The Art of Calorimetry

The Art of Calorimetry

Michele Livan Pavia University and INFN

lectures given at the XIX Seminario Nazionale di Fisica Nucleare e SubnucleareOtranto 21-27 Settembre 2006

M. Livan Pavia University & INFN

Main focus on the physics of calorimetric measurements, very little on calorimetric techniques

Topics:

Introduction to calorimetry

The development of electromagnetic and hadron showers

Energy response and compensation

Fluctuations

The state of the art (towards ILC calorimetry)


References

Wigmans, R. (2000). Calorimetry: Energy measurement in particle physics. International Series of Monographs on Physics Vol. 107, Oxford University Press

Wigmans, R. Calorimetry. Proceeding of the 10th ICFA School on Instrumentation in Elementary Particle Physics. Itacuruça, Brazil, December 2003.

AIP Conference Proceedings - Volume 674


Aknowlegments

These lectures are an enlarged version of lectures given by Richard Wigmans at the Pisa University in 2005.

Thanks to Richard for allowing me to use his lectures as a starting point.

Introduction to CalorimetryM. Livan

The Art of CalorimetryLecture I


The term Calorimetry finds its origin in thermodynamics

Calorimeters are thermally isolated boxes containing a substance to study

Modern , highly sophisticated versions, are in use in nuclear weapons Laboratories

239 Pu produces heat at a rate of 2 mwatts/g

Calorimetry can provide an accurate measurement of the amount of Plutonium in a non-invasive way


In nuclear and particle physics, calorimetry refers to the detection of particles, and measurements of their properties, through total absorption in a block of matter, called calorimeter.

Common feature of all calorimeters is that the measurement process is destructive.

Unlike, for example, wire chambers that measure particle properties by tracking in a magnetic field, the particles are no longer available for inspection once the calorimeter is done with them.

The only exception to this rule concerns muons. The fact that muons can penetrate substantial amounts of matter (as a calorimeter) is an important mean for muon identification

In the absorption process, almost all the particle’s energy is eventually converted to heat, hence the term calorimetry.


LHC beam: Total stored energy

E = 1014 protons x 14·1012 eV ≈ 1·108 J

Which mass of water Mwater could one heat up (ΔT =100 K) with this amount of energy (cwater = 4.18 J g-1 K-1) ?

Mwater = E/(c ΔT) = 239 kg

What is the effect of a 1 GeV particle in 1 liter of water (at 20° C) ?

ΔT = E/(c· Mwater) = 3.8·10-14 K !

1 calorie ≈ 107 TeV !

The rise in temperature of the calorimeter is thus negligible More sophisticated methods are needed to determine particle properties.

CDF Calorimeters


First calorimetric measurements: late 1940’s

fluorescence, invention of PMT, anthracene and NaI

α , β and γ from nuclear decays

Semiconductor detectors developed in the ‘60s

Li doped Si and Ge crystals

Nuclear radiation Detectors

γ-ray spectrum from Uranium nuclei measured with scintillation and semiconductor detectors.Semiconductor technology offers spectacularly improved resolution.


Calorimetry is a widespread technique in Particle Physics:

Shower counters

Instrumented targets

Neutrino experiments

Proton decay/Cosmic Ray detectors

4π detectors (our main topic)

Calorimetry makes use of various detection mechanisms:

Scintillation

Čerenkov radiation

Ionization

Cryogenic phenomena

Calorimetry in Particle Physics


Primary use in early experiments: measure γs from π0 → γγ

Alternate method: use sheets of material to convert photons into e+e- pairs ⇒ low efficiency

NaI(Tl) (hygroscopic), CsI and many other types of scintillating crystals

High light yield ⇒ excellent energy resolution

Scintillation light has two components: fast and slow.

Decay time of slow component can be quite sizable ( 230 ns in NaI)

In the 60’s development of shower counters (Pb-Glass) based on Čerenkov light production.

High-density material but light yield several orders of magnitude smaller than for scintillating crystals ⇒ worst energy resolution

Čerenkov light instantaneous ⇒ extremely fast signals

Shower counters I


Homogeneous calorimeters:

Scintillating crystals and Pb-Glass

Entire volume is sensitive to particles and may contribute to the signal

Sampling calorimeters:

The functions of particle absorption and signal generation are exercised by different media:

Passive medium: high density material (Fe, Cu, Pb, U, ....)

Active medium: generates light or charge that produce the signal

Scintillator, gas, noble liquids, semiconductors,.............

Only a small fraction of the energy is deposited in the active material ⇒ worse energy resolution (at least for electrons and γs)

Cheaper ⇒ used in large systems

Shower counters II


Bubble chambers: both target and detector

Electronic detectors: the two functions are usually separated.

Target

Detector

Determine if interesting interactions are taking place in the target (Triggering)

Measure the properties of the reaction products

Instrumented targets: combination of the functions of target and detector are mantained

Neutrino experiments

Proton decay experiments

Cosmic Rays experiments

Instrumented targets


Neutrino experiments ν interaction probability in a 1 kTon detector ≈ 10-9

⇒ intense beams and very massive detectors

Example WA1 (CDHS)

Slabs of Fe (absorber) interleaved with layers of scintillator.In the rear: wire chambers to track muons generated in charged currents interactions and/or charmed particles production


Cosmic Rays Atmospheric neutrinos

Result of the decay of π and Κ in the Earth atmosphere

Solar neutrinos

Produced in the nuclear fusion of H into He and some higher-order processes

High Energy Cosmic Rays

Energies up to 1 Joule (6·1018 eV)

Very large instrumented masses are needed

KASCADE Cosmic ray experiment near Karlsruhe (Germany).Large TMS (Tetramethylsilane) calorimeter located in the central building, surrounded by numerous smaller, plastic -scintillator counters to detect ionizing particles


Proton decay In many theories Barion Number conservation breaks down ⇒

proton decay is allowed

Current experimental limit on the proton lifetime based on the decay p → e+ π0 is > 1032 years

Need for large instrumented mass (300 m3 of water = 1032 protons)

SuperKamiokandeWater Čerenkov calorimeter:Enormous volume of high purity waterviewed by large number of photomultipliers: p → e+ π0 decay produces 5 relativistic particles, the positron and two e+ e- pairs from the two γs from the π0 decay.The energy carried by these particles adds up to the proton rest mass, 938.3 MeV.


4π detectors

Onion-like structure

Tracking

(Particle ID)

Electromagnetic Calorimetry

Hadronic Calorimetry

Muon spectrometry

Muons Muons ((µµ))

Hadrons (h)Hadrons (h)ee±±, , γγ

Charged TracksCharged Tracksee±±, , µµ±, ±, hh±±

Heavy absorber,(e.g., Fe)Heavy absorber,(e.g., Fe)Zone where Zone where νν and and µµ remain remain

High Z materials, e.g.,High Z materials, e.g.,lead lead tungstate tungstate crystalscrystals

Heavy material, IronHeavy material, Iron+ active material+ active material

LightweightLightweight


Why Calorimeters ? Sensitive to both charged and neutral particles

Differences in the shower patterns ⇒ some particle identification is possible (h/e/µ/ν(missing ET) separation)

Calorimetry based on statistical processes

⇒ σ(E)/E ∝ 1/√E

Magnetic spectrometers ⇒ Δp/p ∝ p

Increasing energy ⇒ calorimeter dimensions ∝ logE to contain showers

Fast: response times < 100 ns feasible

No magnetic field needed to measure E

High segmentation possible ⇒ precise measurement of the direction of incoming particles


Why Calorimeters ? Moving from fixed

target to (Hadron) Colliders emphasis :

from detailed reconstruction of particle four-vectors

to energy flow (jets, missing ET) especially when observed in combination with electrons and muons

CDF Top event

Bubble Chamber event


Particle Identification

e

γ

π+

µ

ν

Tracking

precision normal Particle ID

Calorimeters

electromagnetic hadronic Muon

Tracking

vertex momentum ID em energy h energy Muon ID,p


e/π separation (No longitudinal segmentation !)

