Mauricio Barbi University of Regina TRIUMF Summer...

Calorimetry Calorimetry -- 11

Mauricio BarbiUniversity of Regina

TRIUMF Summer InstituteJuly 2007

Some Literature

1. “Detector for Particle Radiation”, Konrad Kleinknecht, Cambridge University Press

2. “Introduction to Experimental Particle Physics”, Richard Fernow, Cambridge University Press

3. “Techniques in calorimetry”, Richard Wigmans, Cambridge University Press4. Particle Data Group (PDG): http://pdg.lbl.gov/

Thanks to Michele Levin (INFN and PaviaUniversity) for letting me use some of his material and examples in these lectures

Principles of CalorimetryPrinciples of Calorimetry(Focus on Particle Physics)(Focus on Particle Physics)

Lecture 1:Lecture 1:i. Introductionii. Interactions of particles with matter (electromagnetic)iii. Definition of radiation length and critical energy

Lecture 2:i. Development of electromagnetic showersii. Electromagnetic calorimeters: Homogeneous, sampling.iii. Energy resolution

Lecture 3:i. Interactions of particle with matter (nuclear) ii. Development of hadronic showers iii. Hadronic calorimeters: compensation, resolution

Introductionàà http://http://en.wikipedia.org/wiki/Calorimeteren.wikipedia.org/wiki/Calorimeter:

– A calorimeter is a device used for calorimetry– Calorimetry is the science of measuring the heat generated or absorbed in a chemical reaction

or physical process.

à The word Calorimeter comes from the Latin calor meaning heat, and from the Greek metrymeaning to measure.

à A primitive calorimeter was invented by Benjamin Thompson (17th century): “When a hot object is set within the water, the system's temperature increases. By measuring the

increase in the calorimeter's temperature, factors such as the specific heat (the amount of heat lost per gram) of a substance can be calculated.” (http://www.bookrags.com/Calorimeter)

Bomb calorimeter

IntroductionSpecific heat is the amount of heat per unit mass required to raise the temperature by one Kelvin:

Q = heat added (energy)c = specific heatm = mass∆T = change in temperature

tcmQ ∆=

0.20.84Glass0.190.79Granite0.492.05Ice (-10 C)

14.186Water0.582.4Alcohol(ethyl)

0.0330.14Mercury0.09250.387Zinc0.03210.134Tungsten0.05580.233Silver0.03050.128Lead0.03010.126Gold0.0920.38Brass

0.09230.386Copper0.02940.123Bismuth0.2150.9Aluminum

c in cal/gm Kc in J/gm KSubstance

How to measure the energy of a particle?

Let’s consider that we have a calorimeter with 1 liter of water as absorber. Using the formula and table from previous slide, let’s solve the following problems?

What is the effect of a 1 GeV particle (e.g., at LHC) in the calorimeter?

This is a far too small temperature change to be detected in the calorimeter.

New techniques of detection are needed in particle physics.

Introduction

KcM

ET

water

14108.3 −×=×

=∆

IntroductionStill at Still at http://http://en.wikipedia.org/wiki/Calorimeteren.wikipedia.org/wiki/Calorimeter:à In particle (and nuclear) physics, a calorimeter is a component of a

detector that measures the energy of entering particles

IntroductionMain goals:ð Provide information to fully reconstruct the 4-vector pµ= (E,p) of a particleð Complementary to tracking detectors at very high energies:

ð Provide particle ID based on different energy deposition pattern for different particles species (e/p, etc)ü Though neutrinos are not directly detected, they can be identified from the missing

energy needed for energy conservation to hold

ð Segmentation of th calorimeter can also provide space coordinates of particles. Time information also possible with high resolution achievable

ð Usually important in removing background (cosmic rays, beam spills, etc)

energymissingmeasureddirectly

==

+=

miss

vis

missvis

EE

EEE

pp

? pEE

E∝∝ :chambers drifiting;

1)( :rsCalorimeteσ

IntroductionBasic principles:ð Sensitive to both charged

(e±, µ±, p±, etc) and neutral particles (γ, p0, etc)

ð Total energy absorptionü Particle is “completely destroyed”

Destructive processð The mechanism evolves as:ü Entering particle interact with matter

ü Energy deposition by development of showers of decreasingly lower-energy particles produced in the interactions of particle with matter

