Calorimetry for particle physics
Christian W. Fabjan and Fabiola Gianotti
CERN, 1211 Geneva 23, Switzerland
(Published 15 October 2003)
Calorimetry has become a well-understood, powerful, and versatile measurement method. Besides
perfecting this technique to match increasingly demanding operation at high-energy particle
accelerators, physicists are developing low-temperature calorimeters to extend detection down to ever
lower energies, and atmospheric and deep-sea calorimeters to scrutinize the universe up to the highest
energies. The authors summarize the state of the art, with emphasis on the physics of the detectors and
innovative technologies.
CONTENTS
I. Introduction 1243
II. Electromagnetic Calorimetry 1244
A. Physics of the electromagnetic cascade 1244
B. Energy resolution of electromagnetic
calorimeters 1246
1. Stochastic term 1247
2. Noise term 1247
3. Constant term 1247
4. Additional contributions 1248
C. Main techniques and examples of facilities 1249
1. Homogeneous calorimeters 1249
a. Semiconductor calorimeters 1249
b. Cherenkov calorimeters 1250
c. Scintillation calorimeters 1251
d. Noble-liquid calorimeters 1254
2. Sampling calorimeters 1256
a. Scintillation sampling calorimeters 1257
b. Gas sampling calorimeters 1257
c. Solid-state sampling calorimeters 1258
d. Liquid sampling calorimeters 1258
III. Hadron Calorimetry 1260
A. Physics of the hadronic cascade 1261
B. Energy resolution of hadron calorimeters 1263
C. Monte Carlo codes for hadronic cascade
simulation 1267
1. Shower physics modeling techniques 1267
2. Applications: Illustrative examples 1268
D. Examples of hadron calorimeter facilities 1269
IV. Calorimeter Operation in Accelerator Experiments 1270
A. Performance requirements 1270
B. Integration 1272
1. Impact of material 1272
2. Particle identification 1273
C. Calorimeter calibration 1273
V. Low-Temperature Calorimeters 1276
A. Introduction 1276
B. Main technologies 1276
1. Thermal detectors 1276
2. Phonon sensors 1277
3. Superheated superconducting granules 1278
C. Representative applications 1278
1. Search for dark matter 1278
2. Neutrinoless double-beta decay 1278
3. Microcalorimeters for x-ray astronomy 1279
4. Superconducting tunneling junctions for
ultraviolet to infrared spectroscopy in
astronomy 1279
VI. Citius, Altius, Fortius 1280
A. Introduction 1280
B. Atmospheric calorimeters 1280
1. Setting the energy scale 1283
2. Energy resolution 1283
C. Deep-water calorimeters 1283
VII. Conclusions 1284
Acknowledgments 1284
References 1284
I. INTRODUCTION
Calorimetry is an ubiquitous detection principle in
particle physics. Originally invented for the study of
cosmic-ray phenomena, this method was developed and
perfected for accelerator-based particle physics experi-
mentation primarily in order to measure the energy of
electrons, photons, and hadrons. Calorimeters are
blocks of instrumented material in which particles to be
measured are fully absorbed and their energy trans-
formed into a measurable quantity. The interaction of
the incident particle with the detector (through electro-
magnetic or strong processes) produces a shower of sec-
ondary particles with progressively degraded energy.
The energy deposited by the charged particles of the
shower in the active part of the calorimeter, which can
be detected in the form of charge or light, serves as a
measurement of the energy of the incident particle.
Calorimeters can be broadly divided into electromag-
netic calorimeters, used mainly to measure electrons and
photons through their electromagnetic interactions (e.g.,
bremsstrahlung, pair production), and hadronic calorim-
eters, used to measure mainly hadrons through their
strong and electromagnetic interactions. They can be
further classified according to their construction tech-
nique into sampling calorimeters and homogeneous
calorimeters. Sampling calorimeters consist of alternat-
ing layers of an absorber, a dense material used to de-
grade the energy of the incident particle, and an active
medium that provides the detectable signal. Homoge-
neous calorimeters, on the other hand, are built of only
one type of material that performs both tasks, energy
degradation and signal generation.
Today particle physics reaches ever higher energies of
experimentation, and aims to record complete event in-
REVIEWS OF MODERN PHYSICS, VOLUME 75, OCTOBER 2003
0034-6861/2003/75(4)/1243(44)/$35.00 ©2003 The American Physical Society1243
formation. Calorimeters are attractive in this field for
various reasons:
• In contrast with magnetic spectrometers, in which the
momentum resolution deteriorates linearly with the
particle momentum, in most cases the calorimeter en-
ergy resolution improves with energy as 1/
冑
E, where
E is the energy of the incident particle. Therefore
calorimeters are very well suited to high-energy phys-
ics experiments.
