Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part III)

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Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part III)

Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part III)

Peter LochPeter LochUniversity of ArizonaUniversity of Arizona

Tucson, ArizonaTucson, ArizonaUSAUSA

Peter LochPeter LochUniversity of ArizonaUniversity of Arizona

Tucson, ArizonaTucson, ArizonaUSAUSA

2P. LochP. Loch

U of ArizonaU of ArizonaFebruary 09, 2010February 09, 2010

Calorimeter Basics

Full absorption detectorFull absorption detector Idea is to convert incoming particle energy into detectable signalsIdea is to convert incoming particle energy into detectable signals

Light or electric currentLight or electric current Should work for charged and neutral particlesShould work for charged and neutral particles

Exploits the fact that particles entering matter deposit their energy in particle Exploits the fact that particles entering matter deposit their energy in particle cascadescascades Electrons/photons in electromagnetic showersElectrons/photons in electromagnetic showers Charged pions, protons, neutrons in hadronic showersCharged pions, protons, neutrons in hadronic showers Muons do not shower at all in generalMuons do not shower at all in general

Principal design challengesPrincipal design challenges Need dense matter to absorb particles within a small detector volumeNeed dense matter to absorb particles within a small detector volume

Lead for electrons and photons, copper or iron for hadronsLead for electrons and photons, copper or iron for hadrons Need “light” material to collect signals with least lossesNeed “light” material to collect signals with least losses

Scintillator plastic, nobel gases and liquidsScintillator plastic, nobel gases and liquids Solution I: combination of both features Solution I: combination of both features

Crystal calorimetry, BGOCrystal calorimetry, BGO Solution II: sampling calorimetrySolution II: sampling calorimetry

3P. LochP. Loch


Calorimeter Basics (2)

Sampling calorimetersSampling calorimeters Use dense material for absorption power… Use dense material for absorption power…

No direct signal No direct signal

……in combination with highly efficient active material in combination with highly efficient active material Generates signalGenerates signal

Consequence: only a certain fraction of the incoming energy is directly Consequence: only a certain fraction of the incoming energy is directly converted into a signalconverted into a signal Typically 1-10%Typically 1-10%

Signal is therefore subjected to sampling statisticsSignal is therefore subjected to sampling statistics The same energy loss by a given particle type may generate different signalsThe same energy loss by a given particle type may generate different signals Limit of precision in measurementsLimit of precision in measurements

Need to understand particle responseNeed to understand particle response Electromagnetic and hadronic showersElectromagnetic and hadronic showers

4P. LochP. Loch


Electromagnetic Cascades in Calorimeters

Electromagnetic showersElectromagnetic showers Particle cascade generated by Particle cascade generated by

electrons/positrons and photons in electrons/positrons and photons in mattermatter

Developed by bremsstrahlung & pair-Developed by bremsstrahlung & pair-productionproduction

Compact signal expectedCompact signal expected Regular shower shapesRegular shower shapes

Small shower-to-shower fluctuationsSmall shower-to-shower fluctuations Strong correlation between longitudinal Strong correlation between longitudinal

and lateral shower spreadand lateral shower spread

RD3 note 41, 28 Jan 1993

0

20

0

Approximation good within 2% for all materials

radiation length

Helium (5% low)

Shower depth scales in :716.4

g cm278

1 ln

except Sh Molierower width scales

21 Me

e i Ra

1

d

V

n :ii

M

M

S

c

AX

Z ZZ

ER X

E

X

R

Z

0

00.0265 1.2

(90% energy containment radius)

with 21 Me

.2800 MeV

800 MeV1.

V

2

s

cEZ

X

E

X Z

C. Amsler et al. (Particle Data Group), Physics Letters B667, 1 (2008) and 2009 partial update for the 2010 edition

5P. LochP. Loch









RD3 note 41, 28 Jan 1993C. Amsler et al. (Particle Data Group), Physics Letters B667, 1 (2008) and 2009 partial update for the 2010 edition

