The Principles of Calorimetry
Kerstin Borras
Deutsches Elektronen-Synchrotron
> Introduction
> Electromagnetic Showers
> Hadronic Showers
> Example of calorimeters
Readout and calibration
> Lessons learned in CMS
Recent Reviews:
5th Detector Workshop of the Helmholtz Alliance "Physics at the Terascale"
https://indico.desy.de/conferenceOtherViews.py?view=standard&confId=5126
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
A Generic Collider Detector
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
CMS Detector
ECAL
Barrel
ECAL
Endcap
CASTOR
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Introduction
Calorimeters =
Instruments for measuring thermal effects which were
produced by chemical, biological or physical
processes.
The energy deposited in a defined volume is
calculable with the change of temperature and the
heat capacity.
Historic Example: Meitner & Orthmann (1930)
Measurement of the average energy deposition by the
beta decay of 210Bi with a differential calorimeter:
3,3µ
µW of a 7,6 Ci [1Ci=3,7 107Bq] source deposited in a
copper block,
measured, average energy ~ average kinetic energy
principle of energy measurement of particles works!
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
The Principle
High-energy particles produce secondary particles in
matter through electromagnetic effects or strong
interactions that in turn can produce further particles so
that
a particle shower is created.
Two types of showers: electromagnectic and hadronic
electron shower in a cloud
chamber with lead absorber
(photon emission caused by
bremsstrahlung, pair production, etc.)
Energy detection: particle deceleration by absorption
excitation & ionization
generation of charge or scintillation light
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Necessity of Calorimeters
calorimeter 
resolution: σ(E)/E ~ 1/√E
improvement in high E
drift chamber
σ(p)/p ~ p
deterioration in great p
calorimeters are indispensable in current experiments!
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Advantages of Calorimeters
• good energy measurements for high particle
energies
• required size of a calorimeter grows only
logarithmically with energy
• detection of charged and neutral particles
• segmented calorimeters:
• spatial information about the particle track
• information on the particle type through the
shape of the energy deposition
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Types of Calorimeters
• homogeneous calorimeters:
• absorber = medium of detection
• energy resolution limited by: optical homogeneity and
transversal/longitudinal losses of energy
d e te c to rs
a b s o rb e rs
• large volume, large readout cells
• sampling calorimeters:
• absorber ≠ medium of detection
d
• absorber with a high density (Pb,Fe,U) for particle
absorption on short tracks
compact construction
• medium of detection according to the readout signal:
• scintillation light: plastic scintillatators, crystals
• charge: ionization chambers with liquids or gases,
counters made of silicon
• deposited energy only partly detected
caused by sampling fluctuations
Kerstin Borras
worse resolution
Calorimetry, HEPHY Vienna , 13 June 2012
Electromagnetic Showers
• interactions of electrons / positrons and
photons
• shower development
• energy measurement in sampling calorimeters
• resolution
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Interactions for e- and e+
bremsstrahlung:
stopping of e-/e+ in the
Colombfield of an atomic
nucleus with the emission of a
photon, until E too small:
+ liq
E solid
=
c
610MeV
Z + 1.24
E gas
=
c
710MeV
Z + 1.24
Ee < Ec:= critical energy
ionization and excitation
processes
annihilation:
•
annihilation of a positron with an electron into two photons
scattering processes:
•
Møller scattering (scattering of e- at e-)
•
Bhabha scattering (scattering of e- at e+)
•
Multiple scattering on a atomic nuclei
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Bremsstrahlung
Radiation of a photon in the Coulomb
field of a nucleus.
Z,A
Significant contribution to the particle
production in a shower
Dominant energy loss mechanism for
high-energy e± (and ultra-relativistic µ
with E>1000 GeV)
dE
Z2 2
183
Strong dependency on the atomic
−
= 4α ⋅ NA
re E ln 1
3
dx
A
Z
number of the absorber
−
x/X
dE E
0
⇒ E(x) = E ⋅ e
−
=
Material independent specification with
dx X 0
X0 =
the radiation length X0:
A
4α ⋅ NA Z 2re ln
2
X0(cm)
183
1
Z3
A
X 0 ≈ 180 2
Z
 g 
 cm 3 
Szint.
LAr
Fe
Pb
W
34
14
1.76
0.56
0.35
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Ionization and Excitation
Loss of energy for heavy, charged particles:
Bethe-Bloch-Formalism

1− 1− β2
dE 2π ⋅ e 4 n   m e c 2 β 2 T 
2
2
 − (2 1 − β − 1 + β )ln2 +
−
=
ln
− δ
dx m e c 2 β 2   2I2 (1 − β 2 ) 
8


e = elementary charge
me= rest mass of an electron
β = v/c
T = kinetic energy
n = density of electrons
I = medium ionization potential
δ = density correction function
according to Sternheimer
mip = minimum ionizing
particle
E
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Interactions for Photons
Beer‘s Law:
Iγ = I0 e −µx
µ = µphoto + µCompton + µpair + ...
Coefficient for mass absorption
[
]
NA
σ i cm 2 /g
A
• atomic photo effect
(ττ) (absorption of a photon through
µi =
an atom and emission of e)
• Compton Scattering (σ
σINCOH)
(incoherent scattering of photons
at the electrons of the atom)
• Rayleigh-Streuung (σ
σCOH) (coherent scattering of
photons at the electrons
of an atom)
• pair production at the nucleus (κn) and at the electron (κe)
• nuclear photo effect (σ
σPH.N.)
