Calorimetry - 1 Mauricio Barbi University of Regina TRIUMF Summer Institute July 2007 Some Literature 1. “Detector for Particle Radiation”, Konrad Kleinknecht, Cambridge University Press 2. “Introduction to Experimental Particle Physics”, Richard Fernow, Cambridge University Press “Techniques in calorimetry”, Richard Wigmans, Cambridge University Press Particle Data Group (PDG): http://pdg.lbl.gov/ 3. 4. Thanks to Michele Livan (INFN and Pavia University) for letting me use some of his material and examples in these lectures Principles of Calorimetry (Focus on Particle Physics) Lecture 1: i. ii. iii. Introduction Interactions of particles with matter (electromagnetic) Definition of radiation length and critical energy Lecture 2: i. Development of electromagnetic showers ii. Electromagnetic calorimeters: Homogeneous, sampling. iii. Energy resolution Lecture 3: i. Interactions of particle with matter (nuclear) ii. Development of hadronic showers iii. Hadronic calorimeters: compensation, resolution Introduction http://en.wikipedia.org/wiki/Calorimeter: A calorimeter is a device used for calorimetry Calorimetry is the science of measuring the heat generated or absorbed in a chemical reaction or physical process. The word Calorimeter comes from the Latin calor meaning heat, and from the Greek metry meaning to measure. Bomb calorimeter A primitive calorimeter was invented by Benjamin Thompson (17th century) “When a hot object is set within the water, the system's temperature increases. By measuring the increase in the calorimeter's temperature, factors such as the specific heat (the amount of heat lost per gram) of a substance can be calculated.” (http://www.bookrags.com/Calorimeter) Introduction Specific heat is the amount of heat per unit mass required to raise the temperature by one Kelvin: Substance Q c m T Aluminum c in cal/gm K 0.9 0.215 Bismuth 0.123 0.0294 Copper 0.386 0.0923 0.38 0.092 Gold 0.126 0.0301 Lead 0.128 0.0305 Silver 0.233 0.0558 Tungsten 0.134 0.0321 Zinc 0.387 0.0925 0.14 0.033 2.4 0.58 4.186 1 Ice (-10 C) 2.05 0.49 Granite 0.79 0.19 Glass 0.84 0.2 Brass Q = heat added (energy) c = specific heat m = mass T = change in temperature c in J/gm K Mercury Alcohol(ethyl) Water Introduction How to measure the energy of a particle? Let’s consider that we have a calorimeter with 1 liter of water as absorber. Using the formula and table from previous slide, let’s solve the following problems? What is the effect of a 1 GeV particle (e.g., at LHC) in the calorimeter? T E M water c 3.8 10 14 K This is a far too small temperature change to be detected in the calorimeter. New techniques of detection are needed in particle physics. Introduction Still at http://en.wikipedia.org/wiki/Calorimeter: In particle (and nuclear) physics, a calorimeter is a component of a detector that measures the energy of entering particles Introduction Main goals: Provide information to fully reconstruct the 4-vector p= (E,p) of a particle Complementary to tracking detectors at very high energies: Calorimete rs : (E) E 1 E ; drifiting chambers : Δp p p Provide particle ID based on different energy deposition pattern for different particles species (e/π, etc) Though neutrinos are not directly detected, they can be identified from the missing energy needed for energy conservation to hold E Evis Emiss Evis directly measured Emiss missing energy Segmentation of the calorimeter can also provide space coordinates of particles. Time information also possible with high resolution achievable Usually important in removing background (cosmic rays, beam spills, etc) Introduction Basic principles: Sensitive to both charged (e±, ±, π±, etc) and neutral particles (, π0, etc) Total energy absorption Destructive process The mechanism evolves as: Entering particle interact with matter Energy deposition by development of showers of decreasingly lower-energy particles produced in the interactions of particle with matter Particle is “completely destroyed” Electromagnetic showers produced by electromagnetic processes Hadronic showers produced by hadronic processes (+ EM components) The energy of the particles produced in the showers is