Italo- Hellenic School of Physics The Physics at LHC

(1)

Lucia Silvestris Lucia Silvestris

INFN INFN - - Bari Bari

Italo- Hellenic School of Physics The Physics at LHC

Martignano (Le) Italy

Tracking

Tracking at at

LHC LHC

(2)

9--14 June 200514 June 2005 Tracking at LHC L. Silvestris

Outline Outline

– Large Hadron Collider

• The machine

• Physics Program

– LHC Detectors

– Tracking Detector

• ATLAS & CMS tracking systems

– Tracking Reconstruction &

Performances

• Track Reconstruction Algorithms

• Examples for High Level Trigger Studies

– Summary

(3)

Lecture 1

(4)

Large Hadron Collider &

Physics Program

(5)

Will be installed in the existing LEP tunnel

– need B = 8.4 T dipole magnets (limits energy)

E_cm = 14 TeV

– ~7 times higher than present highest energy machine (Tevatron: 2 TeV)

Under construction: pilot run in June 2007 L ~ 10 ³²cm^-2s^-1

2008 L ~ 2x 10 ³³ cm^-2s^-1

Design luminosity: L = 10³⁴ cm^-2s^-1

– ~100 times larger than present machines (Tevatron: 10³² cm^-2s^-1)

Energy and luminosity gives LHC an accessible energy range extended by a factor of 10 compared to the Tevatron.

Search for:

– new massive particles up to m ~ 5 TeV – rare processes with small cross-sections

One year at L = 10³⁴ cm^-2s^-1 →→→→ ∫ Ldt ≈ 100 fb^-1

Large Hadron Collider

(6)

L L arge arge H H adron adron C C ollider ollider

(7)

L L arge arge H H adron adron C C ollider ollider

27 km around

(8)

L L arge arge H H adron adron C C ollider ollider

27 km around

(9)

L L arge arge H H adron adron C C ollider ollider

27 km around

(10)

pp Cross Section and Pile

pp Cross Section and Pile - - up up

Operating conditions:

1) A “good” event containing a Higgs decay + 2) ~20 extra “bad” (minimum bias) interactions

(11)

Interactions/s:

• Lum = 10³⁴ cm^–2s^–1 = 10⁷ mb^–1 Hz

• σ_inel(pp) = 70 mb

• Interaction Rate, R = 7×10⁸ Hz Events / beam crossing:

• ∆t = 25 ns = 2.5×10^–8 s

• Interactions/crossing = 17.5 Not all proton bunches are full:

• Approximately 4 out of 5 are full

• Interactions/“active” crossings = 17.5 × 3564/2835 = 23

pp Cross Section and Pile

pp Cross Section and Pile - - up up

(12)

Interactions/s:

• Lum = 10³⁴ cm^–2s^–1 = 10⁷ mb^–1 Hz

• ∆t = 25 ns = 2.5×10^–8 s

H →ZZ* → 2e2µ H →ZZ* → 2e2µ

pp Cross Section and Pile

pp Cross Section and Pile - - up up

(13)

Interactions/s:

• Lum = 10³⁴ cm^–2s^–1 = 10⁷ mb^–1 Hz

• ∆t = 25 ns = 2.5×10^–8 s

H →ZZ* → 2e2µ H →ZZ* → 2e2µ

µµµµ µµµµ

e e

All tracks with p_T > 1 GeV

pp Cross Section and Pile

pp Cross Section and Pile - - up up

(14)

Pile Pile - - up up

“In-time” pile-up: particles from the same crossing but from a different pp

interaction

Long detector response/pulse shapes:

– “Out-of-time” pile-up: left-over

signals from interactions in previous crossings

– Need “bunch-crossing identification”

(15)

Physics Program Physics Program

Cross-sections of physics

processes vary over many orders of magnitude:

– inelastic: 10⁹ Hz

– b b production: 10⁶-10⁷ Hz – W → l ν: 10² Hz

– t t production: 10 Hz

– Higgs (100 GeV/c²): 0.1 Hz – Higgs (600 GeV/c²): 10^–2 Hz

Only 100 ev/sec on tape for ALL interesting events

→ Selection needed: 1:10^10-11

Trigger is a challenging task at LHC

In tomorrow’s lecture, how Tracking detector influence this task.