(absorption of a photon by a nucleus and the
emission of a nucleon.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Interactions for Photons
atomic photo effect:
e-
only possible in the environment of a
three body collision
predominantly
electrons from the K-level :
1
2
Eγ
 32 
K
4
5
e
σ photo =  7  α Z σ Th
ε =
σ eTh =
2
m ec
 ε 
1
σ
= 4π ⋅ r α Z
ε
Compton scattering:
K
photo
2
e
4
5
γ + e → γ' +e'
E′γ = E γ
atomic cross section:
X+
γ + Atom → Atom + + e −
8
3
π ⋅ r e2
(Thomson)
µphoto ∝ Z 4...5 /E γ
1
1 + ε (1 − cosθ γ )
Eγ
0: Thompson-Scattering
Eγ >> mc2: Klein-Nishina Formel
µ compton ∝ Z/E γ
X
σ ec ∝
θγ
lnε
ε
σ cAtom = Z ⋅ σ ec
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Pair Production
e-
pair production:
e+
only possible in the
Coulomb field of a nucleus
or an electron, if
Z
γ + nucleus →
γ + e− →
E γ ≥ 2m e c 2
cross section:
 7 183 
σ pair ≈ 4α ⋅ re2 Z 2  ln 1 
9
Z3 
7 A 1
≈
9 NA X 0
≈
λ pair =
µPaar ∝
A 1
N A λ pair
9
X0
7
7 -1
X0
9
independent of the
energy
e + e − + nucleus
e+e− + e−
topology:
E± ≈
Eγ
2
becomes asymmetric at
high energies
Θ2
mc 2
=
E
approximation for a
shower model
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Interactions for Photons
cross section has a minimum
at about Eγ≈ 1...5 MeV
medium free length of path
λγ has a maximum with
λ γ > X0
e.g. Pb:
λ γ /X 0 ≈ 3.5
important for:
• lateral shower propagation
• electromagnetic shielding
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
The Shower Development
simple model of the shower development (Heitler):
• account only for bremsstrahlung and pair production
• interactions after every single radiation length
• symmetric energy distribution
after t radiation lengths: 2t particles with an energy of E0/2t
particle production, until the particle energy falls below EC,
after that only ionization processes
tmax= ln(E0/ EC)/ln(2)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Longitudinal Shower Profile
profile function:
dE
∝ t α e −t
dt
particle
production
particle
absorption
shower maximum:
t max
E0
= ln
−a
Ec
a=-1.0 für e± und 0,5 für γ
shower containment:
t 95% ≈ t max + 0.08Z + 9.6
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Transversal Shower Profile
transversal shower propagation through:
• opening angle in production processes
Θ
2
mc 2
=
E
(pair production)
• multiple scattering of produced electrons
2
< ΘM
>=
21MeV
x
⋅
Ec
X0
main contribution through multiple scattering of
Molière Length:
electrons with Ee≈ EC
RM
21MeV
A g 
=
⋅ X0 ≈ 7 
EC
Z  cm 2 
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Transversal Shower Profile
Further enlargement of the shower through photons at an
energy, where the absorption cross section is minimal and
thus the medium free length of path is large:
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Transversal Shower Profile
shower containment:
R(90%) ≈ 1 RM
R(95%) ≈ 2 RM
R(99%) ≈ 4 RM
two different factors:
• rapid decline of the differential energy deposition till about 1 RM
• thereafter propagation of the shower and the lower differential
energy deposition caused by low-energy photons with evolving
shower development
1 dE
= a ⋅ e −r/R M + b ⋅ e −r/λ min
E dr
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
a
c
=
⊕b⊕
E
E
E
• inhomogeneities
• stochastic fluctuations
in shower development
• non-linearities
• electronic
noise
• inter-calibration
between calorimeter •
• sampling fluctuations
cells
with sampling
•
calorimeters
• with measurements
on the test beam:
• photo-electron statistic
energy variation of
•
beam particles
• decisive factor at
high energies
quality factor!
Kerstin Borras
radioactivity
overlapping /
pileup of
events
little impact at
high energies
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
a
Term
∝
E
E
• stochastic fluctuations in the shower:
(shower fluctuations: NShower ~ E and Poisson statistic)
Ntotal ∝
E0
Ec
E0
T∝
X0
Ec
Tdet = F(ξ )T
total number of track segments
total track length
visible track length
F(ξ
ξ): function for the description
of effects caused by energy
threshold Ecut for the signal
production
E
ζ ∝ cut
Ec
resolution:
σ(E) σ (Tdet )
∝
∝
E
Tdet
1
Tdet
∝
1
E0
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Resolution in Sampling Calorimeters
σ(E)
a
term (contination)
∝
E
E
• sampling fluctuations
T
N = det
d
visible track length in
the detection medium
E X0
= F(ξ )
Ec d
resolution:
Ec
σ (E )
N
1
∝
∝
E
N
F(ξ ) E
d
X0
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Resolution in Sampling Calorimeters
σ(E)
a
term
∝
(continuation)
E
E
• path length fluctuations
d eff =
d
cosθ
< cosΘ >=
resolution:
θ
21MeV
π ⋅ Ec
d
Ec
σ(E)
1
∝
E
F(ξ ) E
d
X 0 ⋅ < cosΘ >
• Landau fluctuations
contribution from detection layers
in gaseous detectors
small for thin layers of a few mm
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
a
∝
E
E
term
(continuation)
• stochastic fluctuations in the analysis:
• photo-electron statistic for the detector (photo multiplier,
diodes) : Ne ~ Nγ ~ NShower ~E and Poisson statistic
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
∝ b term
E
• absorption loss (leakage)
• inhomogeneities and non-linearities
• inter-calibration between calorimeter cells
• with measurements on the test beam: energy variation of
beam particles
resolution approaches a
saturation value
quality factor!
