Calorimeters
• Purpose of calorimeters
• EM Calorimeters
• Hadron Calorimeters
Graduate lectures HT
'08
T. Weidberg
1
EM Calorimeters
• Measure energy (direction) of electrons and
photons.
• Identify electrons and photons.
• Reconstruct masses eg
– Z  e+ e p0 g g
– H gg
• Resolution important:
• Improve S/N
• Improve precision of mass measurement.
Graduate lectures HT
'08
T. Weidberg
2
EM Calorimeters
• Electron and photon interactions in
matter
• Resolution
• Detection techniques
• Sampling calorimeters vs all active
• Examples
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'08
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3
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, variation with bg)
m+ can
capture eEmc = critical energy
defined via:
dE/dxion.=dE/dxBrem.
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'08
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4
Charged particles in matter
(Bremsstrahlung = Brakeing Radiation)
• Due to acceleration of incident charged particle in nuclear
Coulomb field
g
• Radiative correction to Rutherford Scattering. ee• Continuum part of x-ray emission spectra.
Ze
• Emission often confined to incident electrons because
– radiation ~ (acceleration)2 ~ mass-2.
• Lorentz transformation of dipole radiation from incident
particle centre-of-mass to laboratory gives narrow (not sharp)
cone of blue-shifted radiation centred around cone angle of
=1/g.
• Radiation spectrum very uniform in energy.
• Photon energy limits:
– low energy (large impact parameter) limited through shielding of
nuclear charge by atomic electrons.
– highlectures
energy
incident particle energy.
Graduate
HT limited by maximum
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'08
5
12.2 Charged particles in matter
(Bremsstrahlung  EM-showers, Radiation length)
• dT/dx|Brem~T (see Williams p.247)  dominates over dT/dx|ionise ~ln(T) at
high T.
• For electrons Bremsstrahlung dominates in nearly all materials above few
10 MeV. Ecrit(e-) ≈ 600 MeV/Z
• If dT/dx|Brem~T  dT/dx|Brem=T0exp(-x/X0)
• Radiation Length X0 of a medium is defined as:
– distance over which electron energy reduced to 1/e.
– X0~Z2 approximately.
• Bremsstrahlung photon can undergo pair production (see later) and start
an em-shower (or cascade)
• Length scale of pair production and multiple scattering are determined by
X0 because they also depend on nuclear coulomb scattering.
 The development of em-showers, whether started by primary e or g is
measured in X0.
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'08
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6
Very Naïve EM Shower Model
• Simple shower model
assumes:
– E0 >> Ecrit
– only single Brem-g or pair
production per X0
• The model predicts:
– after 1 X0, ½ of E0 lost by
primary via Bremsstrahlung
– after next X0 both primary and
photon loose ½ E again
– until E of generation drops
below Ecrit
– At this stage remaining Energy
lost via ionisation (for e+-) or
compton scattering, photoeffect (for g) etc.
– Abrupt end of shower happens at t=tmax = ln(E0/Ecrit)/ln2
Graduate lectures HT
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–
Indeed
observe
logarithmic
depth
dependence
'08
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13.1 Photons in matter
•
•
Rayleigh scattering
– Coherent, elastic scattering of the entire atom (the blue sky)
 g + atom  g + atom
– dominant at lg>size of atoms
Compton scattering
–

–
–
•
•
(Overview)
Incoherent scattering of electron from atom
g + e-bound  g + e-free
possible at all Eg > min(Ebind)
to properly call it Compton requires Eg>>Ebind(e-) to approximate free e-
Photoelectric effect
– absorption of photon and ejection of single atomic electron
 g + atom  g + e-free + ion
– possible for Eg < max(Ebind) + dE(Eatomic-recoil, line width) (just above k-edge)
Pair production
– absorption of g in atom and emission of e+e- pair
– Two varieties:
 g + nucleus  e+ + e- + nucleus (more momentum transfer to nucleusdominates)
 g + Z atomic electrons  e+ + e- + Z atomic electrons
• both summarised via: g + g(virtual)  e+ + e– Needs Eg>2mec2
– Nucleus has to recoils to conserve momentum  coupling to nucleus needed 
strongly Z-dependent crossection
Graduate lectures HT
'08
T. Weidberg
8
13.1 Photons in matter
(Note on Pair Production)
• Compare pair production with Bremsstrahlung
Typical Lenth =
Radiation Length
X0
Pair production
Bremsstrahlung
g
g
e-
Typical Lenth =
Pair Production
Length L0
ee-*
e-*
eZe
e-
Ze
• Very similar Feynman Diagram
• Just two arms swapped
L0=9/7 X0
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'08
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13.1 Photons in matter
(Crossections)
Lead
Carbon
•
•
•
R  Rayleigh
PE  Photoeffect
C  Compton
Graduate lectures HT
'08
•
•
•
PP  Pair Production
PPE  Pair Production on atomic electrons
PN  Giant Photo-Nuclear dipole
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resonance
10
Transverse Shower Size
• Moliere radius = 21 MeV X0/Ec
Electrons
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'08
Photons
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11
Sampling vs All Active
• Sampling: sandwich of passive and
active material. eg Pb/Scintillator.
