STFC
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An introduction to calorimeters for
particle physics
Bob Brown
STFC/PPD
Graduate lectures 2009/10
R M Brown - RAL
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Overview
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
Introduction

Electromagnetic cascades

Hadronic cascades

Calorimeter types

Energy resolution

e/h ratio and compensation

Measuring jets
 Energy flow calorimetry
 DREAM approach
Graduate lectures 2009/10

CMS as an illustration of practical calorimeters
 EM calorimeter (ECAL)
 Hadron calorimeter (HCAL)

Summary

General principles
 Items not covered
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General principles
Calorimeter: A device that measures the energy of a particle by absorbing
‘all’ the initial energy and producing a signal proportional to this energy.

There is an absorber and a detection medium (may be one and the same)

Absorption of the incident energy is via a cascade process leading to n
secondary particles, where n  EINC

The charged secondary particles deposit ionisation that is detected in the active
elements, for example as a current pulse in Si or light pulse in scintillator.

The energy resolution is limited by statistical fluctuations on the detected
signal, and therefore grows as n, hence the relative energy resolution:
sE / E  1/n  1/ E

The depth required to contain the secondary shower grows only logarithmically.
In contrast, the length of a magnetic spectrometer scales as p in order to
maintain sp /p constant

Charged and neutral particles, and collimated jets of particles can be measured.

Hermetic calorimeters provide inferred measurements of missing (transverse)
energy in collider experiments and are thus sensitive to , o etc
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The electromagnetic cascade
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A high energy e or g
incident on an absorber
initiates a shower of
secondary e and g
via pair production
and bremsstrahlung
Absorber
1 X0
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Depth and radial extent of em showers
Longitudinal development in a given medium is characterised by radiation length:
The distance over which, on average, an electron loses all but 1/e of its energy.
X0  180 A / Z2 g.cm-2
For photons, the mean free path for pair production is:
Lpair = (9 / 7) X0
The critical energy is defined as the energy at which energy losses by an electron
through ionisation and radiation are, on average, equal:
eC  560 / Z (MeV)
The lateral spread of an em shower arises mainly from the multiple scattering of
non-radiating electrons and is characterised by the Molière radius:
RM = 21X0 /eC  7A / Z g.cm-2
For an absorber of sufficient depth, 90% of the shower energy is contained
within a cylinder of radius 1 RM
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Average rate of Bremsstrahlung energy loss
E
E(x) = Ei exp(-x/X0)
dE/dx (x=0) = - Ei/X0
Ei
Ei/e
X0
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x
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EM shower development in liquid krypton
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EM shower development in krypton (Z=36, A=84)
GEANT simulation of a 100 GeV electron shower in the NA48 liquid Krypton calorimeter (D.Schinzel)
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Hadronic cascades
High energy hadrons interact with nuclei producing secondary particles (mostly p ,p )
±
0
The interaction cross section depends on the nature of the incident particle, its energy
and the struck nucleus.
Shower development is determined by the mean free path between inelastic collisions,
the nuclear interaction length, given (in g.cm-2) by:
lI = (NAsI / A)-1 (where NA is Avogadro’s number)
In a simple geometric model, one would expect sI  A2/3 and thus lI  A1/3.
In practice:
lI  35 A1/3 g.cm-2
The lateral spread of a hadronic showers arises from the transverse energy of the
secondary particles which is typically <pT>~ 350 MeV/c.
Approximately 1/3 of the pions produced are p0 which decay p0 gg in ~10-16 s
Thus the cascades have two distinct components: hadronic and electromagnetic
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Hadronic cascade development
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lI

eg Cu:
X0 = 12.9 g.cm-2
lI = 135 g.cm-2
In dense materials: X0  180 A / Z << lI  35 A
and the em component develops more rapidly than the hadronic component.
2
1/3