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
term
∝ b (continuation)
E
• absorption losses
caused by leakages:
longitudinal losses are
more problematic than
lateral losses
simple model:
∆E ≈ ∆t • (dE/dt)|te
≈ (dE/dt)|tmax ~ E,
loss at the end of the detector
≈ 1 , fluctuation in position of the shower maximum
∆E ~ E
constant term for resolution
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution
σ(E)
• absorption losses caused by
∝ b term
(continuation)
inactive material in front of
E
the calorimeter
material of drift chambers,
coils, cables, etc. leads to
a start of the shower in
front of the calorimeter
important effect at small
particle energies
compensation through socalled presampler
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Summary ELM Calorimeters
> calorimeters measure the energy of particles through absorption
> the generation of a particle shower through elm processes:
e+/e- : bremsstrahlung, annihilation, ionization and excitation,
scattering processes (Møller,Bhabha,Multiple)
photon: pair production, photo-effect (atom & nucleus), Compton
and Rayleigh scattering
> material independent description of shower profiles: X0,RM
dE/dt ~ tα e-t
tmax ~ ln E,
> energy resolution:
σ(E)
a
c
=
⊕b⊕
E
E
E
t 95% ≈ t max + 0.08Z + 9.6
• stochastic fluctuations in the shower development
• sampling fluctuations with sampling calorimeters
• photo-electron statistic
• electronicnoise
• inhomogeneities
• radioactivity
• non-linearities
• overlapping of events
• inter-calibration between calorimeter cells
• little impact at high energies
• with measurements on the test beam: energy variation of the beam particles
• decisive factor at high energies
quality factor!
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadronic Showers
• particle absorption through a complex interplay of
different processes with strong interaction
• studies for the optimization of calorimeters with Monte
Carlo simulations, which contain the probabilities for
the different processes in parametrized form as
measured in experiments
• definition of characteristic sizes and profiles possible,
however strong fluctuations because of the number of
possible processes
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
The Spallation Model
Evolution of the processes in two steps with different time
scales:
Step 1: 10-22s
Step 2:
10-18s - 10-13s
material-dependent probability of nuclear fission:
cross section (U) ≈ 16 x cross section (Pb)
different contributions to the energy deposition:
Eion, Eem, Einv, En
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadronic Shower Components
> ionization and excitation energy (Eion):
largest share of the energy loss,
produced, slow protons have 10-100-times ionization density
saturation effects in scintillators (Birk´s Law) or recombination effects
in LAr
> electromagnetic contribution(Eelm):
particularly at the beginning of the shower: production of neutral π-, ηmesons through charge exchange processes: π-p π0n, π+n π0p
Dominant decay: π0
γγ
strong fluctuation from event to event,
energy dependance: Eem ≈ 0,181 + 0,095 lnE [GeV]
> undetectable contribution (Einv):
Losses through binding energy during the fission of nuclei: heavy
remnants of the nuclei deposit only their kinetic energy, partial
compensation through neutrons caputerde by other with following
emission of a photon
production of υ and fast µ,
Recoil energy of heavy nuclei
> production of slow n during evaporation (En):
loss of energy through scattering with protons or capture through nuclei
signal contribution dependent on the properties of the detection medium
concnerning the strong interaction
(e.g. LAr: little detection
contribution to Einv)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Measurements of Hadronic
Showers
elegant experiment:
C.Leroy, Y.Sirois, R.Wigmans NIM A 252 (1986) 4
measurement of the signals of
hadronic showers in a pile of 3mm
thick 238U plate, separated by a
0.5mm Fe-foil
> induced radioactivity is a snap-shot in the shower development
within the uranium plate
> Eγγ and T1/2 used to identify the mechanism of production
> 48V from spallation reactions in Fe-foil
> 239Np from the capture of slow n in 238U
> 237U from nuclear reactions (n,2n), (γγ,n) (p,α
α) ...
> 140Ba, 131I, 90Mo ... from nuclear fission
> electromagnetic component from dosimeter signal
> hadronic component from dosimeter signal and β-activity
Spallation: nuclear fragmentation, multiple fragmentation into small particles (α-particles…)
through high-energy particles. Nuclear fission: nuclear fission in 2-3 fragments, mainly through
neutrons or photons.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Mesurement of Hadronic Showers
electromagnetic
component
vanished ~ 5 λint
1.9 λint
elektromagnetic
component
concentrated
around the
shower axis
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadronic Shower Components
• Ep < ca. 20 GeV:
Eion dominant
• Ep > ca. 20 GeV:
Eem dominant
• Einv: 25%(Ep=1GeV)
10% (Ep>150GeV)
• En: 10%(Ep=1GeV)
5% (Ep>150GeV)
Relative energy contributions
is a function of the energy of
the primary particle
(important for calorimeter optimization)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Description of Hadronic Showers
material independent description:
σinel ≈ σ0 A0,7 mit σ0 ≈ 35mb
(almost independent of the hadron energy(>1GeV) and hadron type)
hadronic absorption length (analog to X0):
λabs = A / (NA σinel ) ~ A¼
hadronic interaction length:
λint = A / (NA σtotal ) ~ A1/3 ≅ 35 A1/3[g/cm2]
comparison of X0 and λ :
Material
Z
Hydrogen (gas)
Helium (gas)
Beryllium
Carbon
Nitrogen (gas)
Oxygen (gas)
Aluminium
Silicon
Iron
Copper
Tungsten
Lead
Uranium
1
2
4
6
7
8
13
14
26
29
74
82
92
A
1.01
4.00
9.01
12.01
14.01
16.00
26.98
28.09
55.85
63.55
183.85
207.19
238.03
ρ [g/cm3]
0.0899 (g/l)
0.1786 (g/l)
1.848
2.265
1.25 (g/l)
1.428 (g/l)
2.7
2.33
7.87
8.96
19.3
11.35
18.95
X0 [g/cm2]
λa [g/cm2]
63
94
65.19
43
38
34
24
22
13.9
12.9
6.8
6.4
6.0
50.8
65.1
75.2
86.3
87.8
91.0
106.4
106.0
131.9
134.9
185.0
194.0
199.0
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadronic Shower Profiles
longitudinal profile:
lateral profile:
t max (λ int ) ≈ 0.2 ⋅ lnE[GeV] + 0.7
• high energy deposition along the
shower axis
t 95% (λ int ) ≈ t max (λ int ) + λ att
λ att (λ int ) ≈ (E[GeV]) 0,13
e.g. iron: t95% ≈ 80cm
• low energy deposition in the far
tails
L 95% (λ int ) ≈ λ int
≈ 16,7cm for iron
hadronic showers are more extensive than electromagnetic:
t
95%
in Uran for 30 GeV π 80cm and for 30 GeV e- 10cm.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron Shower Signals
efficiencies for the detection of hadronic and electromagnetic components are
different:
εh= hadr. efficiency, εe= electromagnetic efficiency
S =ε E +ε E
h
h
h
e
e
Eh
= 1 − f π 0 = 1 − k ⋅ lnE (GeV)
E
signals
non-linear
signal
k ≈ 0.1
signals not
gauß-shaped
em component dependent on energy
signal(h)≠
≠signal(e)
resolution is
worse
ε
σ (E)
a
=
+ b ⋅ e −1
E
εh
E
εe/εh>1
εe/εh=1
εe/εh<1
E (hadron)
compensation:
increase εh, decrease εe, offline-weighting
Kerstin Borras
sampling calorimeter
Calorimetry, HEPHY Vienna , 13 June 2012
Sampling Fractions
E dep = E vis + E inv
sampling fraction:
E vis
Sf =
E dep
varies with different particles
Regarding a MIP (minimum ionizing particle), a fictitious particle that
independent of its speed always experiences a loss of energy through
ionization and excitation.
