Transcript Calorimetry - 2 - University of Regina

Calorimetry - 2
Mauricio Barbi
University of Regina
TRIUMF Summer Institute
July 2007
1
Principles of Calorimetry
(Focus on Particle Physics)
Lecture 1:
i.
ii.
iii.
Introduction
Interactions of particles with matter (electromagnetic)
Definition of radiation length and critical energy
Lecture 2:
i.
Development of electromagnetic showers
ii.
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
2
Interactions of Particles with Matter
Interactions of Photons
Last lecture:
σ  σ p.e.  σ Comp  σ pair  ...
Photoeletric effect
p.e.  P hot oelectric effect
Comp  Comptonscat t ering
pair  e  e - pair product ion
Pair production
Energy range versus Z for more
likely process:
Rayleigh
scattering
Compton
http://pdg.lbl.gov
3
Michele Livan
Interactions of Particles with Matter
Interactions of Electrons
Ionization (Fabio Sauli’s lecture)
For “heavy” charged particles (M>>me: p, K, π, ), the rate of energy loss (or
stopping power) in an inelastic collision with an atomic electron is given by the BetheBlock equation:
2
  2me c 2  2 2Wmax 
dE
C
2
2 Z z
2



 2N A re me c
ln

2
β

δ
(


)

2



dx
A β 2  
I2
Z


cm 
MeV

g 

http://pdg.lbl.gov
(βγ) : density-effect correction
C: shell correction
z: charge of the incident particle
β = vc of the incident particle ;  = (1-β2)-1/2
Wmax: maximum energy transfer in one collision
I: mean ionization potential
4
Interactions of Particles with Matter
Interactions of Electrons
Ionization
For electrons and positrons, the rate of energy loss is similar to that for “heavy”
charged particles, but the calculations are more complicate:
 Small electron/positron mass
 Identical particles in the initial and final state
 Spin ½ particles in the initial and final states
 






2
dE
C 
cm 
2
2 Z 1   k (k  2 ) 

 2πN A re me c
ln

F
(
k
,

,

)



2
MeV
dx
A β2    I 2
Z  
g 

  2 m c 2  

e

  

k = Ek/mec2 : reduced electron (positron) kinetic energy
F(k,β,) is a complicate equation
However, at high incident energies (β1)  F(k)  constant
5
Interactions of Particles with Matter
Interactions of Electrons
Ionization
At this high energy limits (β1), the energy loss for both “heavy” charged particles
and electrons/positrons can be approximate by

dE   2me c 2 
  A ln γ  B 

 2 ln
dx   I 

Where,
electrons
heavy charged particles
A
3
4
B
1.95
2
The second terms indicates that the rate of relativistic rise for electrons is slightly smaller than
for heavier particles. This provides a criterion for identification between charge
particles of different masses.
6
Interactions of Particles with Matter
Interactions of Electrons
Bremsstrahlung (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:
d
Z 2 ln E
 2
dE mi E
mi2 factor expected since classically
radiation  a   F 
 mi 
2
2
i
 Makes electrons and positrons the only significant contribution to this process for
energies up to few hundred GeV’s.
 dσ 


 dE  e
2
m

 μ
 37103

me 
 dσ 



 dE  μ
7
Interactions of Particles with Matter
Interactions of Electrons
Bremsstrahlung
The rate of energy loss for k >> 137/Z1/3 is giving by:

dE
N  183
 re2 4αZ 2 A  ln 1  E
dx
A  Z 3
Recalling from pair production
A
1
X0 
N A r 2 4αZ 2 ln183 Z 13 
e



dE
E

dx
X0
 E(x)  E0e

x
X0
The radiation length X0 is the layer thickness that reduces the electron energy by a
factor e (63%)
8
Interactions of Particles with Matter
Interactions of Electrons
Bremsstrahlung
Radiation loss in lead.
http://pdg.lbl.gov
9
Interactions of Particles with Matter
Interactions of Electrons
Bremsstrahlung and Pair production
 Note that the mean free path for photons for pair production is very similar to X0
for electrons to radiate Bremsstrahlung radiation:
λ pair
9
 X0
7
 This fact is not coincidence, as pair production and Bremsstrahlung have very
similar Feynman diagrams, differing only in the directions of the incident
and 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  shower development.
10
Interactions of Particles with Matter
Interactions of Electrons
Bremsstrahlung (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:
Other definition  Rossi
http://pdg.lbl.gov
Ec 
dE
dE
(Ec )

