Tracker - Hong Kong University of Science and Technology

Tracker

2

Tracker Functions

•  Charged particle trajectory •  Momentum measurement

•  Requires magnetic field •  Primary and secondary vertex determination •  Particle ID (in conjunction with other detectors):

•  e/γ discrimination •  Electron ID using transition radiation •  p/K/π separation using dE/dx vs p •  p/K/π separation in combination with Cerenkov angle

•  Integral part of energy flow measurement •  Trigger

3

Typical Tracking Detectors

•  Silicon •  Resolution ~ 10 µm (sometimes poorer to save cost) •  Very high granularity possible •  Expensive •  Small number of layers, N ~ 10 (CMS: 3 pixel + 10 strip pairs)

•  Wire chamber •  Resolution ~ 100 µm transverse, (much) worse along wire •  Poor granularity •  Relatively cheap •  Many hit layers, N ~ 100 (UA1: ~70; CDF: 96)

•  Time projection chamber •  Resolution ~ 100+ µm (in 3D) •  Good granularity because of 3D •  Very long integration time

-  ALEPH: ~50 µsec; ALICE: ~90 µsec -  CEPC bunch crossing ~ 3 µsec

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ILC: Silicon or TPC

Momentum Resolution

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Momentum Resolution

Intrinsic contributions determined by design •  Measurement precision •  Multiple scattering Other contributions that are in principle reducible •  Magnetic field map •  Detector alignment •  Pulse height slewing if timing used •  Etc

Enabled by proper design, construction

and monitoring

7

Three-Point Measurement

Assumptions: •  Uniform magnetic field B •  Three equally spaced measurement points •  L = bend plane distance from 1st to 3rd measurement •  Same precision σx for each measurement

(0,x1)

(L/2,x2)

(L,x3) s

s = x2 −x1 + x32

≈L2

8ρ=0.3BL2

8pTσ s = 3 2σ x

σ pT

pT=σ s

s= 8 3

2σ x pT0.3BL2#

$%

&

'( ≈ 9.8

σ x pT0.3BL2#

$%

&

'(

Units: •  B in Tesla •  L in m •  pT in GeV/c

pT means transverse to B field, not necessarily transverse to z.

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Gluckstern Paper

•  Considers the general case of unequal spacing between hits and different precision among the hits.

•  Formulae for direction as well as momentum resolution. •  Incorporated into codes such as TRKERR and others •  Optimized (but not necessarily practical) layouts •  For best momentum resolution •  For best direction

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N Equally Spaced Measurements with Fixed Precision

Assumptions: •  Uniform magnetic field B •  L = bend plane distance from 1st to Nth measurement •  Ignore multiple scattering, i.e. high-momentum limit

σ pT

pT≈

720N + 4

σ x pT0.3BL2"

#$

%

&' for large N

When you see (N+5) in some references, check

their definition of N!

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What Is Large?

10.1 (Gluckstern Large-N Formula for N=3) 9.8 (3-point formula)

Resolution scales as ~ 1/sqrt(N).

25 points ~2x better than 3-point measurement.

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CMS Example

•  N = 3 (pixel) + 10 (strip pairs) •  Not evenly spaced …

•  σx ~ 30 µm (average) •  B = 4 T •  L = 1 m

σ pT

pT≈

720N + 4

σ x pT0.3BL2"

#$

%

&'

=1.63×10−4 pT

~1.5% for 100 GeV

from

200

8 JI

NS

T 3

S08

004

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TPC and Silicon Tracker

•  TPC point resolution ~10x worse than silicon. •  Would need 100x more points to compensate.

•  May not be practical •  Common remediation:

•  More measurement points (but less than100x) •  Larger tracking volume

σ pT

pT≈

720N + 4

σ x pT0.3BL2"

#$

%

&'

13

Resolutions  are  well  estimated  using  Gluckstern  formula.    

Before  there  is  an  advanced  detector  design  including  realistic  supports  and  services,  detailed  simulation  can  be  misleading:  precision  achieved  beyond  Gluckstern  formula  is  compromised  by  inaccuracies  due  to  poorly  understood  material  inventory  etc.      

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Vector-Vector Approach

•  Uniform magnetic field B •  L = bend plane distance of field •  Assume vector measurements before and after B field

•  No measurements inside magnet •  Bend angle Δφ

Δφ =

0.3BLpT

Units: •  B in Tesla •  L in m •  pT in GeV/c •  φ in radian

Δφ

L φ1 φ2

Multiple Scattering

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From PDG

x is total path length, not path length L transverse to B field x = L / sin(λ) λ = angle between track and B field

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Multiple Scattering

s = 0.3BL2

8pT

σ s =σ splane=14 3

Lsinλ!

"#

$

%&θ0

=14 3

Lsinλ!

"#

$

%&×0.014β p

z Lsinλ!

"#

$

%& X0 1+ 0.038ln

Lsinλ!

"#

$

%& X0

(

)*

+

,-

./0

123

σ pT

pT=σ s

s≈840.0140.3 3

!

"#

$

%&×

Lsinλ!

"#

$

%&×1p

Lsinλ!

"#

$

%& X0 ×

psinλBL2

=0.052

B X0Lsinλ

Magnetic Field

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Magnet for Central / Barrel Tracking

Common magnetic field configuration: Solenoid •  Field parallel to beam direction •  Same amount of bend for + and - charge •  Sub-optimal for forward tracks •  Impact on circulating beams Experiment Solenoid Field (T) Tracker Radius (m)

ALEPH 1.5 1.8

DELPHI 1.2 2

L3 0.5 0.5

OPAL 0.4 2

SLD 0.6 1

CDF 1.4 1.4

D0 Upgrade 2 0.7

ATLAS 2 1

CMS 4 1

FCC-hh 6? 3?