for example myons:
• for Mµ≈
µ≈105
MeV
µ≈
myon with Eµ
µ of a few MeV good approximation for a MIP
• at larger Eµ
µ
higher loss of energy particularly in the absorber
Sf(µ
µ) decreases µ/mip < 1, µ/mip ≈0.7 at Eµ≈
µ≈100
GeV
µ≈
nomenclature: Sf(mip)=mip, Sf(µ
µ)=µ
µ, Sf(e)=e, Sf(h)=h , Sf(π
π)= π
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Electron Sampling Fraction
high Ee: e/mip <1
Mehr niederenergetische
γ`s in großer
Showertiefe.
electromagnetic showers:
transition- (migration-)effekt
Absinken von
e/mip ist Z
abhängig.
OberflächenEffekt
in the shower production of γ with
Eγγ≤1MeV
wide range in the detction medium
(Z small)
Crosses the absorber and enters at
small range in the absorber
(Compton-Eff.~ Z, Photo-Eff.~ Z4...5)
produced electron has low E and is
stopped in the absorber
e/mip <1 for em showers
possibility of compensation
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron Sampling Fraction
π = fem • e + (1 – fem) • h
fem=
electrom. deposited energy fraction
fion + fγγ + fn + fbind = fhad = 1-fem
h = fion • ion + fγγ • γ + fn • n + fbind • b
fion=
fγγ =
fn
through charged particles
deposited energy fraction
through γ deposited energy fraction
=
fbind=
through n deposited energy fraction
through binding energy deposited
energy fraction
e/π
π signal ratio:
e
e
(E) =
≅
π
fem ⋅ e + (1 − fem ) ⋅ h
e
h
1 + 0,11⋅ lnE(
mit fem ≅ 0,11•lnE
e
− 1)
h
measurement of intrinsic e/h
low E: hadrons deposit E without nuclear
interaction
little losses through
undectectable energy deposition
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hardware Compensation
e
e/mip
(E) =
π
fem ⋅ e/mip + (1 − fem ) ⋅ h/mip
possibilities of compensation with the goal:
e/mip = h/mip
• decrease e/mip:
through transition effect possible to a limited extend with larger
layer thickness, absorber with high Z,
detection medium with low Z
• increase h/mip:
through the different contributions and sampling fractions
h/mip = fion • ion/mip + fγγ • γ/mip + fn • n/mip + fbind • b/mip
fion decreases at high Z (Z/A decreases),
fn increases at high Zabs ((A-Z)/Z increases), however it
can only be used if the detection medium is sensitive to n.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Compensation of the Hadronic Part
h/mip = fion • ion/mip + fγγ • γ/mip + fn • n/mip + fbind • b/mip
individual contributions are
correlated:
• fbind and fn
• fγγ and fn ( excitation of the
nuclei through captureof the n)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Compensation with ion/mip
ion/mip depends on the spectrum of p from nuclear fissions and
on dE/dx. Because of the high ionization density due to slow p
the following needs to be observed:
saturation effects e.g. Birk´s law in scintillators or
recombination effects e.g. Onsager effect in LAr.
dS
dE/dx
=S
dx
1 + k B ⋅ dE/dx
kB= Birk´s constant
≈ 0.01g cm-2 MeV-1
specific ionization:
• mip: ≈ 1MeV g-1 cm-2
• dE/dx 100-times higher:
light efficiency 2-times
lower
• dE/dx 1000-times
higher:
light efficiency 11times lower
electron-energy: 0.1....0.005 MeV
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Compensation with ion/mip
Dependencies on the layer thickness of the absorber and
the detection medium:
• thicker detection layers: loss of energy in these layers shifts the
energy spectrum of the spallation protons towards lower energies
minor signal
ion/mip falls
• thickness of the absorber layers:
• dabs << Rspallation: all p out of the spallation reach the detection
medium, ion/mip rises with growing dabs
• dabs >> Rproton: only p on the surface produce a signal,
saturation expected
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Compensation with n/mip
Neutrons deposit their energy through
collisions or through γ production in
inelastic scatterings, uranium
fission or n-capture.
In collisions the n transfers
∆E ~ En/Mdetect
to their collision partner
low masses desired in the detection
medium e.g. a high hydrogen
content
n lose ~En/2 to p and p deposits
through ionization and excitation
scintillator optimal (preferable via
Birk´s Law)
n/mip rises with Rd=dabs/ddetect:
• n are only decelerated in detection
medium, independent of dabs
mip
• mip falls with Rd
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Compensation of fbind
When uranium is used as an absorber the loss of the undetectable
binding energy is replaced by energy arising out of nuclear fission.
This additional energy is released mainly in the form of low-energy n and
soft γ.