_

LHC High Luminosity

High Luminosity

(16)

99--14 June 200514 June 2005 Tracking at LHCTracking at LHC L. SilvestrisL. Silvestris 10

Physics Program Physics Program

Tracking detectors essential not only for tracking but also for Trigger and particle identification and energy flow in the full

energy range

S.M. Higgs search MSSM Higgs Bosons

A, H, H^± cross-section ~ tg²β

Best sensitivity from A/H → ττ, H^± → τν

mm_h_h < 135 < 135 GeVGeV

mm_A_A ≈≈ mm_H_H ≈m≈m_H_H_±_± at large at large mm_A_A

(17)

Physics Program Physics Program --22

• Search for SUperSYmmetric (SUSY) particles and New Physics

• Heavy Flavour and precision physics: CP violation of B hadrons; rare B decays; top mass & couplings, W mass &

couplings

• Heavy Ions physics

(18)

Experiments at the LHC Experiments at the LHC

Two super-conducting magnet rings in the LEP tunnel

Opal

Delphi

SPS

PS

LEP - LHC

Aleph

L3

LHCb Alice

CMS

ATLAS

Experiments:

ATLAS A Toroidal LHC ApparatuS (Study of Proton-Proton collisions)

CMS Compact Muon Solenoid (Study of Proton-Proton collisions)

ALICE A Large Ion Collider Experiment (Study of Ion-Ion collisions)

LHCb Study of CP violation in B-meson decays at the LHC

(19)

LHC detector &

Tracking Detector

(20)

LHC Detector Requirements LHC Detector Requirements

Very good electromagnetic calorimetry for electron and photon identification (H->gamma gamma)

Good hadronic calorimeter jet reconstruction and missing transverse energy measurement;

Efficient and high-resolution tracking for particle

momentum measurements, b-quark tagging, τ tagging, vertexing (primary and secondary vertex)

Excellent muon identification with precise momentum reconstruction

(21)

A Generic Multipurpose LHC Detector A Generic Multipurpose LHC Detector

µ

e

n p ν

γ

About 10 λ are needed to shield the muon system from hadrons produced in p-p collision

(22)

Gas detectors Gas detectors

Most of gas detectors are based on the principle of proportional detector:

– Multi-Wire Proportional chamber (MWPC) – Drift chambers

– Straw tubes

– Cathode strip or pad chambers – Time Projection Chamber (TPC) – Micro-Strip Gas Chamber (MSGC)

(23)

MWPCMWPC

Cathode planes Anode wires

• Many proportional counters in one gas volume

• The anode wires act as independent detectors

• Typical dimensions

– cathode - anode ~ 1 cm – wire pitch d = 1 - 2 mm – wire diameter 20 - 50 µm

• Spatial resolution d/√12 = 300 - 600 µm Charpak 1968

(24)

Drift chambers Drift chambers

Proportional chamber with a large anode wire pitch (few cm)

– coordinate - measuring the time of arrival

– typical speed of electron drift up to ~ 5 cm/µs

– time resolution of 1ns gives spatial precision of 50µm – can be improved using higher gas pressure

Different configurations of cathode electrodes in order to achieve a constant field towards anode

Various geometries used:

– planar, cylindrical, jet chamber

Worse timing and load characteristics compare to MWPC’s, left-right ambiguity

(25)

Straw tubes Straw tubes Type of a drift chamber

– composed of individual straws (diameter of ~ 5mm) with an anode wire in their center

– no common gas volume, tolerates higher load

– a coarse time measurement gives spatial resolution about 150µm – can be used to construct a `continuos tracker’ packing many layers

of straw tube together

(26)