• In contrast with magnetic spectrometers, calorimeters
are sensitive to all types of particles, charged and neu-
tral (e.g., neutrons). They can even provide indirect
detection of neutrinos and their energy through a
measurement of the event missing energy.
• They are versatile detectors. Although originally con-
ceived as devices for energy measurement, they can
be used to determine the shower position and direc-
tion, to identify different particles (for instance, to dis-
tinguish electrons and photons from pions and muons
on the basis of their different interactions with the
detector), and to measure the arrival time of the par-
ticle. Calorimeters are also commonly used for trigger
purposes, since they can provide fast signals that are
easy to process and to interpret.
• They are space and therefore cost effective. Because
the shower length increases only logarithmically with
energy, the detector thickness needs to increase only
logarithmically with the energy of the particles. In
contrast, for a fixed momentum resolution, the bend-
ing power BL
2
of a magnetic spectrometer (where B
is the magnetic field and L the length) must increase
linearly with the particle momentum p.
Besides perfecting this technique to match the physics
potential at the major particle accelerator facilities, re-
markable extensions have been made to explore new
energy domains. Low-temperature calorimeters, sensi-
tive to phonon excitations, detect particles with unprec-
edented energy resolution and are sensitive to very-low-
energy deposits which cannot be detected in
conventional devices. The quest to understand the ori-
gin, composition, and spectra of energetic cosmic rays
has led to imaginative applications in which the atmo-
sphere or the sea are instrumented over thousands of
cubic kilometers.
A regular series of conferences (CALOR, 2002) and a
comprehensive recent monograph (Wigmans, 2000) tes-
tify to the vitality of this field.
In this paper we review major calorimeter develop-
ments with emphasis on applications at high-energy ac-
celerators. First, the physics, the performance, and prac-
tical realizations of electromagnetic calorimetry are
discussed (Sec. II). Next, the physics of hadronic calo-
rimeters and the processes determining their perfor-
mance are presented (Sec. III). A section on calorimetry
for accelerators (Sec. IV) concludes with a discussion of
integration issues. Section V is dedicated to an overview
of low-temperature calorimeters. The achievements and
projects in atmospheric and water calorimeters are ana-
lyzed in Sec. VI. Section VII is devoted to the conclu-
sions.
The success of calorimeters in modern experiments
rests also on remarkable developments in the field of
high-performance readout electronics that have allowed
optimum exploitation of the intrinsic potential of these
detectors. A discussion of calorimeter readout tech-
niques is beyond the scope of this paper. A very good
review has been made by de La Taille (2000).
II. ELECTROMAGNETIC CALORIMETRY
In this section we discuss the physics and the perfor-
mance of electromagnetic calorimeters. The main tech-
niques used to build these detectors are also reviewed,
and their merits and drawbacks are described. Examples
of calorimeters operated at recent or present high-
energy physics experiments, or under construction for
future machines, are given as illustration.
A. Physics of the electromagnetic cascade
In spite of the apparently complex phenomenology of
shower development in a material, electrons and pho-
tons interact with matter via a few well-understood
QED processes, and the main shower features can be
parametrized with simple empirical functions.
The average energy lost by electrons in lead and the
photon interaction cross section are shown in Fig. 1 as a
function of energy. Two main regimes can be identified.
For energies larger than ⬃10 MeV, the main source of
electron energy loss is bremsstrahlung. In this energy
range, photon interactions produce mainly electron-
positron pairs. For energies above 1 GeV both these
processes become roughly energy independent. At low
energies, on the other hand, electrons lose their energy
mainly through collisions with the atoms and molecules
of the material thus giving rise to ionization and thermal
excitation; photons lose their energy through Compton
scattering and the photoelectric effect.
As a consequence, electrons and photons of suffi-
ciently high energy (⭓1 GeV) incident on a block of
material produce secondary photons by bremsstrahlung,
or secondary electrons and positrons by pair production.
These secondary particles in turn produce other par-
ticles by the same mechanisms, thus giving rise to a cas-
cade (shower) of particles with progressively degraded
energies. The number of particles in the shower in-
creases until the energy of the electron component falls
below a critical energy
⑀
, where energy is dissipated
mainly by ionization and excitation and not in the gen-
eration of other particles.
