Track reconstruction for the Mu3e experiment Alexandr Kozlinskiy (Mainz, Institut für Kernphysik) on behalf of the Mu3e collaboration

Track reconstruction for the Mu3e experiment

Alexandr Kozlinskiy (Mainz, Institut für Kernphysik) on behalf of the Mu3e collaboration

DPG 2019 @ Aachen (.03.26, T42.1)

Mu3e Experiment

Mu3e experiment:

• Search for Lepton Flavor Violation (LFV)

• Decay: µ⁺→e⁺e⁺e⁻

• Standard Model: Br<10⁻⁵⁴(not observable)

• Enhanced in New Physics (NP) models

• Any observed decay will point to NP

• Location: Paul Scherrer Institute (PSI)

• Commission in 2020-21 Current experimental status:

• SINDRUM (1988)Nucl.Phys.B299(1988)1

• Br<10⁻¹²at 90% c.l

Mu3e aim for sensitivity of one in10¹⁵µ-decays

• With existing beam line at PSI:10⁸µ/s

• Better sensitivity with new beam line (10⁹µ/s)

e⁺

µ⁺ νµ νe e⁺ W⁺

e⁻

Neutrino mixing γ^∗ SMµ⁺→e⁺e⁺e⁻

Signal & Background

Signal:

• Three tracks

• Decay at rest

• P

Ee=mµ (Ee<53 MeV/c)

• P pe= 0

• Common vertex & time

Background:

• Random combinations:

• µ⁺→e⁺+ 2ν,e^± scattering

• Fake tracks

• Not same vertex, time, etc.

• Internal conversion:

• µ⁺→e⁺e⁺e⁻+2ν

• Missing momentum & energy

µ→3e+ 2ν

e⁺ e⁺

e−

ν_µ ¯ν_e

101 102 103 104 105 106

Internal conversion background 10⁻¹⁸

10⁻¹⁶ 10⁻¹⁴

e⁺e⁺e−mass [MeV/c²]

Background

Signal

µ→3e(signal)

e⁺ e⁺

e−

Mu3e Detector (1)

Target µ⁺beam

Inner pixel e⁺ e⁺

e⁻ tiles

layers Helium atmosphere

mag.field:B= 1T 12 cm

r1≈23mm r2≈30mm O(10⁸)µ⁺/s

pµ≈28MeV/c

Muons stop and decay on target:

• Double cone hollow target

• O(100) µmthickness

• Vertex separation

• Existing beam line at PSI:

• Continuous muon beam

• O(10⁸)µ⁺/s

Inner pixel layers:

• Thin & high granularity

• 99.9% efficiency

• As close as possible to target

• Reduce effect of Multiple Scattering (MS) and pixel size

• Improve vertex resolution

Mu3e Detector (2)

Target µ⁺beam

Scintillating fibres

Inner pixel e⁺ e⁺

e⁻ Outer pixel layers

layers

r3≈72mm r4≈85mm

Fibres

Two outer pixel layers:

• Reconstruct momentum

• 1Tesla→minpT ≈12MeV/c (limited by outer layer radius)

Scintillating fibres:

• σt<1ns

• Suppress accidental BG

• Charge ID

Mu3e Detector (3)

Target µ⁺beam

Scintillating fibres

Inner pixel e⁺ e⁺

e⁻ Outer pixel layers Recurl pixel layers

Scintillator tiles

layers Tiles

Particles bend back in magnetic field:

• Dedicated ’recurl’ stations

• Improve momentum resolution (factor 5-10 improvement)

constraint on radius:

pixel size (minσp)

Recurl stations:

• Two pixel layers (same as central station)

• Scintillating tiles

• σt<100ps

• Suppress accidentals

HV-MAPS

High Voltage - Monolithic Active Pixel Sensor

• Commercially available technology

• Large area (2×2 cm²)

• High granularity (pixel size80×80µm²)

• Thin (50µm)

• Fast - charge collection via drift (HV,σt≈15 ns)

• High efficiency (>99%)

P-substrate

N-well E field

Particle

I.Peric, NIM A582(2007)876

SeeT-27.1andT-27.2

"Motivation"

A lot of data from detector:

• 10⁸µ/sstop and decay on target

≈same number of electrons

• O(10¹⁰) pixel hits/s + fibre & tile hits Need reconstruction:

• Fast (online tracking @ filter farm)

• →fast fit

Triplet fit

Track in mag.field:

• Helical trajectory

• Require minimum 3 hits

If no pixel uncertainty and no energy loss:

• Triplet - trajectory with Multiple Scattering (MS) in middle point

• One parameter - curvaturer(momentump)

• MS angles -ϕM S(r), λM S(r) Fit - minimizeχ² (scattering angle):

• χ²=ϕ²_{M S}(r)/σ²_{M S}+λ²_{M S}(r)/σ²_{M S}

• No analytical solution

• Small MS angles→linearization around known solution (circle inxy-plane)

ϕM S

y x

hit 1 hit 2 hit 3 B

NIM A844(2017)135

Track fit

Track/Segment:

• Sequence of triplets

• 3D radius:

• Minimize combinedχ²

• Simple solutionr=

Pri/σi²

1/σ²i

where ri - individual triplet solution (weighted average)

Note:

• Theoretically individual triplets can be fitted in parallel and then combined.

• In practice start from seed triplet and then add more hits.

triplet 1

triplet 2

Reconstruction: triplets

Hits

Fibres

combine hits

Fake triplets (red) Truth (MC) triplets

(black)

Combine hits of first 3 layers:

• 10 hits per layer per event (50 ns)

• O(1K) triplet combinations

• Factor 50 reduction with geometrical selections

• 10⁸ triplet fits each second Result:

• Collection of triplets (seeds)

• Fake rate≈1(1 fake per truth track)

Reconstruction: short tracks

r z

Make short tracks:

• Use triplets as seeds

• Estimate hit at last layer

• Lookup inϕ/z window

• Combine 4 hits (triplet + hit)

• 2 triplets (2 shared hits)

• Fit (weighted average) O(10) short tracks

• Fake rate≈1.0%

Reconstruction: long tracks

long 8-hit track (2 short tracks)

long 6-hit track (short + 2 hits)

Long (6- and 8-hit) tracks:

• Combine short track with pair of hits or another short tracks

• Fake rate≈3.7%

• ≈0.5%true random combinations

• Rest - hits from same tracks, different turns

Acceptance & efficiency

Full Geant4 simulation of Mu3e detector

• Decay: µ⁺→e⁺νν (≈5 decays within frame)

• 50 ns frame (event size) Reconstruction efficiency:

• Acceptance: ǫacc≈80%

• Require minimum 4 hits (1 per layer)

• minpT, etc.

• Short tracks: εS ≈95%·εacc

• Geometrical andχ² cuts

• Long tracks: εL ≈80%·εS

• Used for analysis (vertex fit, etc.)

Reconstruction efficiency: long tracks

−1.5 −1 −0.5 0 0.5 1 1.5

[rad]

λ

0 10 20 30 40 50 60

p [MeV/c]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Target µ⁺beam

Scintillating fibres

Inner pixel e⁺ e⁺

e⁻ Outer pixel layers Recurl pixel layers

Scintillator tiles

layers (polar angle) minpT

≈10MeV/c End of recurl

stations

Service areas between stations

Momentum resolution

Short tracks(4 hits)

• hσpi ≈1.4MeV/c

• Depends linearly on momentum

Long tracks (6 and 8 hits)

• hσpi ≈0.2MeV/c

• minσp≈100KeV/c

−5 −4 −3 −2 −1 0 1 2 3 4 5 [MeV/c]

- pmc

prec 0

0.05 0.1 0.15 0.2 0.25 106

×

Long tracks σp≈0.2MeV/c

Short tracks σp≈1.4MeV/c

0 10 20 30 40 50

[MeV/c]

pmc 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

[MeV/c]pσ

minσp≈100KeV/c (pmindepends onλ)

Sensitivity

• Vertex fit (3 long tracks and/or short track)

• Fit invariant mass

• Better tracking→narrow mass distribution

• With current design and10¹⁵µ/s: SES≈2·10⁻¹⁵

2] [MeV/c mrec

96 98 100 102 104 106 108 110

2Events per 0.2 MeV/c

4

10− 3

10− 2

10− 1

10−

1 10 102

at 10-12

eee

→ µ

at 10-13

eee

→ µ

at 10-14

eee

→ µ

at 10-15

→ eee µ ν

ν eee

→ µ

Bhabha +Michel

muons/s muon stops at 108

1015

Mu3e Phase I

Questions

2

] [MeV/c m

96 98 100 102 104 106 108 110

2

Events per 0.2 MeV/c

−4

10

3

10

10

10

1 10 10

at 10

eee

→ µ

at 10

→ eee µ

at 10

eee

→ µ

at 10

eee

→ µ ν

ν eee

→ µ

Bhabha +Michel

muons/s muon stops at 10

10

Mu3e Phase I