The Art of Calorimetry

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The Art of Calorimetry

  1. 1. The Art of Calorimetry Michele Livan Pavia University and INFN lectures given at the XIX Seminario Nazionale di Fisica Nucleare e Subnucleare Otranto 21-27 Settembre 2006
  2. 2. ✦ Main focus on the physics of calorimetric measurements, very little on calorimetric techniques ✦ Topics: ✦ Introduction to calorimetry ✦ The development of electromagnetic and hadron showers ✦ Energy response and compensation ✦ Fluctuations ✦ The state of the art (towards ILC calorimetry) M. Livan Pavia University & INFN
  3. 3. ✦ References ✦ Wigmans, R. (2000). Calorimetry: Energy measurement in particle physics. International Series of Monographs on Physics Vol. 107, Oxford University Press ✦ Wigmans, R. Calorimetry. Proceeding of the 10th ICFA School on Instrumentation in Elementary Particle Physics. Itacuruça, Brazil, December 2003. AIP Conference Proceedings - Volume 674 M. Livan Pavia University & INFN
  4. 4. ✦ Aknowlegments ✦ These lectures are an enlarged version of lectures given by Richard Wigmans at the Pisa University in 2005. ✦ Thanks to Richard for allowing me to use his lectures as a starting point. M. Livan Pavia University & INFN
  5. 5. Introduction to Calorimetry M. Livan The Art of Calorimetry Lecture I
  6. 6. ✦ The term Calorimetry finds its origin in thermodynamics ✦ Calorimeters are thermally isolated boxes containing a substance to study ✦ Modern , highly sophisticated versions, are in use in nuclear weapons Laboratories ✦ 239 Pu produces heat at a rate of 2 mwatts/g ✦ Calorimetry can provide an accurate measurement of the amount of Plutonium in a non-invasive way M. Livan Pavia University & INFN
  7. 7. ✦ In nuclear and particle physics, calorimetry refers to the detection of particles, and measurements of their properties, through total absorption in a block of matter, called calorimeter. ✦ Common feature of all calorimeters is that the measurement process is destructive. ✦ Unlike, for example, wire chambers that measure particle properties by tracking in a magnetic field, the particles are no longer available for inspection once the calorimeter is done with them. ✦ The only exception to this rule concerns muons. The fact that muons can penetrate substantial amounts of matter (as a calorimeter) is an important mean for muon identification ✦ In the absorption process, almost all the particle’s energy is eventually converted to heat, hence the term calorimetry. M. Livan Pavia University & INFN
  8. 8. ✦ LHC beam: Total stored energy ✦ E = 1014 protons x 14·1012 eV ≈ 1·108 J ✦ Which mass of water Mwater could one heat up (ΔT =100 K) with this amount of energy (cwater = 4.18 J g-1 K-1) ? ✦ Mwater = E/(c ΔT) = 239 kg ✦ What is the effect of a 1 GeV particle in 1 liter of water (at 20° C) ? ✦ ΔT = E/(c· Mwater) = 3.8·10-14 K ! ✦ 1 calorie ≈ 107 TeV ! ✦ The rise in temperature of the calorimeter is thus negligible ➯ More sophisticated methods are needed to determine particle properties. M. Livan Pavia University & INFN
  9. 9. CDF Calorimeters
  10. 10. Nuclear radiation Detectors ✦ First calorimetric measurements: late 1940’s ✦ fluorescence, invention of PMT, anthracene and NaI ✦ α , β and γ from nuclear decays ✦ Semiconductor detectors developed in the ‘60s ✦ Li doped Si and Ge crystals γ-ray spectrum from Uranium nuclei measured with scintillation and semiconductor detectors. Semiconductor technology offers spectacularly improved resolution. M. Livan Pavia University & INFN
  11. 11. Calorimetry in Particle Physics ✦ Calorimetry is a widespread technique in Particle Physics: ✦ Shower counters ✦ Instrumented targets ✦ Neutrino experiments ✦ Proton decay/Cosmic Ray detectors ✦ 4π detectors (our main topic) ✦ Calorimetry makes use of various detection mechanisms: ✦ Scintillation ✦ Čerenkov radiation ✦ Ionization ✦ Cryogenic phenomena M. Livan Pavia University & INFN
  12. 12. Shower counters I ✦ Primary use in early experiments: measure γs from π0 → γγ ✦ Alternate method: use sheets of material to convert photons into e+e- pairs ⇒ low efficiency ✦ NaI(Tl) (hygroscopic), CsI and many other types of scintillating crystals ✦ High light yield ⇒ excellent energy resolution ✦ Scintillation light has two components: fast and slow. ✦ Decay time of slow component can be quite sizable ( 230 ns in NaI) ✦ In the 60’s development of shower counters (Pb-Glass) based on Čerenkov light production. ✦ High-density material but light yield several orders of magnitude smaller than for scintillating crystals ⇒ worst energy resolution ✦ Čerenkov light instantaneous ⇒ extremely fast signals M. Livan Pavia University & INFN
  13. 13. Shower counters II ✦ Homogeneous calorimeters: ✦ Scintillating crystals and Pb-Glass ✦ Entire volume is sensitive to particles and may contribute to the signal ✦ Sampling calorimeters: ✦ The functions of particle absorption and signal generation are exercised by different media: ✦ Passive medium: high density material (Fe, Cu, Pb, U, ....) ✦ Active medium: generates light or charge that produce the signal ✦ Scintillator, gas, noble liquids, semiconductors,............. ✦ Only a small fraction of the energy is deposited in the active material ⇒ worse energy resolution (at least for electrons and γs) ✦ Cheaper ⇒ used in large systems M. Livan Pavia University & INFN
  14. 14. Instrumented targets ✦ Bubble chambers: both target and detector ✦ Electronic detectors: the two functions are usually separated. ✦ Target ✦ Detector ✦ Determine if interesting interactions are taking place in the target (Triggering) ✦ Measure the properties of the reaction products ✦ Instrumented targets: combination of the functions of target and detector are mantained ✦ Neutrino experiments ✦ Proton decay experiments ✦ Cosmic Rays experiments M. Livan Pavia University & INFN