converted into ionization or excitation of the matter which compounds the calorimeter energy loss The calorimeter response is proportional to the energy of the entering particle (note the statistical process in the previous item) σ(E)/E=A/E-1/2 Introduction Calorimeter is a complicate device: Particle has to be completely absorbed in order to have its energy fully detected Several things happen during this process Showers are product of competing physics interactions between particle and matter Again, this depends on detector material Particle ID and energy measurement through development of showers (with exception of muons) Depends on detector material, its size and geometry Statistical processes fluctuations detector resolution Depends on the energy of the particle, calorimeter uniformity, etc Detector material, its size and geometry to fully contain the showers Different calorimeter types for different physics goals Faster response? Better energy resolution? Spatial coordinates? Hadronic particles? EM particles? Etc….. Introduction More about EM interaction of particle with matter in this lecture εL Atomic electron atom Free electron Compton scattering εK e detectors Development of showers and energy resolution in the next lecture EM shower in a sampling calorimeter d absorbers Introduction Some applications of calorimetry in particle physics Basic mechanism used in calorimetry in particle physics to measure energy Cherenkov light Scintillation light Ionization charge Introduction Neutrino physics Super-Kamiokande (SK) - Japan Measurement of neutrino oscillations Water as active material Energy measurement through Cherenkov radiation ~12K PMTs 50K metric ton of water Introduction Ultra high energy cosmic ray The Pierre Auger Observatory (world’s largest calorimeter) Measure charged particles with E > 1019 eV Atmosphere as the calorimeter Surface detectors to measure energy and shower profile Air shower 16K water Cherenkov detectors 3000 Km2 Introduction Collider experiments ZEUS at HERA e-p collider, Germany Study the proton structure and confront QCD predictions Uranium-scintillator sampling calorimeter Energy measured using scintillating light Rear calorimeter Forward calorimeter Central tracking Barrel calorimeter Introduction Collider experiments ATLAS at LHC p-p collider, Switzerland Search for Higgs, SUSY particles, CP violation, QCD, etc Liquid Argon/Pb (EM) and Cu (or W) (Hadron) sampling Calorimeter Energy measured using ionization in the liquid argon Muon Detectors Electromagnetic Calorimeters Solenoid Forward Calorimeters EndCap Toroid Barrel Toroid Inner Detector Hadronic Calorimeters Shielding Interactions of Particles with Matter We have seen that the calorimeter is based on absorption It is important to understand how particles interact with matter Several physics processes involved, mostly of electromagnetic nature Energy deposition, or loss, mostly by ionization or excitation of matter One can initially separate the interactions into two classes Electromagnetic (EM) processes (this lecture): Main photon interactions with matter: Compton scattering Pair Production Photoelectric effect Main electron interactions with matter: Bremsstrahlung Ionization Cherenkov radiation (not covered in this lecture) Hadronic processes: more complicate business than EM nuclear interactions between hadrons (charged or neutral) and matter Interactions of Particles with Matter Interactions of Photons For a beam of photons traversing a layer of material (Beer-Lambert’s law): I(X) I 0 e μx I 0 e μ ρX α = /ρ is called mass absorption coefficient. I 0 initial beam intensity x thickness of the layer [cm] ρ density of the material [ g cm 3 ] X ρx mass thickness [ g cm 2 ] μ linear absorption coefficien t [cm-1 ] Also, I(X) I 0 e X λ ρ x P 1 eX λ λ = α-1 [g/cm2] = photon mass attenuation length Probability that the photon will interact in thickness X of material Interactions of Particles with Matter Interactions of Photons Photon attenuation length for different elemental absorbers versus photon energy http://pdg.lbl.gov Note the different patterns for different elements different response to photons as a