1

0 0

max

( ), with

( )

1 1.0 ln ,

with and

0.5 for 0.5 for

a bt

j

c

j

dE bt eE b t x X

dt a

t a b y C

y E E

eC

6P. LochP. Loch









RD3 note 41, 28 Jan 1993

G.A. Akopdzhanov et al. (Particle Data Group), Physics Letters B667, 1 (2008) and 2009 partial update for the 2010 edition

( ) ( )1( ) ( )E r E rdE

a E e b E eE dr

P. Loch (Diss.), University of Hamburg 1992

7P. LochP. Loch


Hadronic Cascades in Calorimeters

Hadronic signalsHadronic signals Much larger showersMuch larger showers

Need deeper developmentNeed deeper development Wider shower spreadWider shower spread

Large energy losses without signal Large energy losses without signal generation in hadronic shower generation in hadronic shower componentcomponent Binding energy lossesBinding energy losses Escaping energy/slow particles Escaping energy/slow particles

(neutrinos/neutrons)(neutrinos/neutrons) Signal depends on size of Signal depends on size of

electromagnetic componentelectromagnetic component Energy invested in neutral pions lost Energy invested in neutral pions lost

for further hadronic shower for further hadronic shower developmentdevelopment

Fluctuating significantly shower-by-Fluctuating significantly shower-by-showershower

Weakly depending on incoming Weakly depending on incoming hadron energyhadron energy

Consequence: non-compensationConsequence: non-compensation Hadrons generate less signal than Hadrons generate less signal than

electrons depositing the same energyelectrons depositing the same energy 30 GeV electrons

30 GeV pions


8P. LochP. Loch


Shower Features Summary

ElectromagneticElectromagnetic CompactCompact

Growths in depth ~log(E)Growths in depth ~log(E) Longitudinal extension scale is radiation Longitudinal extension scale is radiation

length length XX00

Distance in matter in which ~50% of Distance in matter in which ~50% of electron energy is radiated offelectron energy is radiated off

Photons 9/7 XPhotons 9/7 X00

Strong correlation between lateral and Strong correlation between lateral and longitudinal shower developmentlongitudinal shower development

Small shower-to-shower fluctuationsSmall shower-to-shower fluctuations Very regular developmentVery regular development

Can be simulated with high precisionCan be simulated with high precision 1% or better, depending on features1% or better, depending on features

HadronicHadronic Scattered, significantly biggerScattered, significantly bigger

Growths in depth ~log(E)Growths in depth ~log(E) Longitudinal extension scale is interaction Longitudinal extension scale is interaction

length length λλ >> >> XX00 Average distance between two inelastic Average distance between two inelastic

interactions in matterinteractions in matter Varies significantly for pions, protons, Varies significantly for pions, protons,

neutronsneutrons Weak correlation between longitudinal Weak correlation between longitudinal

and lateral shower developmentand lateral shower development Large shower-to-shower fluctuationsLarge shower-to-shower fluctuations

Very irregular developmentVery irregular development Can be simulated with reasonable Can be simulated with reasonable

precisionprecision ~2-5% depending on feature~2-5% depending on feature

9P. LochP. Loch


Electromagnetic Signals

Signal features in sampling Signal features in sampling calorimeterscalorimeters Collected from ionizations in Collected from ionizations in

active material active material Not all energy deposit Not all energy deposit

converted to signalconverted to signal Proportional to incoming Proportional to incoming

electron/photonelectron/photon C.f. Rossi’s shower model, C.f. Rossi’s shower model,

Approximation B Approximation B Only charged tracks contribute

to signal Only pair-production for

photons Energy loss is constant

Signal proportional to Signal proportional to integrated shower particle pathintegrated shower particle path

Stochastical fluctuationsStochastical fluctuations Sampling characterSampling character

