tracking - istituto nazionale di fisica nucleare · development of particle detectors, in...

Tracking

gianluigi cibinetto

Issue I Lecture 3

Outline

•  Introduction and terminology

•  Tracking devices

•  Tracking algorithms

•  Momentum resolution

high energy physics lab detection techniques - tracking 2

What is Tracking?

•  A coordinated system of hardware and software for detecting and measuring charged particles

•  A tool to visualize the trajectory of individual stable particles (and their unstable progenitors)

•  A connection between the quantum world of particles and the classical world of macroscopic instruments


History of tracking

•  1992 Nobel Prize, Georges Charpak "for his invention and development of particle detectors, in particular the multiwire proportional chamber"


•  Cloud Chamber 1936 Nobel Prize Carl Anderson "for his discovery of the positron”

•  1968 Nobel Prize, Luis Alvarez, "... hydrogen bubble chamber and data analysis”

Why Discuss Tracking

•  Tracks are the core of (most) analyses

•  Charged particle content of final state

•  Precise kinematic and vertex information

•  Tracks are required for everything else

•  Tracks are potential charged particles dEdx, DIRC, e identification, muons, neutrals, ...

•  Could also be background, scattering, fakes decays, bad calibration, software bugs,...

•  Analysis must take all these into account!


Tracking Terminology

•  Stable charged particles ∈ e, μ, π, K, P

•  Trajectory ≡ path of a charged particle (directional 1-D object in 3-space)

•  Tracking Detector ≡ highly-segmented detector capable of sensing a charged particle without greatly changing its P

•  Hit ≡ position measurement in a single active element of a tracking detector

•  Track ≡ collection of hits presumably from one particle, reconstructed to estimate the particle P and trajectory


A real example


Why do we need a magnet?

•  Magnet + tracking = magnetic spectrometer •  momentum ⇒ geometry (curvature) •  Requires a ~uniform B-field: solenoid •  Approximately constant field inside volume

–  Double windings at the end minimize distortions –  Iron contains return flux


B(0,0,L/2) = 0.5×B(0,0,0)

FB = qv×B

The Drift Chamber

•  5 m3 gas volume

•  Al Endplates

•  Inner (Be+Al) cylinder

•  Outer (CF) cylinder

•  Wires –  ~32 kNewtons tension –  ≤ 200μm sag

•  ~1% X0 total (active region)


Measuring the right time

•  Signal time depends on ionization (track) position

•  Field irregularities due to shaping wires

•  Asymmetric trajectory due to Lorentz force

•  Measured using tracking data in-situ. Translate time (TDC) to ‘distance to wire’ using a time to distance (T2D) function


DCH hits


dE/dx calibration

•  Use: –  p from Λ decay (p π-)

–  K from D* decay –  π from Ks decay

–  µ from µµγ events –  e from rad BhaBha events

•  Bethe Block parametrization


The Silicon Vertex Detector

•  340 double-sided Si wafers: ~1m2 Si

•  5 layers: independent tracker

•  Unique arch in outer layer

•  CF support structure 4% X0 total

•  ~90% of Ω

•  Mounted to the Be beam-pipe.


Silicon detectors are diodes

•  Doped bulk, Implants creates diode

•  Reverse-bias depletes conduction carriers from the bulk

•  Tracks ionize bulk –  electron-hole pairs

collected at implants –  charge collection and

amplification

•  Diode separation allows spatial signal –  resolution given by pitch,

charge sharing


The Success of Si Vertex Detectors

•  Standard industrial manufacturing

•  <1μm precision features on cm-scale wafers

•  Signals from both charge carriers

•  Charge drift distance ~ 100μm

–  geometric position reconstruction

•  Compatibility with IC electronics

•  Disadvantage: material (0.3 mm Si, 0.5% X0)


SVT readout and resolution

•  AToM (“A Time Over threshold Machine”) chip measures when signal is over threshold and how long (time over threshold)

•  Adjacent strips above threshold are clustered •  Cluster position from charge distribution

–  Diffusion + capacitive coupling allow interpolation: better resolution than pitch/√12


Tracking algorithms

•  Track Finding

•  Track Fitting


Track Finding

•  Track Finding = pattern recognition – Associate all hits from a single particle

•  Requirements – maximally efficient at finding tracks: some lost hits is OK

–  Low mis-association rate: single wrong hit can spoil resolution

•  Computationally affordable: combinatoric problem


Tracks looks obvious


But not at first


A common tracking strategy

•  Find tracks in Dch first –  Fewer background hits (especially outer layers) –  More redundancy (40 vs 5 layers) –  only tracks with Pt > 150 MeV