Silicon detectors Silicon detectors Principle of detection

– to produce one pair of charge carrier in silicon (electron - hole pair) one needs only 3.6 eV energy compare to ~ 30 eV in a gas – density of silicon is much higher than that of a gas

• MIP produces about 100 electron - hole pairs per 1µm of silicon

• to produce this charge in gas one needs cm’s

– a typical silicon detector is produced from a plate of high resistivity n-doped silicon of ~ 300µm thickness

– on one side a thin p-doped layer is produced

(27)

Solid state detectors Solid state detectors

All LHC experiment will use trackers based on silicon devices

– silicon micro-strip detectors – silicon pixel detectors

– silicon drift detectors

Development of radiation hard silicon detectors (RD42) and cryogenic silicon detectors (RD39)

Another development is diamond tracking detectors (RD42)

– due to their potentially better radiation hardness

(28)

Silicon detectors Silicon detectors Principle of detection

– a reverse bias voltage is applied (i.e. positive potential on n-side, negative on on p-side) in order to

• fully deplete the silicon of free charge carriers

• to produce the electric field for drifting electron and holes to opposite surfaces where a read out structure is organized

– a MIP produces in a typical detector a charge of about 25 000 electrons

• no amplification inside the detector (unlike in gas detectors) is needed

– benefiting from well developed silicon technology different readout structures can be produced

(29)

Silicon strip detectors Silicon strip detectors

– on one side of silicon plate a thin (a few µm) Al strips are produced with pitch of ~ 50 µm

– the charge collected on the strip is integrated in electronics and read out or as an amplitude or as an digital information

– position resolution is for digital readout strip pitch/√12 (~ 15 µm for 50 µm pitch) or slightly better for amplitude readout

– strips can produced on both sides on the silicon plate in order to

measure two coordinates simultaneously - double sided silicon detectors Al strips

Al layer

n p

(30)

Silicon Pixel detectors Silicon Pixel detectors

instead of strips an Al pixel structure is produced on one side of the silicon plate

typical dimensions ~ 50 x 400 µm²

– at least in one dimension resolution as for strip detector

problem is how to read it out, to each pixel an amplifier circuitry has to be connected

– use of special designed readout chip bump-bonded on the detector silicon

– development of monolithic detectors with CCD type of electronics

(31)

Silicon Pixel detectors Silicon Pixel detectors

Advantages:

– a true two dimensional micro-detector – very low noise (small capacitance)

– relatively fast detector (depends on multiplexing)

– excellent pattern recognition capability for high particle density

Disadvantages:

– very fragile

– challenging technology

bump bonds

(32)

What LHC means on Tracking…

Luminosity

– low-luminosity: 10³³cm^-2s^-1 (first 3 years) – high-luminosity: 10³⁴cm^-2s^-1

–

• ~20 minimum bias events per bunch crossing

• ~1000 charged tracks per event

Radius: 2cm 10cm 25cm 60cm N_Tracks/(cm²*25ns) 10.0 1.0 0.10 0.01

Severe radiation damage to detectors

H → bb event

@ high luminosity Challenging requirements for the Tracking system

(33)

What LHC means on Tracking… H → bb event

Luminosity

–

H → bb event

(34)

What LHC means on Tracking… H → bb event

Plus 22 minimum bias events

Luminosity

–

H → bb event

(35)

Tracker Requirements Tracker Requirements

Efficient & robust Pattern Recognition algorithm

– Fine granularity to resolve nearby tracks

– Fast response time to resolve bunch crossings

Ability to reconstruct narrow heavy object

– 1~2% p_t resolution at ~ 100 GeV

Ability to operate in a crowded environment

– Nch/(cm²*25ns) = 1.0 at 10 cm from PV

Ability to tag b/τ through secondary vertex

– Good impact parameter resolution

Reconstruction efficiency

– 95% for hadronic isolated high p_t tracks – 90% for high p_t tracks inside jets

Ability to operate in a very high radiation environment

– Silicon detectors will operate at -7°C ÷ -10°C to contain reverse annealing and limit leakage current

(36)

Different Strategies....