The importance of energy resolution


Partons ⇒ Particles ⇒ Jets

Processes creating jets are very complicated, and consist of parton fragmentation, then both electromagnetic and hadronic showering in the detector

Reconstructing jets is, naturally, also very difficult. Jet energy scale and reconstruction is one of the largest sources of systematic errors


Resolution for Jets (LHC)In jet detection also factors

other than calorimeter resolution play an

important role: the jet algorithm and the

contributions of underlying events to the signal.

This effect become less important as energy

increases and jets become more collimated.

At high energy e+e- Colliders high resolution

jet measurement will become reality


Scintillators and Light Detectors

HPD

Anode

PhotoCathode

Dynodes

PM

SiPM

Pixel size: ~25 x 25 µm2 to ~100 x 100 µm2

Array size:

0.5 x 0.5 µm2 to 5 x 5 µm2


Wavelength shiftersScintillating fibers


Čerenkov radiation

Pb-GlassOPALLEP

Quarz FibersDREAM

R&D for ILC


Ionization Gas Calorimeters

Bad resolution

Landau fluctuations

Pathlenght fluctuations

Noble liquids

Potentially slow

Liquid purity problems

Stable calibration

Semiconductors

Excellent resolution

Fast

Expensive

ATLAS LAr


Cryogenic phenomena Highly specialized detectors

Dark matter, solar νs, magnetic monopoles, double β decay

Very precise measurements of small energy deposits

Phenomena that play a role in the 1 Kelvin to few milli-Kelvin range

Bolometers

Real calorimeters: temperature increase due to E deposit is measured by a resistive thermometer

Superconducting Tunnel Junctions

Use Cooper pairs excited by incident radiations that tunnel through a thin layer separating two superconductors

Superheated Superconducting Granules

Use transition from superconducting to normal state induced by energy deposition


Choosing a calorimeter Many factors:

Choices: active, passive materials, longitudinal and lateral segmentation etc.

Physics, radiation levels, environmental conditions, budget

CAVEAT: Test beam results sometimes misleading

Signals large integration time or signal integration over large volume could be not possible in real experimental conditions

Miscellaneous materials (cables, support structures, electronics etc.) present in the real experiment can spoil resolution

Jet resolution not measurable in a test beam


Basic Electromagnetic Interactions (Reminder)


Energy loss by charged particles

Main energy loss mechanism for charged particles traversing matter:

Inelastic interaction with atomic electrons

If the energy is sufficient to release atomic electrons from nuclear Coulomb field ⇒ ionization

Other processes:

Atomic excitation

Production of Čerenkov light

At high energy: production of δ-rays

At high energy: bremsstrahlung

At very high energy: nuclear reactions


The Bethe-Block Formula

dE/dx in [Mev g-1cm2]

Valid for “heavy particles

First approximation: medium simply characterized by Z/A ~ electron density

dE

dx= −4πNAr2

ec2z2 Z

A

1β2

12

ln2mec2γ2β2

I2Tmax − β2 − δ

2


Critical energy Ec

For electrons:

Ec(e-) in Cu (Z=29) = 20 MeV

For muons

Ec(µ) in Cu = 1 TeV

Unlike electrons, muons in multi-GeV range can traverse thick layers of dense matter.

Interaction of charged particles

dE

dx

Brems

=dE

dx

ion

Esolid+liqc =

610MeV

Z + 1.24Egas

c =710MeV

Z + 1.24

Emuc = Eelec

c

mµ

me

2 Energy loss (ion+rad)of e and p in Cu


Energy loss by charged particles


Energy loss by Bremsstrahlung

Radiation of real photons in the Coulomb field of the nuclei of the absorber medium

For electrons:

radiation length [g/cm2]

Interaction of charged particles

−dE

dx= 4αNA

Z2

Az2r2

eE ln183Z

13

−dE

dx=

E

X0=⇒ E = E

− xX0

0

X0 = A

4αNAZ2A z2r2

eE ln 183

Z13

−dE

dx= 4αNA

Z2

Az2(

14π0

e2

mc2)2E ln

183Z

13∝ E

m2


Interaction of photons In order to be detected a photon has to create charged particles

and/or transfer energy to charged particles

Photoelectric effect

Most probable process at low energy

P.e. effect releases mainly electrons from the K-shell

Cross section shows strong modulation if Eγ≈ Eshell

At high energies (ε>>1)

σKphoto = 4πr2

eα4Z5 1

σphoto ∝ Z5 σphoto ∝ E−3

σKphoto =

327

12

α4Z5σeTh =

Eγ

mec2σe

Th =83πr2

e (Thomson)


Photoelectric effect


Interaction of photons Compton scattering

Assume electrons quasi-free

Klein-Nishina

At high energy approximately

Atomic Compton cross-section

Compton Cross-section (Klein-

Nishina)

dσ

dΩ(θ, )

σec ∝ ln

σatomicc = Zσe

c

γ + e ⇒ γ’ + e’

σCompton ∝ E−1


Scattering Compton For all but the high Z materials: most probable process for γs in

the range between few hundred keV and 5 MeV

Typically at least 50% of the total energy is deposited by such γs

in the absorption process of multi GeV e+, e- and γs

Compton scattering is a very important process to understand the fine details of calorimetry

Angular distribution of recoil electrons shows a substantial

isotropic component. Many γs in the MeV range are absorbed by a sequence of Compton scatterings ⇒ most of the Compton

electrons produced in this process are isotropically distributed


Interaction of photons Pair production

Only possible in the field of a nucleus (or an electron) if

Eγ > 2mec2

Cross-section (High energy approximation)


Summaryµ = γ mass attenuation coefficient

Iγ = I0e−µx µi =

NA

Aσi

µ = µphoto + µcompton + µpair + ... Gammas

Electrons


Summary (Z dependence)

Z(Z + 1)

Z(Z + 1)

Z

Z Z4÷5


Z dependence

Gammas Electrons


Photon absorption

Energy domains in which photoelectric effect, Compton scattering and pair production are the most likely processes to occur as a function of the Z value of the absorber material

Electromagnetic and hadronic showers development

M. LivanThe Art of Calorimetry

Lecture II


Summary (Z dependence)

Z(Z + 1)

Z(Z + 1)

Z

Z Z4÷5


A simple shower


Simple shower model Consider only Bremsstrahlung and (symmetric) pair

production

Assume X0 ∼ λpair

After t X0:

N(t) = 2t

E(t)/particle = E0/2t

Process continues until E(t)<Ec

E(tmax) = E0/2tmax = Ec

tmax = ln(E0/Ec)/ln2

Nmax ≈ E0/Ec


Electromagnetic Showers Differences between high-Z/low-Z materials

Energy at which radiation becomes dominant

Energy at which photoelectric effect becomes dominant

Energy at which pair production becomes dominant

Showers ⇒ Particle multiplication ⇒ little material needed to contain shower

100 GeV electrons: 90% of shower energy contained in 4 kg of lead

Shower particle multiplicity reaches maximum at shower maximum

Depth of shower maximum shifts logarithmically with energy


Electromagnetic shower profiles (longitudinal)

Depth of shower max increases logarithmically

with energy


Electromagnetic Showers Longitudinal development governed by radiation length (X0)

Defined only for GeV regime

there are important differences between showers induced by e, γ:

e.g. Leakage fluctuations, effects of material upstream, ....

