calorimetry in particle physics experimentspersonalpages.to.infn.it/~arcidiac/calo_2.pdf · r....

Calorimetry in particle physicsexperiments

Unit n. 3Detector response: energy resolution

Roberta Arcidiacono

R. Arcidiacono Calorimetria a LHC 2

Lecture Overview

● Energy Resolution of electromagnetic calorimeters– Stochastic term

– Noise term

– Constant term

– Additional contributions

● Energy Resolution of hadron calorimeters● Position and Time Measurement


Energy Resolution

The energy resolution of a calorimeter is determined by many factors:

1. Linearity of energy deposited in active medium (resolution vs energy)

2. Actual energy deposited in calorimeter (sampling fluctuations)

3. Leakage of energy outside the calorimeter

4. Noise (e.g. from electronics or pickup)

5. Ion or light collection efficiency

Usually, the dominant term in the energy resolution is due to sampling fluctuations which are Poissonian in nature.

σE

E= a

√E


Energy in EM Calorimeters

Measurement based on principle that E released by ionization/excitation is proportional to particle energy

Total track length T0 (g/cm2) X0 E0/Ec

ionization tracks signal produced by charged tracks ionization tracks signal produced by charged tracks E E00

Intrinsic energy resolution of IDEAL ECAL is due to fluctuations of the track length T0 → stochastic process


Energy Resolution of EM Calorimeters

Intrinsic resolution:

s (E) T0 s (E)/E 1/ T0 1/ E0

Energy resolution of REAL detectors:

stochastic noise

constant

σE

E= a

√E+ bE

+c


Energy Resolution of EM Calorimeters

CMS ECAL in test beam

stochasticnoiseconstant

σE

E= S

√E+ NE

+C


Stochastic Term a

Due to fluctuations related to the physical development of the shower

● homogeneous cal: term very small; in most cases s (E)/E s (E)/E is better than statistical expectation by a factor called Fano* factor

typical values ~ few%

● sampling cal: event by eventevent by event fluctuations in number of charged particles Nsample crossing the active layers

typical values ~ 5-20%

** energy loss in a collision not purely statistical. The process giving rise to each individual charge carrier is not independent as the number of ways an atom may be ionized is limited by the discrete electron shells. The net result is a higher energy resolution than predicted by purely statistical considerations.


Stochastic Term a

Sampling calorimeters:

➢ sampling fluctuations (d > 0.8)(d > 0.8)

the distance d can increase due to multiple scattering

detectors absorbers

d

in Pb:

➢ Landau fluctuations: due to large variations in number of collisions and energy transferred in ionization processes (thin detector layers)

x = thickness layer (g/cm2)σ LandauE

∝ 1

N sample

2

ln104⋅x

σsampleE

∝ 1

√N sample

∝ √d√E

d eff=d

⟨cosθ⟩→

σ sample

E∝√ d

⟨cosθ⟩1

√E ⟨cosθ⟩≈0.57


Stochastic Term a

➢ Landau fluctuations: Landau fluctuations:

Minimum ionizing particles traversing a thickness x of material give an asymmetric distribution of deposited energy e.

The tail on the high energy loss side is due to d rays which can lose all their energy in the sensitive layer.

Worsening of the sampling resolution depends on the thickness x of the active layer (almost negligible per x ~ 1 g/cm2)


Stochastic Term a

➢ Path Length fl uctuations:

From low energy electrons (large multiple scattering-large angle with shower axis )

Low contribution (~ Landau fluctuations) in calorimeters with dense material not too thin.


More on Landau fl uctuations

● Bethe-Bloch describes the average energy loss● Actual energy loss will scatter around the mean

value: fluctuation described by asymmetric distr. → the Landau distribution

● Difficult to calculate– parametrization exist in GEANT and some

standalone software libraries– Energy loss distribution is often used for

calibrating the detector


Landau Fluctuations

● Landau function

normalized deviation from most probable energy loss DE (which depends on the thickness x of the layer)

● Landau-Vavilov distribution is more accurate


Energy loss: average-most probable


Landau function

3 GeV electron in thin gap multi wired chamber


Landau fl uctuations for Si detectors


Noise Term b

Due to electronic noise of the readout chain, depends on detector technique and features of readout circuit

● 'light' cal'light' cal: when high-gain multiplication (phototube) is present in the first step of electronic chain, noise very small

● ''charge' cal:charge' cal: noise is larger due to preamplifiers

● noise can become dominant below few GeV noise-equivalent energy required << 100 MeV


Constant Term c

Calorimeter Quality factor!

Determined by energy independent contributions

● non-uniformities from instrumental effects

– detector geometry

– imperfections in mechanical structure

– temperature gradients

– radiation damage

● term very important at high energies

● typicallytypically 1 % 1 %


Additional Contributions

● Longitudinal leakage

● Lateral leakage

● Upstream energy losses

● Non-hermetic coverage

dominate at high energies for homogeneous calorimeters since stochastic term very small


Longitudinal Leakage


Energy in Hadron CalorimetersRecall: nuclear effects in hadronic showers produce a

form of invisible energy (delayed photons, soft neutrons, binding energy...), not detectable by practical instruments or with reduced efficiency.

