb detector
The whole detector will have to be aligned
I concentrate on the Inner Tracker for now
The Outer Tracker should follow shortly
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 3/23 December 11, 2006
Different types of misalignments
Aligned detector
Internal misalignments
Global shifts or rotations
Global distortions
Other possible effects: scaling, ...
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 4/23 December 11, 2006
Alignment framework
Upstream processingUpstream processing(tracking algs, etc…)(tracking algs, etc…)
AlignToolsAlignTools
Align Data objectsAlign Data objects
Align AlgorithmsAlign Algorithms
Stores/DBsStores/DBs
Transient event storeTransient event store
Transient detector storeTransient detector store
Conditions DBConditions DB
SolvingSolving
Track Track SelectionSelection
Track ModelTrack Model
UpdateUpdate
Book-keeping Book-keeping of alignable of alignable geometrygeometry
etc…etc…
Tracking infoTracking info
Geometry infoGeometry info
iterate
LHCb BrunelLHCb Brunel
environmentenvironment
Job done in collaboration between LPHE, CERN, NIKHEF, Zurich and Heidelberg
© A. Hicheur @ 1st LHC
Detector Alignment
Workshop, CERN, 09.06
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 5/23 December 11, 2006
Use of residuals to recover the motion and rotation of the detection planes.
For N planes, 6N parameters to determine
Figure of merit: 2 = (ri/i)2
How to spot a misalignment?
© A. Hicheur @ Tracking &
Alignment Workshop, Zurich,
07.06
Misalignments change the tracks' path and hence the vertices. The vertex position is of utmost importance for the precise measurements of the Standard Model physics parameters.
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 6/23 December 11, 2006
Several solving methods are combined
Global/Collective modes not constrained: singularities appear in the
solving procedure
These singularities must be avoided (use constraints on alignment params)
Global fit: correlate different planes
Alignment problem M a = b
One method: Diagonalize matrix: With M = UT D U ==> a = UT D-1 U b
Hierarchical alignment:
Stations
Boxes
Layers
Ladders
Solving the mathematical problem©
A. H
iche
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Ali
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07.0
6
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 7/23 December 11, 2006
σ ~ 0.51% σ ~ 0.90%
Bia
s
© J
. Nar
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rack
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Example of the effect of misalignments on Physics
σ ~ 23 MeV
σ ~ 41 MeV
•Worst Misalignment: T1 and T3 moved in Opposite directions in all the 6 d.o.f. of 0.5 mm for translations and 0.5 mrad for rotations
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 8/23 December 11, 2006
Motivations of the track selection and monitoring tool
Physics motivations: • Select proper tracks for alignment
Reject ghost tracks
Select isolated tracks Provide monitoring variables for the alignment
e.g. ladder and box overlaps (see next slides)
Technical motivation:• Set a tool usable as pre-filter for tracks used for alignment studies
Steps to perform :• Save a standard monitoring NTuple (used later as monitoring tool)• Offline analysis of this NTuple
Define a set of cuts in order to achieve the physics motivations• Use this set of cuts in the track selection tool
Configuration: Code developed in LHCb reconstruction software packages Analysis done using ~25k B --> J/ (-->) Ks events
Quality selection: residuals and pull
Pull of the residual for non-ghost tracks:
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 9/23 December 11, 2006
Plot of hits residuals:
not measurable (1.58 for black curve above)
The large peak is not quite understood yet
Quality selection: pull of momentum
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 10/23 December 11, 2006
Fraction of non-ghost tracks
vs. track momentum:
= 1.14
Understood by the tracking experts
Pull of the momentum for
non-ghost tracks:
Quality selection: Track – Muon matching
We want to match track with muons:
In case of no B field, we know that the particles reaching the muon chambers
have a momentum of p > 5 GeV
Loop on all muon tracks
Extrapolate track and muon track to a defined z (set as property)
Calculate a chi2 of the position of these states:
(X_track-X_muon)²X_track
X_muon
) + (Y_track-Y_muon)²Y_track
Y_muon
)
If chi2 < C (C is a property) set flag to 1
==> 1.55 % of all tracks matched to muons for B->J/psi(mu mu) Ks data
Warning: This is not a matching efficiency!
