Page 28

Tobias Golling

Alignment Validation

LHC Alignment Workshop – September 05 2006

Introduction & Overview

Mass resonances: J/, , Z

Resolution Effects

Degenerate Modes

Monitoring

Validation with MC

Summary

Tobias Golling on behalf of

Page 28

Tobias Golling

Outline

All 4 experiments have roughly the same ideas for alignment

validation

Much is in common – there are some experiment-dependent

peculiarities

All: Much work to do for the validation of the alignment

I will present the general ideas, using examples (incomplete)

from the LHC but also from the Tevatron or the SLAC experiments

At the end I will be more specific about the differences

between ALICE, ATLAS, CMS and LHCb

Page 28

Tobias Golling

Why Validate?

The residual based alignment has limitations:

A 1-dimensional measure is used to determine 6 DoF per module

(underconstrained) – this leads to more than one solution

Physics is biased

Validate to detect “wrong solutions”

Go one step further: Validation ⇒ Constraint

Use as alignment correction, make alignment more robust

however, then we cannot use it anymore to monitor

Rule of thumb:

“Practical constraint” ⇒ feed back into alignment algorithm as

additional constraint (straightforward in global algorithms)

Else: use as monitor

Page 28

Tobias Golling

More Reasons for Validation

Alignment monitoring sensitive to all kinds of

(other) problems: tracking, reconstruction,...

We only need to align what has an impact on physics

⇒ Invert the argument:

If all physics observables look as expected then we have good

reason to believe that our detector is sufficiently aligned

Goal for Day 1: working tracking reconstruction!

It's always easy to blame alignment – be prepared for this!

Page 28

Tobias Golling

Possible Handles

Tracks correlating different modules, not from beamspot

Cosmics ⇒ Barrel, off-axis tracks (can reconstruct?), “two arms”

muon trigger, ATLAS: ~40Hz through Inner Detector, ~1Hz through Pixel

Caveats: Illumination not uniform / low statistics / low momentum

Halo muons ⇒ Endcap

Beam-gas, Caveat: low momentum (ECM=113GeV)

Parasitic collisions at 0.9TeV

Rate, trigger? - ATLAS: Minbias scintillating trigger

Alignment algorithms more robust

if parameter matrix well populated

Page 28

Tobias Golling

Possible Handles cont'd

Standard candles: J/, , Z,...

Mass resolution probes pT resolution

Caveat: Measure only convolution of material description,

B-field uncertainty, misalignments ⇒ Disentangle!

Rate, trigger?

Overlap hits in the same layer: residualouter - residualinner

Not affected by misalignments elsewhere in the detector

Errors on residualouter/inner are highly correlated and subtract out

Less sensitive to MS, use lower pT and higher track density

Circumference constraint

Caveats: Low statistics

Usually used already in alignment algorithm

Use redundancy of detectors: E/p, eta-phi match between

tracking and calorimetry

Alignment monitoring:

Lifetime, mass, residuals vs. eta, phi, pT, charge, module position,...

Page 28

Tobias Golling

Possible Handles cont'd

Biased track parameters can probe some degenerate modes

e.g. IP distribution, charge asymmetries,...

Vertex constraint: common vertex for a group of tracks

Compare track-based alignment with survey and hardware alignment

Survey & hardware based alignment doesn't have the problem of

“wrong solutions”

Magnet-off data can eliminate some “wrong solutions”

Caveat: turning B-field on and off changes the geometry,

no pT measurement

Disentangle E-loss, B-field, Misalignments

Page 28

Tobias Golling

Use mass resonances: J/, ,Z

decaying to µ+µ-

Plot m(µ+µ-) vs pT

At low pT sensitive to E-loss

B-field effect independent of pT

At high pT more sensitive to

misalignments

Procedure:

First fix material budget to make mass ~independent of pT

Iterative process, also cross check with conversions

Residual discrepancy attributed to B-field scale (or misalignment)

Handle: magnetic field effect independent of charge, alignment effect

charge dependent ⇒ Look for charge asymmetry of muons

Run alignment with magnet off data

Small global corrections expected with magnet on

Residual effects due to B-field or material

J/ and Z Mass

Page 28

Tobias Golling

Z mass

J/ mass

Probe at different scales: J/, Z

Z important for validation of muon

alignment

M2 = 2P1P2(1-cos12)

P → P(1+),  = dP/P

(M+dM)2 = 2P1P2(1+)2(1-cos12)

dM / M ~  = dP / P = dB / B = d/

With P = 0.3 B(T) (m)

100x

4GeV

6GeV

Page 28

Tobias Golling

J/ and  accessible by Trigger?