ü Electromagnetic showers à produced by electromagnetic processes

ü Hadronic showers à produced by hadronic processes (+ EM components)

ü The energy of the particles produced in the showers is converted into ionization or excitation of the matter which compounds the calorimeterà energy loss

ð The calorimeter response is proportional to the energy of the enteringparticle (note the statistical process in the previous item)

IntroductionCalorimeter is a complicate device: ð Particle has to be completely absorbed in order to have its

energy fully detectedØ Depends on detector material, its size and geometry

ð Several things happen during this processØ Showers are product of competing physics interactions between particle and

matter ü Again, this depends on detector material

ð Particle ID and energy measurement through development of showers or (with exception of muons)Ø Statistical processes à fluctuations à detector resolutionØ Depends on the energy of the particle, calorimeter uniformity, etcØ Detector material, its size and geometry to fully contain the showers

ð Different calorimeter types for different physics goalsØ Faster response? Better energy resolution? Spatial coordinates? Hadronic

particles? EM particles? Etc…..

Introductionq More about EM interaction of particle with matter in this

lecture

q Development of showers andenergy resolution in the next lecture

detec to rs absorbers

d

EM shower in a sampling calorimeter

eK

eL

e

γ

γ

θ

atomAtomic electron

φ

Free electron

Compton scattering

IntroductionSome applications of calorimetry in particle physics

Ø Basic mechanism used in calorimetry in particle physics to measure energy

Ø Cherenkov light

Ø Scintillation light

Ø Ionization charge

IntroductionNeutrino physicsØ Super-Kamiokande (SK) - JapanØ Measurement of neutrino oscillationsØ Water as active materialØ Energy measurement through Cherenkov

radiation

~12K PMTs50K metric ton of water

IntroductionUltra high energy cosmic rayØ The Pierre Auger Observatory (world’s largest calorimeter)Ø Measure charged particles with E > 1019 eVØ Atmosphere as the calorimeterØ Surface detectors to

measure energy and shower profile

3000 Km2

Air shower

16K water Cherenkov detectors

IntroductionCollider experimentsØ ZEUS at HERA e-p collider, GermanyØ Study the proton structure and confront QCD predictionsØ Uranium-scintillator sampling calorimeterØ Energy measured using scintillating light

Rear calorimeter

Central tracking

Forward calorimeter

Barrel calorimeter

IntroductionCollider experimentsØ ATLAS at LHC p-p collider, SwitzerlandØ Search for Higgs, SUSY particles, CP violation, QCD, etcØ Liquid Argon/Pb (EM) and Cu (or W) (Hadron) sampling CalorimeterØ Energy measured using ionization in the liquid argon

Solenoid Forward Calorimeters

Muon DetectorsElectromagnetic Calorimeters

EndCap Toroid

Barrel Toroid Inner Detector Hadronic Calorimeters Shielding

Interactions of Particles with MatterWe have seen that the calorimeter is based on absorptionØ It is important to understand how particles interact with matterØ Several physics processes involved, mostly of electromagnetic natureØ Energy deposition, or loss, mostly by ionization or excitation of matter

One can initially separate the interactions into two classes

Ø Electromagnetic (EM) processes (this lecture):Ø Main photon interactions with matter: Ø Compton scatteringØ Pair ProductionØ Photoelectric effect

Ø Main electron interactions with matter:Ø BremsstrahlungØ IonizationØ Cherenkov radiation (not covered in this lecture)

Ø Hadronic processes (next lecture): more complicate business than EMà nuclear interactions between hadrons (charged or neutral) and matter

Interactions of Particles with MatterInteractions of PhotonsInteractions of Photons

For a beam of photons traversing a layer of material (Beer-Lambert’s law):

a = µ/? is called mass absorption coefficient.

Also,

? = a-1 [g/cm2] = photon mass attenuation length

( )X?µµx eIeII(X) −− == 00

][cmµ

]cmg[?xX

]cmg [?

