Detector Concept 5

A 3D Track Fit with Multiple Scattering for the Mu3e Experiment

Moritz Kiehn for the Mu3e Collaboration

Physikalisches Institut, Universität Heidelberg

Connecting The Dots, Berkeley, 2015-02-10

The Mu3e Experiment 2

• Precision experiment

• Search for µ⁺→e⁺e⁻e⁺ In this talk

• Experimental concept

• Track fitting in different regimes

• Triplet fit for Mu3e

• Performance comparisons

µ → eee in the Standard Model 3

Features

• Charged lepton flavor violating

• Expected BR(µ→eee)≪10⁻⁵⁰

• Current limit from Sindrum

BR(µ→eee)<1·10⁻¹² @90 % CL

Nucl.Phys. B299(1) 1988 (1–6)

• Our Sensitivity: 1 in 10¹⁶ decays Importance

• Observable rate only from New Physics

Signal and Backgrounds 4

Signal

e⁺

e⁺ e^-

Backgrounds Internal Conversion

e^- e⁺

e^{+ ν}

ν

Accidental

e⁺

e⁺ e^-

• Common vertex

•

Pp~i =0

• p <53 MeV

• Common vertex

•

P~pi 6=0

• In-time

• No common vertex

• Out-of-time Requiresσp<0.3 MeV

σ_t<1 ns

Detector Concept 5

Target μ Beam

28 MeV/c

Magnetic field∼1 T

Environment

• >10⁹ µ⁺ decays/s (continous)

• Electrons p <53 MeV/c

Pixel Tracker

• Monolithic active pixels

• 50 µm silicon, 80 µm pixel size

• Continous readout

Detector Concept 5

Target Inner pixel layers

Scintillating fibres

Outer pixel layers μ Beam

28 MeV/c

Magnetic field∼1 T

Environment

• >10⁹ µ⁺ decays/s (continous)

• Electrons p <53 MeV/c

Pixel Tracker

• Monolithic active pixels

• 50 µm silicon, 80 µm pixel size

• Continous readout

Detector Concept 5

Target Inner pixel layers

Scintillating fibres

Outer pixel layers Recurl pixel layers

Scintillator tiles

μ Beam

28 MeV/c

Magnetic field∼1 T

Environment

• >10⁹ µ⁺ decays/s (continous)

• Electrons p <53 MeV/c

Pixel Tracker

• Monolithic active pixels

• 50 µm silicon, 80 µm pixel size

• Continous readout

Multiple Scattering 6

Ω MS

θMS

B

θ

∼

p x /X

Mu3e Example

• p = 35 MeV/c

• 50 µm Si

• ΩR=5 cm

→ ∆y ≈320 µm

→ Scattering dominates

Tracking Models 7

Position Resolution

σ

ΘMS ^Scattering

d

Scattering scale factor:

d ·θMS

σ ≪1

Dominated byhit resolution Reconstruction

• Helix fit

1. Circle fit in xy-plane

e.g. Karimaeki 1991

2. Straight line in sz-space

• 2.5D fit, global parameters

Tracking Models (cont’d) 8

Position Resolution

σ

ΘMS ^Scattering

d

Scattering scale factor:

d ·θMS

σ ≈1

Reconstruction

• Kalman filter

e.g. Fruewirth 1987

• General Broken Lines

Blobel,Kleinwort 2011

• 3D fit

Tracking Models / General Broken Lines 9

☓ ☓ ☓ ☓

u_i u_i+1 u_i-1

Θi

reference trajectory

reference trajectory Global Trajectory (3D)

Local Trajectory (2D)

☓ ☓ ☓ ☓

linearize around reference

Minimize u_i andθi

see Kleinwort 2012

Tracking Models (cont’d) 10

Position Resolution

σ

ΘMS ^Scattering

d

Scattering scale factor:

d ·θ_MS

σ ≫1

Dominated byscattering Reconstruction

• Kalman filter

• General Broken Lines

• Anything else?

A Triplet of Hits 11

Sensor 1 Sensor 2

Sensor 3

# parameters

+ 9 data points

- 3 start position - 2 direction angles - 1 curvature / radius - 2 path lengths

+ 1 constraints

A Triplet of Hits (cont’d) 12

Sensor 1 Sensor 2

Sensor 3

θMS,2 θMS,1

# parameters

+ 9 data points

- 3 start position - 2 direction angles - 1 curvature / radius - 2 path lengths - 2 scattering angles

- 1 constraints

Additional constraints

• < θ_MS,i >=0

• < θ²_MS,i >=PDG

• ∆E ≈0

A Triplet of Hits (cont’d) 12

Sensor 1 Sensor 2

Sensor 3

θMS,2 θMS,1

# parameters

+ 9 data points

- 3 start position - 2 direction angles - 1 curvature / radius - 2 path lengths - 2 scattering angles

- 1 constraints

Additional constraints

• < θ_MS,i >=0

• < θ²_MS,i >=PDG

• ∆E ≈0

Triplet Fit 13

s01 s12

c2 c1

r01 r12

h0 h2

h1

ϕ01x

ϕ12x

ϕM S

d01 d12

ϕ01

ϕ12

x y

z s

z01 z12

h2

h1

h0

θ12

θ01

s01

s12

θM S

Assumptions:

• No position error

• No energy loss

• Thin scatterer at middle hit

Minimize:

χ²_i(R3D) = ϕMS(R3D)²

σ_ϕ² +θMS(R3D)² σ_θ² Problem: highly non-linear

Solution: linearize around circle.