function of the photon energy Why? Next slide Interactions of Particles with Matter Interactions of Photons Cross-section for photon absorption Total cross-section σ for photon absorption is related to the total mass attenuation length λ: 1 A σ λ NA A Atomic mass of the material [g mol ] N A 6.022 141 99(47) 10 23 mol -1 Avogrado' s number Several processes contribute to the total cross-section: σ σ p.e. σ Comp σ pair ... Therefore, different p.e. Photoelect ric effect processes contributes with Comp Compton scattering different attenuations: 1 A λ i pair e e - pair production σi N A http://pdg.lbl.gov i p.e., Comp, pair, ... The “+…” in the above expression includes: Rayleigh scattering, where the atom is neither ionized or excited Photonuclear absorption Interactions of Particles with Matter Interactions of Photons Cross-section for photon absorption Since a calorimeter has to fully absorb the energy of an interacting photon: Important to understand the cross-sections as a function of the photon energy in different material Will ultimately define the geometry and composition of a calorimeter The cross-section calculations are difficult due to atomic effects, but there are fairly good approximations: Depend on the absorber material Depend on the photon energy Let’s then visit some of the processes cited in the previous slide Interactions of Particles with Matter Interactions of Photons Photoelectric effect e + X X atom (X) ion (X ) e Can be considered as an interaction between a photon and an atom as a whole Can occur if a photon has energy E > Eb (Eb = binding energy of an electron in the atom). The photon energy is fully transferred to the electron Electron is ejected with energy T = E - Eb Discontinuities in the cross-section due to discrete energies Eb of atomic electrons (strong modulations at E=Eb; L-edges, K-edges, etc) p.e. cross-section in Pb Dominating process at low ’s energies ( < MeV ). Gives low energy electrons Kleinknecht E Interactions of Particles with Matter Interactions of Photons Photoelectric effect εL εK Cross-section: Let ε p.e. cross-section in Pb Eγ me c 2 (reduced photon energy) For εK < ε < 1 ( εK is the K-absorption edge): σ K p.e. 32 7 ε 1 2 8 e σTh πre2 (Thomson ) 3 e α 4 Z 5σTh 1 α , (fine structure constant) 137 re Classical electron radius For ε >> 1 (“high energy” photons): σ K p.e. 1 4πr α Z ε 2 e 4 5 σp.e goes with Z5/ε εK ε=1 E Interactions of Particles with Matter Interactions of Photons Compton scattering A photon with energy E,in scatters off an (quasi-free) atomic electron εL Atomic electron A fraction of E,in is transferred to the electron atom Free electron εK e atom (X) ion (X ) e The resulting photon emerges with E,out < E,in and at different direction me c 2 Using conservation of energy and momentum: cos θ 1 (E γ,in E γ,out ) E γ,in E γ,out The energy of the outgoing photon is: Eγ,out Eγ,in 1 ε(1 cos θ) , where ε E γ,in me c 2 E Interactions of Particles with Matter Interactions of Photons Compton scattering The energy transferred to the electron: Te Eγ,in Eγ,out me c 2 E,out / E,in http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm ε ( 1 cos θ) 1 ε(1 cos θ) 2 Coherent scattering (Rayleigh) Incoherent scattering (electron is removed from atom) Two extreme cases of energy loss: 0 : E,out E,in ; Te 0 No energy transferred to the electron Eγ,out Backscattered at = π : me c 2 1 2ε 2 Eγ,in εK E,in [MeV] , for ε 1 E Compton edge me c 2 2ε 2 2ε 1 Te me c Eγ,in E ,in 1 E ,in , for 1 1 2ε 1 2ε 2 2 2 ε=1 Interactions of Particles with Matter Interactions of Photons Compton scattering Total Compton cross-section per electron given by Klein-Nishina (QED) (1929): .