• All active: eg Lead Glass.
• Pros/cons
– Resolution
– Compactness  costs.
Graduate lectures HT
'08
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12
Detection Techniques
•
•
•
•
•
Scintillators
Ionisation chambers
Cherenkov radiation
(Wire chambers)
(Silicon)
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'08
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13
Organic Scintillators (1)
• Organic molecules (eg Naphtalene) in
plastic (eg polysterene).
• excitation  non-radiating deexcitation to first excited state 
scintillating transition to one of many
vibrational sub-states of the ground
state.
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'08
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Organic Scintillators (2)
• gives fast scintillation light, deexcitation time O(10-8 s)
• Problem is short attenuation length.
– Use secondary fluorescent material to
shift l to longer wavelength (more
transparent).
– Light guides to transport light to PMT or
– Wavelength shifter plates at sides of
calorimeter cell. Shift blue  green (K27)
 longer attenuation length.
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'08
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15
Inorganic Scintillators (1)
• eg NaI activated (doped) with Thallium, semiconductor, high density: r(NaI=3.6),  high stopping
power
• Dopant atom creates energy level (luminescence
centre) in band-gap
• Excited electron in conduction band can fall into
luminescence level (non radiative, phonon emission)
• From luminescence level falls back into valence
band under photon emission
• this photon can only be re-absorbed by another
dopant atom  crystal remains transparent
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'08
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16
Inorganic Scintillators (2)
• High density of inorganic crystals  good
for totally absorbing calorimetry even at very
high particle energies (many 100 GeV)
• de-excitation time O(10-6 s) slower then
organic scintillators.
• More photons/MeV  Better resolution.
• PbWO4. fewer photons/MeV but faster and
rad-hard (CMS ECAL).
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'08
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Detectors (1)
• Photomultiplier:
– primary electrons liberated by photon from photo-cathode (low
work function, high photo-effect crossection, metal, hconversion≈¼ )
– visible photons have sufficiently large photo-effect cross-section
– acceleration of electron in electric field 100 – 200 eV per stage
– create secondary electrons upon impact onto dynode surface
(low work function metal)  multiplication factor 3 to 5
– 6 to 14 such stages give total gain of 104 to 107
– fast amplification times (few ns)  good for triggers or veto’s
– signal on last dynode proportional to #photons impacting
PMT
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'08
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18
Detectors (2)
• APD (Avalanche Photo Diode)
– solid state alternative to PMT
– strongly forward biased diode gives
“limited” avalanche when hit by photon
Graduate lectures HT
'08
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19
13.2 Detectors
• Ionisation Chambers
– Used for single particle and flux measurements
– Can be used to measure particle energy up to few
MeV with accuracy of 0.5% (mediocre)
– Electrons more mobile then ions  medium fast
electron collection pulse O(ms)
– Slow recovery from ion drift
Graduate lectures HT
'08
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20
Resolution
• Sampling fluctuations for sandwich calorimeters.
• Statistical fluctuations eg number of photo-electrons or number
of e-ion pairs.
• Electronic noise.
• Others
– Non-uniform response
– Calibration precision
– Dead material (cracks).
– Material upstream of the calorimeter.
– Lateral and longitudinal shower leakage
• Parameterise resolution as
– a Statistical
– b noise
– c constant
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'08
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E
a
b

 c
E
E E
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Classical Pb/Scintillator
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'08
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Lead Glass
• All active
• Pb Glass
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'08
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BGO
• Higher resolution
 (E)
E
~ 1% ( E  1GeV )
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'08
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Liqiuid Argon
• Good resolution eg
NA31.