Mean free path of γs = 9/7 X0

Distribution of energy fraction deposited in the first

5 X0 by 10 GeV electrons and γs showering in Pb.

Results of EGS4 simulations


Electromagnetic Showers Scaling with X0 is not perfect

In high-Z materials, particle multiplication continues longer and decreases more slowly than in low-Z materials

The number of positrons strongly increases with the Z value of the absorber material

Example: number of e+/GeV in Pb is 3 times larger than in Al

Need more X0 of Pb to contain shower at 90% level


Scaling is NOT perfect


Electromagnetic shower leakage (longitudinal)

• The absorber thickness needed to contain a

shower increases logarithmically with

energy

• The number of X0 needed to fully contain

the shower energy can be as much as 10 X0 going from high Z to low Z

absorbers

• More X0 needed to contain γ initiated

showers


Electromagnetic Showers

Phenomena at E < Ec determine important calorimeter properties

In lead > 40% of energy deposited by e± with E < 1 MeV

Only 1/4 deposited by e+, 3/4 by e- (Compton, photoelectrons!)

The e+ are closer to the shower axis, Compton and photoelectrons in halo


Importance of SOFT particles

10 GeV e-

• The composition of em showers. Shown are the percentages of the energy of 10 GeV electromagnetic showers deposited through shower particles with energies below 1 MeV, below 4 MeV or above 20 MeV as function of the Z of the absorber material.

• Results of EGS4 simulations


Electromagnetic Showers

Lateral shower width scales with Molière radius ρM

ρM much less material dependent than X0

Lateral shower width determined by:

Multiple scattering of e± (early, 0.2 ρM)

Compton γs travelling away from axis (1 - 1.5 ρM)

ρM = EsX0

EcEs = mec

2

4π/α

X0 ∝ A/Z2, Ec ∝ 1/Z ⇒ ρM ∝ A/Z


Lateral profile Material

dependence

Radial energy deposit profiles for 10 GeV electrons showering in Al, Cu and Pb

Results of EGS4 calculations


Lateral profile

Radial distributions of the energy deposited by 10

GeV electron showers in Cu.

Results of EGS4 simulations


Electrons and positrons

The number of positrons increases by more than a factor 3 going from Al to U

Aluminum (∼18 e+/GeV)

Uranium (∼60 e+/GeV)

Increase due to the fact that particle multiplication in showers developing in high-Z absorber materials continues down to much lower energies than in low-Z materials


Contributions to signal


Lateral shower leakage

• No energy dependence

• A (sufficiently long) cylinder will contain the same fraction of energy of a 1 GeV or 1 TeV em shower

• Results of EGS4 simulations


Muons in calorimeters

Muons are not minimum ionizing particles

The effects of radiation are clearly visible in calorimeters, especially for high-energy muons in high-Z absorber material

Ec(µ) =mµ

me

2× Ec(e)

=⇒ Ec(µ) ≈ 200 GeV in Pb


Muon signals in a calorimeter

Signal distributions for muons of 10, 20, 80 and 225 GeV traversing the SPACAL detector


Hadron showers

Extra complication: the strong interaction Much larger variety may occur both at the particle level

and at the level of the stuck nucleus Production of other particles, mainly pions Some of these particles (π0, η) develop electromagnetic

showers Nuclear reactions: protons, neutrons released from nuclei Invisible energy (nuclear binding energy, target recoil)


Hadron vs em showers Hadron showers ⇒ much more complex than em showers

Invisible energy em showers: all energy carried by incoming e or γ goes to ionization had showers: certain fraction of energy is fundamentally

undetectable em showers

e± ⇒ continuous stream of events ( ionization + bremsstrahlung) γ ⇒ can penetrate sizable amounts of material before losing energy

had showers ionization (as a µ) then interaction with nuclei development similar to em shower but different scale ( λ vs. X0) Particle sector Nuclear sector


The electromagnetic fraction, fem

em decaying particles : π0, η0 ⇒ γ γ % of hadronic energy going to em fluctuates heavily On average 1/3 of particles in first generation are π0s π0s production by strongly interacting particles is an irreversible

process (a ”one-way street”) Simple model

after first generation fem = 1/3 after second generation fem = 1/3 + 1/3 of 2/3 = 5/9 after third generation fem = 1/3 + 1/3 of 2/3 + 1/3 of 4/9 = 19/27 after n generations fem = 1 - (1- 1/3)n

the process stops when the available energy drops below the pion production threshold and n depends on the average multiplicity of mesons produced per interaction <m> ⇒ n increases by one unit every time E increases by a factor <m>

fem increases with increasing incoming hadron energy


The electromagnetic fraction, fem

But other particles than pions are produced (factor 1/3 wrong) <m> is energy dependent barion number conservation neglected → lower fem in proton

induced showers than in pion induced ones Using a more realistic model

< fem > = 1- (E/E0)(k-1)

E0= average energy needed to produce a π0

(k-1) related to the average multiplicity < fem > slightly Z dependent

Consequences: Signal of pion < signal of electron (non-compensation) e/π signal ratio energy dependent (non-linearity)


Energy dependence em component

SPACAL: Pb - scintillating fibers QFCAL: Cu - quartz fibers


Signal non-linearity


Non em component Breakdown of the non-em component in Lead

Ionizing particles 56% (2/3 from spallation protons)

Neutrons 10% (37 neutrons/GeV)

Invisible 34%

Spallation protons carry typically 100 MeV

Evaporation neutrons 3 MeV


Where does the energy go ?

Energy deposit and composition of the non-em component of hadronic showers in lead and iron.

The listed numbers of particles are per GeV of non-em energy


A typical process Nuclear interaction (nuclear star) induced by a proton of

30 GeV in a photographic emulsion

Protons(isotropic)

Fast pions and fast spallation protons( non-isotropic)

Spallation neutrons( non-visible)


Neutron production spectra

dN

dE=√

E exp(−E/T )


Hadronic shower profiles

Shower profiles are governed by the

Nuclear interaction lenght, λint

λint (g cm-2) ∝ A1/3

Fe 16.8 cm, Cu 15.1 cm, Pb 17.0 cm, U 10.0 cm


Longitudinal profile


Hadronic showers fluctuations

Very interesting measurements of the longitudinal energy deposition in em and hadronic showers were made with the “Hanging file calorimeter”


Fluctuations (em showers)

Hanging file calorimeter

170 GeV electrons


Fluctuations (hadronic showers)


270 GeV pions


Fluctuations (hadronic showers)


270 GeV pions


Hadronic lateral shower profiles

Lateral shower profile has two components:

Electromagnetic core (π0)

Non-em halo (mainly non-relativistic shower particles)

Spectacular consequences for Čerenkov calorimetry

Čerenkov light is emitted by particles with β > 1/n e.g. quartz (n= 1.45) : Threshold 0.2 MeV for e, 400 MeV

for p





Nonrelativistic particles dominate tails in hadron showers


Lateral distribution shower particles

Np produced by thermal neutron capture

Mo fission product of U produced by non-thermal neutrons (MeV)

U produced by γ (10 GeV) induced reactions present in the em core


Shower containment

Shower containment:

Depth to contain showers increases with log E

Lateral leakage decreases as the energy goes up ! <fem> increases with energy Electromagnetic component concentrated in a narrow cone

around shower axis ⇒ Energy fraction contained in a cylinder with a given radius

increases with energy


Hadronic shower leakage (longitudinal)


Hadronic shower leakage (lateral)

This energy dependence is a direct consequence of the energy of <fem>. The average energy fraction carried by the em shower component increases with energy and since this component is concentrated in a narrow cone around the shower axis, the energy fraction contained in a cylinder with a given radius increases with energy as well.


