Energy response and Compensation1

M. LivanThe Art of Calorimetry

Lecture II

✦ 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,....)2

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 3

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 4

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

✦ 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

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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 (unless…..)

fem function of energy

� = fem · e + (1� fem) · h

�/e = fem + (1� fem) · h/e

e/� =e/h

1� fem[1� e/h]6

Hadron Showers Energy dependence EM component

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

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e/� =e/h

1� fem[1� e/h]< fem > = 1- (E/E0)(k-1)E=1GeV; k=0.82

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”)

✦ 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 9

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

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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

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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 12

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 13

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 14

✦ 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

R� = fem e + [1� fem] h ⇥ e/� =e/h

1� fem[1� e/h]

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Response function of a non compensating calorimeter

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Signal non-linearity

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Compensation✦ In order to understand how compensation could be achieved, one

should understand in detail the response to the various types of particles that contribute to the calorimeter signals

✦ 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

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

✦ rel, p, n and inv denote the calorimeter responses✦ Normalizing to mips and eliminating the last term

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

✦ For compensation the response to neutron is crucial✦ Despite the fact that n carry typically not more than

~10% of the non-em energy, their contribution to the signal can be much larger than that

h = frel · rel + fp · p + fn · n + finv · invfrel + fp + fn + finv = 1

e

h=

e/mip

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

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Compensation - The role of neutrons✦ Neutrons only loose their energy through the products of the

nuclear reactions they undergo✦ Most prominent at the low energies typical for hadronic shower

neutrons is the elastic scattering. ✦ In this process the transferred energy fraction is on average:

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

✦ Pb/H2 calorimeter structure (90/10)✦ 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!20

⇒ n/mip = 45⇒ n/mip = 350

Compensation in a Uranium/gas calorimeter

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Compensation: the crucial role of the sampling fraction

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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)

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Compensation✦ 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,…….✦ No way to get compensation in homogeneous calorimeters ✦ No way to get compensation in sampling calorimeters with

non hydrogenous active medium, e.g. LAr or Si

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Fluctuations25

Calorimetric measurement✦ Discussing calorimeter response 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 process26

Fluctuations (1)✦ Calorimeter’s energy resolution is determined by fluctuations✦ 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 (many, but not all):✦ Energy E gives N signal quanta, with σ = √N

✦ ⇒ σ√E ∝ √N√N = cE ⇒ σ/E=c/√E

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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%

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Signal quantum fluctuations dominate

✦ Quartz window transmit a larger fraction of the Čerenkov light (UV component) 29

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

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Sampling fluctuations in em calorimeters Determined by sampling fraction and sampling frequency

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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

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Contribution of leakage fluctuations to energy resolution

✦ Longitudinal shower fluctuations and therefore leakage are essentially driven 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 particles33

Fluctuations (5)

✦ Instrumental effects

✦ Structural differences in sampling fraction

✦ “Channelling” effects

✦ Electronic noise, light attenuation,.....

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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+......

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The em resolution of the ATLAS em calorimeter

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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)

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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)

✦ 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

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Hadron showers: Fluctuations in em shower fraction (fem)

Pion showersDue 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

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✦ 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

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�

E=

a1⇥E� a2

�

E=

a1�E

+ a2

�

E=

a1⇥E� a2

⇤�E

E0

⇥l�1⌅ �E

=a1pE

� a2E�0.28

Hadronic resolution of non-compensating calorimeters

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ATLAS Fe-scintillator

prototype