880.P20 Winter 2006 Richard Kass 1 Energy Measurement (Calorimetry) Why measure energy ? I) Not always practical to measure momentum. An important contribution to momentum resolution is proportional to the momentum. Example: suppose we want to measure the momentum of a charged particle such that we can tell whether it is positively or negatively charged (to within 3). We demand: p /p < 0.33 From previous notes, we found for measuring trajectory in a wire chamber (e.g. drift chamber) Use BaBar or CDF-like parameters: B=1T, L=1m, n=100, =150m and find p : ) ( ) 3 . 0 ( 4 720 2 T GeV/c, m, BL p n p p GeV/c 2 4 2 2 10 5 . 2 10 5 . 1 ) 1 )( 1 )( 3 . 0 ( 720 104 ) 33 . 0 ( ) 3 . 0 ( 720 4 ) 33 . 0 ( BL n p 250 GeV/c we can’t reliably measure the charge of the particle at e practical limits on the values of B, L, , n, etc. teresting particles do not have electrical charge. asurement using B-field only works for charged particles. photons, 0 ’s and ’s (both decay to ), K L ’s, neutrons, et
Transcript
880.P20 Winter 2006Richard Kass 1
Energy Measurement (Calorimetry)Why measure energy ?
I) Not always practical to measure momentum. An important contribution to momentum resolution is proportional to the momentum.Example: suppose we want to measure the momentum of a charged particlesuch that we can tell whether it is positively or negatively charged (to within 3). We demand: p/p < 0.33From previous notes, we found for measuring trajectory in a wire chamber (e.g. drift chamber)
Use BaBar or CDF-like parameters: B=1T, L=1m, n=100, =150m and find p:
)()3.0(4
7202 TGeV/c,m,
BLp
npp
GeV/c24
22
105.2105.1
)1)(1)(3.0(720104)33.0()3.0(
7204)33.0(
BLnp
Thus above 250 GeV/c we can’t reliably measure the charge of the particle at the 3 level. There are practical limits on the values of B, L, , n, etc.
II) Some interesting particles do not have electrical charge.Momentum measurement using B-field only works for charged particles.What about photons, 0’s and ’s (both decay to ), KL’s, neutrons, etc ?
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Energy Measurement (Calorimetry)A calorimeter is used to measure the energy of a charged and/or neutral particle The calorimeter should absorb all of the energy of an incident particleEnergy measurement by a calorimeter is a DESTRUCTIVE process. Original particle no longer exists after the measurement.Calorimeter usually located behind charged particle tracking chambers MWPCs, drift chambers, silicon trackers are non-destructive measuring devices
The energy resolution of a calorimeter is determined by many factors: Actual energy deposited in calorimeter (sampling fluctuations) Leakage of energy out of the calorimeter Noise (e.g. from electronics or pickup) Ion or light collection efficiencyUsually, the dominant term in the energy resolution is due to sampling fluctuationswhich are Poisson in nature. Thus this term in the energy resolution varies like:
EAEE // A is a constant
A more complete description of the energy resolution is:
22222
)ln( EDCEB
EA
EE
B=contribution due to electronics (e.g. ADC resolution)C=contribution due to calibration errors and other systematic effectsD=contribution due to energy leakage
Since C and D are usually smallenergy resolution improves as Eincreases. This is different thanmomentum resolution which getsworse as momentum increases.
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CalorimetryCalorimeter information can also be used to:
identify particles (e.g. ’s, e’s)measure space coordinates of particles (no B-field necessary)form a “trigger” to signal an interesting eventeliminate background events (e.g. cosmic rays, beam spill)can be optimized to measure electromagnetic or hadronic energy
Calorimeter usually divided into active and passive parts:Active: responsible for generation of signal (e.g. ionization, light)Passive: responsible for creating the “shower”
Many choices for the “active” material in a calorimeter: inorganic crystals (CsI used by CLEO, BELLE, BABAR)organic crystals (ancthracene) {mainly used a reference for light output}plastic scintillator (ZEUS, CDF)liquid scintillator (used by miniBoone)Noble liquids (liquid argon used by D0, ATLAS)gas (similar gases as used by wire proportional chambers)glass (leaded or doped with scintillator)water (SuperK)
Many choices for the “passive” material in a calorimeter:high density stuff: marble, iron, steel, lead, depleted uranium lower(er) density stuff: sand, ice, water
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“Typical” CalorimetersFrom PDG 2004
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Energy Deposition and ShoweringThe key to calorimetry is the showering process. In a shower the original particle interacts with the passive material creating manylower energy particles. The low energy particles deposit energy (via ionization) in the active material. The amount of ionization (or light) is proportional to the amount of energy deposited in the calorimeter.
Cloud chamber photo of an electromagnetic shower. A highenergy electron initiates the shower.The electron radiates photons viabremsstrahlung when it goes throughthe first lead plate. The photons areconverted to electrons and positronsby the lead and they in turn create new photons. This processcontinues until the photons areno longer energetic enough to undergo pair production.
Lead plates
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Electromagnetic ShowerRecall: for energiesabove 10 MeV thedominant EM processis pair production.