(Ec )
dx
dx
Brem
ion
Ec 
800MeV
Z  1.2
11
Interactions of Particles with Matter
Summary of the basic EM interactions
e+ / eIonisation
P.e. effect

dE/dx

g
s
Z
E
E
Bremsstrahlung
dE/dx

Z5
Comp. effect

s
Z(Z+1)
Z
E
E
Pair production

s
Z(Z+1)
12
E
Electromagnetic Shower Development
Detecting a signal:
 The contribution of an electromagnetic interaction to energy loss usually depends
on the energy of the incident particle and on the properties of the absorber
 At “high energies” ( > ~10 MeV):
 electrons lose energy mostly via Bremsstrahlung
 photons via pair production
 Photons from Bremsstrahlung can create an electron-positron pair which can
radiate new photons via Bremsstrahlung in a process that last as long as the
electron (positron) has energy E > Ec
 At energies E < Ec , energy loss mostly by ionization and excitation
 Signals in the form of light or ions are collected by some readout system
Building a detector
 X0 and Ec depends on the properties of the absorber material
 Full EM shower containment depends on the geometry of the detector
13
Electromagnetic Shower Development
A simple shower model (Rossi-Heitler)
Considerations:
B. Rossi, High Energy Particles, New York, Prentice-Hall (1952)
W. Heitler, The Quantum Theory of Radiation, Oxford, Claredon Press (1953)
 Photons from bremsstrahlung and electron-positron from pair production produced
at angles  = mc2/E (E is the energy of the incident particle)  jet character
Assumptions:
 λpair  X0
 Electrons and positrons behave identically
 Neglect energy loss by ionization or excitation for E > Ec
 Each electron with E > Ec gives up half of its energy to bremsstrahlung photon
after 1X0
 Each photon with E > Ec undergoes pair creation after 1X0 with each created
particle receiving half of the photon energy
 Shower development stops at E = Ec
 Electrons with E < Ec do not radiate  remaining energy lost by collisions
14
Electromagnetic Shower Development
A simple shower model
Shower development:
Start with an electron with E0 >> Ec
 After 1X0 : 1 e- and 1  , each with E0/2
 After 2X0 : 2 e-, 1 e+ and 1  , each with E0/4
.
 Number of particles
.
N(t)  2 t  e t ln 2
increases
 After tX0 :
E
exponentially with t
E(t)  0 t
2
 equal number of e+, e-, 
ln E 0 E 
ln 2
 Depth at which the energy of a shower particle equals
some value E’
1 E0
N(E  E ) 
ln 2 E   Number of particles in the shower with energy > E’
lnE0 Ec 
t max 
Maximum number of particles reached at E = Ec 
ln 2
N max  e t max ln 2  E0 Ec
[ X0 ]
t(E ) 
15
Electromagnetic Shower Development
A simple shower model
Concepts introduce with this simple mode:
 Maximum development of the shower (multiplicity) at tmax
 Logarithm growth of tmax with E0 :
 implication in the calorimeter longitudinal dimensions
 Linearity between E0 and the number of particles in the shower
16
Electromagnetic Shower Development
A simple shower model
What about the energy measurement?
Assuming, say, energy loss by ionization
 Counting charges:
 Total number of particles in the shower:
t max
N all   2t  2  2t max  1  2  2t max  2
t 0
E0
Ec
 Total number of charge particles (e+ and e- contribute with 2/3 and  with 1/3)
E
2
4 E0
N e e    2 0 
3
Ec 3 Ec
 Measured energy proportional to E0
17
Electromagnetic Shower Development
A simple shower model
What about the energy resolution?
Assuming Poisson distribution for the shower statistical process:
 (E)
E
 (E)
E

1

N e e 

1
E
3Ec
2
Resolution improves with E
E
Example: For lead (Pb), Ec  6.9 MeV:
More general term:
 (E)
Statistic fluctuations
E

σ(E)