Hadronic shower profiles

The λint/X0 ratio is important for particle ID

In high-Z materials: λint/X0 ∼ 30 ⇒ excellent e/π separator

1 cm PB + scintillator plate makes spectacular preshower detector


Comparison em/hadronic calorimeter properties

Ratio of the nuclear interaction lenght and the radiation lenght as a function of Z


Particle ID with a simple preshower detector


Lessons for calorimetry In absorption process, most of the energy is deposited by very

soft particles Electromagnetic showers:

3/4 of the energy deposited by e-, 2/4 of it by Compton, photoelectrons

These are isotropic, have forgotten direction of incoming particle ⇒ No need for sandwich geometry

The typical shower particle is a 1 MeV electron, range < 1mm ⇒ important consequences for sampling calorimetry

Hadron showers: Typical shower particles are a 50-100 MeV proton and a 3 MeV

evaporation neutron Range of 100 MeV proton is 1 - 2 cm Neutrons travel typically several cm What they do depends critically on detail of the absorber


Angular distributiom


Range of protons generated in hadron showers

Average range of protons in various absorber materials, as a function of energy

Energy Response and Compensation


Lecture III


Lessons for calorimetry In absorption process, most of the energy is deposited by very

soft particles Electromagnetic showers:

3/4 of the energy deposited by e-, 2/4 of it by Compton, photoelectrons

These are isotropic, have forgotten direction of incoming particle ⇒ No need for sandwich geometry

The typical shower particle is a 1 MeV electron, range < 1mm ⇒ important consequences for sampling calorimetry

Hadron showers: Typical shower particles are a 50-100 MeV proton and a 3 MeV

evaporation neutron Range of 100 MeV proton is 1 - 2 cm Neutrons travel typically several cm What they do depends critically on detail of the absorber



Response = Average signal per unit of deposited energy

e.g. # photoelectrons/GeV, picoCoulombs/MeV, etc

A linear calorimeter has a constant response

The Calorimeter Response Function

• Electromagnetic calorimeters are in general linear

• All energy deposited through ionization/excitation of absorber

• If not linear ⇒ instrumental effects (saturation, leakage,....)


Signal linearity for electromagnetic showers

Example: Saturation effects in

PMTs Voltage between last

dynodes lowered by high current

⇒ lower PMT gain


Saturation in ”digital” calorimeters Gaseous detector operated in “digital” mode

Geiger counters or streamer chambers Intrinsically non linear:

Each charged particle creates an insensitive region along the stuck wire preventing nearby particles to be registered

Density of particles increases with increasing energy ⇒ calorimeter response decreases with increasing energy

Example: Calorimeter read out using wire chambers in “limited

streamer” mode Energy varied by depositing n (n = 1-10) positrons of 17.5

GeV simultaneously in the calorimeter Energy deposit profile not energy dependent Calorimeter longitudinally subdivided in 5 sections


Saturation in ”digital” calorimeters

At n=6 Non linearity:

1 - 14.5 % 2 - 14.8 % 3 - 9.3 % 4 - 2.4 % 5 - 0.5 %

Non-linearity in sect. 1 more than 6 times the one in sect. 4 Energy deposit in sect. 1 less than half of the one in sect. 4 Particle density in sect. 1 larger than in sect. 4


Fluctuations due to instrumental effects (readout)

Electrons from shower leakage traversing SPDs generate signals order of magnitude larger than the ones generated by scintillation photons


Homogeneous calorimeters I Homogeneous: absorber and active media are the same Response to muons

because of similarity between the energy deposit mechanism response to muons and em showers are equal

⇒ same calibration constant ⇒ e/mip=1 Response to hadrons and jets

Due to the invisible energy π/e < 1 e/mip =1 ⇒ π/mip < 1 Response to hadron showers smaller than the electromagnetic

one Electromagnetic fraction (fem) energy dependent ⇒ response to electromagnetic component increases with energy

⇒ π/e increases with energy


Homogeneous calorimeters II Calorimeter response to non-em component (h) energy

independent ⇒ e/h > 1 (non compensating calorimeter) e/π not a measure of the degree of non-compensation

part of a pion induced shower is of em nature fem increases with energy ⇒ e/π ⇒ tends to 1

e/h cannot be measured directly

fem function of energy

π = fem · e + (1− fem) · h

π/e = fem + (1− fem) · h/e

e/π =e/h

1− fem[1− e/h]


Hadron showers: e/h and the e/π signal ratio


Homogeneous calorimeters III Response to jets Jet = collection of particles resulting from the fragmentation of a

quark, a diquark or a hard gluon From the calorimetric point of view absorption of jets proceeds

in a way that is similar to absorption of single hadrons (Minor) difference:

em component for single hadrons are π0 produced in the calorimeter jets contain a number of π0 (γ from their decays) upon entering the

calorimeter (“intrinsic em component”) <fem> for jets and single hadrons different and depending on the

fragmentation process No general statement can be made about differences between

response to single hadrons and jets but: response to jets smaller than to electrons or gammas response to jets is energy dependent


Sampling calorimeters Sampling calorimeter: only part of shower energy deposited

in active medium Sampling fraction fsamp

fsamp is usually determined with a mip (dE/dx at minimum)

N.B. mip’s do not exist ! e.g. D0 (em section):

3 mm 238U (dE/dx = 61.5 MeV/layer) 2 x 2.3 mm LAr (dE/dx = 9.8 MeV/layer) fsamp = 13.7%

fsamp =energy deposited in active medium

total energy deposited in calorimeter


The e/mip ratio D0: fsamp = 13.7%

However, for em showers, sampling fraction is only 8.2% ⇒ e/mip ≈ 0.6

e/mip is a function of shower depth, in U/LAr it decreases e/mip increases when the sampling frequency becomes very high

What is going on ? Photoelectric effect: σ ∝ Z5, (18 / 92)5 = 3 · 10-4

⇒ Soft γs are very inefficiently sampled Effects strongest at high Z, and late in the shower development The range of the photoelectrons is typically < 1 mm Only photoelectrons produced near the boundary between active

and passive material produce a signal ⇒ if absorber layers are thin, they may contribute to the signals


Sampling calorimeters: the e/mip signal ratio

e/mip larger for LAr (Z=18) than for scintillator e/mip ratio determined by the difference in Z values between

active and passive media


Gammas

At high energy γ/mip ≈ e/mip Below 1 MeV the efficiency for γ detection drops

spectacularly due to the onset of the photoelectric effect


The EM sampling fraction changes with depth !

e/mip changes as the shower develops The effect can be understood from the the changing composition of

the showers Early phase: relatively fast shower particles (pairs) Tails dominated by Compton and photoelectric electrons

Very relevant for the calibration of longitudinally segmented em calorimeters !

