Track Based Alignment of the Mu3e Detector

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Track Based Alignment of the Mu3e Detector

Ulrich Hartenstein

for the Mu3e Collaboration

DPG-Fr¨ujahrstagung 03.03.16

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1 The Mu3e Experiment

2 The Detector

3 Misalignment Studies

4 Alignment Strategy

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The Mu3e Experiment

2 The Detector

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The Mu3e Experiment

Goal

Observe

µ⁺→e⁺e⁻e⁺ ifBR>10⁻¹⁶ or

exclude a BR of >10⁻¹⁶ with CL=90%

Motivation

in SM suppressed byBR<10⁻⁵⁴ new physics?!

current status (SINDRUM 1988):

BR<10⁻¹²

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The Detector

2 The Detector

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The Detector

Building the Detector

muon beam

target

HV-MAPS pixel size = 80µm mount to 2x2cm²sensors thinned to 50µm

Kapton as support structure

impossible to have sufficient alignment after construction!

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The Detector

Building the Detector

muon beam

target

inner pixel layers

impossible to have sufficient alignment after construction!

(8)

The Detector

Building the Detector

outer pixel layers

muon beam

target

inner pixel layers

impossible to have sufficient alignment after construction!

(9)

The Detector

Building the Detector

impossible to have sufficient alignment after construction!

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The Detector

Building the Detector

impossible to have sufficient alignment after construction!

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The Detector

Building the Detector

impossible to have sufficient alignment after construction!

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Misalignment Studies

2 The Detector

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Misalignment

xy-view of the silicon sensors

perfect alignment

misaligned sensors

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Misalignment

xy-view of the silicon sensors

perfect alignment misaligned sensors

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Misalignment Studies

what does that mean?

→ need for alignment algorithm

for track based alignment tracks are needed!

→ despite of misalignment reconstruction possible?

how well aligned to be able to align?

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Misalignment Studies

Produce Misalignment in a Simulated Detector

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Misalignment Studies

Produce Misalignment in a Simulated Detector

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Momentum Reconstruction Efficiency

For Misalignment of Individual Sensors

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Standard Deviation of Shifts [mm]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

]°Standard Deviation of Rotations [

0 0.2 0.4 0.6 0.8 1 1.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Efficiency

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Momentum Reconstruction Resolution

For Misalignment of Individual Sensors

1.7 1.8 1.9 2 2.1 2.2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

]°Standard Deviation of Rotations [

0 0.2 0.4 0.6 0.8 1 1.2

1.7 1.8 1.9 2 2.1 2.2

momentum resolution from RMS ofprec−pMC

for random sensor shifts & rotations in MeV/c

Resolution

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Alignment Strategy

2 The Detector

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Alignment Strategy

Used Software

after construction:

σposition ≤80µm σorientation≤0.3^◦ track based alignment

Mu3e software package

General Broken Lines (V. Blobel, C. Kleinwort, arXiv:1201.4320v1) Millepede-II (V. Blobel, C. Kleinwort, arXiv:1103.3909v1)

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Alignment Strategy

Used Software

after construction:

σposition ≤80µm σorientation≤0.3^◦ track based alignment Mu3e software package

General Broken Lines (V. Blobel, C. Kleinwort, arXiv:1201.4320v1) Millepede-II (V. Blobel, C. Kleinwort, arXiv:1103.3909v1)

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Alignment Strategy

General Broken Lines Fit

An Advanced Track Fitting Method

multiple scattering & energy loss→ more advanced track models track refit (seeding needed!)

→ complete covariance matrix of all parameters

→ track based alignment withMillepede-II computing time of O(n)

by exploiting sparsity of matrix (n = number of measurements)

V. Blobel, C. Kleinwort,

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Alignment Strategy

Millepede-II

Least Squares Fits with a Large Number of Parameters

fit track & alignment parameters simultaneously

→ very large minimisation problem!

solve irrespectively of track parameters

→ reduced to an×n matrix equation (n =number of alignment parameters) reasonable computing time

even for up to 100,000 alignment parameters

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Alignment Strategy

Current Status & Outlook

misalignment StudiesX basic software X

improvements & bug fixing

use telescope to practice use of MP-II (March ’16) blinded tests of alignment software

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Backup

Misalignment Studies - Momentum Resolution Sigma

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 4-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

]° Standard Deviation of Rotations [

0 0.2 0.4 0.6 0.8 1 1.2

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 4-hit-segments

0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 6-hit-segments

0 0.1 0.2 0.3 0.4 0.5 0.6

0 0.2 0.4 0.6 0.8 1 1.2

0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 6-hit-segments

0.15 0.2 0.25 0.3 0.35 8-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 0.2 0.4 0.6 0.8 1 1.2

