An introduction to calorimeters for particle physics

1
An introduction to calorimeters for particle
physics

• Bob Brown
• STFC/PPD

2
Overview

• Introduction
• General principles
• 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
• 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
• Absorption of the incident energy is via a
  cascade process leading to n secondary
  particles, where ?n? ? EINC
• Calorimeters have an absorber and a detection
  medium (may be one and the same)
• 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
• Calorimeters can measure charged and neutral
  particles, and collimated jets of particles.
• 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 a thick absorber
initiates a shower of secondary e and g via pair
production and bremsstrahlung
1 X0
5
Depth and radial extent of em showers
Longitudinal development in a given material 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 energy loss via Bremsstrahlung
E
E(x) Ei exp(-x/X0) dE/dx (x0) Ei/X0
Ei
Ei/e
x
X0
7
EM shower development in liquid 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 l ? 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. 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
In dense materials X0 ? 180 A / Z2 ltlt lI ? 35
A1/3 (eg Cu X0 12.9 g.cm-2, lI 135
g.cm-2) and the EM component develops more
rapidly than the hadronic component. 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
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 from fluctuations in the electromagnetic
fraction
11
Calorimeter types
12
Energy Resolution
The energy resolution of a calorimeter is usually
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
includes- 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 The
goal of calorimeter design is to find, for a
given application, the best compromise between
the contributions from the three terms For EM
calorimeters, energy resolution at high energy is
usually dominated by c
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 in the crystal, F 1
(Compared with a GeLi g detector, where F
0.1) Furthermore, inherent fluctuations in the
avalanche multiplication process of an APD give
rise to a gain noise (excess noise factor)
leading to F 2 for thecrystal /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 stochasic 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 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 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 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 the
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 contribute
inter-calibration errors, response non-uniformity
(both laterally and in depth), energy leakageand
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
Sampling fluctuations also degrade the energy
resolution. As for EM calorimeters ssamp / E
?? d where d is the absorber thickness (empirica
lly, the resolution does not improve for d ? 2 cm
(Cu)) ZEUS at HERA employed 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 For this calorimeter sintr / E
26/? E and ssamp / E 23/? E Giving an
excellent 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
Measure electromagnetic component of shower
independently event-by-event
20
DREAM test results
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
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 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
ECAL design objectives
26
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
27
Lead tungstate properties
28
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
29
Correction for impact position
30

Energy resolution random impact

31
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
32
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
33
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
34
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)
35
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
36
Search for heavy gauge bosons
37
Summary

• Calorimeters are key elements of almost all
  particle physics experiments
• A variety of mature technologies are available
  for their implementation
• Design optimisation is dictated by physics goals
  and experiment conditions
• Compromises may be necessary eg high
  resolution hadron calorimetry vs high resolution
  EM calorimetry
• Calorimeters will play a crucial role in
  discovery physics at LHC eg H ? ? ? , ZI ?
  ee- , SUSY (ET)

• Not covered
• Triggering with calorimeters
• Particle identification
• Di-jet mass resolution