Must use different calibration constants


The e/mip ratio: dependence on sampling frequency

Only photoelectrons produced in a very thin absorber layer near the boundary between active and passive materials are sampled

Increasing the sampling frequency (thinner absorber plates) increases the total boundary surface


The hadronic response is not constant fem, and therefore e/π signal ratio is a function of energy If calorimeter is linear for electrons, it is non-linear for hadrons

Energy-independent way to characterize hadron calorimeters: e/h e = response to the em shower component h = response to the non-em shower component → Response to showers initiated by pions:

e/h is inferred from e/π measured at several energies (fem values) Calorimeters can be

Undercompensating (e/h > 1) Overcompensating (e/h < 1) Compensating (e/h =1)

Hadronic shower response and the e/h ratio

Rπ = fem e + [1− fem] h → e/π =e/h

1− fem[1− e/h]


Hadron Showers Energy dependence EM component


Hadronic signal (non)-linearity at low energy

At low energy response to hadrons resembles the one for mips at low energy, and if e/mip ≠1 ⇒ the calorimeter is by definition non linear, regardless the degree of compensation


Hadronic signal (non)-linearity: dependence on e/h


Non-linearity and e/h Non-linearity determined by e/h value of the calorimeter Measurement of non-linearity is one of the methods to

determine e/h Assuming linearity for em showers:

Linearity (at least for E > 5 GeV) is only one of the main advantages of compensating calorimeters

π(E1)π(E2)

=fem(E1) + [1− fem(E1)](e/h)−1

fem(E2) + [1− fem(E2)](e/h)−1

e/h = 1⇒ π(E1)π(E2)

= 1


Non-em calorimeter response I Energy deposition mechanisms that play a role in the

absorption of the non-em shower energy: Ionization by charged pions (Relativistic shower component).

The fraction of energy carried by these particles is called frel

Ionization by spallation protons (non-relativistic shower component). The fraction of energy carried by these particles is called fp

Kinetic energy carried by evaporation neutrons may be deposited in a variety of ways. The fraction of energy carried by these particles is called fn

The energy used to release protons and neutrons from calorimeter nuclei, and the kinetic energy carried by recoil nuclei do not lead to a calorimeter signal. This energy represent the invisible fraction finv of the non-em shower energy


Non-em calorimeter response II h can be written as follows:

rel, p, n and inv denote the calorimeter responses Normalizing to mips and eliminating the last term (inv =0)

The e/h value can be determined once we know its response to the three components of the non-em shower components

h = frel · rel + fp · p + fn · n + finv · inv

frel + fp + fn + finv = 1

e

h=

e/mip

frel · rel/mip + fp · p/mip + fn · n/mip


Compensation (I) Need to understand response to typical shower particles

(relative to mip)

Relativistic charged hadrons Even if relativistic, these particles resemble mip in their

ionization losses ⇒ rel/mip = 1

Spallation protons and Neutrons Spallation protons

More efficient sampling Signal saturation


Aspects of compensation: sampling of soft shower protons

Results from Monte Carlo simulation Quite complicated picture, many effects contribute:

ratio of specific ionization in the active and passive materials ↑,

multiple scattering effects ↓, sampling inefficiencies due to limited range ↓ saturation and recombination effects in the active medium ↓


Aspects of compensation: sampling of soft shower protons


Aspects of compensation: saturation effects

dL

dx= S

dE/dx

1 + kb · dE/dxBirk’s Law


Compensation: the spallation proton/mip signal ratio


Compensation: the spallation proton/mip signal ratio

Response to spallation protons depends on: spallation protons energy spectrum Z value of the absorber fsamp and ffreq saturation properties of the active medium


Compensation (II) Need to understand response to typical shower particles

(relative to mip)

Spallation protons and Neutrons

Neutrons (n, n’γ) inelastic scattering: not very important (n, n’) elastic scattering: most interesting (n, γ) capture (thermal): lots of energy, but process is slow (µs)


Compensation (III) - The role of neutrons Elastic scattering felastic = 2A/(A+1)2

Hydrogen felastic = 0.5 Lead felastic = 0.005 Pb/H2 calorimeter structure (50/50)

1 MeV n deposits 98% in H2

mip deposits 2.2% in H2

Recoil protons can be measured! ⇒ Neutrons have an enormous potential to amplify

hadronic shower signals, and thus compensate for losses in invisible energy

Tune the e/h value through the sampling fraction! e.g. 90% Pb/10% H2 calorimeter structure

1 MeV n deposits 86.6% in H2


⇒ n/mip = 45

⇒ n/mip = 350


Compensation in a Uranium/gas calorimeter


Compensation: the importance of soft neutrons


Compensation (III) - The role of neutrons Elastic scattering felastic = 2A/(A+1)2

Hydrogen felastic = 0.5 Lead felastic = 0.005 Pb/H2 calorimeter structure (50/50)

1 MeV n deposits 98% in H2


Recoil protons can be measured! ⇒ Neutrons have an enormous potential to amplify

hadronic shower signals, and thus compensate for losses in invisible energy

Tune the e/h value through the sampling fraction! e.g. 90% Pb/10% H2 calorimeter structure

1 MeV n deposits 86.6% in H2


⇒ n/mip = 45

⇒ n/mip = 350


Compensation: the crucial role of the sampling fraction


Compensation in practice: Pb/scintillator calorimeters


Compensation in Fe/scintillator calorimeters ?


Compensation: slow neutrons and the signal’s time structure

Average time between elastic n-p collisions: 17 ns in polystyrene

Measured value lower (10 ns) due to elastic or inelastic neutron scattering off other nuclei present in the calorimeter structure (Pb, C and O)


Compensation: effects of slow neutrons on the signals


Non-hydrogenous calorimeters: Z dependence of e/h


Compensation (IV) All compensating calorimeters rely on the contribution

of neutrons to the signals Ingredients for compensating calorimeters

Sampling calorimeter Hydrogenous active medium (recoil p!) Precisely tuned sampling fraction

e.g. 10% for U/scintillator, 3% for Pb/scintillator,....... Uranium absorber

Helpful, but neither essential nor sufficient

Fluctuations


Lecture IV


Calorimetric measurement In the previous lecture we examined the average signals

produced during absorption To make a statement about the energy of a particle:

relationship between measured signal and deposited energy (calibration)

energy resolution (precision with which the unknown energy can be measured)

Resolution is limited by: fluctuations in the processes through which the energy is degraded

(unavoidable) ultimate limit to the energy resolution in em showers (worsened by detection

techniques)

not a limit for hadronic showers ? (clever readout techniques can allow to obtain resolutions better than the limits set by internal fluctuations

technique chosen to measure the final products of the cascade process


Fluctuations (1) Calorimeter’s energy resolution is determined by fluctuations

→ applying overall weighting factors (offline compensation) has no merit in this context

Many sources of fluctuations may play a role, for example: Signal quantum fluctuations (e.g. photoelectron statistics)

Sampling fluctuations

Shower leakage

Instrumental effects (e.g. electronic noise, light attenuation, structural non-uniformity)

but usually one source dominates

Improve performance ⇒ work on that source

Poissonian fluctuations: Energy E gives N signal quanta, with σ = √N

⇒ σ√E ∝ √N√N = cE ⇒ σ/E=c/√E


What excellent resolution does for you


Fluctuations (2)

Signal quantum fluctuations

Ge detectors for nuclear γ ray spectroscopy: 1 eV/quantum

⇒ If E= 1 MeV: 106 quanta, therefore σ/E = 0.1%

Usually E expressed in GeV ⇒ σ/E = 0.003%/√E

Quartz fiber calorimeters: typical light yield ∼ 1 photoelectron/GeV

Small fraction of energy lost in Čerenkov radiation, small fraction of the light trapped in the fiber, low quantum efficiency for UV light

⇒ σ/E = 100%/√E. If E = 100 GeV, σ/E = 10%


Signal quantum fluctuations dominate (1)

