Spring, 2009 Phys 521A 1

Charged particle tracking

Spring, 2009 Phys 521A 2

Charged particle tracking

• Detectors provide position estimates of ionization deposits in either 2D or 3D

• Need to “connect the dots” to determine particle trajectories (tracks)

• Measure momentum trans-verse to a uniform magnetic field

• Detect particle position with a minimum of material (limit interactions, multiple Coulomb scattering)

• Occupancy, 2-track resolution

high point density

low point density

Spring, 2009 Phys 521A 3

Momentum measurement

• Often put detectors in a magnetic field to allow momentum measurement in the plane transverse to the field:– dp/dt = zevxB from which |pT| = zeRB

– For pT in GeV, pT = 0.3zRB, with R in meters, B in Tesla

• Full momentum requires additional measurement of track angle w.r.t. magnetic field

• Curvature is measured; for an arc section this corresponds to measuring the sagitta

• Uncertainty in curvature measurement κ set by detector

• Uncertainty in pt is then δpt = -0.15 z B δκ / κ2 soσ(pt) = pt

2 [σ(κ) / 0.15 z B], i.e. is proportional to pt2.

Spring, 2009 Phys 521A 4

Magnets

• Resolution criteria for charged particle momentum measurements often require strong (Tesla-scale), uniform magnetic fields over large volumes– Enormous physical forces robust mechanical structures– Need to contain field iron return yoke– Now almost always superconducting to reduce power

consumption and cooling requirements

• Geometries:– Fixed target – usually dipole field– Colliding beam – axial (at center), toroidal (at large radii)

• Material budget: magnet plus cryostat represent “dead” material, degrade resolution of external calorimeters– EM calorimeters often designed to sit inside magnet

Spring, 2009 Phys 521A 5

Spring, 2009 Phys 521A 6

Calibration

• Calibration needs– Electronics (gain, time offsets, noise thresholds)– Geometric (field distortions, mechanical tolerances, wire sag…)– Dedicated system required (e.g. a laser)?– Time variation of calibrations

• Once and for all (e.g., endplate hole positions, magnetic field mapping…)

• Continuous (atmospheric pressure, temperature…)• Sporadic (changes in gas mixture or HV settings…)

• Often takes years to get optimum resolution performance, and systematic errors due to calibration can still dominate the measurement of some track parameters (e.g. impact parameter)

Spring, 2009 Phys 521A 7

Alignment

• Bootstrapping calibration using real tracks usually needed; implies statistical uncertainty on calibration parameters systematic uncertainty on hit positions, often correlated between hits

• Alignment withother detectorsalso needed(rotations andoffsets)

Spring, 2009 Phys 521A 8

Calorimeters

Spring, 2009 Phys 521A 9

Electromagnetic calorimeters

• Calorimeters measure deposited energy; initial particle is destroyed

• Recall basic features of EM cascades– Bremsstrahlung and pair production in stages– Particle number grows exponentially until (E0/N) < EC

– Both N and deposited ionization from e± are proportional to E0

– Longitudinal development governed by radiation length X0

– Transverse shower size governed by multiple Coulomb scattering; parameterized using Moliere radius RM

• Two types of EM calorimeters:– Homogeneous (100% active medium)– Sampling (absorber and active layers interspersed)

• Physical size dictated by X0 of medium, so most use high-Z material

Spring, 2009 Phys 521A 10

Spring, 2009 Phys 521A 11

Homogeneous calorimeters

• Not finely segmented• Cost is often high • Issues with uniformity, surface properties (tot. int. refl.)• Measured quantity = light output in ~visible range• Two main types:

– Inorganic scintillators (e.g. CsI(Tl))• High light yield• Slow signal development (100s of ns)

– Cherenkov light (e.g. lead glass)• Lower yield (<0.1% relative to scintillators)• prompt signal

Spring, 2009 Phys 521A 12

Sampling EM calorimeters

• High-z absorber interspersed with sensitive element• Detect number of shower particles or ionization using scintillating

tiles or fibers, MWPC, liquid noble gases, solid state detectors• Flexible segmentation allows measurement of both longitudinal and

transverse shower development• Sampling fraction:

• Resolution:

detectors absorbers

d

E

d

NE sample

sample 1

0Xd

NN eesample

Spring, 2009 Phys 521A 13

Energy resolution

• Shower energy proportional to detected signal (energy or number of particles) σ(E)/E = a / √E

• Contrast with tracking in B field, where σ(pt) = C pt2

• In addition to statistical behavior, systematic uncertainties enter resolution– Shower leakage (lack of containment), gain calibration, non-

linearity of response σ(E)/E = b

– Electronic noise: not proportional to detected energy, so from this source σ(E)/E = c / E

E

cb

E

a

E

E

)(

Statistic fluctuations “Constant term”(calibration, non-linearity, etc

Noise, etc

Spring, 2009 Phys 521A 14

Typical EM energy resolution

• Homogeneous calorimeters:

• Sampling calorimeters:

EMEE

E )%255.7(

%21%32

4

EEE

Spring, 2009 Phys 521A 15

Electromagnetic Shower DevelopmentSome considerations on energy resolutionSome considerations on energy resolution

Energy leakage

Longitudinal leakage

More X0 needed to contain initiated shower

Lateral leakage

~ No energy dependence

EGS4 simulations

From Mauricio Barbi, TSI’07 lectures

Spring, 2009 Phys 521A 16

Spring, 2009 Phys 521A 17

Calorimeter reconstruction

• Transform ADC counts to energy (next slide)

• Form clusters from regions of contiguous energy deposit;– Many algorithms available, e.g. simple nσ noise cut, separate

cuts for cluster seed, surrounding cells (4/2/0…)– separation or not of local cluster maxima into sub-clusters…– Determine cluster position (energy-weighted sum)

• Additional corrections based on environment– Charged track pointing to cluster or not?– Cluster size/shape consistent with e/γ?

Spring, 2009 Phys 521A 18

Calorimeter calibration

• Electronic calibration – response to known input pulses, determine rms noise (pedestal), gain– Changes in time due to aging of sensors, electronics

• Absolute energy calibration: ADC counts / MeV, requires calibration source of known energy (can be from data)– Changes in time as active medium ages (radiation, chemical…)

• Correction for “pile-up” of ionizing radiation– Depends sensitively on response time of detector– Out-of-time energy from previous collisions, cosmic rays,

delayed decays of excited nuclei…– In-time multiple interactions (e.g. at LHC)