ATLAS Inner Detector

ID inside 2T solenoid field

Tracking based on many points Precision Tracking:

• Pixel detector (2-3 points) 5-25 cm

• Semiconductor Tracker – SCT (4 points) 25 –50 cm

Continuous Tracking:

(for pattern recognition & e id)

• Transition Radiation Tracker – TRT (36 points) 55-105cm

(37)

46m Long, 22m Diameter, 7’000 Ton Detector

2.3 m x 5.3 m Solenoid ~ 2 Tesla Field ~ 4 Tesla Toroid Field

ATLAS

(38)

(39)

• High accuracy momentum measurement

made in the central tracker AND in the

external muon system;

• The external system identifies and provide also the muon trigger.

ATLAS

air core toroid

Toroid magnets: allow magnetic

Coverage down to |η| = 2.7 B=0.5T

(40)

Different Strategies…

5.4 m

Outer Barrel (TOB) Inner Barrel (TIB)

End cap (TEC) Pixel

2,4 m

Inner Disks (TID)

volume 24.4 m³

running temperature – 10 ⁰C dry atmosphere for YEARS!

CMS has chosen an

all-silicon configuration CMS Tracker

Inside 4T solenoid field

Tracking rely on “few” measurement layers, each able

to provide robust (clean) and

precise coordinate determination

Precision Tracking:

• Pixel detector (2-3 points)

• Silicon Strip Tracker (220 m²) – SST (10 – 14 points)

Inner Barrel (TIB)

2,4 m

Inner Disks (TID)

(41)

CMS

22m Long, 15m Diameter, 14’000 Ton Detector 13m x 6m Solenoid: 4 Tesla Field

→ Tracking up to η ~ 2.4

ECAL & HCAL Inside solenoid Muon system in return yoke

First muon chamber just after solenoid

→ Extended lever arm for p_t measurement

5.4 m

End cap (TEC) Pixel

2,4 m

Inner Disks (TID)

volume 24.4 m³

CMS has chosen an

Precision Tracking:

Inner Barrel (TIB)

2,4 m

Inner Disks (TID)

(42)

5.4 m

End cap (TEC) Pixel

2,4 m

Inner Disks (TID)

volume 24.4 m³

CMS has chosen an

Precision Tracking:

Inner Barrel (TIB)

2,4 m

Inner Disks (TID)

(43)

High accuracy momentum measurement made in the central tracker;

The external system identifies (and trigger) muon tracks and improves the momentum

Resolution for very high Pt muons

B=4T

Muon Chambers

CMS

Central Solenoid

Central Detector Calorimeter

return yoke

Muon Chambers

(44)

ATLAS & CMS Tracking Performances ATLAS & CMS Tracking Performances

ATLAS ID

CMS µ-System

ATLAS µ-System ATLAS

CMS

Higgs New Physics

(45)

The ATLAS Pixel Detector The ATLAS Pixel Detector

3 barrel layers*

– r = 5.05 cm (B-layer), 9.85 cm, 12.25 cm 3 pairs of Forward/Backward disks

– r= 49.5 cm, 60.0 cm, 65.0 cm

– ~ 2% of tracks with less than 3 hits – Fully insertable detector

Pixel size:

– 50 µm x 300 µm (B layer) & 50 µm x 400 µm

~ 2.0 m² of sensitive area with 8 x 10⁷ ch Hit resolution:

– r-φ σ ~ 12 µm – r-z σ ~ 60 µm

Modules are the basic building elements

– 1456 in the barrel + 288 in the endcaps – Active area 16.4 mm x 60.8 mm

– Sensitive area read out by 16 FE chips each serving a 18 columns x 160 row pixel matrix

* Several changes from TDR

(46)