The main features of electromagnetic showers (e.g.,
their longitudinal and lateral sizes) can be described in
terms of one parameter, the radiation length X
0
, which
depends on the characteristics of the material (Particle
Data Group, 2002),
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Christian W. Fabjan and Fabiola Gianotti: Calorimetry for particle physics
Rev. Mod. Phys., Vol. 75, No. 4, October 2003
X
0
共
g/cm
2
兲
⯝
716 g cm
⫺ 2
A
Z
共
Z⫹ 1
兲
ln
共
287/
冑
Z
兲
, (1)
where Z and A are the atomic number and weight of the
material, respectively. The radiation length governs the
rate at which electrons lose energy by bremsstrahlung,
since it represents the average distance x that an elec-
tron needs to travel in a material to reduce its energy to
1/e of its original energy E
0
,
具
E
共
x
兲
典
⫽ E
0
e
⫺ x/X
0
. (2)
Similarly, a photon beam of initial intensity I
0
travers-
ing a block of material is absorbed mainly through pair
production. After traveling a distance x⫽
9
7
X
0
, its inten-
sity is reduced to 1/e of the original intensity,
具
I
共
x
兲
典
⫽ I
0
e
⫺
共
7/9
兲
共
x/X
0
兲
. (3)
Two slightly different definitions are used for the criti-
cal energy
⑀
. In the first one,
⑀
is the energy at which the
electron ionization losses and bremsstrahlung losses be-
come equal. This energy depends on the features of the
material and is approximately given by
⑀
⫽
610
共
710
兲
MeV
Z⫹ 1.24
共
0.92
兲
(4)
for solids (gases). Figure 1 shows that
⑀
⬃7 MeV in lead.
In the second definition (Rossi, 1952),
⑀
is the energy at
which the ionization loss per X
0
equals the electron en-
ergy E:
dE
dx
共
ionization
兲
⫽
E
X
0
. (5)
Both definitions are equivalent in the approximation
dE
dx
共
bremsstrahlung
兲
⯝
E
X
0
. (6)
Equations (2) and (3) show that the physical scale
over which a shower develops is similar for incident
electrons and photons, and is independent of the mate-
rial type if expressed in terms of X
0
. Therefore electro-
magnetic showers can be described in a universal way by
using simple functions of the radiation length.
For instance, the mean longitudinal profile can be de-
scribed (Longo and Sestili, 1975)
dE
dt
⫽ E
0
b
共
bt
兲
a⫺ 1
e
⫺ bt
⌫
共
a
兲
, (7)
where t⫽ x/X
0
is the depth inside the material in radia-
tion lengths and a and b are parameters related to the
nature of the incident particle (e
⫾
or
␥
). The shower
maximum, i.e., the depth at which the largest number of
secondary particles is produced, is approximately lo-
cated at
t
max
⯝ln
E
0
⑀
⫹ t
0
, (8)
where t
max
is measured in radiation lengths, E
0
is the
incident particle energy, and t
0
⫽⫺0.5 (⫹ 0.5) for elec-
trons (photons). This formula shows the logarithmic de-
pendence of the shower length, and therefore of the de-
tector thickness needed to absorb a shower, on the
incident particle energy. Longitudinal shower profiles for
different energies of the incident particles are shown in
Fig. 2 (left plot). The calorimeter thickness containing
95% of the shower energy is approximately given by
t
95%
⯝t
max
⫹ 0.08Z⫹ 9.6, (9)
where t
max
and t
95%
are measured in radiation lengths.
In calorimeters with thickness ⯝25X
0
, the shower lon-
gitudinal leakage beyond the end of the active detector
is much less than 1% up to incident electron energies of
⬃300 GeV. Therefore, even at the particle energies ex-
pected at the CERN Large Hadron Collider (LHC), of
order ⬃TeV, electromagnetic calorimeters are very
compact devices: the ATLAS lead-liquid argon calorim-
eter (ATLAS Collaboration, 1996b) and the CMS crys-
tal calorimeter (CMS Collaboration, 1997) have thick-
nesses of ⯝45 cm and ⯝23 cm, respectively (the
radiation lengths are ⯝1.8 cm and ⯝0.9 cm, respec-
tively).
The transverse size of an electromagnetic shower is
mainly due to multiple scattering of electrons and posi-
trons away from the shower axis. Bremsstrahlung pho-
tons emitted by these electrons and positrons can also
FIG. 1. (a) Fractional energy lost in lead by electrons and positrons as a function of energy (Particle Data Group, 2002). (b)
Photon interaction cross section in lead as a function of energy (Fabjan, 1987).