Energy resolution subject to strong intrinsic fluctuations

Exitacion and break-up energy rarely detected

High energy muons and neutrinos which escape from calorimeter

Energy used to extract nucleons

Invisible energy fraction ~ 40% of energy lost in non-EM processes

EM interaction of secondaries (0)


Energy in Hadron CalorimetersResponse to EM and Hadronic incoming

particles:

εh = efficiency for detecting hadronic energy

εe = efficiency for detecting em energy

E vise =e E ; E vis

=e F0Eh F h E with F0=1−F h

E vis

E vise = e

−1

=1− 1−he F h


Energy in Hadron Calorimeters

In general εh and εe are different! Response to hadron:

The fraction of the energy deposited hadronically depends on the energy:

n(π 0 )≈ ln E (GeV ) − 4.6

Response becomes non-linear

also, event by event fluctuations of

Fh, F0 worsen energy resolutionworsen energy resolution

σ(E )E

= a

√E+b∣ϵeϵh−1∣

Rh=ϵh E h+ϵe E e

EhE

=1−F π0=1−k ln (E ) k≈0.1


Energy in Hadron Calorimeters

The relative response e/ is the keypoint to optimize the performance of hadron calorimeters.

If e/ = 1 , calorimeter is compensated

If e/ 1 (indeed > 1, since response to hadron will be lower), (non Gaussian) fluctuation of F0 will affect energy resolution AND the response will not be linear with energy

It is possible to tune the e/ response


Compensation of Hadron Calorimeters

HCAL are typically (up to now) sampling calorimeters

fsamp ~ small fraction of E

Compensation can happen via:Compensation can happen via:

● Choice of appropriate passive and active media to achieve full compensation between the EM and hadronic part of the shower, recovering part of the invisible energy ( less fluctuations in the hadronic component), and decreasing the electromagnetic contribution (less fluctuation from the EM component).

● Tuning of the sampling layers thickness.


Compensation of Hadron Calorimeters

increase εh : use Uranium absorber → amplify neutron and

soft � component by fission + use hydrogenous detector → high neutron detection efficiency

decrease εe : combine high Z absorber with low Z detectors.

Suppressed low energy � detection by increasing the

photoelectric cross-section (σphoto ∝ Z5), decreasing the EM

sampling fraction (less energy deposition in the active medium)

offline compensation : requires detailed fine segmented shower data → event by event correction.

large n-p elastic cross section:on average half of the

neutron kinetic energy is transferred


Compensation of Hadron CalorimetersExample:

238U as passive and scintillator as active media

238U:High Z decreases εe ; Slow neutrons induces fission in the 238U;

Fission energy compensates loss due to “invisible” energy carried by the slow neutrons

Slow neutrons can be captured by nucleus of 238U which emits a low energy γ’s. Can further recover the “invisible” energy

Scintillator:Slow neutrons lose their kinetic energy via elastic collisions with

nucleusThe lighter the nuclei, more energy transferred to the active mediumScintillators are rich in Hydrogen


Energy Resolution of Hadron Calorimeters

● For optimized HCAL:For optimized HCAL:

– e/ = 1, which guarantees linearity, E-1/2 scaling of resolution, best resolution

– compensation is possible by proper choice of active/passive/thickness of material

– Intrinsic best resolution ss(E)(E)/E /E 0.2 /0.2 /√√EE– sampling fluct. contributes as

ss(E)/E(E)/E∼∼0.09[0.09[∆∆E(MeV)/E(GeV)]E(MeV)/E(GeV)]1/2 1/2 where

∆E is the energy lost in one sampling cell


Position Measurement

Possible when calorimeter or readout is segmented

➔ The cell must be comparable in size to ( or smaller to) one rM (Moliere radius)

Fine segmentation in order to measure position with good accuracy

Techniques depends on the type of calorimeter

EX: in homogeneous segmented calorimeters Coordinates of incident e/ are measured by computing the center of gravity of the energy deposited in a NxN matrix of cells.


Position Resolution

EM homogeneous lead-glass calorimeter

25 GeV gamma

--- center block

__ average over block face

HCAL iron-scintillator calorimeter

__ 25 GeV pions

--- 40 GeV pions


Position Measurement

Ex: in CMS ECAL (cell size ~ 2x2 cm2)

XECAL = ∑wixi/∑wi sum on 3x3 or 5x5 matrix

wi = wo + log(Ei/ETOT) wo = 5

spatial resolution ~ 0.7 mm


Time Resolution

Time resolution depends on:

● the type of active materialtype of active material used (intrinsic time constant of the signal generation /collection)

● signal processingsignal processing technique

type speed resolution costionization moderate moderate moderatecrystal fast best expensive

scintillating fast moderate cheap

calorimetry in particle physics experimentspersonalpages.to.infn.it/~arcidiac/calo_2.pdf · r....

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