UA1

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Magnet for Central / Barrel Tracking

•  UA1 dipole (now in T2K) •  B field in horizontal direction •  Better than solenoid for forward tracks •  Azimuthal variation in performance •  Potentially large impact on beams

•  What magnetic field??? •  UA2 •  D0 (early 1990’s)

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Magnet for Forward Tracking

ATLAS configuration: Toroid •  rmin of acceptance limited by coil and cryostat •  Different performance for + and - charge

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Magnet for Forward Tracking

LHCb configuration: Dipole •  η coverage down to beam pipe – engineering challenge for detector •  Same performance for + and - charge •  Potentially large impact on beams

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Other Considerations

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Track Trigger Capability

LHC •  Implemented in software High Level Trigger up to now

•  Capable of ~100 KHz input rate •  Output rate ~1 KHz for recording

•  Level-1 hardware trigger for Phase-2 upgrade •  Need to handle 40 MHz input

CMS Phase-2 upgrade •  Two closely layers for pT discrimination

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Track Trigger Capability

Lepton collider •  Low rates so software implementation is sufficient •  How about FCC-ee (with crab waist) peak luminosity up

to ~ 9 x 1036 cm-2 sec-1

• 

from http://tlep.web.cern.ch/content/machine-parameters

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Typical Approach to Pattern Recognition

•  Start with (small) subset of detector layers •  Select hits based on consistency with being a track

•  Subject to constraints as desired, such as IP pointing, minimum momentum and so on

•  Fit track •  Extrapolate / interpolate to other detector layers •  Attach additional hits and iterate

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TPC and Silicon Tracker

Figure from a person working on ILD detector concept

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Why It Is Important to Consider (in Early Design Stage)

•  Number of track candidates driven by all possible combinations of hits

•  Number of combinations scales as high power of Nhit •  Rapid increase at high hit rates •  Sensitive to hard-to-predict background rates •  Can be exacerbated by ill-conceived design

•  All track candidates, accepted or discarded, are computationally expensive

•  No easy fix once detector has been designed

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Crossing Angle in Projective Geometry

•  Projective detector elements (such as wires or strips) rely on second view to determine a “hit”

•  Orthogonal views, e.g. ATLAS and CMS muon chambers •  Number of ghost hits scales as n2

-  Potentially huge impact on pattern recognition

•  Small stereo angles, e.g. ATLAS and CMS silicon strips •  Fewer ghost hits

Real particle hit Ghost hit

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Multiple Projections

•  Further reduce ghost solutions •  Insurance against one projection not functioning

•  Back to two views

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Lookup Table: ATLAS FTK

•  Use simulation to define track patterns •  Match hits to pre-defined patterns •  Execution can be extremely fast

•  Custom hardware •  Massive parallelism

•  Reduced flexibility •  Custom hardware •  Pre-defined patterns

Not appropriate during detector design phase Can be an important tool in a real experiment

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TPC and Silicon Tracker

Figure from a person working on ILD detector concept

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Pattern Recognition in TPC and Silicon Tracker

Unfair visual comparison because •  3D in reality vs 2D in picture •  Measurement resolution much better than picture

granularity •  Algorithms much better than your eyes •  CMS provides existence proof that silicon trackers can

work, even in dense hit environments

Still, TPC-like tracker •  Pattern recognition likely to be simpler / more robust •  More efficient for short tracks

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Silicon Tracker Alignment

•  Many independent modules with typical size (1-2 cm)2

•  Large number of degrees of freedom •  Hierarchy of structures, e.g.

•  Tracker made up of cylindrical layers •  Each layer made up of staves •  Each stave made up of modules

•  If these structures are well constructed and well understood, constraints can be applied to reduce number of degrees of freedom •  Less special alignment data needed •  Faster algorithmic convergence •  Avoid false minimums

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Examples from Silicon Tracker Alignment

ATLAS IBL stave bowing •  Supposed to be free to slide on one end under differential

thermal expansion / contraction •  Actual behavior now understood in measurements on

mock-ups and FEA calculations Silicon sensors curling up •  Thin sensors to reduce multiple scattering •  Flat modules now like potato chip

Lessons learned •  “Reasonable” assumptions can be completely wrong •  Sufficient redundancy to characterize unforeseen problem

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TPC Field Distortion

Two sources of ions in TPC •  From tracks traversing TPC volume •  From avalanche in signal amplification region

•  Minimized with good design Ions drift very slowly to central electrode Distorting TPC drift field for subsequent tracks Elaborate alignment and calibration become an essential part of the TPC design.

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TPC Alignment and Calibration with Lasers ALEPH (see talk)

ALICE

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ILD Tracker

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Impact on Calorimeter

Material in central tracker leads to •  Photon conversion •  Hadronic interactions Minimize the material and to characterize what is there •  Care during design, construction and installation

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Interaction with Machine

•  Power pulsing at ILC •  Reduced heat load •  Air cooling instead of liquid •  Significant reduction of material

•  “Death zone” of beamstrahlung background

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Summary

•  Easy and reliable resolution from Gluckstern formula •  Detailed simulation when there is well developed design •  Pay attention to the many things that can wreck a good-

on-paper design, e.g. •  Material, including services •  Detector stability and alignment •  Pattern recognition and other software implications •  Trigger capability as necessary •  Impact on other systems

Think about the whole experiment