1. 1 Calorimetry - 1 Mauricio Barbi University of Regina TRIUMF Summer Institute July 2007

2. 2 Some Literature 1.“Detector for Particle Radiation”, Konrad Kleinknecht, Cambridge University Press 2.“Introduction to Experimental Particle Physics”, Richard Fernow, Cambridge University Press 3.“Techniques in calorimetry”, Richard Wigmans, Cambridge University Press 4.Particle Data Group (PDG): http://pdg.lbl.gov/ i.B. Rossi. High energy particles, Prentice-Hall 77-79 (1952) Thanks to Michele Levin (INFN and Pavia University) for letting me use some of his material and examples in these lectures

3. 3 Principles of Calorimetry (Focus on Particle Physics) Lecture 1: i.Introduction ii.Interactions of particles with matter (electromagnetic) iii.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

4. 4 Introduction  http://en.wikipedia.org/wiki/Calorimeter  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.  A primitive calorimeter was invented by Benjamin Thompson (17 th 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) Bomb calorimeter

5. 5 Introduction Specific heat is the amount of heat per unit mass required to raise the temperature by one Kelvin: Q = heat added (energy) c = specific heat m = mass  T = change in temperature 0.20.84Glass 0.190.79Granite 0.492.05Ice (-10 C) 14.186Water 0.582.4Alcohol(ethyl) 0.0330.14Mercury 0.09250.387Zinc 0.03210.134Tungsten 0.05580.233Silver 0.03050.128Lead 0.03010.126Gold 0.0920.38Brass 0.09230.386Copper 0.02940.123Bismuth 0.2150.9Aluminum c in cal/gm Kc in J/gm KSubstance

6. 6 Introduction How to measure the particle energy? 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? This is a far too small temperature change to be detected in the calorimeter. New techniques of detection are needed in particle physics.

7. 7 Introduction Still at http://en.wikipedia.org/wiki/Calorimeter 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

8. 8 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:  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  Segmentation of th 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)

9. 9 Introduction Basic principles:  Sensitive to both charged (e ±,  ±, π ±, etc) and neutral particles ( , π 0, etc)  Total energy absorption Particle is “completely destroyed” 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 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 )

10. 10 Introduction  Calorimeter is a complicate device:  Particle has to be completely absorbed in order to have its energy fully detected  Depends on detector material, its size and geometry  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 or (with exception of muons)  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…..

11. 11 Introduction  More about EM interaction of particle with matter in this lecture  Development of showers and energy resolution in the next lecture EM shower in a sampling calorimeter εKεK εLεL e    atom Atomic electron  Free electron Compton scattering

12. 12 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

13. 13 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

14. 14 Introduction Ultra high energy cosmic ray  The Pierre Auger Observatory (world’s largest calorimeter)  Measure charged particles with E > 10 19 eV  Atmosphere as the calorimeter  Surface detectors to measure energy and shower profile 3000 Km 2 Air shower 16K water Cherenkov detectors

15. 15 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 Central tracking Forward calorimeter Barrel calorimeter

16. 16 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 Solenoid Forward Calorimeters Muon DetectorsElectromagnetic Calorimeters EndCap Toroid Barrel ToroidInner DetectorHadronic CalorimetersShielding

17. 17 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 (next lecture): more complicate business than EM  nuclear interactions between hadrons (charged or neutral) and matter

18. 18 Interactions of Particles with Matter Interactions of Photons For a beam of photons traversing a layer of material ( Beer-Lambert’s law ): α =  /ρ is called mass absorption coefficient. Also, λ = α -1 [g/cm 2 ] = photon mass attenuation length Probability that the photon will interact in thickness X of material ρρ x

19. 19 Interactions of Particles with Matter Interactions of Photons Photon attenuation length for different elemental absorbers versus photon energy Note the different patterns for different elements  different response to photons as a function of the photon energy Why?  Next slide http://pdg.lbl.gov

20. 20 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: Several processes contribute to the total cross-section: The “+…” in the above expression includes:  Rayleigh scattering, where the atom is neither ionized or excited  Photonuclear absorption Therefore, different processes contributes with different attenuations: http://pdg.lbl.gov

21. 21 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

22. 22 Interactions of Particles with Matter Interactions of Photons Photoelectric effect  Can be considered as an interaction between a photon and an atom as a whole  Can occur if a photon has energy E  > E b (E b = binding energy of an electron in the atom).  The photon energy is fully transferred to the electron  Electron is ejected with energy T = E  - E b  Discontinuities in the cross-section due to discrete energies E b of atomic electrons (strong modulations at E  =E b ; L-edges, K-edges, etc)  Dominating process at low  ’s energies ( < MeV ).  Gives low energy electrons p.e. cross-section in Pb EE

23. 23 Interactions of Photons Photoelectric effect  Cross-section: Let (reduced photon energy) For ε K < ε < 1 ( ε K is the K-absorption edge): For ε >> 1 (“high energy” photons): σ p.e goes with Z 5 /ε Interactions of Particles with Matter p.e. cross-section in Pb EE εKεK εLεL ε = 1 εKεK

24. 24 Interactions of Particles with Matter Interactions of Photons Compton scattering A photon with energy E ,in scatters off an (quasi-free) atomic electron A fraction of E ,in is transferred to the electron The resulting photon emerges with E ,out < E ,in and at different direction Using conservation of energy and momentum: The energy of the outgoing photon is:, where εKεK εLεL e    atom Atomic electron  Free electron