σ e Comp 1 ε 2( 1 ε) 1 1 3ε 1 2πre2 2 ln 1 2ε ln ( 1 2ε) 2 ε 1 2 ε ε 2 ε 1 2 ε http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm Two extreme cases: ε << 1 : e Comp e Th 1 2 Incoherent scattering only Backward-forward symmetry in distribution 3 8 e e ε >> 1 : Comp Th 1 1 ln 2 2 distribution peaks in the forward direction Cross-section per atom: atomic e Comp Z Comp Includes coherent and incoherent scattering Interactions of Particles with Matter Interactions of Photons Pair Production ee+ An electron-positron pair can be created when (and only when) a photon passes by the Coulomb field of a nucleus or atomic electron this is needed for conservation of momentum. Z γ nucleus e e nucleus + e- e+ + e- + e- + nucleus e+ + e- + nucleus Threshold energy for pair production at E = 2mc2 near a nucleus. E = 4mc2 near an atomic electron Pair production is the dominant photon interaction process at high energies. Cross- section from production in nuclear field is dominant. First cross-section calculations made by Bethe and Heitler using Born approximation (1934). Interactions of Particles with Matter Interactions of Photons Pair Production (Attenuation length) 137 The interesting energy domain is that of several hundred MeV or more, ε 1 . The cross- section per nucleus is: Z 3 σ n pair 7 183 r 4αZ ln 1 9 Z 3 2 e 2 σ npair Z 2 Does not depend on the energy of the photon, but Mass attenuation length for pair creation (check few slides ago): 1 λ n pair NA n 7 1 A 1 σ pair , where X 0 A 9 X0 N A r 2 4αZ 2 ln 183 Z 13 or e λ npair 9 X0 7 Accurate to within a few percent down to energies as low as 1 GeV X0 is called radiation length and corresponds to a layer thickness of material where pair creation has a probability P = 1 – e-7/9 54% Interactions of Particles with Matter Interactions of Photons Pair Production Photon pair conversion probability P=54% P 1 e http://pdg.lbl.gov 7 X 9 X0 Interactions of Particles with Matter Interactions of Photons Pair Production (Attenuation Length) Along with Bremsstrahlung (more later), pair production is a very important process in the development of EM showers X0 is a key parameter in the design of a calorimeter There are more complicate expressions for X0 in the literature: X 01 4αre2 NA 2 Z Lrad f(Z)) ZLrad A (PDG, http://pdg.lbl.gov) Lrad is similar to the expression for X0 in the previous slide L’rad replaces 183Z-1/3 by 1194Z-2/3 f(z) is an infinite sum which, for elements up to U, can be approximate to 1 f(Z) a 2 0 .20206 0 .0369a 2 0 .0083a 4 0 .002a 6 2 1 a Where a = αZ PDG also gives a fitting function: X0 716 A Z(Z 1 ) ln 287 Z g 2 cm Interactions of Particles with Matter Interactions of Photons Pair Production For compound mixtures: wj 1 X0 j Xj Where, wj = weight fraction of each element in the compound j = “jth” element http://pdg.lbl.gov Interactions of Particles with Matter Interactions of Photons Summary σ σ p.e. σ Comp σ pair ... Photoeletric effect p.e. Photoelect ric effect Comp Compton scattering pair e e - pair production Pair production Energy range versus Z for more likely process: Rayleigh scattering Compton http://pdg.lbl.gov Michele Livan Calorimeters? Curiosity Primitive calorimeter invented by Benjamin Thompson (17th century): “We owe the invention of this device to an observation made just before the turn of the nineteenth century by the preeminent scientist Benjamin Thompson ( Count Rumford). While supervising the construction of cannons, Rumford noticed that as the fire chamber was bored out, the metal cannons would heat up. He observed that the more work the drill exerted in the boring process, the greater the temperature increase. To measure the amount of heat generated by this process, Count Rumford placed the warm cannon into a tub of water and measured the increase in the water's temperature. In doing so, he simultaneously invented the science of calorimetry and the first primitive calorimeter. In simplest terms, a modern calorimeter is a water-filled insulated chamber. When a hot object is set within the water, the system's temperature increases. By measuring the increase in the calorimeter's temperature, a scientist can calculate such factors as the specific heat (the amount of heat lost per gram) of a substance. Another application of calorimetry is the determination of the calorific value of certain fuels--that is, the amount of energy obtained when fuel is burned. Engineers burn the fuel completely within a calorimeter system and then measure the temperature increase within the device. The amount of heat generated by this burning is indicative of the fuel's calorific value. “ (http://www.bookrags.com/Calorimeter)