Quartz window transmit a larger fraction of the Čerenkov light (UV component)


Signal quantum fluctuations dominate also here (2)

Asymmetric distribution typical of Poisson distribution

At high energy Gaussian shape (central limit theorem)


Fluctuations (3)

Sampling fluctuations

Determined by fluctuations in the number of different shower particles contributing to signals

Both sampling fraction and the sampling frequency are important

Poissonian contribution : σsamp/E = asamp/√E

ZEUS: No correlation between particles contributing to signals in neighboring sampling layers ⇒ range of shower particles is very small


Sampling fraction and sampling frequency

For fiber calorimeters for equal sampling fraction, better resolution for smaller diameter fibers (higher sampling frequency)


Sampling fluctuations in em calorimetersDetermined by sampling fraction and sampling frequency


How to measure signal quantum fluctuations

Reduce the # of photoelectrons using a neutral density filter by a factor f (f>1)

x = light yield of the calorimeter

# of p.e. for an energy deposit E is xE, σ=√(xE), (σ/E)p.e.=1/√(xE)

Contribution of sampling fluctuations: (σ/E)samp=asamp/√(E)

If f is known ⇒ determine x

Better at low energy where non stochastic contributions are limited

(σ/E)nofilter =

a2samp/E + 1/xE

(σ/E)filter =

a2samp/E + f/xE =

(σ/E)2nofilter + (f − 1)/xE


How to measure signal quantum fluctuations

f = 3 and 10

3, 8,10,15 GeV

1300 ± 90 p.e./GeV

2.8%/√E contribution to resolution

5.7%/√E: total em resolution

5.0%/√E sampling fluctuation contribution

NIM A368 (1996), 640


How to measure the effects of sampling fluctuations (I)

To measure sampling fluctuations:

Choose conditions in which sampling fluctuations contribute substantially to the total energy resolution

Change the sampling fraction keeping everything else the same

Derive the contribution of sampling fluctuations from a comparison of the total energy resolution before and after these changes were made


How to measure the effects of sampling fluctuations (II)

σsum = calorimeter resolution

σdiff = contribution of sampling fluctuations

for em showers σsum = σsamp

σA = σB = σsum√2 = σsamp√2

If fluctuations in A and B completely uncorrelated

σsum = σdiff = σsamp

If other sources contribute → σsum > σdiff and σA , σB < σsum√2

At the extreme (sampling fluctuations not relevant)

σA , σB = σsum√2 and σsamp(A) = σsamp(A+B)√2


How to measure the effects of sampling fluctuations (III)

Measurement of the p.e. statistics

p.e. statisticscontribution

sampling fluctuationscontribution

NIM A290 (1990), 335


How to measure the effects of sampling fluctuations (IV)

Energy resolution for em showers strongly dominated by sampling fluctuations

Sampling fluctuations in good agreement with the formula: Sampling fluctuations strongly dominate the hadron resolution in these

compensating calorimeters Hadronic sampling fluctuations are about a factor 2 larger than the em

ones “Intrinsic” fluctuation contribution scale as E-1/2

asamp = 2.7%

d/fsamp


Sampling fluctuations in em and hadronic showers

em resolution dominated by sampling fluctuations

sampling fluctuations only minor contribution to hadronic resolution in this non compensating

calorimeter


Fluctuations (4)

Shower leakage fluctuations

These fluctuations are non-Poissonian

For a given average containment, longitudinal fluctuations are larger that lateral ones

Difference comes from # of particles responsible for leakage

e.g. Differences between e, γ induced showers


Contribution of leakage fluctuations to energy resolution

Longitudinal shower fluctuations and therefore leakage are essentially driven by by fluctuations in the starting point of the shower, i.e. by the behavior of one single shower particle.

Lateral shower fluctuations generated by many particles


Effects back-, front, and side leakage on em energy resolution

Albedo relevant for particles below 100 MeV


Leakage and leakage fluctuations in electron / γ induced showers

•γ-induced showers may start considerably deeper inside the absorber than electron showers. As a consequence, they are also less contained• Large event-to-event fluctuation in the starting point of γ-induced showers have no equivalent in electron showers


Fluctuations (5)

Instrumental effects

Structural differences in sampling fraction

“Channelling” effects

Electronic noise, light attenuation,.....


Instrumental effects: channelling in fiber calorimeters

•Sampling fraction for em showers: 2%•Electrons entering the calorimeter at 0º exactly at the position of a fiber loose very little energy in the early stages of the shower development and can cause longitudinal leakage•Shower particles escaping from the back traverse a region where there is no more Pb, the fibers are bundled and the sampling fraction is almost 100%


Fluctuations (6)

Different effects have different energy dependence

quantum, sampling fluctuations σ/E ∼ E-1/2

shower leakage σ/E ∼ E-1/4

electronic noise σ/E ∼ E-1

structural non-uniformities σ/E = constant

Add in quadrature σ2tot = σ21 + σ22 + σ23 + σ24+......


The em resolution of the ATLAS em calorimeter


Fluctuations in hadron showers (I)

Some types of fluctuations as in em showers, plus

Fluctuations in visible energy

(ultimate limit of hadronic energy resolution)

Fluctuations in the em shower fraction, fem

Dominating effect in most hadron calorimeters (e/h≠1)

Fluctuations are asymmetric in pion showers (one-way street)

Differences between p, π induced showers

No leading π0 in proton showers (barion # conservation)


Hadron showers: fluctuations in nuclear binding energy losses

Distribution of nuclear binding energy loss that may occur in spallation reaction induced by protons with a kinetic energy of 1 GeV on 238U (more of 300 different reactions contributing)

Estimate of the fluctuations of nuclear binding energy loss in high-Z materials (based on the relative contributions of particles of different energies): σ/ΔEB ≈ 15%/√(ΔEB)

Note the strong correlation between the distribution of the binding energy loss and the distribution of the number of neutrons produced in the spallation reactions

There may be also a strong correlation between the kinetic energy carried by these neutrons and the nuclear binding energy loss


Fluctuations in hadron showers (II)

Some types of fluctuations as in em showers, plus

Fluctuations in visible energy

(ultimate limit of hadronic energy resolution)

Fluctuations in the em shower fraction, fem

Dominating effect in most hadron calorimeters (e/h≠1)

Fluctuations are asymmetric in pion showers (one-way street)

Differences between p, π induced showers

No leading π0 in proton showers (barion # conservation)


Hadron showers: Fluctuations in em shower fraction (fem)

Pion showers Due to the irreversibility of the production of π0s and because

of the leading particle effect, there is an asymmetry between the probability that an anomalously large fraction of the energy goes into the em shower component


Hadronic response function: effect of e/h

Undercompensating calorimeter: showers with anomalously large fem values produce anomalously large signals

Overcompensating calorimeters: such showers produce anomalously small signals

Compensating calorimeters: Gaussian distribution


Fluctuations in fem: differences p/π induced showers

<fem> is smaller in proton-inducer showers than in pion-induced ones: barion number conservation prohibits the production of leading π0s and thus reduces the em component respect to pion-induced showers


Hadronic energy resolution of non-compensating calorimeters does not scale with E-1/2 and is often described by:

Effects of non-compensation on σ/E is are better described by an energy dependent term:

In practice a good approximation is:

Fluctuations in hadron showers (III)

σ

E=

a1√E⊕ a2

σ

E=

a1√E⊕ a2

E

E0

l−1

σ

E=

a1√E

+ a2


Hadronic resolution of non-compensating calorimeters

ATLAS Fe-scintillator

prototype


Hadronic resolution of non-compensating calorimeters

Differences between the two curves become significant only at energies > 400 GeV where experimental data are not available


Fluctuations in hadron showers (IV)

The ultimate limit on hadronic energy resolution is determined by the correlation between ∑En and nuclear binding energy loss

Better in Pb than in Uranium (14%√E vs. 21%√E)


The ultimate limit on hadronic energy resolution


Lessons for calorimeter design (1)

Improve resolution ⇒ work on fluctuation that dominate

example: 60 ton (liquid) scintillator does not make good hadron calorimeter.