Consider an electron with energy E>> Ec. Ec is the critical energy:
The electron is incident on some material that is many radiation lengths (RL) thick. collisionradiation
c dxdE
dxdEE whereenergy
Consider the following simple model of an electromagnetic shower:a) Each electron with E > Ec travels 1 RL then gives up half its energy to a photon via bremsstrahlungb) Each photon with E > Ec travels 1 RL then undergoes pair production with E-=E+=E/2.c) Electrons and positrons E < Ec with do not radiate energy.d) Neglect ionization energy loss for E > Ec .
#RL #e++e- #’s0 1 00-1 1 11-2 3 12-3 5 3
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Electromagnetic ShowersFrom this simple model we can make several “predictions”:The number of particles (N) after t radiation lengths is: N(t)=Ne+(t)+Ne-(t)+N(t)= 2t=etln2
Given an electron with incident energy E0 the average energy E(t) of the particles at depth t is: E(t)=E0/N(t)= E0/ 2t
The shower has the maximum number of particles when E(t)=Ec: tmax=ln(Eo/Ec)/ln2 Nmax= Eo/Ec
Past the distance tmax the shower dies out quickly.The shower also spreads laterally.The lateral spread is characterized by the Moliere radius, Rm: Rm=(21MeV)RL/Ec
95% of the shower is within 2Rm.
To understand energy deposition in more detail we use a Monte Carlo program or build a test module and put it in a beam.
Depth in radiation lengths
Ener
gy d
epos
ition
/uni
t
Radius (Rm units)
Inte
nsity
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Electromagnetic vs Hadronic ShowersHadronic showers are more complicated than EM showers Strong and weak interactions are involved in the hadronic shower processEnergy resolution of hadronic calorimeter usually worse than EM calorimeter neutrinos leak energy out of calorimeter muons will not usually be absorbed by calorimeter (unlikely to bremsstrahlung) long lived particles (Ks, KL, ) may escape calorimeter before decaying or interacting
EM shower
Hadronic shower
MC simulation of hadronic (proton)and EM shower (photon). Hadronicshowers typically have larger lateralspread compared with EM showers.
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Sampling CalorimetersSampling calorimeters have active and passive material interleaved.A few typical examples of SC’s and their active material are given below. a) Scintillatorb) Scintillator with wave shifter readoutc) liquid argon with ionization chamber readoutd) Gas with MWPC readoutFor a)-d) the passive material could be lead or iron.
Energy vs Momentum ResolutionGuidelines for the design of a lead sampling calorimeter: Longitudinal thickness necessary to contain shower: 98% of shower contained in 2.5tmax=2.5ln(Eo/Ec)/ln2 For E0=5 GeV 13.1 cm For E0=100 GeV 19.2 cm Lateral thickness necessary to contain EM shower: 2 Moliere Radi contains 95% of shower (approx. independent of energy) Rm=(21MeV)RL/Ec=1.6 cm 3.2 cm
Compare above lead sampling calorimeter with drift chamber+B-field:Let E/E = 10%/E1/2
E/E= 4.5% @ 5 GeV E/E= 1% @ 100 GeVFor “BaBar/CDF” system (B=1T, L=1m, n=100, =150m) Calculate the following for momentum resolution (not including MS, angle piece)P/p= 0.65% @5 GeV p/p= 13% @ 100 GeV
7204)3.0(
)3.0(4720 2
2nBLAEp
EA
BLp
npEpE
3/22
7204)3.0(
nBLAp
The two resolutions are equal when:For high energyparticles pE.
p=18 GeV/c for our “typical” systems (A=0.1, B=1T, L=1m, n=100, = 150m).
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Crystal CalorimetersThese calorimeters have only active elements (e. g. crystals) that combine a shortradiation length with large light output.
Material PropertiesRL(cm) Rm (cm) a(cm) light energy resolution (%) experiments
BaBar and Belle also have CsI calorimeters, but CLEO’s is the best!
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Electromagnetic Calorimeter
(EMC)
The BaBar CalorimeterBaBar EM calorimeter uses CsI crystals 5760 crystals in barrel 820 crystals in forward region
each crystal has 2 photodiodes
Energy resolution
mrad87.3E
angular resolution
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Particle ID with Calorimeterselectron/positron: Charged particle undergoes EM shower in calorimeter,compare momentum (measured in drift chamber) with energy, require E/p1.Not efficient when electron has same energy as a minimum ionizing particle(both have E/p 1), also background from reactions: 0X.
photon: EM shower in calorimeter not matched to charged track in drift chamber.
muon: Charged track in drift chamber that does not shower in EM calorimeter orinteract in hadron calorimeter. Background from pions (and kaons) that decay in flight () and/or non-interacting /K.
neutrino: Compare visible energy (calorimeter) with measured momentum (drift chamber) and look for imbalance in event. Could be more than one neutrino missing!
neutron or KL: Hadronic shower in calorimeter that does not match to charged track in drift chamber. Need a hadronic calorimeter.
0, : measure invariant mass of combinations.
Problems: How do you tell the charge of track initiating the shower?? What about neutrinos?