  15. 15. Neutrino experiments ✦ ν interaction probability in a 1 kTon detector ≈ 10 -9 ✦ ⇒ intense beams and very massive detectors ✦ Example WA1 (CDHS) Slabs of Fe (absorber) interleaved with layers of scintillator. In the rear: wire chambers to track muons generated in charged currents interactions and/or charmed particles production M. Livan Pavia University & INFN
  16. 16. Cosmic Rays ✦ Atmospheric neutrinos ✦ Result of the decay of π and Κ in the Earth atmosphere ✦ Solar neutrinos ✦ Produced in the nuclear fusion of H into He and some higher-order processes ✦ High Energy Cosmic Rays ✦ Energies up to 1 Joule (6·1018 eV) ✦ Very large instrumented masses are needed KASCADE Cosmic ray experiment near Karlsruhe (Germany). Large TMS (Tetramethylsilane) calorimeter located in the central building, surrounded by numerous smaller, plastic -scintillator counters to detect ionizing particles M. Livan Pavia University & INFN
  17. 17. Proton decay ✦ In many theories Barion Number conservation breaks down ⇒ proton decay is allowed ✦ Current experimental limit on the proton lifetime based on the decay p → e + π0 is > 1032 years ✦ Need for large instrumented mass (300 m3 of water = 1032 protons) SuperKamiokande Water Čerenkov calorimeter: Enormous volume of high purity water viewed by large number of photomultipliers: p → e+ π0 decay produces 5 relativistic particles, the positron and two e+ e- pairs from the two γs from the π0 decay. The energy carried by these particles adds up to the proton rest mass, 938.3 MeV. M. Livan Pavia University & INFN
  18. 18. 4π detectors ✦ Onion-like Muons (µ) structure Hadrons (h) ✦ Tracking e±, γ ✦ (Particle ID) Charged Tracks e±, µ±, h± ✦ Electromagnetic Calorimetry Heavy material, Iron + active material ✦ Hadronic High Z materials, e.g., Calorimetry lead tungstate crystals Heavy absorber,(e.g., Fe) ✦ Muon Zone where ν and µ remain spectrometry Lightweight M. Livan Pavia University & INFN
  19. 19. Why Calorimeters ? ✦ Sensitive to both charged and neutral particles ✦ Differences in the shower patterns ⇒ some particle identification is possible (h/e/µ/ν(missing ET) separation) ✦ Calorimetry based on statistical processes ✦ ⇒ σ(E)/E ∝ 1/√E ✦ Magnetic spectrometers ⇒ Δp/p ∝ p ✦ Increasing energy ⇒ calorimeter dimensions ∝ logE to contain showers ✦ Fast: response times < 100 ns feasible ✦ No magnetic field needed to measure E ✦ High segmentation possible ⇒ precise measurement of the direction of incoming particles M. Livan Pavia University & INFN
  20. 20. Why Calorimeters ? ✦ Moving from fixed target to (Hadron) Colliders emphasis : Bubble Chamber event ✦ from detailed reconstruction of particle four-vectors ✦ to energy flow (jets, missing ET) especially when CDF observed in Top event combination with electrons and muons M. Livan Pavia University & INFN
  21. 21. Particle Identification vertex momentum ID em energy h energy Muon ID,p e γ π+ µ ν precision normal Particle ID electromagnetic hadronic Muon Tracking Calorimeters Tracking M. Livan Pavia University & INFN
  22. 22. e/π separation (No longitudinal segmentation !) M. Livan Pavia University & INFN
  23. 23. The importance of energy resolution
  24. 24. Partons ⇒ Particles ⇒ Jets ✦ Processes creating jets are very complicated, and consist of parton fragmentation, then both electromagnetic and hadronic showering in the detector ✦ Reconstructing jets is, naturally, also very difficult. Jet energy scale and reconstruction is one of the largest sources of systematic errors M. Livan Pavia University & INFN
  25. 25. Resolution for Jets (LHC) In jet detection also factors other than calorimeter resolution play an important role: the jet algorithm and the contributions of underlying events to the signal. This effect become less important as energy increases and jets become more collimated. At high energy e+e- Colliders high resolution jet measurement will become reality M. Livan Pavia University & INFN
  26. 26. Scintillators and Light Detectors Anode PM Photo Cathode Dynodes HPD SiPM Pixel size: ~25 x 25 µm2 to ~100 x 100 µm2 Array size: 0.5 x 0.5 µm2 to 5 x 5 µm2 M. Livan Pavia University & INFN
  27. 27. Wavelength shifters Scintillating fibers M. Livan Pavia University & INFN
  28. 28. Čerenkov radiation Pb-Glass OPAL LEP Quarz Fibers DREAM R&D for ILC M. Livan Pavia University & INFN
  29. 29. Ionization ✦ Gas Calorimeters ATLAS LAr ✦ Bad resolution ✦ Landau fluctuations ✦ Pathlenght fluctuations ✦ Noble liquids ✦ Potentially slow ✦ Liquid purity problems ✦ Stable calibration ✦ Semiconductors ✦ Excellent resolution ✦ Fast ✦ Expensive M. Livan Pavia University & INFN
  30. 30. Cryogenic phenomena ✦ Highly specialized detectors ✦ Dark matter, solar νs, magnetic monopoles, double β decay ✦ Very precise measurements of small energy deposits ✦ Phenomena that play a role in the 1 Kelvin to few milli-Kelvin range ✦ Bolometers ✦ Real calorimeters: temperature increase due to E deposit is measured by a resistive thermometer ✦ Superconducting Tunnel Junctions ✦ Use Cooper pairs excited by incident radiations that tunnel through a thin layer separating two superconductors ✦ Superheated Superconducting Granules ✦ Use transition from superconducting to normal state induced by energy deposition M. Livan Pavia University & INFN
  31. 31. Choosing a calorimeter ✦ Many factors: ✦ Choices: active, passive materials, longitudinal and lateral segmentation etc. ✦ Physics, radiation levels, environmental conditions, budget ✦ CAVEAT: Test beam results sometimes misleading ✦ Signals large integration time or signal integration over large volume could be not possible in real experimental conditions ✦ Miscellaneous materials (cables, support structures, electronics etc.) present in the real experiment can spoil resolution ✦ Jet resolution not measurable in a test beam M. Livan Pavia University & INFN
  32. 32. Basic Electromagnetic Interactions (Reminder) M. Livan Pavia University & INFN