E
a
c
b
E
E
Constant term
(calibration, non-linearity, etc
7 .2%
E [GeV ]
Noise, etc
18
Electromagnetic Shower Development
A simple shower model
copper
Simulation of the energy
deposit in copper as a function
of the shower depth for
incident electrons at
4 different energies showing
the logarithmic dependence of
tmax with E.
Longitudinal profile
of an EM shower
Number of
particle
decreases after
maximum
EGS4* (electron-gamma
shower simulation)
*EGS4 is a Monte Carlo code for doing
simulations of the transport of electrons and
photons in arbitrary geometries.
19
Electromagnetic Shower Development
A simple shower model
Though the model has introduced correct concepts, it is too simple:
 Discontinuity at tmax : shower stops  no energy dependence of the
cross-section
 Lateral spread  electrons undergo multiple Coulomb scattering
 Difference between showers induced by  and electrons
 λpair = (9/7) X0
 Fluctuations : Number of electrons (positrons) not governed by
Poisson statistics.
20
Electromagnetic Shower Development
Shower Profile
 Longitudinal development governed by the radiation length X0
 Lateral spread due to electron undergoing multiple Coulomb
scattering:
 About 90% of the shower up to the shower maximum is
contained in a cylinder of radius < 1X0
 Beyond this point, electrons are increasingly affected by
multiple scattering
 Lateral width scales with the Molière radius ρM
E
M  X0 s
Ec
g
cm
2

, E s  21MeV
95% of the shower is
contained laterally in a
cylinder with radius 2ρM
21
Electromagnetic Shower Development
Shower profile
From previous slide, one expects the longitudinal and transverse developments to scale with X0
EGS4 calculation
EGS4 calculation
Longitudinal development
10 GeV electron
Transverse development
10 GeV electron
 ρM less dependent on Z than X0:
X 0  A Z 2 , Ec  1 Z   M  A Z
22
Electromagnetic Shower Development
Shower profile
Different shower development for photons and electrons
At increasingly depth, photons
carry larger fraction of the
shower energy than electrons
EGS4 calculation
23
Electromagnetic Shower Development
Energy deposition
60%
e± (< 4 MeV)
The fate of a shower is to develop,
reach a maximum, and then decrease
in number of particles once E0 < Ec
Given that several processes compete
for energy deposition at low energies,
it is important to understand how the
fate of the particles in a shower.
40%
e± (< 1 MeV)
 Most of energy deposition by low
energy e±’s.
EGS4 calculation
e± (>20 MeV)
Ionization dominates
24
Electromagnetic Calorimeters
Homogeneous Calorimeters
 Only one element as passive (shower development) and active (charge or light
collection) material
 Combine short attenuation length with large light output  high energy resolution
 Used exclusively as electromagnetic calorimeter
 Common elements are: NaI and BGO (bismuth germanate) scintillators,
scintillating, glass, lead-glass blocks (Cherenkov light), liquid argon (LAr), etc
Material Properties
X0(cm)
ρM (cm) la(cm)
NaI
2.59
4.5
41.4
CsI(TI)
1.85
3.8
36.5
Lead glass 2.6
3.7
38.0
la= nuclear absorption length
light
scintillator
scintillator
cerenkov
energy resolution (%) experiments
2.5/E1/4
crystal ball
2.2/E1/4
CLEO, BABAR, BELLE
5/E1/2
OPAL, VENUS
25
Electromagnetic Calorimeters
Homogeneous Calorimeters
BaBar EM Calorimeter
 CsI as active/passive material
 Total of ~6500 crystals
EM calorimeter
26
Electromagnetic Calorimeters
Sampling Calorimeters
 Consists of two different elements, normally in a sandwich geometry:
 Layers of Active material (collection of signal) – gas, scintillator, etc
 Layers of passive material (shower development)
 Segmentation allows measurement of spatial coordinates
 Can be very compact  simple geometry, relatively cheap to construct
 Sampling concept can be used in either electromagnetic or hadronic calorimeter
 Only part of the energy is sampled in the active medium.
 Extra contribution to fluctuations
27
Electromagnetic Calorimeters
Sampling Calorimeters

Typical elements:
Passive: Lead, W, U, Fe, etc
Active: Scintillator slabs, scintillator fibers, silicon detectors, LAr, LXe, etc.
Typical Energy Resolution
E
(7.5  25)%
EM
E
E
 E (35  80)%

hadronic
E
E
Passive medium Active medium

28
Electromagnetic Calorimeters
Sampling Calorimeters
ATLAS LAr Accordion Calorimeter
Ionization chamber: 1 GeV E-deposit  5 x106 eAccordion shape  Complete Φ symmetry without
azimuthal cracks  better acceptance.
Test beam results, e- 300 GeV
(ATLAS TDR)
 (E) E  a
E b/ E c
Spatial and angular
uniformity 0.5%
Spatial resolution
 5mm / E1/2
29
Electromagnetic Calorimeters
Sampling Calorimeters
detectors
absorbers
Sampling fraction:
The number of particles we see: Nsample
N sample 
N e e 
d X 0 
d = distance between active plates
d
Sampling fluctuation:
 sample
E

1
N sample

d
E
The more we sample, the better is
the resolution
30