Calorimetry for particle physics
Calorimetry: challenges facing present and future experiments
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(history of calorimetry)
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Reason why the EM fraction (i.e. the π0's) depend on the energy of the incoming primary hadron:
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In EM showers, 3/4 of energy is deposited by e-, 2/4 of it by Compton and photoelectrons. These are isotropic processes, so the information on the direction of the incoming particle has been lost: no need for sandwich geometry!
The typical shower particle is a 1 MeV electron, range < 1mm. This has important consequences for sampling calorimeters.
Instead, typical hadron shower particles are a 50-100 MeV proton (range 1-2 cm) and a 3 MeV evaporation neutron (range: several cm). What they do depends critically on the details of the absorber.
"Digital" gas calorimeters (e.g. Geiger counters, streamer chambers) are intrinsically non-linear: each charged particle creates an insensitive region around the wire, preventing nearby particles to be registered; and the density of particles increases with increasing energy (so, the calorimeter response decreases with increasing energy).
In homogeneous calorimeters, response to muons and EM showers is the same (same mechanism: ionization), so e/mip=1. Instead, due to invisible energy, π/e<1 (but increasing with energy, as said above). But the response to the non-EM component (h) is energy independent: e/h>1 (so it's e/h, and not e/π, the variable indicating the degree of non-compensation).
e/h cannot be measured directly, but it's extracted from:
π=feme+(1-fem)h
(with fem function of energy).
From the calorimetric point of view, very little differences between absorption of jet and absorption of single hadrons. Among them:
- there are π0's already between the incident particles ("intrinsic EM component") and not only coming from the showering;
- fem is different and depends on the fragmentation process.
In a sampling calorimeter, e/mip is a function of shower depth.
e/mip increases with increasing sampling frequency.
The reason is that soft γ's are very inefficiently sampled (due to photoelectric effect, which is proportional to Z5 and so is much more probable in the passive than in the active material; and the range of photoelectrons is typically <1 mm), so only photoelectrons produced near the boundary between active and passive material produce a signal.
If absorber layers are thin, they may contribute to the signal.
e/mip ratio is determined by the difference in Z value between active and passive media.
e/mip changes as the shower develops (very important for longitudinally segmented EM calorimeters: must use different calibration constants as a function of depth!). Reasons:
- early phase: relatively fast shower particles (e+e- pairs);
- tails are dominated by Compton and photoelectric electrons (the shower energy is already very degraded).
Energy deposition mechanisms that play a role in the absorption of non-em shower energy:
All compensating calorimeters rely on the contribution of neutron to the signals.
Ingredients (according to the author) for compensating calorimeters:
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Undercompensating calorimeter: showers with anomalously large fem values produce anomalously large signals.
Overcompensating calorimeter: such showers produce anomalously small signals
Compensating calorimeter: Gaussian distribution.
The ultimate limit on hadronic energy resolution is determined by the correlation between the total energy carried by neutrons and nuclear binding energy loss. Better in Pb than in Uranium (14%/√E vs 21%/√E).
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Offline compensation doesn't give any advantage, according to the author of this talk.
High-resolution EM and high-resolution hadronic calorimetry are mutually exclusive:
Compensating calorimeters use materials with hydrogen (for recovering neutron energy) or Uranium (for induced fission).
LAr calorimeter don't compensate, since there is no hydrogen, however compensation can be achieved by prolonging the charge collection time so that the gammas from neutron capture can be detected.
Compensation degrades the energy resolution for EM showers, so ATLAS and CMS chose to have non-compensating EM calorimeters since the main goal is energy resolution in H->γγ.
The advantages of gas sampling calorimeters are the low cost and the high segmentation capability. On the other hand, resolution is poor and there are stability problems due to temperature and pressure changes. All 4 LEP experiments used them, but now they are out of fashion.
Crystal calorimeters: typical resolutions are (1.5%-3.5%)/√E.
"Bolometer": a cryogenic calorimeter. It really works like a "calorimeter", since an increase in temperature is measured.