  33. 33. Energy loss by charged particles ✦ Main energy loss mechanism for charged particles traversing matter: ✦ Inelastic interaction with atomic electrons ✦ If the energy is sufficient to release atomic electrons from nuclear Coulomb field ⇒ ionization ✦ Other processes: ✦ Atomic excitation ✦ Production of Čerenkov light ✦ At high energy: production of δ-rays ✦ At high energy: bremsstrahlung ✦ At very high energy: nuclear reactions M. Livan Pavia University & INFN
  34. 34. The Bethe-Block Formula dE Z 1 1 2me c2 γ 2 β 2 max δ = −4πNA re c z 2 2 2 2 2 ln T 2 −β − dx Aβ I 2 2 ✦ dE/dx in [Mev g-1cm2] ✦ Valid for “heavy particles ✦ First approximation: medium simply characterized by Z/A ~ electron density M. Livan Pavia University INFN
  35. 35. Interaction of charged particles ✦ Critical energy Ec dE dE = dx Brems dx ion ✦ For electrons: 610M eV 710M eV solid+liq Ec = gas Ec = Z + 1.24 Z + 1.24 ✦ Ec(e-) in Cu (Z=29) = 20 MeV m 2 Energy loss (ion+rad) ✦For muons = mu Ec elec Ec me µ of e and p in Cu ✦Ec(µ) in Cu = 1 TeV ✦Unlike electrons, muons in multi-GeV range can traverse thick layers of dense matter. M. Livan Pavia University INFN
  36. 36. Energy loss by charged particles M. Livan Pavia University INFN
  37. 37. Interaction of charged particles ✦ Energy loss by Bremsstrahlung ✦ Radiation of real photons in the Coulomb field of the nuclei of the absorber medium dE Z 2 2 1 e2 2 183 E − = 4αNA z ( ) E ln 1 ∝ 2 dx A 4π0 mc2 Z3 m ✦ For electrons: dE Z2 2 2 183 − = 4αNA z re E ln 1 dx A Z3 dE E −Xx − = =⇒ E = E0 0 dx X0 X0 = 2 A 183 radiation length [g/cm2] 4αNA Z z 2 re E ln A 2 1 Z3 M. Livan Pavia University INFN
  38. 38. Interaction of photons ✦ In order to be detected a photon has to create charged particles and/or transfer energy to charged particles ✦ Photoelectric effect ✦ Most probable process at low energy ✦ P.e. effect releases mainly electrons from the K-shell ✦ Cross section shows strong modulation if Eγ≈ Eshell 1 32 2 Eγ 8 2 K σphoto = α 4 Z 5 σT h e = e σT h = πre (T homson) 7 me c2 3 ✦ At high energies (ε1) 2 4 51 K σphoto = 4πre α Z σphoto ∝ Z 5 σphoto ∝ E −3 M. Livan Pavia University INFN
  39. 39. Photoelectric effect M. Livan Pavia University INFN
  40. 40. Interaction of photons γ + e ⇒ γ’ + e’ ✦ Compton scattering ✦ Assume electrons quasi-free dσ ✦ Klein-Nishina (θ, ) dΩ ✦ At high energy approximately ln e σc ∝ ✦ Atomic Compton cross-section atomic σc = e Zσc Compton Cross- −1 section (Klein- σCompton ∝ E Nishina) M. Livan Pavia University INFN
  41. 41. Scattering Compton ✦ For all but the high Z materials: most probable process for γs in the range between few hundred keV and 5 MeV ✦ Typically at least 50% of the total energy is deposited by such γs in the absorption process of multi GeV e+, e- and γs ✦ Compton scattering is a very important process to understand the fine details of calorimetry ✦ Angular distribution of recoil electrons shows a substantial isotropic component. Many γs in the MeV range are absorbed by a sequence of Compton scatterings ⇒ most of the Compton electrons produced in this process are isotropically distributed M. Livan Pavia University INFN
  42. 42. Interaction of photons ✦ Pair production ✦ Only possible in the field of a nucleus (or an electron) if ✦ Eγ 2mec2 ✦ Cross-section (High energy approximation) M. Livan Pavia University INFN
  43. 43. Summary µ = γ mass attenuation coefficient NA Iγ = I0 e−µx µi = σi A µ = µphoto + µcompton + µpair + ... Gammas Electrons M. Livan Pavia University INFN
  44. 44. Summary (Z dependence) Z Z 4÷5 Z(Z + 1) Z Z(Z + 1) M. Livan Pavia University INFN
  45. 45. Z dependence Gammas Electrons M. Livan Pavia University INFN
  46. 46. Photon absorption ✦ Energy domains in which photoelectric effect, Compton scattering and pair production are the most likely processes to occur as a function of the Z value of the absorber material M. Livan Pavia University INFN
  47. 47. Electromagnetic and hadronic showers development M. Livan The Art of Calorimetry Lecture II
  48. 48. Summary (Z dependence) Z Z 4÷5 Z(Z + 1) Z Z(Z + 1) M. Livan Pavia University INFN
  49. 49. A simple shower M. Livan Pavia University INFN
  50. 50. Simple shower model ✦ Consider only Bremsstrahlung and (symmetric) pair production ✦ Assume X0 ∼ λpair ✦ After t X0: ✦ N(t) = 2t ✦ E(t)/particle = E0/2t ✦ Process continues until E(t)Ec ✦ E(tmax) = E0/2tmax = Ec ✦ tmax = ln(E0/Ec)/ln2 ✦ Nmax ≈ E0/Ec M. Livan Pavia University INFN
  51. 51. Electromagnetic Showers ✦ Differences between high-Z/low-Z materials ✦ Energy at which radiation becomes dominant ✦ Energy at which photoelectric effect becomes dominant ✦ Energy at which pair production becomes dominant ✦ Showers ⇒ Particle multiplication ⇒ little material needed to contain shower ✦ 100 GeV electrons: 90% of shower energy contained in 4 kg of lead ✦ Shower particle multiplicity reaches maximum at shower maximum ✦ Depth of shower maximum shifts logarithmically with energy M. Livan Pavia University INFN
  52. 52. Electromagnetic shower profiles (longitudinal) Depth of shower max increases logarithmically with energy M. Livan Pavia University INFN
  53. 53. Electromagnetic Showers ✦ Longitudinal development governed by radiation length (X0) ✦ Defined only for GeV regime ✦ there are important differences between showers induced by e, γ: ✦ e.g. Leakage fluctuations, effects of material upstream, .... ✦ Mean free path of γs = 9/7 X0 Distribution of energy fraction deposited in the first 5 X0 by 10 GeV electrons and γs showering in Pb. Results of EGS4 simulations M. Livan Pavia University INFN
  54. 54. Electromagnetic Showers ✦ Scaling with X0 is not perfect ✦ In high-Z materials, particle multiplication continues longer and decreases more slowly than in low-Z materials ✦ The number of positrons strongly increases with the Z value of the absorber material ✦ Example: number of e +/GeV in Pb is 3 times larger than in Al ✦ Need more X0 of Pb to contain shower at 90% level M. Livan Pavia University INFN
  55. 55. Scaling is NOT perfect M. Livan Pavia University INFN