Thus the average longitudinal energy deposition profile is characterised by a peak
close to the first interaction, followed by an exponential fall off with scale lI
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Depth profile of hadronic cascades
Average energy deposition as a function of depth for pions incident on copper
Individual showers show large variations from the mean profile, arising from
fluctuations in the electromagnetic fraction
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Calorimeter types
There are two general classes of calorimeter:
Sampling calorimeters:
Layers of passive absorber (such as Pb, or Cu) alternate with active
detector layers such as Si, scintillator or liquid argon
Homogeneous calorimeters:
A single medium serves as both absorber and detector, eg: liquified Xe or Kr,
dense crystal scintillators (BGO, PbWO4 …….), lead loaded glass.
Si photodiode
or PMT
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Energy Resolution
The energy resolution of a calorimeter is often parameterised as:
sE / E = a /E  b / E  c
(where  denotes a quadratic sum)
The first term, with coefficient a, is the stochastic term arising from fluctuations in
the number of signal generating processes (and any further limiting process, such
as photo-electron statistics in a photodetector)
The second term, with coefficient b, is the noise term and includes:
- noise in the readout electronics
- fluctuations in ‘pile-up’ (simultaneous energy deposition by uncorrelated particles)
The third term with coefficient c, is the constant term and arises from:
- imperfections in calorimeter construction (dimensional variations, etc.)
- non-uniformities in signal collection
- channel to channel inter-calibration errors
- fluctuations in longitudinal energy containment
- fluctuations in energy lost in dead material before or within the calorimeter
For em calorimeters, energy resolution at high energy is usually dominated by c
The goal of calorimeter design is to find, for a given application, the best
compromise between the contributions from the three terms
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Intrinsic Energy Resolution of em calorimeters
Homogeneous calorimeters:
The signal amplitude is proportional to the total track length of charged particles above
threshold for detection.
The total track length is the sum of track lengths of all the secondary particles.
Effectively, the incident electron behaves as would a single ionising particle of the same
energy, losing an energy equal to the critical energy per radiation length. Thus:
T=S
N
T
i=1 i
= (E /eC) X0
If W is the mean energy required to produce a ‘signal quantum’ (eg an electron-ion pair
in a noble liquid or a ‘visible’ photon in a crystal), then the mean number of such
‘quanta’ produced is n = E / W . Alternatively n = T / L where L is the average track
length between the production of such quanta.
The intrinsic energy resolution is given by the fluctuations on n.
At first sight:
sE / E =  n / n =  (L / T)
However, T is constrained by the initial energy E (see above). Thus fluctuations on n
are reduced:
sE / E =  (FL / T) =  (FW / E)
where F is the Fano Factor
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Resolution of crystal em calorimeters
A widely used class of homogeneous em calorimeter employs large, dense,
monocrystals of inorganic scintillator. Eg the CMS crystal calorimeter which uses
PbWO4, instrumented (Barrel section) with Avalanche Photodiodes.
Since scintillation emission accounts for only a small fraction of the total energy loss in
the crystal, F ~ 1 (Compared with a GeLi g detector, where F ~ 0.1)
Furthermore, fluctuations in the avalanche multiplication process of an APD give rise to
a gain noise (‘excess noise factor’) leading to F ~ 2 for the crystal /APD combination.
PbWO4 is a relatively weak scintillator. In CMS, ~ 4500 photo-electrons are released in
the APD for 1 GeV of energy deposited in the crystal. Thus the coefficient of the
stochastic term is expected to be:
ape =  (F / Npe) =  (2 / 4500) = 2.1%
However, so far we have assumed perfect lateral containment of showers. In practice,
energy is summed over limited clusters of crystals to minimise electronic noise and