 (E)
E
~ 8% E
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'08
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Fast Liquid Argon
• Problem is long drift time of electrons
(holes even slower).
• Trick to create fast signals is fast pulse
shaping.
– Throw away some of the signal and
remaining signal is fast (bipolar pulse
shaping).
– Can you maintain good resolution and
have high speed (LHC)?
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'08
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26
Accordion Structure
Lead plates
Cu/kapton electrodes
for HV and signal
Liquid Argon in gaps.
Low C and low L cf
cables in conventional
LAr calorimeter.
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'08
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Bipolar Pulse Shaping
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'08
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'08
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ATLAS Liquid Argon
• Resolution
– Stochastic term
~ 1/E1/2.
– Noise ~ 1/E
– Constant (nonuniformity over cell,
calibration errors).
Graduate lectures HT
'08
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30
Calibration
• Electronics calibration
– ADC counts to charge in pC. How?
• For scintillators
– Correct for gain in PMT or photodiode. How?
– Correct for emission and absorption in scintillator
and light guides. How ?
• Absolute energy scale.
– Need to convert charge seen pC  E (GeV). How?
Graduate lectures HT
'08
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31
Hadron Calorimeters
•
•
•
•
Why you need hadron calorimeters.
The resolution problem.
e/pi ratio and compensation.
Some examples of hadron calorimeters.
Graduate lectures HT
'08
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32
Why Hadron Calorimeters
• Measure energy/direction of jets
– Reconstruct masses (eg tbW or h bbar)
– Jet spectra: deviations from QCD  quark
compositeness)
• Measure missing Et (discovery of Ws, SUSY
etc).
• Electron identification (Had/EM)
• Muon identification (MIPs in calorimeter).
• Taus (narrow jets).
Graduate lectures HT
'08
T. Weidberg
33
Hadron Interactions
• Hadron interactions on nuclei produce
– More charged hadrons  further hadronic
interactions  hadronic cascade.
 p0 gg EM shower
– Nuclear excitation, spallation, fission.
– Heavy nuclear fragments have short range
 tend to stop in absorber plates.
– n can produce signals by elastic scattering
of H atoms (eg in scintillator)
• Scale set by lint (eg = 17 cm for Fe, cf
X0=1.76 cm)  next transparency
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'08
T. Weidberg
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'08
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Resolution for Hadron Calorimeters
• e/pi ≠ 1  fluctuations in p0 fraction in
shower will produce fluctuations in
response (typically e/pi >1).
• Energy resolution degraded and no
longer scales as 1/E1/2 and response
will tend be non-linear because p0
fraction changes with E.
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'08
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36
e/h Response vs Energy
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'08
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Resolution Plots (E)/E vs
1/E1/2.
Fe/Scint (poor).
ZEUS U/scint
and SPACAL
(good).
Graduate lectures HT
'08
T. Weidberg
38
Compensation (1)
• Tune e/pi ~= 1 to get good hadronic
resolution.
• U/Scintillator (ZEUS)
– Neutrons from fission of U238 elastic
scatter off protons in scintillator  large
signals  compensate for nuclear losses.
– Trade off here is poorer EM resolution.
Graduate lectures HT
'08
T. Weidberg
39
Compensation (2)
• Fe/Scintillator (SPACAL)
– Neutrons from spallation in any heavy absorber
can scatter of protons in scintillator  large
signals.
– If the thickness of the absorber is increased
greater fraction of EM energy is lost in the passive
absorber.
– tune ratio of passive/active layer thickness to
achieve compensation.
– Needs ratio 4/1 to achieve compensation. No use
for classical calorimeter with scintillator plates
(why).
– SPACAL: scintillating fibres in Fe absorber.
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'08
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40
Scintillator Readout
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'08
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SPACAL
1 mm scintillating
fibres in Fe
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'08
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'08
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Compensation (3)
• Software weighting (eg H1)
• EM component localized  de-weight large
local energies
• Very simplified:
E 'K  EK (1  CEK )
ETOTAL   E 'K
k
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'08
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45
Fine grain Fe/Scintillator Calorimeter
(WA1)
• With weighting resolution
improved.
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'08
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 (E)
E
58%

E
46
H1 Hadronic resolution with weighting
Standard H1 weighting
Improved (Cigdem Issever)
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'08
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