[cm]x

I

-1

2

3

0

t coefficien absorptionlinear

thicknessmass

material theofdensity

layer theof thickness

intensity beam initial

=

==

=

==

?XeII(X) −= 0?XeP −−= 1

Probability that the photon will interact in thickness X of material

?µx

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPhoton attenuation length for different elemental absorbers versus photon energy

Note the different patterns for different elements à different response to photons as a function of the photon energy

Why? à Next slide

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorptionTotal cross-section s for photon absorption is related to the total mass attenuation length ?:

Several processes contribute to the total cross-section:

The “+…” in the above expression includes: Ø Rayleigh scattering, where the atom is neither ionized or excitedØ Photonuclear absorption

ANA

?s

1=

number sAvogrado'mol 10 99(47) 141 6.022N

]molg[ material theof mass AtomicA1-23

A ==

=

productionpair epair

scatteringCompton Compeffect ricPhotoelectp.e.

-+=

==

+++=

e

...ssss pairCompp.e. Therefore, different processes contributes with different attenuations:

Aii N

As

?1

=

... pair, Comp, p.e.,=i

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCross-section for photon absorption

à Since a calorimeter has to fully absorb the energy of an interacting photon:à Important to understand the cross-sections as a function of the photon energy in

different materialà Will ultimately define the geometry and composition of a calorimeter

à The cross-section calculations are difficult due to atomic effects, but there are fairly good approximations:à Depend on the absorber materialà Depend on the photon energy

Let’s then visit some of the processes cited in the previous slide

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPhotoelectric effect

à Can be considered as an interaction between a photon and an atom as a whole

à Can occur if a photon has energy Eγ > Eb(Eb = binding energy of an electron in the atom).

Ø The photon energy is fully transferred to the electron

Ø Electron is ejected with energy T = Eγ - Eb

à Discontinuities in the cross-section due to discreteenergies Eb of atomic electrons(strong modulations at Eγ=Eb; L-edges, K-edges, etc)

à Dominating process at low γ’s energies ( < MeV ).à Gives low energy electrons

−+ +→+ e)(Xion (X) atomγ

e-

X+X

p.e. cross-section in Pb

Eγ

Kleinknecht

Interactions of PhotonsInteractions of PhotonsPhotoelectric effect

à Cross-section:

Let (reduced photon energy)

For eK < e < 1 ( eK is the K-absorption edge):

For e >> 1 (“high energy” photons):

s p.e goes with Z5/e

Interactions of Particles with Matter

2cmE

ee

?=

eTh

Kp.e. sZa

es 54

7

21

32

=

eZaprs e

Kp.e.

14 542=

p.e. cross-section in Pb

Eγ

eK

eL

e = 1eK

radiuselectron Classical r

constant) structure (fine,137

1

)(Thomson 38

e

2

=

=

=

a

prs eeTh

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering

à A photon with energy Eγ,in scatters off an(quasi-free) atomic electron

à A fraction of Eγ,in is transferred to the electron

à The resulting photon emerges with Eγ,out < Eγ,in

and at different direction

Using conservation of energy and momentum:

The energy of the outgoing photon is:

, where

Eγ

)E(EEEcm

? ?,out?,in?,out?,in

e −−=2

1cos

2cm

Ee

e

?,in=?)e(

EE ?,in

?,out cos11 −+=

eK

eL

e

γ

γ

θ

atomAtomic electron

φ

Free electron−+ +→+ e)(Xion (X) atomγ

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsCompton scattering

à The energy transferred to the electron:

Two extreme cases of energy loss:à θ ≈ 0 : Eγ,out ≈ Eγ,in ; Te ≈ 0

ð No energy transferred to the electron

à Backscattered at θ = p :

Compton edge

?)e(?)(e

cmEET e?,out?,ine cos11cos12

2

−+−

=−=

1221

2

>>→+

= , for ecm

e

EE e?,in

?,out

eK 1for ,22

1121

221

2 2

,,

22 >>−=

−→

+=

+= ε

ε γγcmEE

eeE

eecmT e

inin?,inee

Eγ

e = 1eK

Eγ,

out/ E

γ,in Coherent scattering

(Rayleigh)

Incoherent scattering(electron is removed from atom)

Eγ ,in [MeV]

http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm

Interactions of Particles with MatterInteractions of PhotonsInteractions of Photons

Compton scatteringTotal Compton cross-section per electron given by Klein-Nishina (QED) (1929):

.

