Richard Kass

1
Energy Measurement (Calorimetry)
Why measure energy ? I) Not always practical to
measure momentum. An important contribution to
momentum resolution is proportional to the
momentum. Example suppose we want to measure the
momentum of a charged particle such that we can
tell whether it is positively or negatively
charged (to within 3s). We demand sp/p 0.33 From previous notes, we found for measuring
trajectory in a wire chamber (e.g. drift chamber)
Use BaBar or CDF-like parameters B1T, L1m,
n100, s150mm and find p
Thus above 250 GeV/c we cant reliably measure
the charge of the particle at the 3s level. L
There are practical limits on the values of B, L,
s, n, etc.
II) Some interesting particles do not have
electrical charge. Momentum measurement using
B-field only works for charged particles. What
about photons, p0s and hs (both decay to gg),
KLs, neutrons, etc ?
2
Energy Measurement (Calorimetry)
A calorimeter is used to measure the energy of a
charged and/or neutral particle The
calorimeter should absorb all of the energy of an
incident particle Energy measurement by a
calorimeter is a DESTRUCTIVE process.
Original particle no longer exists after the
measurement. Calorimeter usually located behind
charged particle tracking chambers
MWPCs, drift chambers, silicon trackers are
non-destructive measuring devices
The energy resolution of a calorimeter is
determined by many factors Actual energy
deposited in calorimeter (sampling fluctuations)
Leakage of energy out of the calorimeter
Noise (e.g. from electronics or pickup) Ion or
light collection efficiency Usually, the dominant
term in the energy resolution is due to sampling
fluctuations which are Poisson in nature. Thus
this term in the energy resolution varies like
A is a constant
Since C and D are usually small energy resolution
improves as E increases. This is different
than momentum resolution which gets worse as
momentum increases.
A more complete description of the energy
resolution is
Bcontribution due to electronics (e.g. ADC
resolution) Ccontribution due to calibration
errors and other systematic effects Dcontribution
due to energy leakage
3
Calorimetry
Calorimeter information can also be used
to identify particles (e.g. gs, es) measure
space coordinates of particles (no B-field
necessary) form a trigger to signal an
interesting event eliminate background events
(e.g. cosmic rays, beam spill) can be optimized
to measure electromagnetic or hadronic
energy Calorimeter usually divided into active
and passive parts Active responsible for
generation of signal (e.g. ionization,
light) Passive responsible for creating the
shower Many choices for the active material
in a calorimeter inorganic crystals (CsI used
by CLEO, BELLE, BABAR) organic crystals
(ancthracene) mainly used a reference for light
output plastic scintillator (ZEUS, CDF) liquid
scintillator (used by miniBoone) Noble liquids
(liquid argon used by D0, ATLAS) gas (similar
gases as used by wire proportional
chambers) glass (leaded or doped with
scintillator) water (SuperK) Many choices for
the passive material in a calorimeter high
density stuff marble, iron, steel, lead,
depleted uranium lower(er) density stuff sand,
ice, water
4
Typical Calorimeters
From PDG 2004
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Energy Deposition and Showering
The key to calorimetry is the showering process.
In a shower the original particle interacts with
the passive material creating many lower energy
particles. The low energy particles deposit
energy (via ionization) in the active material.
The amount of ionization (or light) is
proportional to the amount of energy deposited
in the calorimeter.
Cloud chamber photo of an electromagnetic
shower. A high energy electron initiates the
shower. The electron radiates photons
via bremsstrahlung when it goes through the first
lead plate. The photons are converted to
electrons and positrons by the lead and they in
turn create new photons. This process continues
until the photons are no longer energetic enough
to undergo pair production.
Lead plates
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Electromagnetic Shower
Recall for g energies above 10 MeV the dominant
EM process is pair production.
Consider an electron with energy E Ec. Ec is
the critical energy The electron is incident
on some material that is many radiation lengths
(RL) thick.
Consider the following simple model of an
electromagnetic shower a) Each electron with E
Ec travels 1 RL then gives up half its energy to
a photon via bremsstrahlung b) Each
photon with E Ec travels 1 RL then undergoes
pair production with E-EEg/2. c) Electrons and
positrons E Neglect ionization energy loss for E Ec .
RL ee- gs 0 1 0 0-1 1 1 1-2 3
1 2-3 5 3
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Electromagnetic Showers
From this simple model we can make several
predictions The number of particles (N) after
t radiation lengths is
N(t)Ne(t)Ne-(t)Ng(t) 2tetln2 Given an
electron with incident energy E0 the average
energy E(t) of the particles at depth t is
E(t)E0/N(t) E0/ 2t The shower has the
maximum number of particles when E(t)Ec
tmaxln(Eo/Ec)/ln2 Nmax Eo/Ec Past
the distance tmax the shower dies out quickly.
The shower also spreads laterally. The lateral
spread is characterized by the Moliere radius,
Rm Rm(21MeV)RL/Ec 95 of the shower is
within 2Rm.
Intensity
To understand energy deposition in more detail
we use a Monte Carlo program or build a test
module and put it in a beam.
Energy deposition/unit
Radius (Rm units)
Depth in radiation lengths
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Electromagnetic vs Hadronic Showers
Hadronic showers are more complicated than EM
showers Strong and weak interactions are
involved in the hadronic shower process Energy
resolution of hadronic calorimeter usually worse
than EM calorimeter neutrinos leak energy out
of calorimeter muons will not usually be
absorbed by calorimeter (unlikely to
bremsstrahlung) long lived particles (Ks, KL,
L) may escape calorimeter before decaying or
interacting
MC simulation of hadronic (proton) and EM shower
(photon). Hadronic showers typically have larger
lateral spread compared with EM showers.
EM shower
Hadronic shower
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Sampling Calorimeters

