1. An introduction to calorimeters for particle physics
Bob Brown
STFC/PPD
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL

3. General principles sE / E  1/n  1/ E
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
Graduate lectures 2009/ R M Brown - RAL

4. The electromagnetic cascade
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
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL

6. Average rate of Bremsstrahlung energy loss
E(x) = Ei exp(-x/X0)
dE/dx (x=0) = - Ei/X0 Ei
Ei/e x X0
Graduate lectures 2009/ R M Brown - RAL

7. EM shower development in liquid krypton
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)
Graduate lectures 2009/ R M Brown - RAL

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 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
Graduate lectures 2009/ R M Brown - RAL

9. Hadronic cascade developmentlI
In dense materials: X0  180 A / Z2 << lI  35 A1/3 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
eg Cu: X0 = 12.9 g.cm-2 lI = 135 g.cm-2  
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL

11. 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
Graduate lectures 2009/ R M Brown - RAL

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 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
Graduate lectures 2009/ R M Brown - RAL

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 = SNi=1Ti = (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
Graduate lectures 2009/ R M Brown - RAL

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, 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%
Graduate lectures 2009/ R M Brown - RAL

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 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)
Graduate lectures 2009/ R M Brown - RAL

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 a hadron shower produces a smaller signal than the em component: e/h > 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 contribute: inter-calibration errors, response non-uniformity (both laterally and in depth), energy leakage and cracks .
Graduate lectures 2009/ R M Brown - RAL

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: E*i = Ei (1- c.Ei )
Using one or more of these methods one can obtain an intrinsic resolution
sintr / E  20%/ E
Graduate lectures 2009/ R M Brown - RAL

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 ± (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
Graduate lectures 2009/ R M Brown - RAL

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°
Graduate lectures 2009/ R M Brown - RAL

20. DREAM test results From W. Vandelli, HEP2007, Manchester
Graduate lectures 2009/ R M Brown - RAL

21. Jet energy resolution S zi = 1, S ei = EJ
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 < 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  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
Graduate lectures 2009/ R M Brown - RAL

22. Particle flow calorimetry
From M. Thomson, HEP2007, Manchester
Graduate lectures 2009/ R M Brown - RAL

23. 3.8 T Compact Muon Solenoid Objectives: Higgs discovery
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
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
Graduate lectures 2009/ R M Brown - RAL

24. Measuring particles in CMS
Electromagnetic Calorimeter
Hadron Calorimeter
Iron field return yoke interleaved with Tracking Detectors
Superconducting Solenoid
Silicon Tracker
Muon
Electron
Hadron
Photon
Cross section through CMS
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL

26. Energy resolution: random impact
22 mm
Series of runs at 120 GeV centred on many points within S(3x3)
Results averaged to simulate the effect of random impact positions
Resolution goal of 0.5% at high energy achieved
Graduate lectures 2009/ R M Brown - RAL

27. Hadron calorimeter The brass absorber under construction
Light produced in the scintillators is tranported through optical fibres to photodetectors
The brass absorber under construction
The HCAL being inserted into the solenoid
Graduate lectures 2009/ R M Brown - RAL

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
(ECAL+HCAL) raw response to pions vs energy (red line is MC simulation)
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL

30. Calorimetry is a powerful tool at very high energy
Search for heavy gauge bosons
ZI(1000 GeV)  m+m-
ZI(800 GeV)  e+e-
Calorimetry is a powerful tool at very high energy
Graduate lectures 2009/ R M Brown - RAL

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  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).
Graduate lectures 2009/ R M Brown - RAL

32. Spare slides
Graduate lectures 2009/ R M Brown - RAL

33. Coloured histograms are separate contributing backgrounds for 1fb-1
ECAL design benchmark
High resolution electromagnetic calorimetry 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)
Coloured histograms are separate contributing backgrounds for 1fb-1
Graduate lectures 2009/ R M Brown - RAL

34. 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
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
But:
Graduate lectures 2009/ R M Brown - RAL

35. Photodetectors Barrel - Avalanche photodiodes (APD)
Two 5x5 mm2 APDs/crystal
Gain: QE: ~75%
Temperature dependence: -2.4%/OC
 = 26.5 mm
MESH ANODE
Endcaps: - Vacuum phototriodes (VPT)
More radiation resistant than Si diodes
(with UV glass window)
- Active area ~ 280 mm2/crystal
Gain (B=4T) Q.E.~20% at 420nm
40mm
Graduate lectures 2009/ R M Brown - RAL

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
Scintillator planes outside coil HO
Coil HB HB
ECAL HE HF
Graduate lectures 2009/ R M Brown - RAL

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°)]
(ECAL+HCAL)
For single pions with cluster-based weighting
Graduate lectures 2009/ R M Brown - RAL

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
Graduate lectures 2009/ R M Brown - RAL