Sampling fractionSampling fraction Describes average fraction of Describes average fraction of

deposited energy generating deposited energy generating the signalthe signal

max

c0

act

0c

c

ive0

v

Integrated shower particle track length:

2 2( )

3 3ln2

(only charged tracks ionize!)Number of crossings of active material:

Deposited energy contributing to the signal:

t

T N t dtE

T

TN

E

T

dE

E

active

is 0

vis 0

0

Stochastic nature of sampling:

( ) ( )

d dEdx E

dx

N N E

N N E

E N E

10P. LochP. Loch


Signal Formation: Sampling Fraction

Characterizes sampling Characterizes sampling calorimeterscalorimeters Ratio of energy deposited in active Ratio of energy deposited in active

material and total energy depositmaterial and total energy deposit Assumes constant energy loss per Assumes constant energy loss per

unit depth in materialunit depth in material Ionization onlyIonization only

Can be adjusted when designing the Can be adjusted when designing the calorimetercalorimeter MaterialMaterial choices choices ReadoutReadout geometry geometry

Multiple scatteringMultiple scattering Changes sampling fractionChanges sampling fraction

Effective extension of particle path Effective extension of particle path in matterin matter

Different for absorber and active Different for absorber and active materialmaterial

Showering Showering Cannot be included in sampling Cannot be included in sampling

fraction analyticallyfraction analytically Need measurements and/or Need measurements and/or

simulationssimulations

activevis active

dep active absorb

active

active

absorber

absorber active

eractive absor

ac

b

tive ab

r

e

e

sorb r

(with Rossi's assumption

and )

dE dx

dE dx dE

dE dx cons

dE dx dES

E dE

t

dE d

dx d dE

x const

x

d

d

x

d

d d

11P. LochP. Loch













active

active absorbe absorbr er active active

vis

absorb r

dep

ecos cosd d

dE dx

dE dx

E

x

S

dE d

E

C. Amsler et al. (Particle Data Group), Physics Letters B667, 1 (2008) and 2009 partial update for the 2010 edition

00

0

Approximation:

13.6 MeV1 0.038 ln

particle velocityparticle momentum

with particle charge numbermaterial thickness in radiation length

(good to 11% for singly charged parti

xz x X

cp X

cpzx X

10

cles with 1 for all

matter and within 10 100)x X

12P. LochP. Loch













vis 0

dep 0

0

( )

( ) is the calorimeter signal from test beamsor simulation, converted to energy units.

E A ES

E E

A E

Showering changes the electron sampling fraction mostly due to the strong dependence of photon capture (photo-effect) on the material (cross-section ~Z5) leading to a non-proportional absorption of energy carried by soft photons deeper in the shower!


1S

5 GeV

30 GeV

80 GeV

Electrons

13P. LochP. Loch


Signal Extraction

Example: charge collection in noble Example: charge collection in noble liquidsliquids Charged particles ionizing active Charged particles ionizing active

medium when traversing itmedium when traversing it Fast passage compared to electron Fast passage compared to electron

drift velocity in mediumdrift velocity in medium Electrons from these ionizations are Electrons from these ionizations are

collected in external electric fieldcollected in external electric field Similar to collection of 1-dim “line of Similar to collection of 1-dim “line of

charges” with constant charge densitycharges” with constant charge density Resulting (electron) current is base of Resulting (electron) current is base of

signalsignal Positive ions much slowerPositive ions much slower Can collect charges or measure currentCan collect charges or measure current

Characteristic featuresCharacteristic features Collected charge and current are Collected charge and current are

proportional to energy deposited in proportional to energy deposited in active mediumactive medium

Drift time for electrons in active Drift time for electrons in active mediummedium Determines charge collection timeDetermines charge collection time Can be adjusted to optimize Can be adjusted to optimize

calorimeter performancecalorimeter performance

visd 0

d ion

( ) ; ( ) ; 2e e

e

N e N e EQ tt I tt N

t E

Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part III)

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Transcript of Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part III)