All fluctuations eliminated, except non-compensation: σ/E > 10% at all energies!

SPACAL (e/h ≈ 1.0, but other sources of fluctuation present): σ/E ≈2% at E=300 GeV


Hadron calorimeters: effects of fem fluctuations on resolution


Lessons for calorimeter design (II) Do not spend your money reducing fluctuations that

do not dominate

Practical examples:

A 2 λint deep calorimeter for extraterrestrial detection of high energy cosmic hadrons is dominated by shower leakage

⇒ A high-quality crystal calorimeter is as good (bad) as a crudely sampling one

A calorimeter system with a crystal em section will have a poor performance for hadron detection, no matter what you choose as hadronic section, because of the large e/h value of homogeneous devices

⇒ Don’t waste your money on the hadronic section


Dominating fluctuations dominate !


Calibration of calorimeter systems Determine relationship between signal (pC, p.e.)

and energy (GeV)

Fundamental problem in sampling calorimeters:

Different shower components are sampled differently

Shower composition changes as shower develops

Sampling fraction changes with shower age (also E dependent)

How to intercalibrate the sections of a longitudinally segmented calorimeter?

See NIM A 409 (1998), 621 and NIM A 485 (2002), 385


Sampling fraction changes as shower develops

Samplig fraction changes as much as 30% !

shower dominated by mip’s

shower dominated by soft γ’s


Consequences of the depth dependence of fsamp

HELIOSCalorimeter


Calibration of longitudinally segmented device

Calibration by minimizing total width: Calibration constants are energy dependent Response non-linearity is introduced Systematic mismeasurement of energy

i = calorimeter towersj = event numbers


Calibrating a segmented device by minimizing total signal widthGIVES WRONG RESULTS


Results of miscalibration: non-linearity


Results of miscalibration: mass dependence


Results of miscalibration: mass dependence


Calibration (hadrons)

Effects are even worse for hadrons

Reconstructed energy depends on starting point of shower

If calorimeter is calibrated with pions, jet energies are systematically mismeasured

Resolution is not only determined by the width of a signal distribution, it is also necessary that the distribution is centered around the correct value


Calibration of hadron calorimeters


Alternative method: each section with its own particles

Problem: how about hadrons that start shower in section A?

Energy systematically mismeasured depending on e/h values of sections A,B

Reconstructed energy depends on starting point of shower


Wrong B/A: response depends on starting point


Conclusions on calibration Calibration is a very delicate issue

Discussed strategies (and several others used in practice) only work for a subset of events

electrons of a certain energy, pions penetrating em section, ...

Negative consequences for the rest of the events

Systematic mismeasurement of energy

Reconstructed energy depends on starting point shower

Signal non-linearity, ...

Correct method: B/A =1

i.e. calibrate all calorimeter sections in the same way (electrons or if not possible muons)

The state of artTowards ILC calorimetry


Lecture V


Important calorimeter features

Energy resolution

Position resolution (need 4-vectors for physics)

Particle ID capability

Signal speed


The importance of energy resolution


Particle ID does NOT require segmetation

e/π separation using time structure of the signals


The importance of signal speed


Important calorimeter features Energy resolution

Position resolution (need 4-vectors for physics)

Signal speed

Particle ID capability

but also

Gaussian response function (avoid bias for steeply falling distributions)

Signal linearity or, at least

Well known relationship between signal and energy (reliable calibration)

Most hadron calorimeter fall short in this respect


High resolution hadron spectroscopy High-resolution Hadron Calorimetry (for jet spectroscopy)

very relevant for Linear high-energy e+e- Colliders

Uncertainties due to jet algorithms/underlying event small

No constrained fits as in LEP (beamsstralhung)

⇒ Intrinsic detector properties limiting factor

High-resolution Electromagnetic and high-resolution Hadronic calorimetry are mutually exclusive:

Good jet energy resolution ⇒ Compensation ⇒ very small sampling fraction (∼ 3%) ⇒ poor electron, photon resolution

Good electromagnetic resolution ⇒ high sampling fraction (100% Crystals, 20% LAr) ⇒ large non compensation ⇒ poor jet resolution


Ultimate hadron calorimetry Why not aim for hadron calorimetry with the same

level of precision as achievable in electromagnetic calorimeters ?

⇒ Need to eliminate/reduce hadron-specific fluctuations

Fluctuations in electromagnetic shower content (fem)

Fluctuations in “visible energy” (nuclear breackup)

Achievable limit: σ/E ~ 15%/√E


Fluctuations in the em shower component (fem)

Why are these important ? Electromagnetic calorimeter response ≠ non-em response (e/h ≠ 1) Event-to-event fluctuations are large and non-Gaussian <fem> depends on shower energy and age

Cause of all common problems in hadron calorimeters Energy scale different from electrons, in energy-dependent way Hadronic non-linearity Non-Gaussian response fuction Poor energy resolution Calibration of the sections of a longitudinally segmented detector

Solutions Compensating calorimeters (e/h = 1), e.g. Pb/plastic scintillator Measure fem event-by-event


High resolution jet spectroscopyCompensating Pb/scintillator calorimetry


What compensation does and does not for you

Compensation does not guarantee high resolution

Fluctuations in fem are eliminated, but others may be very large

Example: Texas Tower effect

Compensation has some drawbacks

Small sampling fraction required → em resolution limited

Relies on neutrons → calorimeter signals have to be integrated over large volume and time. SPACAL’s 30%/√E needed 15 tonnes and 50 ns. Not always possible in practice


Compensation in a U/gas calorimeter


Compensation in gas calorimetersHadronic response function


Compensation requires large integration volume!


High-resolution hadron calorimetry

Non-solution

There is no merit in “offline compensation” (e/π by weighting)

Resolution is determined by fluctuations, not by mean values

Side effect: increased signal non-linearity, response depends on starting point shower,... See NIM A487 (2002) 381


“Dummy” compensation


Particle Flow Analysis (PFA) Use tracking, particle ID and calorimetry to

measure 4-vectors of jets Charged particles represent tipically 65% of the

jet energy However, if only charged jet components are

measured: (σ/Ejet) = 25-30/% independent of jet energy Calorimetry essential

The problem with this method is shower overlap. Need to deconvolute contributions from showering charged particles to avoid double counting

This problem is not solvable with a finer granularity. The showers have certain transverse dimensions and exhibit large fluctuations in all dimensions

Larger distance vertex-calorimeter and larger B-field would help

NIM A495 (2002) 107: Method may give improvement of ~ 30%


Design goal ILC: separate W, Z qq

No kinematic constrains as in LEP (Beamstrahlung)

-

Mjj

Mjj

LEP-like detector ILC design goal

60%/√E 30%/√E


Example of PFA at LEP: ALEPH

Attempt to reconstruct hadronic event structure using particle identification and software compensation


PFA at Hadron Collider No kinematic constraints as at LEP


PFA @ ILC: High Density + Fine Granularity In order to reduce problems of shower overlap, ILC R&D focuses on

reducing the shower dimensions and decreasing the calorimeter cell size

X0 = 1.8 cm, λI=17 cm X0 = 0.35 cm, λI=9.6 cm

Iron Tungsten

How about calibration ?