  56. 56. Electromagnetic shower leakage (longitudinal) • The absorber thickness needed to contain a shower increases logarithmically with energy • The number of X0 needed to fully contain the shower energy can be as much as 10 X0 going from high Z to low Z absorbers • More X0 needed to contain γ initiated showers M. Livan Pavia University INFN
  57. 57. Electromagnetic Showers ✦ Phenomena at E Ec determine important calorimeter properties ✦ In lead 40% of energy deposited by e± with E 1 MeV ✦ Only 1/4 deposited by e+, 3/4 by e- (Compton, photoelectrons!) ✦ The e+ are closer to the shower axis, Compton and photoelectrons in halo M. Livan Pavia University INFN
  58. 58. Importance of SOFT particles • The composition of em showers. Shown are the percentages of the 10 GeV e- energy of 10 GeV electromagnetic showers deposited through shower particles with energies below 1 MeV, below 4 MeV or above 20 MeV as function of the Z of the absorber material. • Results of EGS4 simulations M. Livan Pavia University INFN
  59. 59. Electromagnetic Showers ✦ Lateral shower width scales with Molière radius ρM X0 ρM = Es Es = me c2 4π/α Ec X0 ∝ A/Z 2 , Ec ∝ 1/Z ⇒ ρM ∝ A/Z ✦ ρM much less material dependent than X0 ✦ Lateral shower width determined by: ✦ Multiple scattering of e± (early, 0.2 ρM) ✦ Compton γs travelling away from axis (1 - 1.5 ρM) M. Livan Pavia University INFN
  60. 60. Lateral profile ✦ Material dependence ✦ Radial energy deposit profiles for 10 GeV electrons showering in Al, Cu and Pb ✦ Results of EGS4 calculations M. Livan Pavia University INFN
  61. 61. Lateral profile Radial distributions of the energy deposited by 10 GeV electron showers in Cu. Results of EGS4 simulations M. Livan Pavia University INFN
  62. 62. Electrons and positrons ✦ The number of positrons increases by more than a factor 3 going from Al to U ✦ Aluminum (∼18 e+/GeV) ✦ Uranium (∼60 e+/GeV) ✦ Increase due to the fact that particle multiplication in showers developing in high-Z absorber materials continues down to much lower energies than in low- Z materials M. Livan Pavia University INFN
  63. 63. Contributions to signal M. Livan Pavia University INFN
  64. 64. Lateral shower leakage • No energy dependence • A (sufficiently long) cylinder will contain the same fraction of energy of a 1 GeV or 1 TeV em shower • Results of EGS4 simulations M. Livan Pavia University INFN
  65. 65. Muons in calorimeters ✦ Muons are not minimum ionizing particles m 2 µ Ec (µ) = × Ec (e) me =⇒ Ec (µ) ≈ 200 GeV in P b ✦ The effects of radiation are clearly visible in calorimeters, especially for high-energy muons in high-Z absorber material M. Livan Pavia University INFN
  66. 66. Muon signals in a calorimeter ✦ Signal distributions for muons of 10, 20, 80 and 225 GeV traversing the SPACAL detector M. Livan Pavia University INFN
  67. 67. Hadron showers ✦ Extra complication: the strong interaction ✦ Much larger variety may occur both at the particle level and at the level of the stuck nucleus ✦ Production of other particles, mainly pions ✦ Some of these particles (π0, η) develop electromagnetic showers ✦ Nuclear reactions: protons, neutrons released from nuclei ✦ Invisible energy (nuclear binding energy, target recoil) M. Livan Pavia University INFN
  68. 68. Hadron vs em showers ✦ Hadron showers ⇒ much more complex than em showers ✦ Invisible energy ✦ em showers: all energy carried by incoming e or γ goes to ionization ✦ had showers: certain fraction of energy is fundamentally undetectable ✦ em showers ✦ e± ⇒ continuous stream of events ( ionization + bremsstrahlung) ✦ γ ⇒ can penetrate sizable amounts of material before losing energy ✦ had showers ✦ ionization (as a µ) then interaction with nuclei ✦ development similar to em shower but different scale ( λ vs. X0) ✦ Particle sector ✦ Nuclear sector M. Livan Pavia University INFN
  69. 69. The electromagnetic fraction, fem ✦ em decaying particles : π0, η0 ⇒ γ γ ✦ % of hadronic energy going to em fluctuates heavily ✦ On average 1/3 of particles in first generation are π0s ✦ π0s production by strongly interacting particles is an irreversible process (a ”one-way street”) ✦ Simple model ✦ after first generation fem = 1/3 ✦ after second generation fem = 1/3 + 1/3 of 2/3 = 5/9 ✦ after third generation fem = 1/3 + 1/3 of 2/3 + 1/3 of 4/9 = 19/27 ✦ after n generations fem = 1 - (1- 1/3)n ✦ the process stops when the available energy drops below the pion production threshold and n depends on the average multiplicity of mesons produced per interaction m ⇒ n increases by one unit every time E increases by a factor m ✦ fem increases with increasing incoming hadron energy M. Livan Pavia University INFN
  70. 70. The electromagnetic fraction, fem ✦ But ✦ other particles than pions are produced (factor 1/3 wrong) ✦ m is energy dependent ✦ barion number conservation neglected → lower fem in proton induced showers than in pion induced ones ✦ Using a more realistic model ✦ fem = 1- (E/E0)(k-1) ✦ E0= average energy needed to produce a π0 ✦ (k-1) related to the average multiplicity ✦ fem slightly Z dependent ✦ Consequences: ✦ Signal of pion signal of electron (non-compensation) ✦ e/π signal ratio energy dependent (non-linearity) M. Livan Pavia University INFN
  71. 71. Energy dependence em component ✦ SPACAL: Pb - scintillating fibers ✦ QFCAL: Cu - quartz fibers M. Livan Pavia University INFN
  72. 72. Signal non-linearity M. Livan Pavia University INFN
  73. 73. Non em component ✦ Breakdown of the non-em component in Lead ✦ Ionizing particles 56% (2/3 from spallation protons) ✦ Neutrons 10% (37 neutrons/GeV) ✦ Invisible 34% ✦ Spallation protons carry typically 100 MeV ✦ Evaporation neutrons 3 MeV M. Livan Pavia University INFN
  74. 74. Where does the energy go ? ✦ Energy deposit and composition of the non-em component of hadronic showers in lead and iron. ✦ The listed numbers of particles are per GeV of non-em energy M. Livan Pavia University INFN
  75. 75. A typical process ✦ Nuclear interaction (nuclear star) induced by a proton of 30 GeV in a photographic emulsion Spallation neutrons ( non-visible) Fast pions and fast spallation protons ( non-isotropic) Protons (isotropic) M. Livan Pavia University INFN