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 11/23 December 11, 2006
Fraction of non-ghost tracks vs. number of holes (layers with no hits):
(we want the best possible tracks for alignment, i.e. only tracks with 0 holes will
be selected)
Quality selection: number of holes
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 12/23 December 11, 2006
Quality selection: number of shared hits
Fraction of non-ghost tracks vs. number of shared hits:
(we want the best possible tracks for alignment, i.e. only tracks with 0 shared hits
will be selected)
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 13/23 December 11, 2006
Quality selection: isolated tracks
We need isolated tracks:
Reject tracks with shared hits
Reject tracks with too many neighbouring hits:
For each track, look at each layer if other hits found within n strips on each
side of the track (n is a property):
In case one hit is found in layer, loop on all clusters and compare layer and
strip number
In case no hit is found in layer, extrapolate track to z of layer with hole,
convert extrapolated state position to local position and then to strip number
and compare to all clusters
If more than N hits found, reject the track (N will be a property)
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 14/23 December 11, 2006
Quality selection: isolated tracks
Plot of number of neighbouring hits found inside 2 strips around track (just
showing that I find neighbouring hits...):
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 15/23 December 11, 2006
Quality selection: track 2 Probability
Fraction of non-ghost tracks vs. 2 Probability:
It looks like nothing can be gained from here... except if you look at the ghost rate
as a function of the cut on this variable:
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 16/23 December 11, 2006
Only a few preliminary cuts could be found by looking at the plots:
Number of holes == 0 (we want the best possible tracks)
Number of shared hits == 0 (we want isolated tracks)
Probability of chi2 > 30 % (by looking at significance optimisation)
No cut on momentum in case we run with magnet off
With these three cuts:
==> Isolated tracks (no shared hits, cut on NNeighbouringHits
doesn't change much)
==> Ghost rate reduced from 12.68 % to 0.03 %
==> Selection of non-ghost tracks: efficiency = 3.25 %
==> Rejection of ghost tracks: efficiency = 99.99 %
Alignment will guide us for optimising efficiency vs. ghost rate
e.g. would 1 % ghost rate screw up the alignment?
Need simulated misaligned data to check the efficiency of the selection.
Quality selection: preliminary cuts and results
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 17/23 December 11, 2006
Monitoring tool: Ladder overlaps
What are ladder overlap residuals?
For each IT layer, we have an overlap as follows (old drawing, sorry):
Hence, for each layer, we can have up to two hits.
Definition: if track has two hits in the same layer
by convention: overlap residual = res(Hit higher Z) – res(Hit lower Z)
What are they useful for?
With the distribution of ladder overlap residuals, we can constrain and
monitor the relative motion of ladders contained in a same layer.
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 18/23 December 11, 2006
Monitoring tool: ladder overlap residuals
Plot of ladder overlap residuals:
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 19/23 December 11, 2006
Monitoring tool: box overlaps
What are box overlap residuals?• Same idea as for ladder overlaps: we want to constrain and monitor the relative
motion of two boxes of the same station
If hits are found in two contiguous boxes and at least 4 hits in one of the boxes:
then:• “Fit” piece of track in one box (we don’t want to depend on other stations)• Extrapolate to other box• Compare “piece of track” to hits of other box• Define overlap residual as distance of closest approach
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 20/23 December 11, 2006
Monitoring tool: box overlaps
2 “fit” of the hits in the box with most hits:
xtrack
= azhit
+ b
ytrack
= czhit
+ d
==>
where yglobal
is the y coordinate of the track state at hit z and sigmayglobal
its error.
Ad-hoc model for the moment to test the principle of the method. More
accurate formulation to follow (e.g. using parabolic model of “track”)
Minimise this 2 and get “track” parameters (a, b, c and d)
Extrapolate “piece of track” to z position of hits in other box
Define box overlap residual as distance between hit and fitted piece of track
(several residuals per box overlap)
chi 2= x
hit−x
track2
sigmares
2
yglobal
−ytrack
2
sigmayglobal
2
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 21/23 December 11, 2006
Plot of box overlap residuals:
Strange double peak distribution probably comes from linear approximation to
compute residual. To be confirmed. Sigma is far too large. Refinement to come...
Monitoring tool: box overlap residuals
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 22/23 December 11, 2006
Conclusion
The whole detector needs to be aligned in order to get good physics measurements.
The VeLo already has a working software.
T-station alignment software is on the way to completion: Solving tools are ready,
track selection is close to be finished, global framework is nearly ready, ...
A track selection and monitoring tool has been set up:
• Cuts are there to reject the ghosts and select the good tracks.
• An NTuple and histograms are implemented for monitoring purposes.
We're waiting for misaligned data to check if everything works properly.
Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection 23/23 December 11, 2006
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