1. Calorimeters in HEP Add hermiticity CC event - calibration
Paul Thompson
Add hermiticity
CC event - calibration
DIRC
Charged particles through matter
Electrons and positrons
Electromagnetic/hadronic showers
Calorimeter design
Absorber
Incident particle
Detector

2. What is a Calorimeter? ….. A device for measuring energy!
Charged AND NEUTRAL particles incident on thick dense material
Deposit energy which leads to eg ionisation and thus measurable signal
In total contrast to gaseous tracking detectors, we want particles
to deposit all of their energy in the calorimeter, so we can detect and
measure it.
The measured signal is then (hopefully) linearly proportional to the
particle energy
Different techniques for electromagentic and hadronic calorimetry
How do EM and HAD particles interact with matter?

3. Charged Particles Through Matter
Lose energy through ionization Bethe-Bloch
Tmax is the max. kinetic energy that can be transferred to e in a single collision
for A=1 g/mol

4. Interactions of Electrons and Positrons in Matter
Bremsstrahlung radiation when accelerated by nuclei.
Strongly dependent on particle mass
Dominant energy loss for low mass particles (electrons) at high energy
Define `Radiation length’ X0 = mean free
path of electron before it radiates = distance
over which electron energy reduced to fraction 1/e
Apart from particle mass, X0 depends on material density and ~A/Z2
If thickness expressed in X0, radiation loss independent of material

5. Some Radiation Length DataX0 W Pb Sn
G10 Fe Cu Al
glass Z
k/A
… Z2 expresses charge
of scattering sources,
… 1/A ~ expresses the number
of sources per unit volume
Rate of energy loss ~ 1/X0 X0

6. The Critical Energy
`Critical energy’ when Bremsstrahlung and Ionisation losses equal.
…. Will be important later
dE/dx
10 MeV
1/E dE/dX electrons-positrons
Bremsstrahlung
Ionization
f(Z) 1
Critical Energy
Ionisation energy
loss ~ Z/(A.b2)
(Bethe Bloch)
So Bremsstrahlung
has stronger Z
dependence …
… very roughly, critical
energy Ec~600/Z (MeV)
Projectile energy

7. More on Critical EnergyEc
Roughly Ec~1/Z
…. independent of material density Z

8. Energy Loss for Photons
Photons interact with matter in 3 main ways:
1) Pair production (high energy)
2) Compton scattering (low energy)
3) Photoelectric absorption (even lower energy)
At high energy, electron
Bremsstrahlung plus
photon pair production
can lead to a ``shower’’
Mean free path for ge+e- ~ X0 ~1/Z2

9. Photon scattering cross section
spe= Atomic photo-effect
(electron ejection, photon
absorption)
scoherent = Coherent scattering
(Rayleigh scattering-atom
neither ionised nor excited)
s incoherent = Incoherent scattering
(Compton scattering off an
electron)
kn = Pair production, nuclear field
ke = Pair production, electron field
snuc = Photonuclear absorption
(nuclear absorption, usually
followed by emission of a
neutron or other particle)
Photon total cross sections as a function of energy in carbon and
lead, showing the contributions of different processes
Pair production dominates at high energy

10. Electromagnetic Shower Development
Shower maximum occurs
when shower particles on
average have an energy
equal to the critical
energy

12. Modelling Electromagnetic Showers
Bremsstrahlung and pair production ...
Shower deposits constant energy for each radiation length
Each step the number of particles in the shower doubles
The energy per particle reduces by a factor of two
The emission angles are small so narrow shower develops
Width mainly comes from multiple scattering
When the energy falls below the critical energy
Ionisation and collisions dominate the energy loss
Showers stops over a relatively short distance
Longitudinal
Transverse

13. Hadronic Showers Much more complicated than electromagnetic showers!
Hadrons can interact strongly as well as ionising the sampling material
… nuclear reactions become an important energy loss mechanism.
Define nuclear interaction length l via E(x) = E(0) e-x/l
Roughly, l ~ 35 A1/3 g cm-2, quite long even for dense materials,
so hadronic showers are longer and broader than electromag showers
Other difficulties compared with electromagnetic showers:
`Invisible’ energy caused mainly by neutrons interacting by
exciting or breaking up nuclei. Generates transverse momentum
Large component from p0 -> gg …. Hadronic showers have an
electromagnetic core!