  76. 76. Neutron production spectra dN √ = E exp(−E/T ) dE M. Livan Pavia University INFN
  77. 77. Hadronic shower profiles ✦ Shower profiles are governed by the ✦ Nuclear interaction lenght, λint ✦ λint (g cm-2) ∝ A1/3 ✦ Fe 16.8 cm, Cu 15.1 cm, Pb 17.0 cm, U 10.0 cm M. Livan Pavia University INFN
  78. 78. Longitudinal profile M. Livan Pavia University INFN
  79. 79. Hadronic showers fluctuations ✦ Very interesting measurements of the longitudinal energy deposition in em and hadronic showers were made with the “Hanging file calorimeter” M. Livan Pavia University INFN
  80. 80. Fluctuations (em showers) ✦ Hanging file calorimeter ✦ 170 GeV electrons M. Livan Pavia University INFN
  81. 81. Fluctuations (hadronic showers) ✦ Hanging file calorimeter ✦ 270 GeV pions M. Livan Pavia University INFN
  82. 82. Fluctuations (hadronic showers) ✦ Hanging file calorimeter ✦ 270 GeV pions M. Livan Pavia University INFN
  83. 83. Hadronic lateral shower profiles ✦ Lateral shower profile has two components: ✦ Electromagnetic core (π0) ✦ Non-em halo (mainly non-relativistic shower particles) ✦ Spectacular consequences for Čerenkov calorimetry ✦ Čerenkov light is emitted by particles with β 1/n ✦ e.g. quartz (n= 1.45) : Threshold 0.2 MeV for e, 400 MeV for p M. Livan Pavia University INFN
  84. 84. Hadronic lateral shower profiles M. Livan Pavia University INFN
  85. 85. Hadronic lateral shower profiles ✦ Nonrelativistic particles dominate tails in hadron showers M. Livan Pavia University INFN
  86. 86. Lateral distribution shower particles ✦ Np produced by thermal neutron capture ✦ Mo fission product of U produced by non-thermal neutrons (MeV) ✦ U produced by γ (10 GeV) induced reactions present in the em core M. Livan Pavia University INFN
  87. 87. Shower containment ✦ Shower containment: ✦ Depth to contain showers increases with log E ✦ Lateral leakage decreases as the energy goes up ! ✦ fem increases with energy ✦ Electromagnetic component concentrated in a narrow cone around shower axis ✦ ⇒ Energy fraction contained in a cylinder with a given radius increases with energy M. Livan Pavia University INFN
  88. 88. Hadronic shower leakage (longitudinal) M. Livan Pavia University INFN
  89. 89. Hadronic shower leakage (lateral) ✦ This energy dependence is a direct consequence of the energy of fem. The average energy fraction carried by the em shower component increases with energy and since this component is concentrated in a narrow cone around the shower axis, the energy fraction contained in a cylinder with a given radius increases with energy as well. M. Livan Pavia University INFN
  90. 90. Hadronic shower profiles ✦ The λint/X0 ratio is important for particle ID ✦ In high-Z materials: λint/X0 ∼ 30 ⇒ excellent e/π separator ✦ 1 cm PB + scintillator plate makes spectacular preshower detector M. Livan Pavia University INFN
  91. 91. Comparison em/hadronic calorimeter properties ✦ Ratio of the nuclear interaction lenght and the radiation lenght as a function of Z M. Livan Pavia University INFN
  92. 92. Particle ID with a simple preshower detector M. Livan Pavia University INFN
  93. 93. Lessons for calorimetry ✦ In absorption process, most of the energy is deposited by very soft particles ✦ Electromagnetic showers: ✦ 3/4 of the energy deposited by e-, 2/4 of it by Compton, photoelectrons ✦ These are isotropic, have forgotten direction of incoming particle ⇒ No need for sandwich geometry ✦ The typical shower particle is a 1 MeV electron, range 1mm ⇒ important consequences for sampling calorimetry ✦ Hadron showers: ✦ Typical shower particles are a 50-100 MeV proton and a 3 MeV evaporation neutron ✦ Range of 100 MeV proton is 1 - 2 cm ✦ Neutrons travel typically several cm ✦ What they do depends critically on detail of the absorber M. Livan Pavia University INFN
  94. 94. Angular distributiom M. Livan Pavia University INFN
  95. 95. Range of protons generated in hadron showers ✦ Average range of protons in various absorber materials, as a function of energy M. Livan Pavia University INFN
  96. 96. M. Livan The Art of Calorimetry Lecture III Energy Response and Compensation
  97. 97. Lessons for calorimetry ✦ In absorption process, most of the energy is deposited by very soft particles ✦ Electromagnetic showers: ✦ 3/4 of the energy deposited by e-, 2/4 of it by Compton, photoelectrons ✦ These are isotropic, have forgotten direction of incoming particle ⇒ No need for sandwich geometry ✦ The typical shower particle is a 1 MeV electron, range 1mm ⇒ important consequences for sampling calorimetry ✦ Hadron showers: ✦ Typical shower particles are a 50-100 MeV proton and a 3 MeV evaporation neutron ✦ Range of 100 MeV proton is 1 - 2 cm ✦ Neutrons travel typically several cm ✦ What they do depends critically on detail of the absorber M. Livan Pavia University INFN M. Livan Pavia University INFN
  98. 98. The Calorimeter Response Function ✦ Response = Average signal per unit of deposited energy ✦ e.g. # photoelectrons/GeV, picoCoulombs/MeV, etc ✦ ➞ A linear calorimeter has a constant response • Electromagnetic calorimeters are in general linear • All energy deposited through ionization/excitation of absorber • If not linear ⇒ instrumental effects (saturation, leakage,....) M. Livan Pavia University INFN
  99. 99. Signal linearity for electromagnetic showers ✦ Example: ✦ Saturation effects in PMTs ✦ Voltage between last dynodes lowered by high current ✦ ⇒ lower PMT gain M. Livan Pavia University INFN
  100. 100. Saturation in ”digital” calorimeters ✦ Gaseous detector operated in “digital” mode ✦ Geiger counters or streamer chambers ✦ Intrinsically non linear: ✦ Each charged particle creates an insensitive region along the stuck wire preventing nearby particles to be registered ✦ Density of particles increases with increasing energy ✦ ⇒ calorimeter response decreases with increasing energy ✦ Example: ✦ Calorimeter read out using wire chambers in “limited streamer” mode ✦ Energy varied by depositing n (n = 1-10) positrons of 17.5 GeV simultaneously in the calorimeter ✦ Energy deposit profile not energy dependent ✦ Calorimeter longitudinally subdivided in 5 sections M. Livan Pavia University INFN