Two extreme cases:

e << 1 :

à Backward-forward symmetry in θ distribution

e >> 1 :

à θ distribution peaks in the forward direction

Cross-section per atom:

( )( )

++

−++

+−

++

+

= 222

2131

21ln21

21ln1

21121

2ee

e)(e

eee

e)(e

eprs e

eComp

( )εσσ 21−= eTh

eComp

( )

+= ε

εσσ 2ln

211

83 e

TheComp

eComp

atomicComp Zσσ ≈

Includes coherent and incoherent scattering

Incoherent scattering only

http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm

Interactions of PhotonsInteractions of PhotonsPair Production

à An electron-positron pair can be created when (and only when) a photon passes by the Coulombfield of a nucleus or atomic electron à this isneeded for conservation of momentum.

Threshold energy for pair production atEγ = 2mc2 near a nucleus.Eγ = 4mc2 near an atomic electron

à Pair production is the dominant photon interaction process at high energies. Cross-section from production in nuclear field is dominant.

First cross-section calculations made by Bethe and Heitler using Born approximation (1934).


nucleus eenucleus? +→+ −+

Z

e+

e-

γ + e-à e+ + e- + e-

γ + nucleusà e+ + e- + nucleus

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production (Attenuation length)The interesting energy domain is that of several hundred MeV or more, . The cross- section per nucleus is:

à Does not depend on the energy of the photon, but

à Mass attenuation length for pair creation (check few slides ago):

or

Accurate to within a few percent down to energies as low as 1 GeV

X0 is called radiation length and corresponds to a layer thickness of material where pair creation has a probability P = 1 – e-7/9 ≈ 54%

≈

31

22 183ln

97

4Z

aZrs enpair

31

137

Ze >>

2Zs npair ∝

===3

1220

0 183ln4

1 where,

1971

ZaZrNA

XX

sA

N?

eA

npair

Anpair

079

X?npair =

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production

Photon pair conversion probability

P=54%

097

1 XX

eP−

−=

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production (Attenuation Length)Along with Bremsstrahlung (more later), pair production is a very important process in the development of EM showers à X0 is a key parameter in the design of a calorimeter

There are more complicate expressions for X0 in the literature:

(PDG, http://pdg.lbl.gov)

Lrad is similar to the expression for X0 in the previous slide L’rad replaces 183Z-1/3 by 1194Z-2/3

f(z) is an infinite sum which can be approximate to

Where a = aZPDG also gives a fitting function:

( )[ ]radradA

e LZf(Z))LZA

NarX ′+−=− 221

0 4

−+−+

+= 642

22 00200083003690202060

11

a.a.a..a

af(Z)

+

= 20287ln1

716cm

g

Z)Z(Z

AX

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsPair Production

For compound mixtures:

Where,

wj = weight fraction of each element in the compound

j = “jth” element

http://pdg.lbl.gov

∑=j j

j

X

w

X0

1

Interactions of Particles with MatterInteractions of PhotonsInteractions of PhotonsSummary

http://pdg.lbl.gov

productionpair pair

scatteringCompton Compeffect ricPhotoelectp.e.

-

pairCompp.e.

ee

...ssss

+=

==

+++=

Rayleighscattering

Compton

Pair production

Photoeletric effect

Michele Livan

Energy range versus Z for more likely process:

Interactions of Particles with MatterInteractions of ElectronsInteractions of ElectronsIonization (Fabio Sauli’s lecture)

For “heavy” charged particles (M>>me: p, K, p, µ), the rate of energy loss (or stopping power) in an inelastic collision with an atomic electron is given by the Bethe-Block equation:

δ(ß?) : density-effect correction

C: shell correction

z: charge of the incident particle

ß = vc of the incident particle ; γ = (1-ß2)-1/2

Wmax: maximum energy transfer in one collision

I: mean ionization potential

−−−

=−

gcm

MeVZC

dßI

Wcmßz

AZ

cmrNdxdE e

eeA 2)(22

ln2 22

max222

2

222 βγ

γβπ

http://pdg.lbl.gov

Interactions of Particles with MatterInteractions of ElectronsInteractions of ElectronsIonizationFor electrons and positrons, the rate of energy loss is similar to that for “heavy”charged particles, but the calculations are more complicate:à Small electron/positron massà Identical particles in the initial and final stateà Spin ½ particles in the initial and final states

k = Ek/mec2 : reduced electron (positron) kinetic energyF(k,ß,γ) is a complicate equation

However, at high incident energies (ß≈1)à F(k) ≈ constant(next slide)