• Sampling calorimeters have active and passive
  material interleaved.
• A few typical examples of SCs and their active
  material are given below.
• Scintillator
• Scintillator with wave shifter readout
• liquid argon with ionization chamber readout
• Gas with MWPC readout
• For a)-d) the passive material could be lead or
  iron.

Energy Resolution
Material Properties RL(cm) Ec
(MeV) la(cm) Lead 0.56 7.4 17.2 Iron
1.76 20.7 16.8 Tungsten 0.35 8.0 9.6
la nuclear absorption length
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Energy vs Momentum Resolution
Guidelines for the design of a lead sampling
calorimeter Longitudinal thickness necessary
to contain shower 98 of shower
contained in 2.5tmax2.5ln(Eo/Ec)/ln2
For E05 GeV Þ ³ 13.1 cm For E0100 GeV Þ ³
19.2 cm Lateral thickness necessary to
contain EM shower 2 Moliere Radi
contains 95 of shower (approx. independent of
energy) Rm(21MeV)RL/Ec1.6 cm Þ ³
3.2 cm
Compare above lead sampling calorimeter with
drift chamberB-field Let sE/E 10/E1/2
sE/E 4.5 _at_ 5 GeV sE/E 1 _at_ 100 GeV For
BaBar/CDF system (B1T, L1m, n100, s150mm)
Calculate the following for momentum resolution
(not including MS, angle piece) sP/p 0.65 _at_5
GeV sp/p 13 _at_ 100 GeV
The two resolutions are equal when
For high energy particles pE.
p18 GeV/c for our typical systems (A0.1,
B1T, L1m, n100, s 150mm).
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Crystal Calorimeters
These calorimeters have only active elements (e.
g. crystals) that combine a short radiation
length with large light output.
Material
Properties RL(cm) Rm (cm) la(cm) light
energy resolution () experiments NaI
2.59 4.5 41.4 scintillator 2.5/E1/4
crystal ball CsI(TI) 1.85
3.8 36.5 scintillator 2.2/E1/4 CLEO, BABAR,
BELLE Lead glass 2.6 3.7 38.0 cerenkov 5/E1
/2 OPAL, VENUS la nuclear absorption
length
CLEO II-III
CsI crystals (8000)
Drift chamber
Crystal ball (1000 NaI crystals)
BaBar and Belle also have CsI calorimeters, but
CLEOs is the best!
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The BaBar Calorimeter
Electromagnetic Calorimeter (EMC)
BaBar EM calorimeter uses CsI crystals 5760
crystals in barrel 820 crystals in forward
region
each crystal has 2 photodiodes
Energy resolution
angular resolution
13
Particle ID with Calorimeters
electron/positron Charged particle undergoes EM
shower in calorimeter, compare momentum (measured
in drift chamber) with energy, require E/p1. Not
efficient when electron has same energy as a
minimum ionizing particle (both have E/p 1),
also background from reactions pNp0X. photon
EM shower in calorimeter not matched to charged
track in drift chamber. muon Charged track in
drift chamber that does not shower in EM
calorimeter or interact in hadron calorimeter.
Background from pions (and kaons) that decay in
flight (pmn) and/or non-interacting
p/K. neutrino Compare visible energy
(calorimeter) with measured momentum (drift
chamber) and look for imbalance in event. Could
be more than one neutrino missing! neutron or
KL Hadronic shower in calorimeter that does not
match to charged track in drift chamber. Need a
hadronic calorimeter. p0, h measure invariant
mass of gg combinations.
Problems How do you tell the charge of track
initiating the shower?? What about neutrinos?