0.15 0.2 0.25 0.3 0.35 8-hit-segments

sigma of gaussian fit to the core of the momentum resolution distribution (single sensors) in MeV/c

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Backup

Misalignment Studies - Momentum Reconstruction Efficiency (4-hit segments)

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

reconstruction efficiency

0.5 0.6 0.7 0.8 0.9 1

shift [mm]

0 0.1 0.2 0.3 0.4 0.5

0.5 0.6 0.7 0.8 0.9 1

°] rotation [

0 0.2 0.4 0.6 0.8 1

0.5 0.6 0.7 0.8 0.9 1

°] rotation [

0 0.1 0.2 0.3 0.4 0.5

0.5 0.6 0.7 0.8 0.9 1

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.5 0.6 0.7 0.8 0.9 1

shift [mm]

0 0.1 0.2 0.3 0.4 0.5

0.5 0.6 0.7 0.8 0.9 1

0.6 0.7 0.8 0.9 1

shifts of layer 0 in x-direction shifts of layer 0 in z-direction rotations of layer 0 along x-axis

rotations of layer 0 along z-axis shifts of layers 0 & 1 in x-direction shifts of layers 0 & 1 in x-direction

rotations of layers 0 & 1 along x-axis rotations of layers 0 & 1 along z-axis torsion of the whole detector

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Backup

Momentum Reconstruction Resolution

For Torsion of the Whole Detector

°] torsion angle [ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

reconstruction resolution [MeV]

0 0.5 1 1.5

2 2.5

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Backup

Momentum Reconstruction Efficiency

For Misalignment of Whole Detector Layers

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.5 0.6 0.7 0.8 0.9 1

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Backup

Momentum Reconstruction Resolution

For Misalignment of Whole Detector Layers

momentum resolution [MeV]

0 0.5 1 1.5

2 2.5

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Backup

Misalignment Studies - Momentum Resolution RMS (4-hit segments)

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.5 1 1.5 2 2.5

shift [mm]

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5

°] rotation [

0 0.2 0.4 0.6 0.8 1

0 0.5 1 1.5 2 2.5

°] rotation [

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.5 1 1.5 2 2.5

shift [mm]

0 0.1 0.2 0.3 0.4 0.5

0 0.5 1 1.5 2 2.5

0.5 1 1.5 2 2.5

reconstruction resolution [MeV]0.5 1 1.5 2 2.5

shifts of layer 0 in x-direction shifts of layer 0 in z-direction rotations of layer 0 along x-axis

rotations of layer 0 along z-axis shifts of layers 0 & 1 in x-direction shifts of layers 0 & 1 in x-direction

rotations of layers 0 & 1 along x-axis rotations of layers 0 & 1 along z-axis torsion of the whole detector

(32)

Backup

Momentum Reconstruction Efficiency

For Individual Sensors

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

0 0.2 0.4 0.6 0.8 1 1.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4-hit-segments

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 6-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 0.2 0.4 0.6 0.8 1 1.2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 6-hit-segments

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 8-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.2 0.4 0.6 0.8 1 1.2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 8-hit-segments

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Backup

Momentum Resolution

For Individual Sensors

1.7 1.8 1.9 2 2.1 2.2 4-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0 0.2 0.4 0.6 0.8 1 1.2

1.7 1.8 1.9 2 2.1 2.2 4-hit-segments

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 6-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0 0.2 0.4 0.6 0.8 1 1.2

0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 6-hit-segments

0.4 0.45 0.5 0.55 0.6 8-hit-segments

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0 0.2 0.4 0.6 0.8 1 1.2

0.4 0.45 0.5 0.55 0.6 8-hit-segments

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Backup

The Detector

Baseline Design

Target Inner pixel layers

Outer pixel layers Recurl pixel layers

Scintillator tiles μ Beam

110cm

18cm

barrel detector

two double layers of silicon sensors

scintillating fibre tracker &

scintillating tiles (timing)

hollow double cone target use re-curlers

allow precise momentum measurements

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Backup

The Detector

Baseline Design

110cm

18cm

barrel detector

two double layers of silicon sensors

scintillating fibre tracker &

scintillating tiles (timing)

hollow double cone target use re-curlers

allow precise momentum measurements

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Backup

The Target

100 mm

38 mm

19 mm 20.8°

m Mylar μ 5 8 Mylar

m μ 5 7

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Backup

The Phases of the Mu3e Detector

Scintillating fibres Outer pixel layers μ Beam

Scintillating fibres Outer pixel layers Recurl pixel layers