However, then the properties of the detection medium concerning these
particles are important, e.g. scintillator - good detection of n or LAr little detection.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Software Compensation
The π0-share in hadronic showers deposits its energy with in an electromagnetic
shower very locally with high energy density.
The hadronic share is deposited with only low energy density.
identification of the two different components is possible
define weighting functions for the calorimeter cell i in a way that
the electromagnetic component is suppressed and
the hadronic component is raised
e.g. : Eg,i = Ei • (1 - G•Ei) or
H1:
Eg,i = A • exp (B •(Ei/V)) + C with A=A(E), B=B(E) and C=C(E,θ
θ)
compensation only on average, not on the level of the calorimeter cells
rising em share is
suppressed in the
hadronic shower
maximum energy in a cell of the hadronic calorimeter
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Software Compensation
signal linear within ≈2%
e/h = 1
significant improvement of the
resolution
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Software Compensation
alternative approach with tabulated weights:
define weighting factors on the level of the calorimeter cells as a function of the
energy density in the cell and the energy in the hadronic cluster
reaches besides good linearity and resolution also the reconstruction of the real
energy deposition on the level of the calorimeter cell
multiplicity studies, etc.
are possible.
MC analysis:
• deposited
energy/E0
∆ reconstructs
energy /E0
Ο compensation on
average with
weighting function
∆ compensation on
cell level with
tabulated weights
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Software Compensation
Use of a neural network, that was trained with Monte Carlo data:
neural network
standard-weighting
E<10GeV: better linearity and resolution
E>10GeV: equal quality as standard-weighting
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hardware Compensation at ZEUS
sampling calorimeter of uranium and scintillator
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hardware Compensation at ZEUS
linearity
resolution for hadronic and
electromagnetic showers
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Comparison of Compensation Methods
linearity
resolution
CDHS
software compensation
HELIOS hardware compensation
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Outlook
• principles of calometry acquired (brief repetition)
• further topics:
• types of calorimeters and examples
• Calorimeter readout
• The CMS calorimeters and Lessons Learned
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Summary ELM Calorimeters
> calorimeters measure the energy of particles through absorption,
> the generation of a particle shower through elm processes:
e+/e- : bremsstrahlung, annihilation, ionization and excitation,
scattering processes (Møller, Bhabha, Multiple)
photon: pair production, photo-effect (atom & nucleus), Compton
and Rayleigh scattering
> material independent description of shower profiles: X0,RM
dE/dt ~ tα e-t
tmax ~ ln E,
> energy resolution:
σ(E)
a
c
=
⊕b⊕
E
E
E
t 95% ≈ t max + 0.08Z + 9.6
• stochastic fluctuations in the shower development
• sampling fluctuations with sampling calorimeters
• photo-electron statistic
• electronic noise
• inhomogeneities
• radioactivity
• non-linearities
• overlapping of events
• inter-calibration between the calorimeter cells
• little impact at high energies
• with measurements on the test beam: energy variation of the beam particles
• decisive factor at high energies
quality factor!
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Summary HAD Calorimeters
the spallation model
different contributions to
the energy deposition:
Eion, Eem, Einv, En
different efficiencies for signal generation:
sampling fractions related to mip: e (ion-em), h (ion-had, inv, n, γ)
signals non-linear, not gauss-shaped, different signals for hadrons and
electrons e/h≠1, bad resolution:
εe
σ (E)
a
E
=
E
+b⋅
εh
−1
compensation: increase h, decrease e, compensate inv, …
sampling calorimeter
offline-weighting
networks
material, layer thicknesses
software (on average or on cell level), neural
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Homogeneous
Calorimeters
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Homogeneous Calorimeters
• absorber = detection medium
• good energy resolution, only limited by optical homogeneity and transversal/
longitudinal energy losses
• Larger readout cells limited spatial resolution, esp. in longitudinal direction
• large volume high expenses and large space needed in the detector
it can only be used for the electromagnetic part of the calorimeter
scintillators (crystals)
BGO:
bismuth-germanium-oxyde
(Bi4Ge3O12)
Rad.
Dam.
[Gy]
Comments
230
415
≥10
1005
565
≥10
hydroscopic,
fragile
Slightly
hygroscopic
Slightly
hygroscopic
X0 [cm]
NaI (Tl)
3.67
2.59
CsI (Tl)
4.51
1.86
CSI pure
4.51
1.86
BaF2
4.87
2.03
BGO
PbW04
7.13
8.28
1.13
0.89
5×104
(0.49)
4×104
(0.04)
104
(0.13)
8×103
≈100
Densit
y
[g/cm 3
]
4.08
X 0 [cm]
n
Light yield
[p.e./GeV]
(rel. p.e.)
λ cut [nm]
Rad.
Dam.
[Gy]
2.54
1.67
350
102
5.20
1.69
1.81
350
102
7.66
0.95
1.82
600
(1.5×10−4 )
900
(2.3×10−4 )
2000
(5×10 −4 )
Material
Cherenkov detectors
(light efficiency related to NaI(Tl)
readout with a PM)
λ1 [nm]
Density
[g/cm3]
use of (in general):
SF-5
Lead glass
SF-6
Lead glass
PbF2
Light
Yield
γ/MeV
(rel. yield)
4×104
τ1 [ns]
Scintillator
10
310
36
310
0.6
220
620
310
300
480
440 broad band
530 broad band
Kerstin Borras
103
105
10
104
light yield =f(T)
103
Comments
Not available
in quantity
Calorimetry, HEPHY Vienna , 13 June 2012
BGO EM-Calorimeter L3
Physic: (Z, W+, W-)-Boson,
Beauty und Higgs
11000 crystalls:
21.4 X0 x 0.75 RM
Photo-Diode Readout
Temp.-Monitoring:
Light Yield:
≈ –1.55%/°°C
σ/E < 1% für E>1 GeV
spatial resolution
< 2mm for E>2GeV
extremely good
mass resolution
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Lead Glass EM-Calorimeters OPAL
10500 Lead Glass
Counters
10x10x37cm2 a 24.6 X0
Spatial resolution
(intr.):
11mm at 6GeV
σ(E) E = 0 .06
E ⊕ 0.002
Improvement with pre-sampler: chambers mit
streamertubes
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Energy Resolution with Backing-Calo: ZEUS
Measurement of the incomplete absorbed shower tails behind the
hadronic calorimeter
Test stand with Prototyp:
20 cm iron
7.1 λI
depleted uranium
/scintillator
2.7 λI
Iron/Iarocci
tubes
Measurement with 50 GeV
hadrons:
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Quasi-Homogene Calorimeter: NA48
CP-Violation:
K0L
π0 π0
σ/E ≤ 0.04/√
√E
σx = 1mm
Time resolution:
< 1ns
2γγ-resol.: 4cm
Liquid-Krypton:
ρ: 2.45 g/cm3
X0: 4.76 cm
RM: 4.7 cm
Electrode parallel to
beam direction
Material neglegible
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
LKr Calorimeters of NA48
Installation in the cryostat
View on one half of the
calorimeter
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Performance of LKr-Calorimeters
prototype
full device (prel.)
