Calorimeters

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Calorimeters

• Purpose of calorimeters
• EM Calorimeters
• Hadron Calorimeters

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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.

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EM Calorimeters

• Electron and photon interactions in matter
• Resolution
• Detection techniques
• Sampling calorimeters vs all active
• Examples

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12.2 Charged particles in matter(Ionisation and
the Bethe-Bloch Formula, variation with bg)
m can capture e-
Emc critical energy defined via dE/dxion.dE/dx
Brem.
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Charged particles in matter(Bremsstrahlung
Brakeing Radiation)

• Due to acceleration of incident charged particle
  in nuclear Coulomb field
• Radiative correction to Rutherford Scattering.
• Continuum part of x-ray emission spectra.
• 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/?.
• Radiation spectrum very uniform in energy.
• Photon energy limits
• low energy (large impact parameter) limited
  through shielding of nuclear charge by atomic
  electrons.
• high energy limited by maximum incident particle
  energy.

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12.2 Charged particles in matter(Bremsstrahlung
? EM-showers, Radiation length)

• dT/dxBremT (see Williams p.247) ? dominates
  over dT/dxionise ln(T) at high T.
• For electrons Bremsstrahlung dominates in nearly
  all materials above few 10 MeV. Ecrit(e-) 600
  MeV/Z
• If dT/dxBremT ? dT/dxBremT0exp(-x/X0)
• Radiation Length X0 of a medium is defined as
• distance over which electron energy reduced to
  1/e.
• X0Z2 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 ? is measured in X0.

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Very Naïve EM Shower Model

• Simple shower model assumes
• E0 gtgt 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,
  photo-effect (for g) etc.

• Abrupt end of shower happens at ttmax
  ln(E0/Ecrit)/ln2
• Indeed observe logarithmic depth dependence

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13.1 Photons in matter(Overview)

• Rayleigh scattering
• Coherent, elastic scattering of the entire atom
  (the blue sky)
• g atom ? g atom
• dominant at lggtsize of atoms
• Compton scattering
• Incoherent scattering of electron from atom
• g e-bound ? g e-free
• possible at all Eg gt min(Ebind)
• to properly call it Compton requires
  EggtgtEbind(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 lt max(Ebind) dE(Eatomic-recoil,
  line width) (just above k-edge)
• Pair production
• absorption of g in atom and emission of ee- 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-

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13.1 Photons in matter(Note on Pair Production)

• Compare pair production with Bremsstrahlung

• Very similar Feynman Diagram
• Just two arms swapped

L09/7 X0
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13.1 Photons in matter(Crossections)
Lead
Carbon

• R ? Rayleigh
• PE ? Photoeffect
• C ? Compton

• PP ? Pair Production
• PPE ? Pair Production on atomic electrons
• PN ? Giant Photo-Nuclear dipole resonance

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Transverse Shower Size

• Moliere radius 21 MeV X0/Ec

Electrons
Photons
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Sampling vs All Active

• Sampling sandwich of passive and active
  material. eg Pb/Scintillator.
• All active eg Lead Glass.
• Pros/cons
• Resolution
• Compactness ? costs.

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Detection Techniques

• Scintillators
• Ionisation chambers
• Cherenkov radiation
• (Wire chambers)
• (Silicon)

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Organic Scintillators (1)

• Organic molecules (eg Naphtalene) in plastic (eg
  polysterene).
• excitation ? non-radiating de-excitation to first
  excited state ? scintillating transition to one
  of many vibrational sub-states of the ground
  state.

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Organic Scintillators (2)

• gives fast scintillation light, de-excitation
  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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Inorganic Scintillators (1)

• eg NaI activated (doped) with Thallium,
  semi-conductor, high density r(NaI3.6), ? 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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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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Detectors (1)

• Photomultiplier
• primary electrons liberated by photon from
  photo-cathode (low work function, high
  photo-effect crossection, metal, hconversion¼ )
• 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 vetos
• signal on last dynode proportional to photons
  impacting

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Detectors (2)

• APD (Avalanche Photo Diode)
• solid state alternative to PMT
• strongly forward biased diode gives limited
  avalanche when hit by photon

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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

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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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Classical Pb/Scintillator
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Lead Glass

• All active
• Pb Glass

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BGO

• Higher resolution

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Liqiuid Argon

• Good resolution eg NA31.

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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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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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Bipolar Pulse Shaping
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ATLAS Liquid Argon

• Resolution
• Stochastic term
• 1/E1/2.
• Noise 1/E
• Constant (non-uniformity over cell, calibration
  errors).

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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?

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Hadron Calorimeters

• Why you need hadron calorimeters.
• The resolution problem.
• e/pi ratio and compensation.
• Some examples of hadron calorimeters.

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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).

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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 X01.76
  cm) ? next transparency

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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 gt1).
• 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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e/h Response vs Energy
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Resolution Plots s(E)/E vs 1/E1/2.
Fe/Scint (poor).
ZEUS U/scint and SPACAL (good).
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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.

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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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Scintillator Readout
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SPACAL 1 mm scintillating fibres in Fe
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Compensation (3)

• Software weighting (eg H1)
• EM component localized ? de-weight large local
  energies
• Very simplified

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Fine grain Fe/Scintillator Calorimeter (WA1)

• With weighting resolution improved.

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H1 Hadronic resolution with weighting
Standard H1 weighting
Improved (Cigdem Issever)