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Christian W. Fabjan and Fabiola Gianotti: Calorimetry for particle physics
Rev. Mod. Phys., Vol. 75, No. 4, October 2003
contribute to the shower spread. A measurement of the
transverse size, integrated over the full shower depth, is
given by the Molie
`
re radius (R
M
), which can be ap-
proximated by
R
M
共
g/cm
2
兲
⯝21 MeV
X
0
⑀
共
MeV
兲
. (10)
It represents the average lateral deflection of electrons
at the critical energy after traversing one radiation
length. The definition of critical energy as given in Eq.
(5) should be used here, since it more accurately de-
scribes the transverse electromagnetic shower develop-
ment (Particle Data Group, 2002). On average, about
90% of the shower energy is contained in a cylinder of
radius ⬃1R
M
. Since for most calorimeters R
M
is of the
order of a few centimeters, electromagnetic showers are
quite narrow. In addition, their transverse size is roughly
energy independent. An example of shower radial pro-
file is presented in Fig. 2 (right plot). The cells of a seg-
mented calorimeter must be comparable in size to (or
smaller than) one R
M
if the calorimeter is to be used for
precision measurements of the shower position.
B. Energy resolution of electromagnetic calorimeters
The measurement of energy with an electromagnetic
calorimeter is based on the principle that the energy re-
leased in the detector material by the charged particles
of the shower, mainly through ionization and excitation,
is proportional to the energy of the incident particle.
The total track length of the shower T
0
, defined as
the sum of all ionization tracks due to all charged par-
ticles in the cascade, is proportional to
T
0
共
g/cm
2
兲
⬀X
0
E
0
⑀
, (11)
where the symbol ⬀ indicates proportionality and E
0
/
⑀
is the number of particles in the shower. The above for-
mula shows that a measurement of the signal produced
by the charged tracks of the cascade provides a measure-
ment of the original particle energy E
0
. This measure-
ment can be performed, for instance, by detecting the
light produced in a scintillating material, or by collecting
the charge produced in a gas or in a liquid.
The intrinsic energy resolution of an ideal calorimeter,
that is, a calorimeter with infinite size and no response
deterioration due to instrumental effects (for example,
inefficiencies in the signal collection, mechanical nonuni-
formities), is mainly due to fluctuations of the track
length T
0
. Since T
0
is proportional to the number of
track segments in the shower, and the shower develop-
ment is a stochastic process, the intrinsic energy resolu-
tion is given, from purely statistical arguments, by
共
E
兲
⬀
冑
T
0
, (12)
from which the well-known dependence of the fractional
energy resolution on energy,
共
E
兲
E
⬀
1
冑
T
0
⬀
1
冑
E
0
, (13)
can be derived.
The actual energy resolution of a realistic calorimeter
is deteriorated by other contributions and can be written
in a more general way as
E
⫽
a
冑
E
丣
b
E
丣 c, (14)
where the symbol
丣 indicates a quadratic sum. The first
term on the right-hand side is called the stochastic term,
and includes the shower intrinsic fluctuations mentioned
above; the second term is the noise term; and the
FIG. 2. (a) Simulated shower longitudinal profiles in PbWO
4
, as a function of the material thickness (expressed in radiation
lengths), for incident electrons of energy (from left to right) 1 GeV, 10 GeV, 100 GeV, 1 TeV. (b) Simulated radial shower profiles
in PbWO
4
, as a function of the radial distance from the shower axis (expressed in radiation lengths), for 1 GeV (closed circles)
and 1 TeV (open circles) incident electrons. From Maire (2001).
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Christian W. Fabjan and Fabiola Gianotti: Calorimetry for particle physics
Rev. Mod. Phys., Vol. 75, No. 4, October 2003
third term is the constant term. The relative importance
of the various terms depends on the energy of the inci-
dent particle. Therefore the optimal calorimeter tech-
nique can be very different for experiments operating in
different energy ranges, since the energy resolution is
dominated by different contributions. These contribu-
tions are discussed in turn below.
1. Stochastic term
As already mentioned, this term is due to the fluctua-
tions related to the physical development of the shower.