•  Add Svt hits to Dch tracks –  Improve impact parameter and angle resolution

•  Find Svt (low-Pt) tracks with remains

•  Add Dch hits to tracks found in Svt –  Improve momentum resolution


Issues with tracks reconstruction

•  Material effects –  Multiple scattering ~14MeV/P √X0 –  dE/dx (energy loss)

•  B field inhomogeneity

•  Trajectory needs more params –  2 angles + 1 curvature for materials: ~100 total - Equal number of

extra constraint –  Changes from track to track

•  Standard multi-variable fit is a poor match to the problem


Kalman Track Fitting

•  Progressive least-squares fit – Start with an initial estimate – Add measurements one-at-a-time, in order

–  Add (process) noise (= scattering, dE/dx) – Account for B Field inhomogeneities

•  Final result piecewise helix – position and momentum along track


Other uses of Kalman Fit

•  Track extrapolation (to IP and other detectors)

•  Pattern recognition

•  Add Svt (Dch) hits to Dch (Svt) tracks

•  Vertexing – Consider each track as a decay ‘hit’ – Combine tracks using Kalman formalism – Can fit an entire decay chain at once


Question

•  Which particle emits the most synchrotron radiation light when bent in a magnetic field? (Proton, muon electron).


Question

•  Which particle emits the most synchrotron radiation light when bent in a magnetic field? (Proton, muon electron).

•  Kalman filter can be used also for bremsstrahlung recovery algorithms.


Momentum resolution

•  Typical collider experiment: solenoid magnet (field lines parallel to beam axis)barrel and endcap detectors


•  Typical fixed-target experiment: dipole magnet (field lines orthogonal to beam axis) planar detection layers

Momentum measurement


Using sagitta •  Bending of elementary charge in a magnetic field

–  large radius -> weak bending -> large momentum

–  typically see only a small portion of the circle

–  measurement of momentum is equivalent to a measurement of the sagitta.


( ) )4/(7203.0)(

2

.

+⋅

⋅= N

BLpx

pp T

meas

T

T σσfor N equidistant measurements, one obtains (R.L. Gluckstern, NIM 24 (1963) 381)

( )T

T

TT

pBLs

pBLL

BpqBp

22

83.0

82cos1

3.022sin2

m)(T3.0)cGeV(

≈≈−=

⋅≈→≈=

⋅=→=

αραρ

αααρ

ρρ

( ) ( )2

.

223

23.

)(3.0

8)()()(BLpx

pp

BL

px

s

x

ss

pp T

meas

T

TTmeas

T

T ⋅∝

⋅

⋅===

σσσσσσ231

2xxxs +

−=

Multiple scattering effect


What is the contribution of multiple scattering to ?

Tpp)(σ

0

1045.0)(LXBp

pMS

T

=σ

TT

pxpp

⋅∝ )()(σ

σ

px MS 1)( 0 ∝∝θσ

remember

constant)(=

MS

Tppσ

More precisely:

, i.e. independent of p !

σ (p)/p

σ (p)/p

σ (p)/p

p

MS

meas. total error

Problem


Example:

pt = 1 GeV/c, L = 1m, B = 1 T, N = 10

σ(x) = 200 µm:

Assume detector (L = 1m) to be filled with 1 atm. Argon gas (X0 = 110m),

€

σ(p)pT

MS

≈

€

σ pT( )pT

meas.

≈

Bibliography "   Text books (a selection)

– C. Grupen, Particle Detectors, Cambridge University Press, 1996

– G. Knoll, Radiation Detection and Measurement, 3rd ed. Wiley, 2000

– W. R. Leo, Techniques for Nuclear and Particle Physics Experiments, Springer, 1994

–  R.S. Gilmore, Single particle detection and measurement, Taylor&Francis, 1992

– W. Blum, L. Rolandi, Particle Detection with Drift Chambers, Springer, 1994

– G. Lutz, Semiconductor Radiation Detectors, Springer, 1999

"   Review Articles –  Experimental techniques in high energy physics, T. Ferbel (editor), World Scientific, 1991.

–  Instrumentation in High Energy Physics, F. Sauli (editor), World Scientific, 1992.

– Many excellent articles can be found in Ann. Rev. Nucl. Part. Sci.

"   Other sources –  Particle Data Book (2010) http://pdg.lbl.gov/pdg.html

–  R. Bock, A. Vasilescu, Particle Data Briefbook http://www.cern.ch/Physics/ParticleDetector/BriefBook/

–  Proceedings of detector conferences (Vienna CI, Elba, IEEE, Como)

– Nucl. Instr. Meth. A high energy physics lab detection techniques - tracking 32

tracking - istituto nazionale di fisica nucleare · development of particle detectors, in...

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