pile up. Thus lateral leakage contributes to the stochastic term.
The expected contributions are: aleak = 1.5% (S(5x5)) and aleak =2% (S(3x3))
Thus for the S(3x3) case one expects
a = ape  aleak = 2.9%
This is to be compared with the measured value: ameas = 2.8%
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Resolution of sampling calorimeters
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In sampling calorimeters, an important contribution to the stochastic term comes
from sampling fluctuations. These arise from variations in the number of charged
particles crossing the active layers. This number increases linearly with the
incident energy and (up to some limit) with the fineness of the sampling. Thus:
nch  E / t
(t is the thickness of each absorber layer)
If each sampling is statistically independent (which is true if the absorber layers are
not too thin), the sampling contribution to the stochastic term is:
ssamp / E  1/ nch   (t / E)
Thus the resolution improves as t is decreased. However, for an em calorimeter,
of order 100 samplings would be required to approach the resolution of typical
homogeneous devices, which is impractical.
Typically:
ssamp / E ~ 10%/ E
A relevant parameter for sampling calorimeters is the sampling fraction, which bears
on the noise term:
Fsamp = s.dE/dx(samp) / [s.dE/dx(samp) + t.dE/dx(abs) ]
(s is the thickness of the sampling layers)
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Resolution of hadronic calorimeters
The absorber depth required to contain hadron showers is 10lI (150 cm for Cu),
thus hadron calorimeters are almost all sampling calorimeters
Several processes contribute to hadron energy dissipation, eg in Pb:
Thus in general, the hadronic component of a
hadron shower produces a smaller signal than
the em component: e/h > 1
Nuclear break-up (invisible)
Charged particle ionisation
Neutrons with TN ~ 1 MeV
Photons with Eg ~ 1 MeV
Fp° ~ 1/3 at low energies, increasing with energy
Fp° ~ a log(E)
If e/h  1 :- response with energy is non-linear
(since em component ‘freezes out’)
42%
43%
12%
3%
- fluctuations on Fp° contribute to sE /E
Furthermore, since the fluctuations are non-Gaussian,
sE /E scales more weakly than 1/ E
Constant term: Deviations from e/h = 1 also contribute
to the constant term.
In addition calorimeter imperfections contribute:
inter-calibration errors, response non-uniformity (both
laterally and in depth), energy leakage and cracks .
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Compensating calorimeters
‘Compensation’ ie obtaining e/h =1, can be achieved in several ways:
 Increase the contribution to the signal from neutrons, relative to the
contribution from charged particles:
Plastic scintillators contain H2, thus are sensitive to n via n-p elastic scattering
Compensation can be achieved by using scintillator as the detection medium
and tuning the ratio of absorber thickness to scintillator thickness
 Use 238U as the absorber: 238U fission is exothermic, releasing neutrons that
contribute to the signal
 Sample energy versus depth and correct event-by-event for fluctuations on Fp°
p0 production produces large local energy deposits that can be suppressed
by weighting:
E*i = Ei (1- c.Ei )
Using one or more of these methods one can obtain an intrinsic resolution
sintr / E  20%/ E
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Compensating calorimeters
ZEUS at HERA had an intrinsically compensated 238U/scintillator calorimeter
The ratio of 238U thickness (3.3 mm) to scintillator thickness (2.6 mm) was tuned such
that e/p = 1.00 ± 0.03 (implying e/h = 1.00 ± 0.045)
For this calorimeter the intrinsic energy resolution was:
sintr / E = 26%/ E
However, Sampling fluctuations also degrade the energy resolution.
As for electromagnetic calorimeters calorimeters:
ssamp / E  t where t is the absorber thickness
For the ZEUS calorimeter:
ssamp / E = 23%/ E
Giving a nonetheless excellent overall energy resolution for hadrons:
shad / E ~ 35%/ E
The downside is that the 238U thickness required for compensation (~ 1X0)
led to a rather modest EM energy resolution:
sem / E ~ 18%/ E
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Dual Readout Module (DREAM) approach
From W. Vandelli, HEP2007, Manchester