−−−

+=−

gcm

MeVZC

kF

cmI

)(kkßA

ZcmrpN

dxdE

e

eeA 2),,(2

2ln

12

22

2

222 δγβ

Interactions of ElectronsInteractions of ElectronsIonizationAt this high energy limits (ß≈1), the energy loss for both “heavy” charged particles and electrons/positrons can be approximate by

Where,

The second terms indicates that the rate of relativistic rise for electrons is slightly smaller than for heavier particles


−+

∝− B?A

Icm

dxdE e ln

2ln2

2

A Belectrons 3 1.95heavy charged particles 4 2

Interactions of ElectronsInteractions of ElectronsBremsstrahlung (breaking radiation)

A particle of mass mi radiates a real photon while being decelerated in the Coulomb field of a nucleus with a cross section given by:

à Makes electrons and positrons the only significant contribution to this process for energies up to few hundred GeV’s.


EE

mZ

dEd

i

ln2

2

∝σ mi

2 factor expected since classically radiation2

2

=∝

ii m

Fa

32

1037 ×≈

=

e

µ

µ

em

m

dEds

dEds

Interactions of ElectronsInteractions of ElectronsBremsstrahlung

The rate of energy loss for high energy electrons ( k >> 137/Z1/3 ), is giving by:

Recalling from pair production

à

The radiation length X0 is the layer thickness that reduces the electron energy by a factor e (≈63%)


EZA

NaZr

dxdE A

e

≈−

31

183ln4 22

=3

1220

183ln4

1

ZaZrNA

Xe

A

00

0

Xx

eEE(x)XE

dxdE −

=⇒−=

Interactions of ElectronsInteractions of ElectronsBremsstrahlung

Radiation loss in lead.


http://pdg.lbl.gov

Interactions of ElectronsInteractions of ElectronsBremsstrahlung and Pair production

à Note that the mean free path for photons for pair production is very similar to X0

for electrons to radiate Bremsstrahlung radiation:

à This fact is not coincidence, as pair production and Bremsstrahlung have very similar Feynman diagrams, differing only in the directions of the incidentand outgoing particles (see Fernow for details and diagrams).

In general, an electron-positron pair will each subsequently radiate a photon by Bremsstrahlung which will produce a pair and so forth à shower development.


079

X?pair =

Interactions of ElectronsInteractions of ElectronsBremsstrahlung (Critical Energy)Another important quantity in calorimetry is the so called critical energy. One definition is that it is the energy at which the loss due to radiation equals that due to ionization. PDG quotes the Berger and Seltzer:


( ) ionc

Bremcc )(E

dxdE)(E

dxdE

.ZMeVE =+

≈ when21

800http://pdg.lbl.gov

http://pdg.lbl.govOther definition à Rossi

Summary of the basic EM interactionsSummary of the basic EM interactions


e+ / e-

§ Ionisation

§ Bremsstrahlung

§ Photoelectric effect

§ Compton effect

§ Pair production

E

E

E

E

E

γ

dE

/dx

dE

/dx

σ

σ

σ

Z

Z(Z+1)

Z5

Z

Z(Z+1)

Calorimeters?Curiosity à Primitive calorimeter invented by Benjamin Thompson (17th century):

“We owe the invention of this device to an observation made just before the turn of the nineteenth century by the preeminent scientist Benjamin Thompson ( Count Rumford). While supervising the construction of cannons, Rumford noticed that as the fire chamber was bored out, the metal cannons would heat up. He observed that the more work the drill exerted in the boring process, the greater the temperature increase. To measure the amount of heat generated by this process, Count Rumford placed the warm cannon into a tub of water and measured the increase in the water's temperature. In doing so, he simultaneously invented the science of calorimetry and the first primitive calorimeter. In simplest terms, a modern calorimeter is a water-filled insulated chamber. When a hot object is set within the water, the system's temperature increases. By measuring the increase in the calorimeter's temperature, a scientist can calculate such factors as the specific heat (the amount of heat lost per gram) of a substance. Another application of calorimetry is the determination of the calorific value of certain fuels--that is, the amount of energy obtained when fuel is burned. Engineers burn the fuel completely within a calorimeter system and then measure the temperature increase within the device. The amount of heat generated by this burning is indicative of the fuel's calorific value. “ (http://www.bookrags.com/Calorimeter)

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