Spatial resolution: σx < 1mm für E>20GeV
σ/E=3.5%/√
√E ⊕ 4.0%/E ⊕ 0.42%
σx,y ≤ 1 mm
σt ≈ 230 ps
Test measurements in 97:
Capacitor -problems
Reduced drift field:
1,5kV/cm instead of 5kV/cm
Time resolution τ < 0.5ns
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
PbW04 EM-Calorimeter CMS
Higgs-Search: H0
γγ
σM/M = σ1/E1 ⊕ σ2/E2 ⊕ σθ/tanθ
θ/2
• intrinsic ≤2%/√
√E
• constant ≤0.5%
• noise ~ 150MeV
• σθ ≤50mrad/√
√E für η≤1
η≤
Light yield temperature dependent:
PbWO4:
ρ: 8.28g/cm3, X0: 0.89cm, RM: 2cm
τ: 10ns, 80 γ`s pro MeV
n(θ
θ) × n(η
η) = 432×
×216 für η≤1
η≤
mit 25,8 X0 × 1 RM
Readout with silicium-avalanche
photodiode (APD)
pre-shower detector: 3X0 Pb with
Si-Strip-Detector
temperature stability: ± 0.05K
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
PbW04 EM-Calorimeter CMS
σ/E = 0.036/√
√E ⊕ 0.0035
Longitudinal leakage: charged
particles produce charge in in APD
Improvement using readout via
two APDs
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Sampling
Calorimeters
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
EM Sampling Calorimeter
• Absorber ≠ detection medium (solid matter , liquid, gas)
• Absorber with high density (Pb,Fe,U) for large stopping power on short tracks
compact construction
• Deposited energy only partially detected
fluktuations
worse resolution through sampling-
• Detection medium = readout medium:
• Scintillation light: plastic scintillators, crystals, optical fibers
• Charge: ionisation chambers mit liquids or gases, MWPC‘s, Streamer-Tubes,
Silicium-semiconductor-counter
Pb - Sc: ARGUS, H1-SPACAL
Pb/Fe - Sc: CDF
Pb - LAr: H1, SLD
Pb - Gas: DELPHI, ALEPH
U - Sc: ZEUS,
Kerstin Borras
U - LAr: D0
Calorimetry, HEPHY Vienna , 13 June 2012
Signal Readout in Sampling Calorimetern
• Scintillators and optical fibers:
• Mode of operation
• Saturation effects: Birks law …
• MWPC und TPC:
• Ionisation chambers, for example here LAr
• Signal generation
• Pulse generation
• Drift velocity
• Ionisation charge, saturation effects, pollution
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Ionization chamber:
Point source:
Line source:
Electron drift crucial for the signal, velocity of Ar+-Ions neglegible,
Maximal current depends only on the drift velocity and the layer thickness:
N • e= c• d with c=ionisation density =charge per length,
Qmax=N • e/2, z.B. H1 LAr: Sampling-Fraction=8%
3,4 106 Ion pairs
0.08GeV/GeV Primary energy
Qmax= 0,272 pC/GeV
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Forming the Signal Pulse
Vdrift ≈ 2-3km/s, d ≈ 2-3mm
tdrift≈
≈1µ
µs
Very long drift times compared to
interactions rate in collider
Use of bi-polar pulse shaper, which
measure onyl part of the generated charge
Avoid net-shifts in the signal due to pile-up of
events in under high event rate conditions
Areas in the positive region = area in the
negative range
Pulse shaping in c) is much faster comparedto
b), but the ratio signal / noise is much worse,
since only a very small part of the
ionisationcharge is read out.