The ATLAS Pixel Detector The ATLAS Pixel Detector

3 barrel layers*

– r = 5.05 cm (B-layer), 9.85 cm, 12.25 cm 3 pairs of Forward/Backward disks

– r= 49.5 cm, 60.0 cm, 65.0 cm

– ~ 2% of tracks with less than 3 hits – Fully insertable detector

Pixel size:

– 50 µm x 300 µm (B layer) & 50 µm x 400 µm

~ 2.0 m² of sensitive area with 8 x 10⁷ ch Hit resolution:

– r-φ σ ~ 12 µm – r-z σ ~ 60 µm

– 1456 in the barrel + 288 in the endcaps – Active area 16.4 mm x 60.8 mm

– Sensitive area read out by 16 FE chips each serving a 18 columns x 160 row pixel matrix

* Several changes from TDR

(47)

The ATLAS SCT Detector The ATLAS SCT Detector

Hit resolution:

–r-φ σ ~ 16 µm –r-z σ ~ 580 µm

5.6 m 1.53 m

1.04 m

Barrel: 4 layers

• pitch ~ 80 µm

• radii: 284 – 335 – 427 – 498 mm

• 2112 modules, with 2 detectors per side, read out in the middle

498 mm

modules, with 2 detectors per side,

Endcap: 9 wheel pairs

• pitch 70 - 80 µm

• 3 types of modules

Inner (400)

Middle (640 incl. 80 shorter)

Outer (936) All detectors are double-sided

(40 mrad stereo angle)

• 4088 modules

• 61 m² of silicon

• 6.3 x 10⁶ channels

Hit resolution:

–r –r

(48)

The ATLAS SCT Detector The ATLAS SCT Detector

Hit resolution:

–r-φ σ ~ 16 µm –r-z σ ~ 580 µm

5.6 m 1.53 m

1.04 m

Barrel: 4 layers

• pitch ~ 80 µm

• radii: 284 – 335 – 427 – 498 mm

• 2112 modules, with 2 detectors per side, read out in the middle

498 mm

modules, with 2 detectors per side,

Endcap: 9 wheel pairs

• pitch 70 - 80 µm

• 3 types of modules

Inner (400)

Middle (640 incl. 80 shorter)

Outer (936) All detectors are double-sided

(40 mrad stereo angle)

• 4088 modules

• 61 m² of silicon

• 6.3 x 10⁶ channels

Hit resolution:

–r –r

(49)

The CMS Pixel Detector The CMS Pixel Detector

3 barrel layers

– r = 4.1 – 4.6 cm, 7.0 – 7.6 cm, 9.9 – 10.4 cm – ~ 60 x 10⁶ pixels

2 pairs of Forward/Backward disks – Radial coverage 6 < r < 15 cm

– Average z position: 34.5 cm, 46.5 cm

– Later update to 3 pairs possible (<z> ~ 58.2 cm) – Per Disk: ~3 x 10⁶ pixels

⇒ 3 high resolution space points for η < 2.2

Pixel size: 100 µm x 150 µm driven by FE chip

⇒ Hit resolution:

– r-φ σ ~ 10-20 µm

(Lorentz angle 23° in 4 T field) – r-z σ ~ 17 µm

– 800 in the barrel + 315 in the endcaps

10.4 cm

58.2 cm)

Occupancy is ~ 10^-4

Pixel seeding fastest starting point for track reconstruction despite the

extremely high track density

(50)

3 barrel layers

– r = 4.1 – 4.6 cm, 7.0 – 7.6 cm, 9.9 – 10.4 cm – ~ 60 x 10⁶ pixels

⇒ Hit resolution:

– r-φ σ ~ 10-20 µm

10.4 cm

58.2 cm)

(51)

3 barrel layers

– r = 4.1 – 4.6 cm, 7.0 – 7.6 cm, 9.9 – 10.4 cm – ~ 60 x 10⁶ pixels

⇒ Hit resolution:

– r-φ σ ~ 10-20 µm

10.4 cm

58.2 cm)

