An introduction to calorimeters for particle physics

Graduate lectures 2007/8 R M Brown - RAL 1

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RAL

An introduction to calorimeters for particle physics

Bob BrownSTFC/PPD


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RAL 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


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RAL 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:

E / 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 p /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


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RAL The electromagnetic cascade

Absorber

A high energy e or incident on a thick absorber initiates a shower of secondary e and via pair production and bremsstrahlung

1 X0


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RALDepth 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:

C 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 /C 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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RAL

Average rate of energy loss via Bremsstrahlung

E

xX0

Ei

Ei/e

E(x) = Ei exp(-x/X0)

dE/dx (x=0) = Ei/X0


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RAL

EM shower development in liquid 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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RAL Hadronic cascades

High energy hadrons interact with nuclei producing secondary particles (mostly ±,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:

= (NA / A)-1 (where NA is Avogadro’s number)

In a simple geometric model, one would expect A2/3 and thus A1/3.In practice: 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.

Approximately 1/3 of the pions produced are 0 which decay 0 in ~10-16 s

Thus the cascades have two distinct components: hadronic and electromagnetic


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RAL Hadronic cascade development

In dense materials: X0 180 A / Z2 << 35 A1/3

(eg Cu: X0 = 12.9 g.cm-2, = 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


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RAL 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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RAL Calorimeter typesThere 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 photodiodeor PMT


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RAL Energy ResolutionThe energy resolution of a calorimeter is usually parameterised as:E / 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 calorimeterThe goal of calorimeter design is to find, for a given application, the best compromise between the contributions from the three termsFor EM calorimeters, energy resolution at high energy is usually dominated by c


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RAL

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 = N

i=1Ti = (E /C) 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:E / E = n / n = (L / T)However, T is constrained by the initial energy E (see above). Thus fluctuations on n are reduced: E / E = (FL / T) = (FW / E) where F is the Fano Factor


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RALResolution 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 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% ((5x5)) and aleak =2% ((3x3))Thus for the (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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RALResolution 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:samp / 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: samp / 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)


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RALResolution of hadronic calorimeters

The absorber depth required to contain hadron showers is 10 (150 cm for Cu), thus hadron calorimeters are almost all sampling calorimetersSeveral 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 > 1F° ~ 1/3 at low energies, increasing with energyF° ~ 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 E ~ 1 MeV 3%

If e/h 1 :- response with energy is non-linear- fluctuations on F° contribute to E /E

Furthermore, since the fluctuations are non-Gaussian, E /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 .


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RAL 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 scatteringCompensation 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 F° :

0 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

intr / E 20%/ E


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RAL Compensating calorimeters

Sampling fluctuations also degrade the energy resolution. As for EM calorimeters:samp / E d where d is the absorber thickness(empirically, the resolution does not improve for d ≾ 2 cm (Cu))ZEUS at HERA employed an intrinsically compensated 238U/scintillator calorimeterThe ratio of 238U thickness (3.3 mm) to scintillator thickness (2.6 mm) was tuned such that e/ = 1.00 ± 0.03For this calorimeter:

intr / E = 26%/ E and samp / E = 23%/ E

Giving an excellent energy resolution for hadrons:

had / E ~ 35%/ E

The downside is that the 238U thickness required for compensation (~ 1X0) led to a rather modest EM energy resolution:

EM / E ~ 18%/ E


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RALDual Readout Module (DREAM) approach

Measure electromagnetic component of shower independently event-by-event


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RAL DREAM test results


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RAL Jet energy resolutionAt colliders, hadron calorimeters serve primarily to measure jets and missing ET:For a single particle: E / E = a / E c At low energy the resolution is dominated by a, at high energy by cConsider a jet containing N particles, each carrying an energy ei = zi EJ

zi = 1, ei = EJ

If the stochastic term dominates: ei = a ei and: EJ = (ei )2 =

a2ei

Thus: 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: EJ (cei )2 = cEJ (zi )2

Thus: EJ / EJ = c (zi )2 and since (zi )2 < zi = 1 the error on Jet energy is less than for a single particle of the same energyFor example, in a calorimeter withE / E = 0.3 / E 0.05 a 1 TeV jet composed of four hadrons of equal energy has

EJ = 25 GeV, compared to E = 50 GeV, for a single 1 TeV hadron


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RAL Particle flow calorimetry


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RAL Compact Muon Solenoid4 T magnetic field4 T magnetic field

Objectives:• Higgs discovery• Physics beyond the Standard Model

Current data suggest a light Higgs Favoured discovery channel H Intrinsic width very small Measured width, hence S/B given by experimental resolutionHigh resolution electromagneticcalorimetry is a hallmark of CMS

