Track Based Alignment for the Mu3e Pixel Detector

(1)

Track Based Alignment for the Mu3e Pixel Detector

U. Hartenstein

DPG-Fr¨uhjahrstagung 2017

For the Mu3e Collaboration

(2)

The Mu3e Experiment

(3)

Mu3e - In the Standard Model

1/8

µ

⁺

→ e

⁺

e

⁻

e

⁺

(4)

µ

⁺

→ e

⁺

e

⁻

e

⁺

(5)

1/8

µ

⁺

→ e

⁺

e

⁻

e

⁺

BR < 10

⁻⁵⁴

(6)

Beyond the Standard Model?

Motivation

• new physics?!

- predictions from SUSY, Leptoquarks, . . .

• current status (SINDRUM 1988): BR<10⁻¹²

Goal

µ⁺→e⁺e⁻e⁺

with a sensitivity ofO(10⁻¹⁶)

(7)

The Detector

(8)

Building the Detector

µ-beamline at PSI withO(10⁸⁽⁹⁾)µ/s

muon beam

target

• ”MuPix”: HighVoltage

Monolithic ActivePixelSensors

(I.Peric,Nucl.Instr.Meth.,2007, A582, 876)

• 2×2cm² sensors

• 80×80µm² pixels

• thinned to 50µm

impossible to have sufficient alignment after construction!

(9)

3/8 muon beam

target

inner pixel layers

MonolithicActive PixelSensors

impossible to have sufficient alignment after construction!

(10)

outer pixel layers

muon beam

target

inner pixel layers

impossible to have sufficient alignment after construction!

(11)

3/8

impossible to have sufficient alignment after construction!

(12)

impossible to have sufficient alignment after construction!

(13)

3/8

• thinned to 50µm alignment goal: σ ≈2µm

impossible to have sufficient alignment after construction!

(14)

impossible to have sufficient alignment after construction!

(15)

3/8

impossible to have sufficient alignment after construction!

(16)

impossible to have sufficient alignment after construction!

(17)

Track Based Alignment

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Track Based Alignment and the Software for it

• with cosmics, lower rate, . . .

→σ_position≤80µm,σorientation ≤0.3^◦ (from misalignment studies)

→ track based alignment

→ σ≈2µm

• Mu3e software package

• General Broken Lines (GBL)(V. Blobel, C. Kleinwort, arXiv:1201.4320v1)

• Millepede-II (MP-II) (V. Blobel, C. Kleinwort, arXiv:1103.3909v1)

(19)

Track Based Alignment and the Software for it

4/8

• with cosmics, lower rate, . . .

→σ_position≤80µm,σorientation ≤0.3^◦ (from misalignment studies)

→ track based alignment

→ σ≈2µm

• Mu3e software package

• General Broken Lines (GBL)(V. Blobel, C. Kleinwort, arXiv:1201.4320v1)

• Millepede-II (MP-II) (V. Blobel, C. Kleinwort, arXiv:1103.3909v1) Mu3e Track-Reconstruction:

A. Kozlinskiy - Thu,16:45 T 116.1

(20)

General Broken Lines Fit

5/8

• multiple scattering & energy loss

→ more advanced track models: e.g. GBL

• track refit to account formultiple scattering

• complete covariance matrix of all track parameters at any point

→ track based alignment withMillepede-II

V. Blobel, C. Kleinwort,

(21)

5/8

• multiple scattering & energy loss

→ more advanced track models: e.g. GBL

• track refit to account formultiple scattering

• complete covariance matrix of all track parameters at any point

→ track based alignment withMillepede-II

V. Blobel, C. Kleinwort, arXiv:1201.4320v1

(22)

Millepede-II

A least squares fit with a very large number of parameters

6/8

eachtrack j has

measurements: m_ij ±σ_ij and is modelled byf_ij(q_j,p)

(23)

Millepede-II

6/8

eachtrack j has

measurements: m_ij ±σ_ij and is modelled byf_ij(q_j,p)

χ² =

tracks

X

j

measurements

X

i

mij −fij(qj,p) σ_ij

2

(24)

Millepede-II

6/8

• minimiseχ²

- 1.5 mio track parametersqj

- 45 000 alignment parametersp

→invert a 1545000×1545000 matrix - MP-II→reduction to 45000×45000

χ² =

tracks

X

j

measurements

X

i

2

(25)

Millepede-II

6/8

• minimiseχ²

→invert a 1545000×1545000 matrix

- MP-II→reduction to 45000×45000

χ² =

tracks

X

j

measurements

X

i

2

(26)

Millepede-II

6/8

• minimiseχ²

→invert a 1545000×1545000 matrix - MP-II→reduction to 45000×45000

χ² =

tracks

X

j

measurements

X

i

2

(27)

Surface Deformations

(28)

Surface Deformations

• 50µm chips won’t be rigid!