Measure electromagnetic component of shower independently event-by-event
Independent measurements of the scintillation and
Cerenkov light yields allow an estimation of the two
components, thus measuring Fp°
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DREAM test results
From W. Vandelli, HEP2007, Manchester
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Jet energy resolution
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At colliders, hadron calorimeters serve primarily to measure jets and missing ET:
For a single particle: sE / E = a / E  c
At low energy the resolution is dominated by a, at high energy by c
Consider a jet containing N particles, each carrying an energy ei = zi EJ
S zi = 1, S ei = EJ
d ei = a ei and: d EJ =  S (d ei )2 =  S a2ei
d EJ / EJ = a / EJ
If the stochastic term dominates:
Thus:
 the error on Jet energy is the same as for a single particle of the same energy
d EJ   S (cei )2 = cEJ S (zi )2
d EJ / EJ = c S (zi )2 and since S (zi )2 < S zi = 1
If the constant term dominates:
Thus:
 the error on Jet energy is less than for a single particle of the same energy
For example, in a calorimeter with sE / E = 0.3 / E  0.05
a 1 TeV jet composed of four hadrons of equal energy has
d EJ = 25 GeV,
compared to d E = 50 GeV, for a single 1 TeV hadron
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Particle flow calorimetry
From M. Thomson, HEP2007, Manchester
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Compact Muon Solenoid
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4 TTmagnetic field
3.8
 Length ~ 22 m
 Diameter ~ 15 m
 Weight ~ 14.5 kt
Current data suggest a light Higgs
 Favoured discovery channel H  gg
Intrinsic width very small
 Measured width, hence S/B
given by experimental resolution
High resolution electromagnetic
calorimetry is a hallmark of CMS
Objectives:
• Higgs discovery
• Physics beyond the
Standard Model
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Target ECAL energy resolution for
photons: ≤ 0.5% above 100 GeV
 120 GeV SM Higgs discovery (5s)
with 10 fb-1 (100 d at 1033 cm-2s-1)
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Measuring particles in CMS
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Muon
Electron
Hadron
Photon
Electromagnetic
Calorimeter
Silicon
Tracker
Hadron
Calorimeter
Superconducting
Solenoid
Iron field return yoke interleaved
with Tracking Detectors
Cross section
through CMS
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The Electromagnetic Calorimeter
RAL
Barrel: 36 Supermodules (18 per half-barrel)
61200 Crystals (34 types) – total mass 67.4 t
Endcaps: 4 Dees (2 per Endcap)
14648 Crystals (1 type) – total mass 22.9 t
Full Barrel ECAL installed in CMS
The crystals are slightly
tapered and point towards
the collision region
22 cm
Pb/Si Preshowers:
Each crystal weighs ~ 1.5 kg
4 Dees (2/Endcap)
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Energy resolution: random impact
Series of runs at 120 GeV centred on many points within S(3x3)
Results averaged to simulate the effect of random impact positions
22 mm
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Resolution goal
of 0.5%
at high energy
achieved
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Hadron calorimeter
Light produced in the scintillators is
tranported through optical fibres to
photodetectors
The HCAL being inserted into the solenoid
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The brass absorber under construction
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Hadron calorimetry in CMS
Compensated hadron calorimetry & high precision em calorimetry are incompatible
In CMS, hadron measurement combines HCAL (Brass/scint) and ECAL(PbWO4) data
This effectively gives a hadron calorimeter divided in depth into two compartments
Neither compartment is ‘compensating’: e/h ~ 1.6 for ECAL and e/h ~ 1.4 for HCAL
 Hadron energy resolution is degraded and response is energy-dependent
(ECAL+HCAL) raw response to pions vs energy
(red line is MC simulation)
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Particle-Flow Event Reconstruction in CMS
The design of CMS detector is almost ideally suited to particle-flow reconstruction at LHC:
- Strong magnetic field,