PFA method: “π” jet

The circles indicate the characteristic size of the showers initiated by the jet fragments, i.e. ρM for em showers and λint for the hadronic ones


Improvement of energy resolution expected with PFA


ILC R&D example (PFA): CALICE


Measuring the electromagnetic shower content

Measure fem event-by-event

Pioneered by WA1 around 1980

Used characteristics of energy deposit profile to disentangle em/non-em shower components

Works better as energy increases

Does not work for jets (collection of γs, πs showering simultaneously in the same area)


WA1: determine fem event by event


The DREAM principle Quartz fibers are only sensitive to em shower component !

Production of Čerenkov light ⇒ Signal dominated by electromagnetic component

Non-electromagnetic component suppressed by a factor 5 ⇒ e/h=5 (CMS)

Hadronic component mainly spallation protons Ek ∼ few hundred MeV ⇒non relativistic ⇒ no Čerenkov light

Electron and positrons emit Čerenkov light up to a portion of MeV

Use dual-readout system:

Regular readout (scintillator, LAr, ...) measures visible energy

Quartz fibers measure em shower component Eem

Combining both results makes it possible to determine fem and the energy E of the showering hadron

Eliminates dominant source of fluctuations


Quartz fibers calorimetry

Radial shower profiles in: SPACAL (scintillating fibers)QCAL (quartz fibers)


Radial hadron shower profiles (DREAM)


DREAM calorimeter DREAM: Dual REAdout Module

Composition:

Cu : scintillator : quartz fibers : air

69.3 : 9.4 : 12.6 : 8.7

Filling fraction (active material/absorber) = 31.7%

Sampling fraction for mip in Cu/scintillator = 2.1%

DREAM Collaboration: Cosenza, Iowa State, Pavia, Roma I, Texas Tech, Trieste, UCSD


DREAM prototype

Basic structure:4x4 mm2 Cu rods2.5 mm radius hole7 fibers3 scintillating4 Čerenkov

DREAM prototype:5580 rods, 35910 fibers, 2 m long (10 λint)16.2 cm effective radius (0.81 λint, 8.0 ρM)1030 KgX0 = 20.10 mm, ρM =20.35 mm19 towers, 270 rods eachhexagonal shape, 80 mm apex to apexTower radius 37.10 mm (1.82 ρM)Each tower read-out by 2 PMs (1 for Q and 1 for S fibers)1 central tower + two rings


DREAM prototype

DREAM prototype:tested at the CERN H4 beam lineData samples:π from 20 to 300 GeV“Jets” from 50 to 330 GeV“Jets” mimicked by π interaction on 10 cm polyethylene target in front of the detector


Experimental setup for DREAM test beam


Calibration with 40 GeV electrons

Tilt 2˚ respect to the beam direction to avoid channelling effects

Modest energy resolution for electrons (scintillator signal):σ

E=

20.5%√E

+ 1.5%


100 GeV single pions (raw signals)

Signal distribution

Asymmetric, broad, smaller signal than for e-

Typical features of a non-compensating calorimeter e-

e-


Hadronic response (non-linearity)


The (energy independent) Q/S method

Q

S=

RQ

RS=

fem + 0.20(1− fem)fem + 0.77(1− fem)

S = E

fem +

1(e/h)S

(1− fem)

Q = E

fem +

1(e/h)Q

(1− fem)

R(fem) = E

fem +

1e/h

(1− fem)

e/h = 1.3(S), 5(Q)


DREAM: relationship between Q/S ratio and fem


Effect of selection based on fem


Finally a way to measure e/h

Cu/scintillator e/h = 1.3 Cu/quartz e/h = 4.7

R(fem) = p0 + p1fem withp1

p0= e/h− 1


Dual-Readout Calorimetry in Practice

The (energy-independent) Q/S method Hadronic response (normalized to electrons)

Q/S response ratio related to fem value find fem from Q/S

Correction to measured signals (regardless of energy)

R(fem) = fem +1

e/h[1− fem], e/h = 1.3(S), 5(C)

Q

S=

RQ

RS=

fem + 0.20(1− fem)fem + 0.77(1− fem)

Scorr = Smeas

1 + p1/p0

1 + fem · p1/p0

, with

p1

p0= (e/h)s − 1

Qcorr = Qmeas

1 + p1/p0

1 + fem · p1/p0

, with

p1

p0= (e/h)C − 1


Hadronic response:Effect Q/S correction


DREAM: Effect of corrections (200 GeV “jets)


DREAM: Energy resolution “jets”

After corrections the energy resolution is dominated by leakage fluctuations


CONCLUSIONS from tests DREAM offers a powerful technique to improve

hadronic calorimeter performance:

Correct hadronic energy reconstruction, in an instrument calibrated with electrons !

Linearity for hadrons and jets

Gaussian response functions

Energy resolution scales with √E

σ/E < 5% for high-energy “jets”, in a detector with a mass of only 1 ton ! (dominated by fluctuations in shower leakage)


Published Papers


How to improve DREAM performance Build a larger detector → reduce effects side leakage

Increase Čerenkov light yield

DREAM: 8 p.e./GeV → fluctuations contribute 35%/√E

No reason why DREAM principle is limited to fiber calorimeters

Homogeneous detector ?!

Good solution for an ILC calorimeter:

Homogeneous em calorimeter + DREAM

⇒Need to separate the light into its Č, S components


Čerenkov component in light from PbWO4 crystals ?

Light yield typically 10 p.e./MeV (dependent on T, readout)

Lead glass 500 - 1000 p.e./GeV from Čerenkov effect (3 - 5%/√E)

→ Expect substantial Č component in PbWO4 signals

How to detect/isolate Čerenkov component ?

Directionality of Čerenkov component

Time structure of signals

Spectral differences

Preliminary test performed with cosmic rays show that the Čerenkov component can be detected

Test beam at CERN foreseen before the end of the year

Possible future test: Pb-glass doped with red (?)scintillator


How to improve DREAM performance Build a larger detector → reduce effects side leakage

Increase Čerenkov light yield

DREAM: 8 p.e./GeV → fluctuations contribute 35%/√E

No reason why DREAM principle is limited to fiber calorimeters

Homogeneous detector ?!

⇒ Need to separate the light into its Č, S components

For ultimate hadron calorimetry (15%/√E) Measure Ekin (neutrons).

Is correlated to nuclear binding energy loss (invisible energy)

Can be measured with third type of fiber TREAM


Conclusions on DREAM The DREAM approach combines the advantages

of compensating calorimetry with a reasonable amount of design flexibility

The dominating factors that limited the hadronic resolution of compensating calorimeters (ZEUS; SPACAL) to 30 - 35%/√E can be eliminated

The theoretical resolution limit for hadron calorimeters (15%/√E) seems within reach

The DREAM project holds the promise of high-quality calorimetry for all types of particles, with an instrument that can be calibrated with electrons


Conclusions In the past 20 years calorimetry has become a mature

art

The next major challenge will be the experimentation at the ILC where the physics will require jet spectroscopy at the 1% level (σ/E ~ 30%/√E)

Two techniques (PFA and Dual Readout) are trying to cope with this challenge

An R&D project (DREAM) aims to demonstrate in the next few years that the ultimate hadron resolution (15%/√E) is at reach

Documents

The Art of Calorimetry