• Idea: align not only for rotations and shifts but also for - surface deformations

- temperature effects (∆T ≈70K)

• 3rd order polynomials for modelling sensors

50µm silicon

(29)

Surface Deformations

7/8

• 50µm chips won’t be rigid!

• Idea: align not only for rotations and shifts but also for - surface deformations

- temperature effects (∆T ≈70K)

• 3rd order polynomials for modelling sensors

x

10 5 0 5 10

y 1050510

h(x,y)

0.200.150.100.05 0.00 0.050.100.150.20

a deformed sensor

(30)

Outlook

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Status & Outlook

8/8

• misalignment StudiesX

• basic software X

• MP-II testbed for the “MuPix-Telescope” X

• missing bits and pieces

• blinded tests of alignment software

(32)

Status & Outlook

h

Entries 986896

Mean 3.563e−05

RMS 0.02265

/ ndf

χ2 1.075e+04 / 48

Constant 1.814e+05 ± 2.355e+02 Mean 5.187e−05 ± 2.173e−05 Sigma 0.02147 ± 0.00002

−00.3 −0.2 −0.1 0 0.1 0.2 0.3

20 40 60 80 100 120 140 160 180 103

× Entries ^h 986896

Mean 3.563e−05

RMS 0.02265

/ ndf

χ2 1.075e+04 / 48

Residuals

pitch≈100µm σ≈22µm

(33)

Status & Outlook

8/8

h

Entries 986896

Mean 3.563e−05

RMS 0.02265

/ ndf

χ2 1.075e+04 / 48

residual in mm

−00.3 −0.2 −0.1 0 0.1 0.2 0.3

20 40 60 80 100 120 140 160 180 103

× Entries ^h 986896

Mean 3.563e−05

RMS 0.02265

/ ndf

χ2 1.075e+04 / 48

Residuals

pitch≈100µm σ≈22µm

(34)

Backup

(35)

Parametrization

• span sensors by two orthonormal vectors u and v

• use right-handed local coordinate system u,v,w

• w =w(u,v) parametrized withLegendre-polynomials and surface coefficients

x

10 5 0 5 10

y 1050510

h(x,y)

0.200.150.100.05 0.000.050.100.150.20

Figure 1: Legendre-Plane: coefficients of 0−30µm

(36)

Parametrization

• spanned by two orthonormal vectors defining the local u- &

v-coordinates

• w-coordinate defined via u×v with a value ofh(u,v)

h(x,y) =

N

X

i=0 i

X

j=0

c_ijPi−j(x)P_j(y), (1) withLegendre-ploynomials

P_n(x) = 2ⁿ

n

X

k=0

n k

n+k−1 2

n

x^k. (2) and surface coefficientsc_ij

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Alignment Procedure

Watson

● Track (re-)fit with GBL

● Jacobian calculation

Geometry information

● Global positions & orientations

● Surface coefficients

● Temperature scaling

Hit information

● Local hit information

● Sensor ID's

MilleBinary & Steering File(s)

● Local & global derivatives

● “instructions” for pede

Interpret & update

produce

pass (not tested)

Pede

● Least squares fit

● Alignment corrections

(39)

Misalignment

• perfect alignment

• misaligned sensors

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Misalignment

• perfect alignment • misaligned sensors

(41)

Misalignment Studies

• what does that mean?

→ need foralignment algorithm

• for track based alignment tracks are needed!

• “how well(mechanically) aligned to be able to align(with software)?”

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Misalignment Studies

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Momentum Reconstruction Efficiency

Randomly Misaligned 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

• normalised to the efficiency of a perfectly aligned detector

• efficiency plateau

Efficiency

(47)

Momentum Reconstruction Resolution

Randomly Misaligned 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

(48)

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

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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

°] 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

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

0.5 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

(50)

°] 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

• torsion of the whole detector

• maximum rotation angle of each detector end (total: 4^◦)

• fairly insensitive to torsion

(51)

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

• shifts of the innermost layer in x-direction

(52)

shift [mm]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

momentum resolution [MeV]

0 0.5 1 1.5

2 2.5

• shifts of the innermost layer in x-direction

(53)

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

°] 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

°] 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

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

(54)

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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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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The Detector

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

(57)

The Phases of the Mu3e Detector

Scintillating fibres Outer pixel layers μ Beam

Outer pixel layers Recurl pixel layers

Scintillating fibres Outer pixel layers Recurl pixel layers