  101. 101. Saturation in ”digital” calorimeters ✦ At n=6 ✦ Non linearity: ✦ 1 - 14.5 % ✦ 2 - 14.8 % ✦ 3 - 9.3 % ✦ 4 - 2.4 % ✦ 5 - 0.5 % ✦ Non-linearity in sect. 1 more than 6 times the one in sect. 4 ✦ Energy deposit in sect. 1 less than half of the one in sect. 4 ✦ Particle density in sect. 1 larger than in sect. 4 M. Livan Pavia University INFN
  102. 102. Fluctuations due to instrumental effects (readout) ✦ Electrons from shower leakage traversing SPDs generate signals order of magnitude larger than the ones generated by scintillation photons M. Livan Pavia University INFN
  103. 103. Homogeneous calorimeters I ✦ Homogeneous: absorber and active media are the same ✦ Response to muons ✦ because of similarity between the energy deposit mechanism response to muons and em showers are equal ✦ ⇒ same calibration constant ⇒ e/mip=1 ✦ Response to hadrons and jets ✦ Due to the invisible energy π/e 1 ✦ e/mip =1 ⇒ π/mip 1 ✦ Response to hadron showers smaller than the electromagnetic one ✦ Electromagnetic fraction (fem) energy dependent ✦ ⇒ response to electromagnetic component increases with energy ⇒ π/e increases with energy M. Livan Pavia University INFN
  104. 104. Homogeneous calorimeters II ✦ Calorimeter response to non-em component (h) energy independent ⇒ e/h 1 (non compensating calorimeter) ✦ e/π not a measure of the degree of non-compensation ✦ part of a pion induced shower is of em nature ✦ fem increases with energy ⇒ e/π ⇒ tends to 1 ✦ e/h cannot be measured directly π = fem · e + (1 − fem ) · h π/e = fem + (1 − fem ) · h/e e/h e/π = fem function of energy 1 − fem [1 − e/h] M. Livan Pavia University INFN
  105. 105. Hadron showers: e/h and the e/π signal ratio M. Livan Pavia University INFN
  106. 106. Homogeneous calorimeters III ✦ Response to jets ✦ Jet = collection of particles resulting from the fragmentation of a quark, a diquark or a hard gluon ✦ From the calorimetric point of view absorption of jets proceeds in a way that is similar to absorption of single hadrons ✦ (Minor) difference: ✦ em component for single hadrons are π0 produced in the calorimeter ✦ jets contain a number of π0 (γ from their decays) upon entering the calorimeter (“intrinsic em component”) ✦ fem for jets and single hadrons different and depending on the fragmentation process ✦ No general statement can be made about differences between response to single hadrons and jets but: ✦ response to jets smaller than to electrons or gammas ✦ response to jets is energy dependent M. Livan Pavia University INFN
  107. 107. Sampling calorimeters ✦ Sampling calorimeter: only part of shower energy deposited in active medium ✦ Sampling fraction f samp energy deposited in active medium fsamp = total energy deposited in calorimeter ✦ fsamp is usually determined with a mip (dE/dx at minimum) ✦ N.B. mip’s do not exist ! ✦ e.g. D0 (em section): ✦ 3 mm 238U (dE/dx = 61.5 MeV/layer) ✦ 2 x 2.3 mm LAr (dE/dx = 9.8 MeV/layer) ✦ fsamp = 13.7% M. Livan Pavia University INFN
  108. 108. The e/mip ratio ✦ D0: fsamp = 13.7% ✦ However, for em showers, sampling fraction is only 8.2% ✦ ⇒ e/mip ≈ 0.6 ✦ e/mip is a function of shower depth, in U/LAr it decreases ✦ e/mip increases when the sampling frequency becomes very high ✦ What is going on ? ✦ Photoelectric effect: σ ∝ Z5, (18 / 92)5 = 3 · 10-4 ✦ ⇒ Soft γs are very inefficiently sampled ✦ Effects strongest at high Z, and late in the shower development ✦ The range of the photoelectrons is typically 1 mm ✦ Only photoelectrons produced near the boundary between active and passive material produce a signal ✦ ⇒ if absorber layers are thin, they may contribute to the signals M. Livan Pavia University INFN
  109. 109. Sampling calorimeters: the e/mip signal ratio ✦ e/mip larger for LAr (Z=18) than for scintillator ✦ e/mip ratio determined by the difference in Z values between active andINFN M. Livan Pavia University passive media
  110. 110. Gammas ✦ At high energy γ/mip ≈ e/mip ✦ Below 1 MeV the efficiency for γ detection drops spectacularly due to the onset of the photoelectric effect M. Livan Pavia University INFN
  111. 111. The EM sampling fraction changes with depth ! Very relevant for the calibration of longitudinally segmented em calorimeters ! Must use different calibration constants ✦ e/mip changes as the shower develops ✦ The effect can be understood from the the changing composition of the showers ✦ Early phase: relatively fast shower particles (pairs) ✦ Tails dominated by Compton and photoelectric electrons M. Livan Pavia University INFN
  112. 112. The e/mip ratio: dependence on sampling frequency ✦ Only photoelectrons produced in a very thin absorber layer near the boundary between active and passive materials are sampled ✦ Increasing the sampling frequency (thinner absorber plates) increases the total boundary surface M. Livan Pavia University INFN
  113. 113. Hadronic shower response and the e/h ratio ✦ The hadronic response is not constant ✦ fem, and therefore e/π signal ratio is a function of energy ✦ ➙ If calorimeter is linear for electrons, it is non-linear for hadrons ✦ Energy-independent way to characterize hadron calorimeters: e/h ✦ e = response to the em shower component ✦ h = response to the non-em shower component ✦ → Response to showers initiated by pions: e/h Rπ = fem e + [1 − fem ] h → e/π = 1 − fem [1 − e/h] ✦ e/h is inferred from e/π measured at several energies (fem values) ✦ Calorimeters can be ✦ Undercompensating (e/h 1) ✦ Overcompensating (e/h 1) ✦ Compensating (e/h =1) M. Livan Pavia University INFN
  114. 114. Hadron Showers Energy dependence EM component M. Livan Pavia University INFN
