Louis Nicolas – LPHE-EPFL T-Alignment: Track Selection December 11, 2006 Track Selection for...

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


Different types of misalignments

Aligned detector

Internal misalignments

Global shifts or rotations

Global distortions

Other possible effects: scaling, ...


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


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.


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©

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σ ~ 0.51% σ ~ 0.90%

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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


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:


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


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!


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


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)


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)


Quality selection: isolated tracks

Plot of number of neighbouring hits found inside 2 strips around track (just

showing that I find neighbouring hits...):


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:


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


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.


Monitoring tool: ladder overlap residuals

Plot of ladder overlap residuals:


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


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


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


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 December 11, 2006 Track Selection for...

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