25. 25 Interactions of Particles with Matter Interactions of Photons Compton scattering  The energy transferred to the electron: Two extreme cases of energy loss:    0 : E ,out  E ,in ; T e  0  No energy transferred to the electron  Backscattered at  = π : Compton edge εKεK EE ε = 1 εKεK E ,out / E ,in Coherent scattering (Rayleigh) Incoherent scattering (electron is removed from atom) E ,in [MeV] http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm

26. 26 Interactions of Particles with Matter Interactions of Photons Compton scattering Total Compton cross-section per electron given by Klein-Nishina (QED) (1929):. Two extreme cases: ε << 1 :  Backward-forward symmetry in  distribution ε >> 1 :   distribution peaks in the forward direction Cross-section per atom: Includes coherent and incoherent scattering Incoherent scattering only http://www.mathcad.com/Library/LibraryContent/MathML/compton.htm

27. 27 Interactions of Photons Pair Production 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. Threshold energy for pair production at E  = 2mc 2 near a nucleus. E  = 4mc 2 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  + e -  e + + e - + e -  + nucleus  e + + e - + nucleus

28. 28 Interactions of Particles with Matter Interactions of Photons Pair Production (Attenuation length) The interesting energy domain is that of several hundred MeV or more,. The cross- section per nucleus is:  Does not depend on the energy of the photon, but  Mass attenuation length for pair creation (check few slides ago): or Accurate to within a few percent down to energies as low as 1 GeV X 0 is called radiation length and corresponds to a layer thickness of material where pair creation has a probability P = 1 – e -7/9  54%

29. 29 Interactions of Particles with Matter Interactions of Photons Pair Production Photon pair conversion probability P=54% http://pdg.lbl.gov

30. 30 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  X 0 is a key parameter in the design of a calorimeter There are more complicate expressions for X 0 in the literature: (PDG, http://pdg.lbl.gov ) L rad is similar to the expression for X 0 in the previous slide L’ rad replaces 183Z -1/3 by 1194Z -2/3 f(z) is an infinite sum which can be approximate to Where a = αZ PDG also gives a fitting function:

31. 31 Interactions of Particles with Matter Interactions of Photons Pair Production For compound mixtures: Where, w j = weight fraction of each element in the compound j = “j th ” element http://pdg.lbl.gov

32. 32 Interactions of Particles with Matter Interactions of Photons Summary http://pdg.lbl.gov Rayleigh scattering Compton Pair production Photoeletric effect Michele Livan Energy range versus Z for more likely process:

33. 33 Interactions of Particles with Matter Interactions of Electrons Ionization (Fabio Sauli’s lecture) For “heavy” charged particles (M>>m e : p, K, π,  ), the rate of energy loss (or stopping power) in an inelastic collision with an atomic electron is given by the Bethe- Block equation:  (βγ) : density-effect correction C: shell correction z: charge of the incident particle β = vc of the incident particle ;  = (1-β 2 ) -1/2 W max : maximum energy transfer in one collision I: mean ionization potential http://pdg.lbl.gov

34. 34 Interactions of Particles with Matter Interactions of Electrons Ionization For electrons and positrons, the rate of energy loss is similar to that for “heavy” charged particles, but the calculations are more complicate:  Small electron/positron mass  Identical particles in the initial and final state  Spin ½ particles in the initial and final states k = E k /m e c 2 : reduced electron (positron) kinetic energy F(k,β,  ) is a complicate equation However, at high incident energies (β  1)  F(k)  constant (next slide)

35. 35 Interactions of Electrons Ionization At this high energy limits (β  1), the energy loss for both “heavy” charged particles and electrons/positrons can be approximate by Where, The second terms indicates that the rate of relativistic rise for electrons is slightly smaller than for heavier particles Interactions of Particles with Matter A B electrons 3 1.95 heavy charged particles 4 2

36. 36 Interactions of Electrons Bremsstrahlung (breaking radiation) A particle of mass m i radiates a real photon while being decelerated in the Coulomb field of a nucleus with a cross section given by:  Makes electrons and positrons the only significant contribution to this process for energies up to few hundred GeV’s. Interactions of Particles with Matter m i 2 factor expected since classically radiation

37. 37 Interactions of Electrons Bremsstrahlung The rate of energy loss for high energy electrons ( k >> 137/Z 1/3 ), is giving by: Recalling from pair production   The radiation length X 0 is the layer thickness that reduces the electron energy by a factor e (  63%) Interactions of Particles with Matter

38. 38 Interactions of Electrons Bremsstrahlung Radiation loss in lead. Interactions of Particles with Matter http://pdg.lbl.gov

39. 39 Interactions of Electrons Bremsstrahlung and Pair production  Note that the mean free path for photons for pair production is very similar to X 0 for electrons to radiate Bremsstrahlung radiation:  This fact is not coincidence, as pair production and Bremsstrahlung have very similar Feynman diagrams, differing only in the directions of the incident and outgoing particles ( see Fernow for details and diagrams ).  In general, an electron-positron pair will each subsequently radiate a photon by Bremsstrahlung which will produce a pair and so forth  shower development. Interactions of Particles with Matter

40. 40 Interactions of Electrons Bremsstrahlung (Critical Energy)  Another important quantity in calorimetry is the so called critical energy. It is define as the energy at which the loss due to radiation equals that due to ionization. There are several definitions for critical energy. PDG quotes the Berger and Seltzer Interactions of Particles with Matter http://pdg.lbl.gov

41. 41 Summary of the basic EM interactions Interactions of Particles with Matter e + / e -  Ionisation  Bremsstrahlung  Photoelectric effect  Compton effect  Pair production E E E E E  dE/dx    Z Z(Z+1) Z5Z5 Z

42. 42 Calorimeters? Primitive calorimeter invented by Benjamin Thompson (17 th 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 fuelenergy 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)