(52)

The CMS Silicon Strip Tracker The CMS Silicon Strip Tracker

Outer Barrel (TOB): 6 layers

• Thick sensors (500 µm)

• Long strips

Endcap (TEC): 9 Disk pairs

• r < 60 cm thin sensors

• r > 60 cm thick sensors

Inner Barrel (TIB): 4 layers

• Thin sensors (320 µm)

• Short strips

z view

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800

1000 1100 1200

6 layers 6 layers TOB TOB 4 layers 4 layers TIBTIB

3 disks TID 3 disks TID

Radius ~ 110cm, Length ~ 270cm

Radius ~ 110cm, Length ~ 270cm ηηηηηηηη~1.7~1.7

ηηηη~2.4ηηηη~2.4

9 disks TEC 9 disks TEC

Inner Disks (TID): 3 Disk pairs

• Thin sensors

Black: total number of hits Green: double-sided hits

Red: ds hits - thin detectors Blue: ds hits - thick detectors

(53)

Cell size & strip pitch Cell size & strip pitch

Efficient & clean track reconstruction is ensured provided occupancy below few %

SST SST

∆P_t/ P_t~ 0.1*P_t (P_t in TeV)

allows to reconstruct Z to µ⁺µ⁻ with

∆m_Z < 2GeV up to P_t ~ 500GeV Φ

ΦΦ Φ

Occupancy = Φ x pitch x strip length

At small radii need cell size < 1cm² and fast (~25ns) shaping time

This condition is relaxed at large radii 12 layers with (pitch/√12) spatial

resolution and 110 cm radius give a momentum resolution ofof



 



 



 



 



 



 



 



≈ 

∆

Tev p B

T L

m m

pitch p

p

1 4

1 . 1 12 100

. 0

2 1 1

µ

A typical pitch of order 100µm is required in the φ coordinate To achieve the required resolution

Strip length ranges from 10 cm in the inner layers to 20 cm in the outer layers.

Pitch ranges from 80µm in the inner layers to near 200µm in the outer layers

(54)

Cell size & strip pitch Cell size & strip pitch

Efficient & clean track reconstruction is ensured provided occupancy below few %

SST SST

∆P_t/ P_t~ 0.1*P_t (P_t in TeV)

allows to reconstruct Z to µ⁺µ⁻ with

∆m_Z < 2GeV up to P_t ~ 500GeV Φ

ΦΦ Φ

Occupancy = Φ x pitch x strip length

At small radii need cell size < 1cm² and fast (~25ns) shaping time

This condition is relaxed at large radii At small radii need cell size < 1cm² 12 layers with (pitch/√12) spatial resolution and 110 cm radius give a momentum resolution ofof



 



 



 



 



 



 



 



≈ 

∆

Tev p B

T L

m m

pitch p

p

1 4

1 . 1 12 100

. 0

2 1 1

µ

A typical pitch of order 100µm is required in the φ coordinate To achieve the required resolution

Strip length ranges from 10 cm in the inner layers to 20 cm in the outer layers.

Pitch ranges from 80µm in the inner layers to near 200µm in the outer layers

(55)

Lecture 2

(56)

Track Reconstruction

And Performances

(57)

Geometry Modeling Geometry Modeling

Pixel module

Support structures Support structures

Care has been taken to Care has been taken to model localized heavy model localized heavy material (e.g. Aluminum material (e.g. Aluminum

Cable paths

(58)

Geometry Modeling Geometry Modeling

Inter Connect Bus for signal distribution

Inter Connect Cards carrying opto electronic

Module support blocks connected to the cooling

Cooling pipe

Patch panel for opto fibers

Pixel module

Cable paths

(59)

Geometry Modeling Geometry Modeling

Inter Connect Bus for signal distribution

Inter Connect Cards carrying opto electronic

Module support blocks connected to the cooling

Cooling pipe

Patch panel for opto fibers

Interaction Length Radiation Length

Pixel module

Cable paths

(60)

Tracker Detector Response Tracker Detector Response

Simulated energy loss in the detector material is simulated in Geant4

A Simulated Hit basically knows only energy loss, detector unit, entry and exit point.