  115. 115. Hadronic signal (non)-linearity at low energy ✦ At low energy response to hadrons resembles the one for mips at low energy, and if e/mip ≠1 ⇒ the calorimeter is by definition non linear, regardless the degree of compensation M. Livan Pavia University INFN
  116. 116. Hadronic signal (non)-linearity: dependence on e/h M. Livan Pavia University INFN
  117. 117. Non-linearity and e/h ✦ Non-linearity determined by e/h value of the calorimeter ✦ Measurement of non-linearity is one of the methods to determine e/h ✦ Assuming linearity for em showers: π(E1 ) fem (E1 ) + [1 − fem (E1 )](e/h)−1 = π(E2 ) fem (E2 ) + [1 − fem (E2 )](e/h)−1 π(E1 ) e/h = 1 ⇒ =1 π(E2 ) ✦ Linearity (at least for E 5 GeV) is only one of the main advantages of compensating calorimeters M. Livan Pavia University INFN
  118. 118. Non-em calorimeter response I ✦ Energy deposition mechanisms that play a role in the absorption of the non-em shower energy: ✦ Ionization by charged pions (Relativistic shower component). The fraction of energy carried by these particles is called frel ✦ Ionization by spallation protons (non-relativistic shower component). The fraction of energy carried by these particles is called fp ✦ Kinetic energy carried by evaporation neutrons may be deposited in a variety of ways. The fraction of energy carried by these particles is called fn ✦ The energy used to release protons and neutrons from calorimeter nuclei, and the kinetic energy carried by recoil nuclei do not lead to a calorimeter signal. This energy represent the invisible fraction finv of the non-em shower energy M. Livan Pavia University INFN
  119. 119. Non-em calorimeter response II ✦ h can be written as follows: h = frel · rel + fp · p + fn · n + finv · inv frel + fp + fn + finv = 1 ✦ rel, p, n and inv denote the calorimeter responses ✦ Normalizing to mips and eliminating the last term (inv =0) e e/mip = h frel · rel/mip + fp · p/mip + fn · n/mip ✦ The e/h value can be determined once we know its response to the three components of the non-em shower components M. Livan Pavia University INFN
  120. 120. Compensation (I) ✦ Need to understand response to typical shower particles (relative to mip) ✦ Relativistic charged hadrons ✦ Even if relativistic, these particles resemble mip in their ionization losses ⇒ rel/mip = 1 ✦ Spallation protons and Neutrons ✦ Spallation protons ✦ More efficient sampling ✦ Signal saturation M. Livan Pavia University INFN
  121. 121. Aspects of compensation: sampling of soft shower protons ✦ Results from Monte Carlo simulation ✦ Quite complicated picture, many effects contribute: ✦ ratio of specific ionization in the active and passive materials ↑, ✦ multiple scattering effects ↓, ✦ sampling inefficiencies due to limited range ↓ ✦ saturation and recombination effects in the active medium ↓ M. Livan Pavia University INFN
  122. 122. Aspects of compensation: sampling of soft shower protons M. Livan Pavia University INFN
  123. 123. Aspects of compensation: saturation effects dL dE/dx Birk’s Law =S dx 1 + kb · dE/dx M. Livan Pavia University INFN
  124. 124. Compensation: the spallation proton/mip signal ratio M. Livan Pavia University INFN
  125. 125. Compensation: the spallation proton/mip signal ratio ✦ Response to spallation protons depends on: ✦ spallation protons energy spectrum ✦ Z value of the absorber ✦ fsamp and ffreq ✦ saturation properties of the active medium M. Livan Pavia University INFN
  126. 126. Compensation (II) ✦ Need to understand response to typical shower particles (relative to mip) ✦ Spallation protons and Neutrons ✦ Neutrons ✦ (n, n’γ) inelastic scattering: not very important ✦ (n, n’) elastic scattering: most interesting ✦ (n, γ) capture (thermal): lots of energy, but process is slow (µs) M. Livan Pavia University INFN
  127. 127. Compensation (III) - The role of neutrons ✦ Elastic scattering felastic = 2A/(A+1)2 ✦ Hydrogen f elastic = 0.5 Lead felastic = 0.005 ✦ Pb/H2 calorimeter structure (50/50) ✦ 1 MeV n deposits 98% in H2 ✦ mip deposits 2.2% in H2 }⇒ n/mip = 45 ✦ Recoil protons can be measured! ✦ ⇒ Neutrons have an enormous potential to amplify hadronic shower signals, and thus compensate for losses in invisible energy ✦ Tune the e/h value through the sampling fraction! ✦ e.g. 90% Pb/10% H calorimeter structure 2 ✦ 1 MeV n deposits 86.6% in H2 ✦ mip deposits 0.25% in H2 M. Livan Pavia University INFN } ⇒ n/mip = 350
  128. 128. Compensation in a Uranium/gas calorimeter M. Livan Pavia University INFN
  129. 129. Compensation: the importance of soft neutrons M. Livan Pavia University INFN
  130. 130. Compensation (III) - The role of neutrons ✦ Elastic scattering felastic = 2A/(A+1)2 ✦ Hydrogen f elastic = 0.5 Lead felastic = 0.005 ✦ Pb/H2 calorimeter structure (50/50) ✦ 1 MeV n deposits 98% in H2 ✦ mip deposits 2.2% in H2 }⇒ n/mip = 45 ✦ Recoil protons can be measured! ✦ ⇒ Neutrons have an enormous potential to amplify hadronic shower signals, and thus compensate for losses in invisible energy ✦ Tune the e/h value through the sampling fraction! ✦ e.g. 90% Pb/10% H calorimeter structure 2 ✦ 1 MeV n deposits 86.6% in H2 ✦ mip deposits 0.25% in H2 M. Livan Pavia University INFN } ⇒ n/mip = 350
  131. 131. Compensation: the crucial role of the sampling fraction M. Livan Pavia University INFN
  132. 132. Compensation in practice: Pb/scintillator calorimeters M. Livan Pavia University INFN
  133. 133. Compensation in Fe/scintillator calorimeters ? M. Livan Pavia University INFN
  134. 134. Compensation: slow neutrons and the signal’s time structure ✦ Average time between elastic n-p collisions: 17 ns in polystyrene ✦ Measured value lower (10 ns) due to elastic or inelastic neutron scattering off other nuclei present in the calorimeter structure (Pb, C and O) M. Livan Pavia University INFN
  135. 135. Compensation: effects of slow neutrons on the signals M. Livan Pavia University INFN
  136. 136. Non-hydrogenous calorimeters: Z dependence of e/h M. Livan Pavia University INFN