J/ rate from B decay?

⇒ Lower threshold using vertex

and invariant mass cut

J/ and  are “barrel-poor”

4 GeV trigger threshold possible

at low luminosity?

⇒ Use high cross section

resonances

Also Ks in Minbias?

Scale down by 100x

for 0.9TeV run

Mass Resolution vs. Momentum Resolution

Page 28

Tobias Golling

Bs→π+K-

Mass resolution is a good measure of the

momentum resolution

4x

worse

Momentum resolution sensitive

to both B-field inhomogeneities

& misalignments

B known with

uncertainty < 0.03%

⇒ momentum resolution

affected by < 10%

Page 28

Tobias Golling

Weakly Defined Degrees of Freedom

Alignment algorithms based on minimization of track residuals suffer from

a class of detector deformations (degenerate modes or 2 invariant deformations) that alter the shape of tracks in such a way that they are still helical but with certain properties of the helix modified:

biased track parameters – physics is biased

Even if tracks with different momenta and sign charge are used

The barrels are left progressively rotated/translated proportional to

ar2 + br + c

Deformations typically of the same size as the initial random misalignments

Low momentum tracks (~< 2 GeV) less affected

Caveat: Multiple scattering

Page 28

Tobias Golling

Rphi Rotation

Quadratic term

Constant term

Barrels are progressively rotated as you move away from the beam-line

Pixel

Silicon Strip

Page 28

Tobias Golling

X / Y Translation & Rotation

Quadratic term

X / Y Translation:

Barrels are progressively translated as you move away from the beam-line

X / Y Rotation:

Barrels are progressively rotated as you move away from the beam-line

Page 28

Tobias Golling

Z Translation

Telescoping (only linear term):

Projection of high momentum helical tracks onto RZ plane is straight line

Z misalignments that grow linearly with z keep the tracks as straight lines

Page 28

Tobias Golling

Deformations are stable vs. Iterations

Pixel

Silicon Strip

Pixel

Silicon Strip

Page 28

Tobias Golling

Methods for Removing RPhi Mode

Observable: Bias of pT and IP distribution

Quadratic term:

bias on curvature

Opposite bias for positively and negatively charged tracks

E/p

Known charge-symmetric distributions

Constant term:

related to transverse impact parameter

Page 28

Tobias Golling

Charge Dependence

Opposite bias for negative and positive

particles

Mismeasurement of ~7GeV at 50 GeV

for misalignment of 0.5mrad at 50cm

Charge flip at ~1 TeV

For charge-symmetric pT distribution:

plot (pos-neg)/(pos+neg) vs. pT

Page 28

Tobias Golling

Charge Dependence

Black: ideal geometry

Red: Rphi rotated geometry

2 and the Z-mass are hardly

affected by this misalignment:

M2 = 2P1P2(1-cos12)

PT distribution of µ+ and µ-

sensitive to this misalignment

Red: -

Blue: +

Page 28

Tobias Golling

E/p - Quadratic Term

Calorimeter calibration:

Only require that E/p distribution is the same for + and – particles when no misalignments are present

40 GeV electrons

Page 28

Tobias Golling

Impact Parameter - Constant Term

Perfect alignment: mean impact parameter expected to be zero

Rphi rotation: mean IP non-zero

If beamspot is offset:

Use profile histogram: Mean IP vs. Phi

Beamspot offset and angle determined

from amplitude and phase

Fit sin plus average IP (offset in y-axis)

Page 28

Tobias Golling

Result of Sagitta Removal for RPhi

Using E/p and the impact paramter:

Page 28

Tobias Golling

X / Y Translations & Rotations

PT and IP bias varies with eta and phi, e.g.

X / Y translation

X / Y rotation

Remark: Very weak sensitivity to

linear term of X /Y translation

Page 28

Tobias Golling

More Generic High Frequency Modes

Detailed study in global 2 algorithm:

Vertex constraint

Track parameter constraint

Invariant mass constraint

Constraint on the geometry /

on the mode itself

Weak modes corresponding to low part of eigen-spectrum:

Constraints easily implemented

in algorithm (same for Millepede)

Very encouraging results to

constrain these modes

Page 28

Tobias Golling

Degenerate Modes at LHCb or Endcaps

LHCb is an endcap kind of detector

VELO Alignment run by run, since

detector moves between runs (3cm)

Degenerate modes determined in

Step 2

Step 0

Misaligned VELO

Step 1

Internally-aligned VELO

Millepede applied on single tracks in the four parts

Step 2

Aligned VELO

Align the 4 parts using vertex constraints, overlap tracks,...