Target ECAL energy resolution: ≤ 0.5% above 100 GeV

120 GeV SM Higgs discovery (5) with 10 fb-1

(100 d at 1033 cm-2s-1)

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


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RAL Measuring particles in CMS

Ele

ctro

mag

netic

C

alor

imet

er

Hadron Calorimeter Iron field return yoke interleaved

with Tracking Detectors

Superconducting Solenoid

Silicon Tracker

MuonElectronHadronPhoton

Cross section through CMS

D:\CMS Outreach\CMS Outreach\CMSmedia\CMSmovies\CMS_Slice.swf


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RAL ECAL design objectives

Coloured histograms are separate contributing backgrounds for 1fb-1

(electronic, pile-up)

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

Aim (TDR): Barrel End cap

Stochastic term: a = 2.7% 5.7% (p.e. stat, shower fluct, photo-detector, lateral leakage)

Constant term: c = 0.55% 0.55% (non-uniformities, inter-calibration, longitudinal leakage)

Noise: Low L b= 155 MeV 770 MeV

High L 210 MeV 915 MeV

( relies on interaction vertex measurement)

Integrated luminosity for 5 discovery (fb-1)

No syst errors

with syst errors

Integrated luminosity for 5 discovery (fb-1)Integrated luminosity for 5 discovery (fb-1)

No syst errors

with syst errors

Optimised analysis


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RAL The Electromagnetic Calorimeter

The crystals are slightly tapered and point towards the collision region

‘Supermodule’

Each crystal weighs ~ 1.5 kg

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

22 cm

Pb/Si Preshowers: 4 Dees (2/Endcap)

Full Barrel ECAL installed in CMS


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RAL Lead tungstate properties

Temperature dependence ~2.2%/OC Stabilise to 0.1OCFormation and decay of colour centresin dynamic equilibrium under irradiation Precise light monitoring systemLow light yield (1.3% NaI) Photodetectors with gain in mag field

But:

Fast light emission: ~80% in 25 nsPeak 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


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RAL PhotodetectorsBarrel - Avalanche photodiodes (APD)Two 5x5 mm2 APDs/crystal- Gain: 50 QE: ~75%- Temperature dependence: -2.4%/OC

20

40m

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

= 26.5 mm

MESH ANODE


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RAL Correction for impact position

120 GeV

E (GeV)

Central impact (4x4 mm2)

0.5%

120 GeV

‘Uniform’ impact (20x20 mm2) after impact-position

correction

E (GeV)

0.5%

Response for (3x3) varies by ~3% with

impact position in central crystal Correction made using information

from crystals alone(works for )

Does not depend onE,,position ( )

(3 x 3) around Crystal 184(3 x 3) around Crystal 204

(3 x 3) around Crystal 2244x4 mm2 central region


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RAL

22 mm22 mm

Series of runs at 120 GeV centred on many points within (3x3) Results averaged to simulate the effect of random impact positions

Resolution goal of 0.5%

at high energyachieved

Energy resolution: random impact


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RAL Hadron calorimeters in CMSHad Barrel: HB

Had Endcaps: HE

Had Forward: HF

Had Outer: HO

HB

HEHF

HO

Hadron Barrel16 scintillator planes ~4 mmInterleaved with Brass ~50 mmplusscintillator plane immediately after ECAL ~ 9mmplus Scintillator planes outside coil

Coil

HB

ECAL


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RAL Hadron calorimeter

The HCAL being inserted into the solenoid The brass absorber under construction

Light produced in the scintillators is tranported through optical fibres to

photodetectors


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RAL Hadron calorimetry in CMSCompensated hadron calorimetry & high precision EM calorimetry are incompatible In CMS, hadron measurement combines HCAL (Brass/scint) and ECAL(PbWO4) dataThis effectively gives a hadron calorimeter divided in depth into two compartmentsNeither 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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RALCluster-based response compensation

Use test beam data to fit for e/h (ECAL) , e/h (HCAL) and F° as a function of the raw total calorimeter energy (E + H ).Then: E = (e/)E . E + (e/)H . H

Where: (e/)E,H = (e/h)E,H / [1 + ((e/h)E,H -1) . F°)]

(ECAL+HCAL)For single pions

with cluster-based weighting


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RAL 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: 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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RAL Search for heavy gauge bosons

ZI(1000 GeV) +-

ZI(800 GeV) e+e-

Calorimetry is a powerful tool at

very high energy


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RAL 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 e+e- , SUSY (ET)

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

An introduction to calorimeters for particle physics

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