The energy is spread into the sensitive volume along the line connecting those points, allowing independent Landau Fluctuations.

Those charges are drifted to the detector surface, taking into account Lorentz angle and diffusion.

Noise charges are generated on a small subset of strips.

Charges are injected into the strips, taking into account interstrip Capacitive coupling (crosstalk).

Only some strips/pixels are selected based on a Zero Suppression algorithm.

SimHits Digis

Landau fluctuations

Lorentz angle and diffusion (less important) Injection

Zero Suppression

(61)

Lorentz

Lorentz angleangle

Detector usually collects the charge of the electrons

produced in primary ionization after some drifting in the detector (gas or silicon)

If the electron velocity (i.e. electric field E) is not parallel to the magnetic field B

– a Lorentz force in the direction ExB acts on the electron which – the electron deviates from its direction given by E

– in the absence of material electron will start to spiral

– when electron scatters on a molecule it forgot its direction and starts again in the direction of E

(62)

Lorentz

Lorentz angleangle

In this way the electron drift direction is deviated from its ideal direction E by some effective angle - Lorentz angle

– it is approx. ∝ B component perpendicular to E

Detector precision usually depends on the particle incident angle (from the normal)

Dependence of position resolution σ on incident angle α can be approximated

σ² = (σ₀ / cos α)² + const ( tan α − tan α_L)² , where α_L is the Lorentz angle

In order to get best resolution for normal incident tracks (i.e. maximal momentum) one can tilt the detector by

Lorentz angle

– but then is not easy to check for various asymmetries in alignment etc. by changing the direction of magnetic field

(63)

Lorentz

Lorentz DriftDrift

The treatment of Lorentz angle should been modeled using Laboratory measurements as well the dependence of

Lorentz Angle with bias irradiation, temperature is correctly Simulated.

Lorentz angle very important for hit resolution:

•Silicon: tan(θ_L) = 0.12 (~6° at 4T); resolution ~40µm

•Pixel: tan (θ_L) = 0.53 (~28° at 4T) ); resolution ~10µm

Several parameters can affect this parameterization:

•Irradiation conditions

•Temperature

•V bias

•Etc…

(64)

Raw data (

Raw data (DigisDigis) coming from detectors..) coming from detectors..

Raw data formation is not reconstruction

For the purpose of on-line reconstruction DAQ is like the post: the front ends send packets...

In the real experiment…

(65)

Reconstruction hierarchy Reconstruction hierarchy

Reconstruction is also hierarchical – Channel level

• e.g. Applying calibration – Detector unit level

• e.g. Finding clusters of strips or pixels in a silicon detector and assigning positions and errors to them – Detector system level

• e.g. Track reconstruction in the muon sytem – Global

• e.g. Combined muon system – inner tracker track reconstruction

(66)

Detector Unit Reconstruction:

Detector Unit Reconstruction: ClusterizationClusterization

This is the process that, given a set of Digis, recreates the cluster, with its position and estimated error.

Important quantities are:

position: the cluster position must be as close as possible to the Simulated hit position, not to bias the reconstruction

error: important for the tracking, to estimate how far a Reconstructed hit is from the expected track intersection with the detector surface

Digis RecHits

(67)

Tracker Performance: Resolution Tracker Performance: Resolution

The distance between SimHits and RecHits has been studied from all the detectors type and position

Typical behavior of Dx = |x_Sim-x_Rec|

Resolutions:

• 10 µm in the pixels

• 20-50 µm in the microstrip resolution

distance pull

(68)

Reconstruction chain (on demand

Reconstruction chain (on demand vsvs scheduled)scheduled) When a track finder is asked for tracks...

