An introduction to calorimeters for particle physics

1
An introduction to calorimeters for particle
physics

• Bob Brown
• STFC/PPD

2
Overview

• Introduction
• Electromagnetic cascades
• Hadronic cascades
• Calorimeter types
• Energy resolution
• e/h ratio and compensation
• Measuring jets
• Energy flow calorimetry
• DREAM approach
• CMS as an illustration of practical calorimeters
• EM calorimeter (ECAL)
• Hadron calorimeter (HCAL)
• Summary
• General principles
• Items not covered

3
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

4
The electromagnetic cascade
A high energy e or g incident on an
absorberinitiates a shower ofsecondary e and
gvia pair productionand bremsstrahlung
1 X0
5
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
6
Average rate of Bremsstrahlung energy loss
E
E(x) Ei exp(-x/X0) dE/dx (x0) - Ei/X0
Ei
Ei/e
x
X0
7
EM shower development in liquid krypton
EM shower development in krypton (Z36, A84)
GEANT simulation of a 100 GeV electron shower in
the NA48 liquid Krypton calorimeter (D.Schinzel)
8
Hadronic cascades
High energy hadrons interact with nuclei
producing secondary particles (mostly p,p0)
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 Avogadros 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 ltpTgt 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
9
Hadronic cascade development
lI
10
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 fromfluctuations in the electromagnetic
fraction
11
Calorimeter types
12
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 inthe
number of signal generating processes (and any
further limiting process, suchas 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
13
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
SNi1Ti (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
14
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 inthe 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 toa 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 inthe APD for 1 GeV
of energy deposited in the crystal. Thus the
coefficient of thestochastic 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 andpile
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
15
Resolution of sampling calorimeters
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 arenot 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 typicalhomogeneous devices, which
is impractical.Typically ssamp / E
10/? E A relevant parameter for sampling
calorimeters is the sampling fraction, which
bearson the noise term Fsamp
s.dE/dx(samp) / s.dE/dx(samp) t.dE/dx(abs)
(s is the thickness of the
sampling layers)
16
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 ahadron
shower produces a smaller signal thanthe em
component e/h gt 1 Fp 1/3 at low energies,
increasing with energy Fp a log(E) (since em
component freezes out)
Nuclear break-up (invisible) 42 Charged particle
ionisation 43 Neutrons with TN 1 MeV
12 Photons with Eg 1 MeV 3

• If e/h ? 1 - response with energy is non-linear
• - 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 contributeinter-calibr
ation errors, response non-uniformity (both
laterally and in depth), energy leakage and
cracks .
17
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
  Ei Ei (1- c.Ei )
• Using one or more of these methods one can
  obtain an intrinsic resolution
• sintr / E ? 20/? E

18
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

19
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
20
DREAM test results
From W. Vandelli, HEP2007, Manchester
21
Jet energy resolution

• 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
• If the stochastic term dominates d ei a? ei
  and d EJ ? S (d ei )2 ? S a2ei
• Thus d EJ / EJ a /? EJ
• ? the error on Jet energy is the same as for a
  single particle of the same energy
• If the constant term dominates d EJ ? ?
  S (cei )2 cEJ? S (zi )2
• Thus d EJ / EJ c? S (zi )2 and since ?S
  (zi )2 lt S zi 1
• 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

22
Particle flow calorimetry
From M. Thomson, HEP2007, Manchester
23
Compact Muon Solenoid

• 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 electromagneticcalorimetry is a
  hallmark of CMS
• 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)

• Length 22 m
• Diameter 15 m
• Weight 14.5 kt

• Objectives
• Higgs discovery
• Physics beyond the Standard Model

24
Measuring particles in CMS
25
The Electromagnetic Calorimeter
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
Supermodule
The crystals are slightly tapered and point
towards the collision region
22 cm
Pb/Si Preshowers 4 Dees (2/Endcap)
Each crystal weighs 1.5 kg
26

Energy resolution random impact

27
Hadron calorimeter
Light produced in the scintillators is tranported
through optical fibres to photodetectors
The brass absorber under construction
The HCAL being inserted into the solenoid
28
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
29
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 the
measurement of Missing Transverse Energy by
almost a factor of 2, compared to a measurement
based on calorimetry alone.
Particle-flow reconstruction improves jet energy
resolution dramatically below 100 GeV/c
30
Search for heavy gauge bosons
31
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 eg H ? ? ? , ZI ?
  ee- , 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).
32
Spare slides
33
ECAL design benchmark
High resolution electromagneticcalorimetry is
central to the CMS design Benchmark process H ?
? ? ?m / m 0.5 ?E1/ E1 ? ?E2/ E2 ? ?? / tan(?
/ 2 ) Where ?E / E a / ? E ? b/ E ? c
(dq is small q measurement relies on
interaction vertex identification)
34
Lead tungstate properties
35
Photodetectors

• Barrel - Avalanche photodiodes (APD)
• Two 5x5 mm2 APDs/crystal
• Gain 50 QE 75
• Temperature dependence -2.4/OC

• Endcaps - Vacuum phototriodes (VPT)
• More radiation resistant than Si diodes
• (with UV glass window)
• - Active area 280 mm2/crystal
• Gain 8 -10 (B4T) Q.E.20 at 420nm

40mm
36
Hadron calorimeters in CMS
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
37
Cluster-based response compensation
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)
38
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