Page 28

Tobias Golling

Parasitic Collisions

At 0.9TeV beams have no crossing angles, LHCb is displaced

⇒ Head-on collisions at LHCb require parasitic collisions at ALICE, ATLAS and CMS, which can be tuned to occur between 3.75m and 11.25m away from the interaction point, and vice verca

O(10%) of the collisions will be parasitic at a luminosity ratio of

~50% for 11.25m and ~90% for 3.75m

Tracks from the ±3.75m points will make it into the tracking detector

without crossing a lot of material

These tracks impose a different set of constraints than tracks from the IP

⇒ add to alignment or use as cross-check

Needs more study:

Possible to trigger on these events – first ATLAS study suggests that Minbias scintillating trigger would work

Effect of timing shift – events occur late by half a nominal beam crossing

pattern recognition / track fitting

Needs simulation study

Alignment Monitoring

Page 28

Tobias Golling

Use monitoring to assess the need for alignment

Decide whether to update alignment constants: human intervention

Jan31 data

with old

alignment

Jan31 data

with new

alignment

Alignment Monitoring cont'd

Page 28

Tobias Golling

Histograms on hit, cluster and track level

Comparison with reference distributions

Fit to expected modes: look for indications of degenerate modes

Semi-automatic, human intervention needed in case of discrepancy

(user-friendly GUI)

Pixel example:

Pattern of residual vs. row and column number can give information about

residual module rotations and translations

module bow and other distortions (Babar)

xy position of primary vertex (mean and sigma) as a function of z,

separately for silicon and TRT (CDF)

µ-pair miss distance (David Brown)

...

Comparison of SCT & TRT Parameters

rphi residual as function of z

Corresponds to a relative twist of SCT and TRT of 0.2 mrad

Page 28

Tobias Golling

ATLAS SCT-TRT cosmics run:

∆r (TRT-SCT)

Page 28

Tobias Golling

Match Subdetectors in  and 

Twist: ∆ varies with 

Calorimeter and tracker for electrons:

Do same for track – cluster as a function of 

Barrel +

Barrel –





e.g. track – cluster as a function of :

Alignment Validation with MC

Page 28

Tobias Golling

See talk by David Brown yesterday

Generate a “matrix” of all typical realistic misalignment sets

Each represents a degenerate mode (e.g. Telescoping, RPhi rotation,...),

random misalignments, or other pathologies, etc.

Apply alignment algorithm and check to what extend the misalignments

can be recovered

This gives an estimate of the expected systematic uncertainties

Tough to cover all possible misalignments

Only data can tell: Be prepared for surprises...

Summary

Page 28

Tobias Golling

Central physics

Cannot use E/p

Forward physics

No cosmics

(acceptance)

High pT physics, a lot of material

Alignment mainly with magnet on data

Do not reverse polarity

Large magnetic field

Soft physics, very little material

Alignment mainly

with magnet off data

Reverse polarity

Small magnetic field

Summary

Page 28

Tobias Golling

Use all possible handles:

Various topologies: cosmics, halo muons, beam gas, parasitics

Overlap hits

Use redundancy of different subdetectors: -match, E/p

Vertex and mass constraints: J/, , Z

Resolutions: mass and IP

Low level residual and alignment distributions

Other external constraints: Survey, hardware alignment,...

If possible add handle as additional constraint in alignment

algorithm

Else: Monitoring, quick turnaround, semi-automatic

including human intervention

Test against expected misalignment scenarios in MC

Be prepared for the unexpected!

Back-Up

Page 28

Tobias Golling

Page 28

Tobias Golling

J/ and  are “Barrel poor”

J/  distribution for two different triggers

  distribution for two different triggers

Page 28

Tobias Golling

Remove Z Translation (Telescoping)

No pT bias but  bias (Caveat:  distribution not known at LHC),

can use forward-backward symmetry?

Modules are tilted in RPhi and RZ -> hits in same barrel have different radius -> Some sensitivity to telescoping (but need high statistics)

Needs more studies

Slide 1

2005-07-25T17:42:16