Track Finder

DetLayer recHits(region)

DetUnit

Clusterizer Detector

Partition

ReadOutUnit recHits

recHits Digis

Digis

On demand scheduled

(69)

Track Reconstruction Track Reconstruction

• Track reconstruction covers:

– Track finding, or “pattern recognition”: the attribution of hits to tracks

– Track fitting, or the determination of the track parameters from a given set of hits

(70)

Track Model Track Model

• In a uniform magnetic field, and in the absence of material, the solution to the equation of motion of a charged particle is a helix.

• Locally magnetic fields “are” uniform, and material

effects vanish, so a helix is also a local approximation, or linearization, of the general case

• A helix is a 5D object:

– Two positions – Two angles – Curvature

• The particular choice of parameterisation, while important, is beyond the scope of the lecture

(71)

Track State Parametrization Track State Parametrization

• A track state can be represented as a point in 5D linear space

• Not the whole story: a track is a measured (fitted)

object, and has uncertainties (errors) on it's parameters

• A track state is fully described by 5 parameters and a 5x5 symmetric error matrix

– Simply called “track state” or “trajectory state” from now on – This is what a global track fit gives as a result

(72)

Track State Propagation Track State Propagation

• A track state can be “propagated” from one place to another, e.g. From one measurement surface to the next.

• Propagation has a purely geometrical part, which is conceptually straightforward, but technically challenging

– Propagation of track parameters is computation of crossing point of a helix with a surface (e.g. Plane)

– Propagation of track errors involves 5D jacobians

• Physics effects, like energy loss and multiple scattering, can be added during propagation

NewState = propagate( SomewhereState, Surface)

(73)

Kalman Filter Kalman Filter

• Since a trajectory state is a local object, and so is a measurement (hit), is there a way to “update” a track state with a hit locally?

– Yes! (found in 1984...). The operation is called “Kalman update”

NewState = update( PredictedState, Hit)

The PredictedState must be on the same surface as the hit.

Essentially a weighted mean of the measurement and the projection of the predicted state, but affecting the whole state, not just the projection

(74)

Kalman Track Fit Kalman Track Fit

• Given some starting state, the track fit is just a sequence of propagations to measurement surfaces in the order in which they are crossed by the track, and updates

• After each update the track is fully fitted with all the hits used so far.

– Only the last updated state contains the full information. Previous states contain partial information.

• All the hits need not be known in advance, since they are used one at a time

– This property is at the basis of Kalman filter track finding

(75)

Is the Kalman Filter the last word?

• The Kalman filter is an optimal estimator of track parameters in case of

– Unbiased measurements with Gaussian errors – Gaussian process noise (multiple scattering etc.) – No outliers (hits that don't belong to the track)

• For the non-Gaussian generalisation based on adaptive algorithms exists and are used:

– Non-gaussian probability density functions (PDFs) of the hit positions don't hurt too much

– Non-gaussian noise (energy loss) can degrade the fit seriously (GSF) – Ambiguous situation require more advanced outlier treatment (DAF)

• The non-Gaussian generalisation are outside the scope of these lectures.

(76)

Kalman Track Finder Kalman Track Finder

• Given a starting state, hits can be found one at a time!

– After using (updating with) each hit, the track parameter

accuracy improves, and the compatibility window for the next hits gets smaller

• The Kalman filter is a track finder!

(77)

Seeding the Kalman Filter Seeding the Kalman Filter

• The Kalman filter requires a “starting state”

– With “infinite” errors, not to bias the fit

– With parameters close to the fitted ones, to work in the “linear regime”

• Starting the search for compatible hits from “zero

knowledge” would be a waist of CPU, since by definition All hits are compatible.

– A seed should constrain (at least roughly) all 5 parameters

(78)

Seed Generators Seed Generators

• A track seed can be

– internal to the tracker (e.g. A pair of hits and a beam spot constraint)

– External (e.g. From calorimetric cluster)

• For internal seeds, all hits of the tracker need not be used

– Usually a small number of “seeding layers” is chosen