14. Development of Hadronic Showers
Nuclear interactions lead to large energy loss, but have long l
(l ~ 50 cm for protons in lead)

15. Breakdown of a Hadronic Shower
20 GeV hadronic showers in copper ….
Charged particles
Full shower
Large transverse component, especially in neutrals

16. Basics of Calorimeter Design
Calorimeters require:
A dense ABSORBER material in which to build shower
A SAMPLER as a means of collecting deposited energy / getting
a signal out!
“Homogeneous” Calorimeters:
Absorber and Sampler are the same thing
Usually built from crystals
Good resolution, but expensive and hard to grow big crystals!
Often used for electromagnetic calorimetry
2) “Sampling Calorimeters:
Alternating layers of absorber and sampler
Used for all hadronic and many electromagnetic calorimeters

17. An Example Homogeneous Calorimeter
Individual lead glass blocks
- OPAL EM Calorimeter
Also used for electromagnetic
calorimeter at CMS
(lead tungstenate crystals)

18. Homogeneous Calorimeters
Use special optical properties of crystals or glasses to generate
detectable signal from electrons and photons in shower:
Scintillation light or Cerenkov radiation.
e.g. Crystal Calorimeters
Electrons and positrons in
electromagnetic shower emit
Cerenkov radiation at optical
wavelengths.
Radiation collected in
photomultiplier tubes
Total light amplitude collected
proportional to total energy
deposited by incident e / g
Cerenkov radiation
Analogous to a supersonic
shockwave.
Charged particle with
v > c/h emits coherent
radiation at an angle
cos q = 1/hb to incident
particle …. photon rings

19. Sampling Calorimeters
Can fill large and awkward volumes at manageable cost
Only a fraction of deposited energy is sampled

20. Some Example Sampling Calorimeter Designs
Scintillator
readout with
wavelength
shifter bars
(or wavelength
shifting fibers)
Scintillator
readout
Noble
liquid
readout
Readout
with
gaseous
detectors
(MWPCs or
streamer tubes)

21. e.g. Hadronic Calorimeter at ALEPH
Iron return yoke of solenoid
used as absorber material
Active material is limited
Streamer tubes

22. e.g. ATLAS Calorimetry EM calorimeter with lead absorbers and
liquid argon
active material
Hadronic
calorimeter with
alternating tiles
of stainless steel
active scintillator
(polystyrene)

23. Calorimeter Resolution

24. Example: CMS At low E, s(E)/E~1/E, dominated by noise, pile-up etc
At high E, s(E)/E~1/E1/2,
dominated by `intrinsic’
statistical sampling error
NB! Calorimeter resolution improves with increasing energy
Tracking resolution deteriorates with increasing energy
… the two types of detector are often complementary!

25. Summary Basic ideas of how particles interact with matter introduced
Differences between EM and HAD showers lead to different designs and materials of calorimeters
Met some of the most common designs in HEP
Concepts such as components of calorimeter resolution useful to know and may arise in your viva!

26. Compensation For EM showers most energy seen as ionisation
For hadronic shower 30% of energy is not seen due to nuclear excitations/break-up
Ways to compensate for `unseen’ energy so that response to EM and hadronic showers is the same
Use software to reweight the hadronic response. Reweighting algorithm based on test beam and simulation. `Artificial’ compensation needs fine segmentation of EM/hadronic parts
Use Uranium 238 fissile isotope releases neutrons and fission products increase the ionisation. But expensive and dangerous to health. Usually worse EM resolution but much better hadronic.