Triplet Fit 13

s01 s12

c2 c1

r01 r12

h0 h2

h1

ϕ01x

ϕ12x

ϕM S

d01 d12

ϕ01

ϕ12

x y

z s

z01 z12

h2

h1

h0

θ12

θ01

s01

s12

θM S

Assumptions:

• No position error

• No energy loss

• Thin scatterer at middle hit

Minimize:

χ²_i(R3D) = ϕMS(R3D)²

σ_ϕ² +θMS(R3D)² σ_θ² Problem: highly non-linear

Solution: linearize around circle.

Triplet Fit (cont’d) 14

triplet 1

triplet 2

1. Define overlapping triplets χ²( ¯R_3D) =X

χ²_i 2a. Minimizeχ² globally

R¯_3D =arg min

x

χ²(x)

2b. Equivalent: minimize each triplet R¯3D =

Pw_iR_3D,i Pw_i

Compared Track Fits 15

What is considered?

Positions Scattering

Helix ✓ ✗

Triplet ✗ ✓

GeneralBrokenLines ✓ ✓

Coordinates and Track Parameters 16

Coordinate System

x y

z

B~ θ φ

λ

Track Parameters

r

z λ x

x_⊥ y Φ

All parameters defined at inner-most layer

Mu3e Geometry 17

0 10 20 30 40 50 60 70 80

x position / mm

0 10 20 30 40 50 60 70 80

y position / mm

• 4 layers

• B = 1 T

• x/X0 = 1 ‰

• σ = 23 µm

• p = 15–53 MeV

Momentum Resolution 18

20 25 30 35 40 45 50

Momentum / MeV/c

0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040

Relative momentum resolution

= 10°

Helix Triplet

GeneralBrokenLines

7.1

Scattering scale factor f = d

/

Dip Angle λ Resolution 19

20 25 30 35 40 45 50

Momentum / MeV/c

0.000 0.005 0.010 0.015 0.020

re so lut ion / r ad

= 10°

Helix Triplet

GeneralBrokenLines

7.1

Scattering scale factor f = d

/

Azimuthal Angle φ Resolution 20

20 25 30 35 40 45 50

Momentum / MeV/c

0.000 0.005 0.010 0.015 0.020 0.025

re so lut ion / r ad

= 10°

Helix Triplet

GeneralBrokenLines

7.1

Scattering scale factor f = d

/

Local Offset x

Resolution 21

20 25 30 35 40 45 50

Momentum / MeV/c

0.00 0.01 0.02 0.03 0.04 0.05 0.06

x re so lut ion / m m

= 10°

Helix Triplet

GeneralBrokenLines

7.1

Scattering scale factor f = d

/

Mu3e Geometry with Recurlers 22

0 50 100 150 200 250 300 350

x position / mm

200 150 100 50 0 50 100 150

y position / mm

• 4 layers, but>4 hits

• B = 1 T

• x/X0 = 1 ‰

• σ = 23 µm

• p = 15–53 MeV

Momentum Resolution 23

20 25 30 35 40 45 50

Momentum / MeV/c

0.000 0.005 0.010 0.015 0.020 0.025 0.030

Relative momentum resolution

= 10°

Helix Triplet GBL/Helix GBL/Triplet

7.1

Scattering scale factor f = d

/

LHC-like Geometry 24

0 50 100 150 200

x position / mm

0 50 100 150 200

y position / mm

• 6 layers

• B = 2 T

• x/X0 = 2 %

• σ = 25 µm

• p = 100–2000 MeV

Momentum Resolution 25

500 1000 1500

Momentum / MeV/c

0.04 0.06 0.08 0.10 0.12

Relative momentum resolution

= 10°

Helix Triplet

GeneralBrokenLines

4.8

Scattering scale factor f = d

/

Speed 26

2·10⁹µ/s 50 ns integration

Prototype online reconstruction Single Nvidia GTX 680

>10⁹Triplets/s

Summary and Outlook 27

Mu3e triplet fit

• 3D fit w/ scattering

• Fast, non-iterative

• Works for us Applications

• Low momentum, dominating scattering

• Fast online reconstruction

• Reference for refit

Next?

• Full paper coming soon

http://www.psi.ch/mu3e

Backup

The Mu3e Collaboration A1

University Geneva Heidelberg University

Karlsruhe Institute of Technology Mainz University

Paul Scherrer Institute ETH Zürich

University Zürich

Performance Full Mu3e Simulation A2

4 Hits

[MeV/c]

- pmc prec

-5 -4 -3 -2 -1 0 1 2 3 4 5

0 10000 20000 30000 40000 50000 60000

70000 µ = -0.24

= 1.43 σ

6 Hits (Recurler)

[MeV/c]

- pmc prec

-5 -4 -3 -2 -1 0 1 2 3 4 5

0 20 40 60 80 100 120

103

×

= -0.35 µ

= 0.22 σ

Geant4 simulation w/ complete detector No energy loss correction