Example ATLAS: td≈500ns, tp≈45ns with about
20 beam interactions (•) during this time
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Drift velocity
Determines duration and form of the charge collection ( I(t), Q(t) )
Simple model:
λ
= average free path length for electronscattering
vth = thermic velocity
tint = λ/vth = time between two collisions
b= e |E|/m = acceleration
vdrift= e |E|/m • λ/vth ,
vdrift << vth
vdrift ~ |E|
vdrift ~ 1/m
vdrift (e-) ≈ 5mm/µ
µs ≈ 105 vdrift(Ar+)
Theory:
Boltzmann equations,
Cross sections,
Shielding effects in liquids,
Texture effects
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Production of Ionization Charge
energy for the production of an electron-ion-pair:
medium ionization energy
W > Ei = ionization energy
Ei [eV]
W[eV]
Wfl[eV]
Ar
15,4
24,4
23,6±
±0,3
Kr
13,0
20,2
20,5±
±1,5
Xe
10,5
15,7
15,6±
±0,3
the energy of the particle is transformed into:
- excitation energy
- ionization energy (for many ion pairs)
- production of electrons below the ionization threshold
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Saturation Effects
Weak ionisation: recombination of the e- mit mother-ion
initial recombination according to Onsager
Strong ionisation: recombination also with neighbor-ions,
dE
dE/dx
| eff =
dx
1 + k B ⋅ dE/dx
columnar recombination
increasing mit increasing ion density: Birks Law
kB =
k
|E|
E-Field dependent, decreases with increasing E-Field
Q/Q0 = 1/ξ
ξ ln(1+ξ
ξ)
ξ ~ N0/(u- • |E|)
ξ→ 0 : Q/Q0 =1
ξ→ ∞ : Q/Q0 =0
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Elektro-negative Pollution
Reduction of the charge collection efficiency due to adsorption
of the generated free electrons, for example: O2+e- O2Point source:
average free path length: dN/dx=-x/λ
λ
N=N0 exp(-x/ λ) , dN/N0 =-dx/λ
λ
path length of the free electron:
df=Nf ∆x=N0 ∆x exp(-∆
∆x/λ
λ)
Path length of the captured electron:
de=∫∫0 ∆x x(dN/dx) dx
= N0 λ(1- exp(-∆
∆x/λ
λ)) – N0 ∆x exp(-∆
∆x/λ
λ)
Total path length:
dT=df+de= N0 λ(1- exp(-∆
∆x/λ
λ))
charge: Q = Q0 λ/d λ/d
λ)
Limit λ→∞ : Q ≈ Q0 λ/d (1- 1+ ∆x/λ
=Q0 (d-x)/d
Line source:
Average over pathlength with constant
ionisation density:
<Q>/Q0= λ/d ∫0 d (1- exp(-x/λ
λ)) dx/d
HV curves in H1 LAr Calorimeter
<Q> = Q0 λ/d {1 - λ/d (1- exp(-d/λλ))}
with λ(O2) =λ
λ(|E|,P) = 0.19 |E| / ρ(O2)
in (ppm cm2) / (kV/cm)
Permament
monitoring of
the
cleanliness
of the Liq Ar
needed:
• Radioactive
sources in
cryostat
• HV-curvs
with cosmics
and Halo-µ
µ
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
LAr Akkordeon EM-Calorimeter: ATLAS
Physic: H0
γγ
good energy- und spatial resolution
Radiation hard: EM 1kGy per year
Ionisation chamber:
Liq -Argon (90K)
Pb/Fe Absorber (1-2mm)
Readout -boards: Multilayerboards
covered with copper
5x106 e- per GeV
Minimimize inactive regions by
accordeon design
LAr is intrinsic radiationhard
Fine segmention possible:
longitudinal: 9X0, 9X0, 7X0
transversal: ∆η=0.018,
∆η
∆φ=0.020
∆φ
Pre-Shower-Detector: x und y
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
LAr Akkordeon EM-Calorimeter: ATLAS
Direct current measurement:
σ/E=0,10/√
√E
fast and insensible to pollution
⊕ 0,28/E
⊕ 0,0035
Spatial
resolution
≈ 5mm /√
√E
Homogeneity
≈ 5% in space
and angle
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
LAr Akkordeon EM-Calorimeter: ATLAS
Influences on the signal height:
Temperature:
Desity variation and Onsager-effect
Ion-flow:
η=2,5 : 5 105 GeV/cm2/s
η=3,2 : 5x 5 105 GeV/cm2/s
Use different HV settings
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
High Density Projection Chamber: DELPHI
Physics:
LEP-Physics OPAL / L3 / ALEPH
TPC as EM calorimeter
Dense Pb-‘‘wire‘‘ = absorber and
generation of the electrical field
Inonisation charge, generated by the
shower in the gas , drifting along the wire
channels and is read out at the end via a
MWPC.
144 moduls
segmented cathods
and
drift times (TPC)
rekonstruktion of
the showers in all 3
dimensions
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
High Density Projection Chamber: DELPHI
HPC modul
Installation of the modules
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
High Density Projection Chamber: DELPHI
Transverse charge distribution in the HPC
single photon
∆ϕ x ∆θ = 1º x 1º
two overlapping photons
∆ϕ x ∆θ = 1º x 1º
Resolution:
σ(E) E = 0.32
E ⊕ 0.043
σ ϕ = 1.7 mrad, σ θ = 1.0 mrad
(quite a lot of material in front of the HPC due to the RICH-Detector )
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Pb-Optische Fasern: H1 Spacal
Physic: DIS @ HERA e- p
e- X
good e/π
π separation (PHP background)
good aczeptance down to small angles (Q2)
good resolution in E, (x,y) und t
ρ: 7,89g/cm3, X0: 0,91cm, RM: 2,5cm
τ: <1ns, 20 γ`s per MeV
1192 modules with 27,5 X0 × 1,6 RM
Channeling:
Homogeneity of signals: ± 4%
Problem for energy
measurement
Optimization of
the modul
orientation
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Pb-optical Fibers: H1 Spacal
Energy resolution:
σ/E = 0.071/√
√E ⊕ 0.01
Sampling fluktuations and
Fluktuations in the light yeild
(const. term)
Spatial resolution:
√E ⊕ 0.3mm
σx = 3.8mm/√
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Electromagnetic Calorimeters
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadronic
Calorimeters
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter: CMS
Hadronic Calorimeter: Cu / scintillator
Within the supra-conducting coil !
