stfc ral graduate lectures 2009/10 r m brown - ral 1 an introduction to calorimeters for particle...

Graduate lectures 2009/10 R M Brown - RAL 1

STFC

RAL

An introduction to calorimeters for particle physics

Bob Brown

STFC/PPD


STFC

RALOverview

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


STFC

RALGeneral 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:

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

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

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:

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

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


STFC

RALThe electromagnetic cascade

Absorber

1 X0

A high energy e or incident on an absorber

initiates a shower ofsecondary e and via pair production

and bremsstrahlung


STFC

RALDepth 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:

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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RALAverage rate of Bremsstrahlung energy loss

E

xX0

Ei

Ei/e

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

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


STFC

RAL EM shower development in liquid krypton

GEANT simulation of a 100 GeV electron shower in the NA48 liquid Krypton calorimeter (D.Schinzel)

EM shower development in krypton (Z=36, A=84)


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RALHadronic 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/c.

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

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/c.

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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RALHadronic cascade development

In dense materials: X0 180 A / Z2 << 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 peakclose to the first interaction, followed by an exponential fall off with scale

In dense materials: X0 180 A / Z2 << 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 peakclose to the first interaction, followed by an exponential fall off with scale

eg Cu: X0 = 12.9 g.cm-2

= 135 g.cm-2


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RALDepth 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

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


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RAL

There are two general classes of calorimeter:Sampling calorimeters:Layers of passive absorber (such as Pb, or Cu) alternate with activedetector 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.

There are two general classes of calorimeter:Sampling calorimeters:Layers of passive absorber (such as Pb, or Cu) alternate with activedetector 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

Calorimeter types


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RALEnergy Resolution

The energy resolution of a calorimeter is often 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 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

The energy resolution of a calorimeter is often 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 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


STFC

RALIntrinsic 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


STFC

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 inthe crystal, F ~ 1 (Compared with a GeLi 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% ((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 arenot 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 typicalhomogeneous devices, which is impractical.Typically: samp / 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)

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:

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 typicalhomogeneous devices, which is impractical.Typically: samp / 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)


STFC

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 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 > 1

F° ~ 1/3 at low energies, increasing with energy

F° ~ a log(E)(since em component ‘freezes out’)

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 leakage and cracks .

Nuclear break-up (invisible) 42%Charged particle ionisation 43%Neutrons with TN ~ 1 MeV 12%Photons with E ~ 1 MeV 3%


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RALCompensating 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 suppressedby weighting: E*i = Ei (1- c.Ei )

Using one or more of these methods one can obtain an intrinsic resolution intr / E 20%/ E


STFC

RALCompensating 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/ = 1.00 ± 0.03 (implying e/h = 1.00 ± 0.045)

For this calorimeter the intrinsic energy resolution was:

intr / E = 26%/ E

However, Sampling fluctuations also degrade the energy resolution.

As for electromagnetic calorimeters calorimeters:

samp / E t where t is the absorber thickness

For the ZEUS calorimeter:

samp / E = 23%/ E

Giving a nonetheless excellent overall 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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RAL Dual Readout Module (DREAM) approach

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 F°

From W. Vandelli, HEP2007, Manchester


STFC

RALDREAM test results

From W. Vandelli, HEP2007, Manchester


STFC

RALJet energy resolution

At 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 c

Consider 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 energy

For 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

At 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 c

Consider 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 energy

For 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


STFC

RALParticle flow calorimetry

From M. Thomson, HEP2007, Manchester


STFC

RALCompact Muon Solenoid

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 for photons: ≤ 0.5% above 100 GeV

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

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

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 for photons: ≤ 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

4 T magnetic field4 T magnetic field3.8 T


STFC

RALMeasuring 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


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RALThe 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

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

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

Resolution goal of 0.5%

at high energyachieved

Energy resolution: random impact


STFC

RALHadron 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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RALHadron calorimetry in CMS

(ECAL+HCAL) raw response to pions vs energy (red line is MC simulation)

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

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


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RAL 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

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


STFC

RALSearch 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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RALSummary

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 …………………………

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

Some useful referencesParticle Detectors, Claus Grupen, Cambridge University Press.Calorimetry for Particle Physics, C.W. Fabian and F. Gianotti, Rev Mod Phys, 75, 1243 (2003).


STFC

RALSpare slides


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RALECAL design benchmark

Coloured histograms are separate contributing backgrounds for 1fb-1

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

( is small – measurement relies on interaction vertex identification)

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

( is small – measurement relies on interaction vertex identification)


STFC

RALLead tungstate properties

Temperature dependence ~2.2%/OC Stabilise to 0.1OC

Formation and decay of colour centresin dynamic equilibrium under irradiation Precise light monitoring system

Low light yield (1.3% NaI) Photodetectors with gain in mag field

But:

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


STFC

RALPhotodetectors

Barrel - 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


STFC

RALHadron calorimeters in CMS

Had 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


STFC

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


STFC

RAL

‘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

Jet energy resolution

stfc ral graduate lectures 2009/10 r m brown - ral 1 an introduction to calorimeters for particle...

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