- High tracking efficiency with low fake rate,
- Fine granularity electromagnetic calorimeter
- Reconstruction of muons with high purity
Particle-flow reconstruction improves jet energy
resolution dramatically below 100 GeV/c
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Particle-flow reconstruction improves the
measurement of Missing Transverse Energy
by almost a factor of 2, compared to a
measurement based on calorimetry alone.
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Search for heavy gauge bosons
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I
Z (1000 GeV)  m+mI
Z (800 GeV)  e+e-
Calorimetry is a
powerful tool at
very high energy
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Summary
 Design optimisation is dictated by physics goals and experiment conditions
 Compromises may be necessary:
eg high resolution hadron calorimetry vs high resolution em calorimetry
 A variety of mature technologies are available for their implementation
 Calorimeters will play a crucial role in discovery physics at LHC:
I
eg: H  g g , Z  e+e- , SUSY (ET)
 Calorimeters are key elements of almost all particle physics experiments
Not covered:
 Triggering with calorimeters
 Particle identification
 Di-jet mass resolution
 …………………………
Some useful references
Particle Detectors, Claus Grupen, Cambridge University Press.
Calorimetry for Particle Physics, C.W. Fabian and F. Gianotti, Rev Mod Phys, 75, 1243 (2003).
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Spare slides
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ECAL design benchmark
High resolution electromagnetic
calorimetry is central to the CMS design
Benchmark process: H  g g
sm / m = 0.5 [sE1/E1  sE2/E2  s / tan( / 2 )]
Where:
sE / E = a /  E  b/ E  c
(d is small –  measurement relies on interaction
vertex identification)
Coloured histograms are
separate contributing
backgrounds for 1fb-1
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Lead tungstate properties
Fast light emission: ~80% in 25 ns
Peak emission ~425 nm (visible region)
Short radiation length: X0 = 0.89 cm
Small Molière radius: RM = 2.10 cm
Radiation resistant to very high doses
But:
Temperature dependence ~2.2%/OC
 Stabilise to  0.1OC
Formation and decay of colour centres
in dynamic equilibrium under irradiation
 Precise light monitoring system
Low light yield (1.3% NaI)
 Photodetectors with gain in mag field
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Photodetectors
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Barrel - Avalanche photodiodes (APD)
Two 5x5 mm2 APDs/crystal
- Gain: 50 QE: ~75%
- Temperature dependence: -2.4%/OC
20
 = 26.5 mm
MESH
ANODE
40mm
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Endcaps: - Vacuum phototriodes (VPT)
More radiation resistant than Si diodes
(with UV glass window)
- Active area ~ 280 mm2/crystal
- Gain 8 -10 (B=4T) Q.E.~20% at 420nm
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Hadron calorimeters in CMS
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Had Barrel: HB
Had Endcaps: HE
Had Forward: HF
Had Outer: HO
Hadron Barrel
16 scintillator planes ~4 mm
Interleaved with Brass ~50 mm
plus
scintillator plane immediately
after ECAL ~ 9mm
plus
Scintillator planes outside coil
HO
Coil
HB
HB
ECAL
HE
HF
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Cluster-based response compensation
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Use test beam data to fit for e/h (ECAL) , e/h (HCAL) and Fp° as a function of the raw
total calorimeter energy (eE + eH ).
Then:
E = (e/p)E . eE + (e/p)H . eH
Where:
(e/p)E,H = (e/h)E,H / [1 + ((e/h)E,H -1) . Fp°)]
(ECAL+HCAL)
For single pions
with clusterbased weighting
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Jet energy resolution
‘Active’ weighting cannot be used for jets, since
several particles may deposit energy in the same
calorimeter cell.
Passive weighting is applied in the hardware: the
first HCAL scintillator plane, immediately behind the
ECAL, is ~2.5 x thicker than the rest.
One expects: d EJ / EJ = 125% / EJ + 5%
However, at LHC, the energy resolution for jets
is dominated by fluctuations inherent to the jets
and not instrumental effects
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