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter: CMS
Influence of the magnet field:
B perpendicular
B parallel
(mixutre of the responses of the
3S- und 1S- niveaus
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter: CMS
e/π≠
π≠1
π≠
not
linear
Energy resolution:
σ/E = 100%/√
√E ⊕ 4% HCAL
σ/E = 127%/√
√E ⊕ 6,5%
ECAL+HCAL
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter ATLAS
Tilecal Design:
Hadron-Tile Calorimeter: Fe / Scintillator
(costs, radiation hardness, performance requirements)
Scintillator plates(3mm) pependicular to the beam, alternating staggering,
readout with wave-lenghtl-shifting optical fibers in the same orientientation,
segmentation by fiber bundeling for the PM-readout ,
about 10000 readout channle
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter ATLAS
>> Punch through << possible,
especially for high energies
e
(E) ≅
π
e
h
1 + 0,11⋅ lnE(
e
− 1)
h
⇒
e
= 1.37
h
Gaussian signal
distribution:
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Hadron-Calorimeter ATLAS
Linearity:
EM: σ/E = 10%/√
√E ⊕ 0,35%
√E ⊕ 1,8%
HAD: σ/E = 42%/√
Comparison with CMS:
EM: σ/E = 4%/√
√E ⊕ 0,45%
Resolution:
HAD: σ/E = 127%/√
√E ⊕ 6,5%
Very good
electromagnetic
calorimetry for H0 γγ
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Calibration of Calorimeters
Two different steps of calibration:
a)
calibration of the readout elektronics
•
Amplification of the primary signal
•
Digitization of the signal
Inject known units of signal (charge , laser light)
b)
calibration of the calorimeter response to deposited energies
•
Kind of particle ( e±, h, µ )
•
Shower evolution
•
Interkalibration of different calorimeter segments and their
boundaries
Measurments in testbeams with known particles and energy,
cosmic µ oder beam-halo µ
Crucial aspects:
•
linearity of the signals with the energy of the primary particle
•
resolution of the energy and position measurement
•
stability in time (elektronics, ageing, pollution)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Calibration of Readout-Electronics
Ionisation chambers, proportional chambers, semi-conductor counter
H1 LAr Calorimeter:
Two possibilities for
charge injection via
coupling capacitors
A: charge is injected
in front of the first preamplifier and readout
through the whole
chain
B: charge injected
directly into the
ionisations chamber
Conversion function from the charge to the amplified and digitized
signal is determined through injection of differently high charge pulses
Its stabibilty in time guarantees:
linearität of amplification, pedestal (response readout for original signal
height =0) and noise intrinsic to the elektronic,
MWPC readout: also gas amplification (wire,temp.,pressure,gas mixture)
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Calibration of Scintillator-Calorimeters
Monitoring of the stability in time of the:
• Light production in the scintillator
• Light collection and –conversion in the wavelenght shifters,
• Liight absorption within scintillator and/or wavelength shifters
• Efficiency of the light detectors
• Amplification of the light detectors (PM exponentially : e.g.. ∆U=100V
or temperature dependent, in APDs even stronger)
factor 2
Calibration of calorimeters mit scintillator counters:
• pulsed laser, with a stability better than 1%, and with light similar to that
produced by the shower particles. The laser light is defocussed, brought to the
calorimeter cells with light fibers and the signal be readout.
• radioactive sources are moved in thin tubes across the calorimeter cells and the
produced signal readout (but: small free range for β-particles and γ‘s ).
• In Uran-calorimeters the signal from the 238U-decay down to 206Pb produced αparticles, β-particles and γ‘s can be continuously monitored (but: isotropically
distributed signal).
Is an instability detected, usually only a combination of these different possibilities
leads to uncover the true reason.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Example UA2 Pb/Fe/Sc-Calorimeter
Procedure:
• No moveable radioactive source within the calorimeter possible
during each possible access to the detector a very strong radioactive
source was placed in front of the detector and the signals
changes in the calibration constants were deducted with the
assumption, that the signal from the source are comparable with those
from particle showers
regular cross checks of the validity of the calibration with a few
calorimeter modules in testbeams.
Stability of the calibration within
2% even after several years of
data taking.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
calibration signal ↔ energy deposition
Energy calibration ≠ draw signal versus beam energy !
Wigmans recipe for calibration:
• Intercalibration of single regions in a longitudinally segmented
calorimeter is only allowed with always the same kind of particle for all
regions
• Produced particle showers are only allowed to be used for the
calibration, if the full shower is contained in the segment (em shower:
transition effect stronger in last shower tail)
• Either all segments are calibrated in a test beam or the intercalibration
is performed starting from a known module towards an unknown module
using muons.
• The in non-compensating calorimeters for hadrons reconstructed
energy,deviating from the deposited energy, can be corrected with an
overall factor as measured in testbeams.
• All other procedures, which go along the optimization of the resolution
or the linearity, can cause unwanted consequences, like a dependence
of the calibration constant on the starting point of the shower, nongaussian distributions, … .
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Example HELIOS
EM-Calorimeter: Uran / Scintillator, HAD-Calorimeter Uran / Copper / Sc.
N
n
n
Calibration ansatz: minimize
Q = ( ∑ E − A ∑ Sem − B∑ Shad )2
i ij
i ij
j=1
with all events j und calo-cells i
for optimization of the energy resolution
B/A energy-dependent:
Transition-Effect leads
to different samplingFractions toward the
end of the showers,
which enters with
higher energy more and
more the HadronCalorimeter.
Hadron-Shower on
average less affected.
Em-weight>Had-weight
Em-weight<Had-weight
Non-Linearity of the calorimeter due to calibration procedure !
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Effects in Non-Linear Calorimeters
In case the non-linearity of a calorimeter is parametrised:
E = c0 + c1S + c2S2 + c3S3 + .....
Problematic cases:
π0 → γ γ : the not resolved γ‘s are per definitionem reconstructed with a
different energy compared to single γ or e- with the same energy.
ω0 → γ γ γ : even worse reconstruction
ρ0→ π0 π0 → γ γ γ γ : absolut worst constellation in this case
More examples for the different calibration ansatzes and their
consequences for the quality of energy reconstructions and with this on
the physics data analysis can be found in:
Wigmans: Calorimetry – Energy Measurement in Particle Physics (ch. 6)
•Calibration is a high grade non-trivial business with possibly
fatal consequences
•Calibration tests in situ with phyiscs events with for
example Z0-Resonanz at LEP or pT-Balance at HERA are
indispensible
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012
Summary
A calorimeter should:
• be linear in the energy signal,
• have a very good energy resolution,
• give same signals for e and h,
• produce homogene signals for all
positions
• have a good time stability.
Kerstin Borras
Calorimetry, HEPHY Vienna , 13 June 2012