1. Calorimeters Purpose of calorimeters EM Calorimeters
Hadron Calorimeters
Graduate lectures HT '08
T. Weidberg

2. 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

3. EM Calorimeters Electron and photon interactions in matter Resolution
Detection techniques
Sampling calorimeters vs all active
Examples
Graduate lectures HT '08
T. Weidberg

4. 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/dxBrem.
Graduate lectures HT '08
T. Weidberg

5. 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. Ze e- g
Graduate lectures HT '08
T. Weidberg

6. 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  is measured in X0.
Graduate lectures HT '08
T. Weidberg

7. 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, photo-effect (for g) etc.
Abrupt end of shower happens at t=tmax = ln(E0/Ecrit)/ln2
Indeed observe logarithmic depth dependence
Graduate lectures HT '08
T. Weidberg

8. 13.1 Photons in matter (Overview)
Rayleigh scattering
Coherent, elastic scattering of the entire atom (the blue sky)
g + atom  g + atom
dominant at lg>size of atoms
Compton scattering
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

9. 13.1 Photons in matter (Note on Pair Production)
Compare pair production with Bremsstrahlung Ze e-
e-* g
Bremsstrahlung Ze
e-* e- g
Pair production
Typical Lenth =
Pair Production
Length L0
Typical Lenth =
Radiation Length X0
Very similar Feynman Diagram
Just two arms swapped
L0=9/7 X0
Graduate lectures HT '08
T. Weidberg

10. 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
Graduate lectures HT '08
T. Weidberg

11. Transverse Shower Size
Moliere radius = 21 MeV X0/Ec
Electrons
Photons
Graduate lectures HT '08
T. Weidberg

12. 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
T. Weidberg

13. Detection Techniques Scintillators Ionisation chambers
Cherenkov radiation
(Wire chambers)
(Silicon)
Graduate lectures HT '08
T. Weidberg

14. 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.
Graduate lectures HT '08
T. Weidberg

15. 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.
Graduate lectures HT '08
T. Weidberg

16. Inorganic Scintillators (1)
eg NaI activated (doped) with Thallium, semi-conductor, 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
Graduate lectures HT '08
T. Weidberg

17. 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).
Graduate lectures HT '08
T. Weidberg

18. 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
Graduate lectures HT '08
T. Weidberg

19. 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
T. Weidberg

20. 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
T. Weidberg

21. Resolution Parameterise resolution as
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
Graduate lectures HT '08
T. Weidberg

22. Classical Pb/Scintillator
Graduate lectures HT '08
T. Weidberg

23. Lead Glass
All active
Pb Glass
Graduate lectures HT '08
T. Weidberg

24. BGO
Higher resolution
Graduate lectures HT '08
T. Weidberg

25. Liqiuid Argon Good resolution eg NA31. Graduate lectures HT '08
T. Weidberg

26. 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)?
Graduate lectures HT '08
T. Weidberg

27. Cu/kapton electrodes for HV and signal
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.
Graduate lectures HT '08
T. Weidberg

28. Bipolar Pulse Shaping
Graduate lectures HT '08
T. Weidberg

29. Graduate lectures HT '08
T. Weidberg

30. ATLAS Liquid Argon Resolution Stochastic term ~ 1/E1/2. Noise ~ 1/E
Constant (non-uniformity over cell, calibration errors).
Graduate lectures HT '08
T. Weidberg

31. Calibration Electronics calibration For scintillators
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
T. Weidberg

32. Hadron Calorimeters Why you need hadron calorimeters.
The resolution problem.
e/pi ratio and compensation.
Some examples of hadron calorimeters.
Graduate lectures HT '08
T. Weidberg

33. 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

34. 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
Graduate lectures HT '08
T. Weidberg

35. Graduate lectures HT '08
T. Weidberg

36. 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.
Graduate lectures HT '08
T. Weidberg

37. e/h Response vs Energy
Graduate lectures HT '08
T. Weidberg

38. Resolution Plots s(E)/E vs 1/E1/2.
Fe/Scint (poor).
ZEUS U/scint and SPACAL (good).
Graduate lectures HT '08
T. Weidberg

39. 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

40. 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.
Graduate lectures HT '08
T. Weidberg

41. Scintillator Readout
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T. Weidberg

42. 1 mm scintillating fibres in Fe
SPACAL
1 mm scintillating fibres in Fe
Graduate lectures HT '08
T. Weidberg

43. Graduate lectures HT '08
T. Weidberg

44. Graduate lectures HT '08
T. Weidberg

45. Compensation (3) Software weighting (eg H1)
EM component localized  de-weight large local energies
Very simplified:
Graduate lectures HT '08
T. Weidberg

46. Fine grain Fe/Scintillator Calorimeter (WA1)
With weighting resolution improved.
Graduate lectures HT '08
T. Weidberg

47. H1 Hadronic resolution with weighting
Standard H1 weighting
Improved (Cigdem Issever)
Graduate lectures HT '08
T. Weidberg