In homogeneous calorimeters intrinsic fluctuations are
small because the energy deposited in the active volume
of the detector by an incident monochromatic beam of
particles does not fluctuate event by event. Therefore in
most cases the intrinsic energy resolution can be better
than the statistical expectation given in Eq. (12) by a
factor called the Fano factor (Fano, 1947). The experi-
mental evidence for Fano factors in semiconductor,
noble gas, and noble-liquid calorimeters for charge or
light collection is discussed in several papers (Alkhazov
et al., 1967; Doke et al., 1976; Seguinot et al., 1995). Typi-
cal stochastic terms of homogeneous electromagnetic
calorimeters are at the level of a few percent in units of
1/
冑
E(GeV) and are dominated by effects other than the
intrinsic resolution (Secs. II.B.3 and II.B.4).
On the other hand, in sampling calorimeters the en-
ergy deposited in the active medium fluctuates event by
event because the active layers are interleaved with ab-
sorber layers. These fluctuations, which are called sam-
pling fluctuations and represent the most important limi-
tation to the energy resolution of these detectors, are
due to variations in the number of charged particles N
ch
that cross the active layers. This number is proportional
to
N
ch
⬀
E
0
t
, (15)
where t is the thickness of the absorber layers in radia-
tion lengths. If one assumes statistically independent
crossings of the active layers, which is reasonable if the
absorber layers are not too thin, then the ‘‘sampling’’
contribution to the energy resolution comes from the
fluctuation of N
ch
, that is (Amaldi, 1981)
E
⬀
1
冑
N
ch
⬀
冑
t
E
0
共
GeV
兲
. (16)
The smaller the thickness t, the larger the number of
times the shower is sampled by the active layers (i.e., the
sampling frequency) and the number of detected par-
ticles, the better the energy resolution. Hence in prin-
ciple the energy resolution of a sampling calorimeter can
be improved by reducing the thickness of the absorber
layers. However, in order to achieve resolutions compa-
rable to those typical of homogeneous calorimeters, ab-
sorber thicknesses of a few percent of a radiation length
are needed, but this is rarely feasible in practice. Al-
though some approximations have been used to derive
Eq. (16), this simplified approach is nevertheless able to
demonstrate the energy dependence of the resolution.
More complete discussions can be found, for instance, in
Wigmans (2000).
The typical energy resolution of sampling electromag-
netic calorimeters is in the range 5 –20 %/
冑
E(GeV).
Another parameter of sampling calorimeters is the
sampling fraction f
samp
, which has an impact on the
noise term of the energy resolution (Sec. II.B.2):
f
samp
⫽
E
mip
共
active
兲
E
mip
共
active
兲
⫹ E
mip
共
absorber
兲
, (17)
where E
mip
(active) and E
mip
(absorber) indicate the en-
ergies deposited by an incident minimum-ionizing par-
ticle in the active part and in the absorber part of the
detector, respectively.
2. Noise term
This contribution to the energy resolution comes from
the electronic noise of the readout chain and depends on
the detector technique and on the features of the read-
out circuit (detector capacitance, cables, etc.).
Calorimeters in which the signal is collected in the
form of light, such as scintillator-based sampling or ho-
mogeneous calorimeters, can achieve small levels of
noise if the first step of the electronic chain is a photo-
sensitive device, like a phototube, which provides a
high-gain multiplication of the original signal with al-
most no noise.
On the other hand, the noise is larger in detectors in
which the signal is collected in the form of charge be-
cause the first element of the readout chain is a pream-
plifier. Techniques like signal shaping and optimal filter-
ing are used to minimize the electronic noise in these
detectors (Cleland and Stern, 1994). Nevertheless, a fun-
damental limitation remains. This can be schematically
described by the relation Q⫽
冑
4kTR
␦
F (where Q is the
equivalent noise charge, k the Boltzmann constant, T
the temperature, R the equivalent noise resistance of
the preamplifier, and
␦
F the bandwidth), which shows
that the noise increases when one wants to operate at a
high rate.
The noise contribution to the energy resolution in-
creases with decreasing energy of the incident particles
[see Eq. (14)] and at energies below a few GeV may
become dominant. Therefore the noise equivalent en-
ergy is usually required to be much smaller than 100
MeV per channel for applications in the several GeV
region.
In sampling calorimeters the noise term can be de-
creased by increasing the sampling fraction, because the
larger the sampling fraction, the larger the signal from
the active medium and therefore the higher the signal-
to-noise ratio.
3. Constant term
This term includes contributions that do not depend
on the energy of the particle. Instrumental effects that
cause variations of the calorimeter response with the
particle impact point on the detector give rise to re-
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