  137. 137. Compensation (IV) ✦ All compensating calorimeters rely on the contribution of neutrons to the signals ✦ Ingredients for compensating calorimeters ✦ Sampling calorimeter ✦ Hydrogenous active medium (recoil p!) ✦ Precisely tuned sampling fraction ✦ e.g. 10% for U/scintillator, 3% for Pb/scintillator,....... ✦ Uranium absorber ✦ Helpful, but neither essential nor sufficient M. Livan Pavia University INFN
  138. 138. M. Livan The Art of Calorimetry Lecture IV Fluctuations
  139. 139. Calorimetric measurement ✦ In the previous lecture we examined the average signals produced during absorption ✦ To make a statement about the energy of a particle: ✦ relationship between measured signal and deposited energy (calibration) ✦ energy resolution (precision with which the unknown energy can be measured) ✦ Resolution is limited by: ✦ fluctuations in the processes through which the energy is degraded (unavoidable) ✦ ultimate limit to the energy resolution in em showers (worsened by detection techniques) ✦ not a limit for hadronic showers ? (clever readout techniques can allow to obtain resolutions better than the limits set by internal fluctuations ✦ technique chosen to measure the final products of the cascade process M. Livan Pavia University INFN
  140. 140. Fluctuations (1) ✦ Calorimeter’s energy resolution is determined by fluctuations ✦ → applying overall weighting factors (offline compensation) has no merit in this context ✦ Many sources of fluctuations may play a role, for example: ✦ Signal quantum fluctuations (e.g. photoelectron statistics) ✦ Sampling fluctuations ✦ Shower leakage ✦ Instrumental effects (e.g. electronic noise, light attenuation, structural non- uniformity) ✦ but usually one source dominates ✦ Improve performance ⇒ work on that source ✦ Poissonian fluctuations: ✦ Energy E gives N signal quanta, with σ = √N ✦ ⇒ σ√E ∝ √N√N = cE ⇒ σ/E=c/√E M. Livan Pavia University INFN
  141. 141. What excellent resolution does for you M. Livan Pavia University INFN
  142. 142. Fluctuations (2) ✦ Signal quantum fluctuations ✦ Ge detectors for nuclear γ ray spectroscopy: 1 eV/quantum ✦ ⇒ If E= 1 MeV: 106 quanta, therefore σ/E = 0.1% ✦ Usually E expressed in GeV ⇒ σ/E = 0.003%/√E ✦ Quartz fiber calorimeters: typical light yield ∼ 1 photoelectron/GeV ✦ Small fraction of energy lost in Čerenkov radiation, small fraction of the light trapped in the fiber, low quantum efficiency for UV light ✦ ⇒ σ/E = 100%/√E. If E = 100 GeV, σ/E = 10% M. Livan Pavia University INFN
  143. 143. Signal quantum fluctuations dominate (1) ✦ Quartz window transmit a larger fraction of the Čerenkov light (UV component) M. Livan Pavia University INFN
  144. 144. Signal quantum fluctuations dominate also here (2) ✦ Asymmetric distribution typical of Poisson distribution ✦ At high energy Gaussian shape (central limit theorem) M. Livan Pavia University INFN
  145. 145. Fluctuations (3) ✦ Sampling fluctuations ✦ Determined by fluctuations in the number of different shower particles contributing to signals ✦ Both sampling fraction and the sampling frequency are important ✦ Poissonian contribution : σsamp/E = asamp/√E ✦ ZEUS: No correlation between particles contributing to signals in neighboring sampling layers ⇒ range of shower particles is very small M. Livan Pavia University INFN
  146. 146. Sampling fraction and sampling frequency ✦ For fiber calorimeters for equal sampling fraction, better resolution for smaller diameter fibers (higher sampling frequency) M. Livan Pavia University INFN
  147. 147. Sampling fluctuations in em calorimeters Determined by sampling fraction and sampling frequency M. Livan Pavia University INFN
  148. 148. How to measure signal quantum fluctuations ✦ Reduce the # of photoelectrons using a neutral density filter by a factor f (f1) ✦ x = light yield of the calorimeter ✦ # of p.e. for an energy deposit E is xE, σ=√(xE), (σ/E)p.e.=1/√(xE) ✦ Contribution of sampling fluctuations: (σ/E)samp=asamp/√(E) (σ/E)nof ilter = samp /E + 1/xE a2 (σ/E)f ilter = a2 samp /E + f /xE = (σ/E)2 ilter + (f − 1)/xE nof ✦ If f is known ⇒ determine x ✦ Better at low energy where non stochastic contributions are limited M. Livan Pavia University INFN
  149. 149. How to measure signal quantum fluctuations ✦ f = 3 and 10 ✦ 3, 8,10,15 GeV ✦ 1300 ± 90 p.e./GeV ✦ 2.8%/√E contribution to resolution ✦ 5.7%/√E: total em resolution ✦ 5.0%/√E sampling fluctuation contribution NIM A368 (1996), 640 M. Livan Pavia University INFN
  150. 150. How to measure the effects of sampling fluctuations (I) ✦ To measure sampling fluctuations: ✦ Choose conditions in which sampling fluctuations contribute substantially to the total energy resolution ✦ Change the sampling fraction keeping everything else the same ✦ Derive the contribution of sampling fluctuations from a comparison of the total energy resolution before and after these changes were made M. Livan Pavia University INFN
  151. 151. How to measure the effects of sampling fluctuations (II) ✦ σsum = calorimeter resolution ✦ σdiff = contribution of sampling fluctuations ✦ for em showers σsum = σsamp ✦ σA = σB = σsum√2 = σsamp√2 ✦ If fluctuations in A and B completely uncorrelated ✦ σsum = σdiff = σsamp ✦ If other sources contribute → σsum σdiff and σA , σB σsum√2 ✦ At the extreme (sampling fluctuations not relevant) ✦ σA , σB = σsum√2 and σsamp(A) = σsamp(A+B)√2 M. Livan Pavia University INFN
  152. 152. How to measure the effects of sampling fluctuations (III) Measurement of the p.e. statistics NIM A290 (1990), 335 sampling fluctuations contribution p.e. statistics contribution M. Livan Pavia University INFN
  153. 153. How to measure the effects of sampling fluctuations (IV) ✦ Energy resolution for em showers strongly dominated by sampling fluctuations ✦ Sampling fluctuations in good agreement with the formula: asamp = 2.7% d/fsamp ✦ Sampling fluctuations strongly dominate the hadron resolution in these compensating calorimeters ✦ Hadronic sampling fluctuations are about a factor 2 larger than the em ones ✦ “Intrinsic” fluctuation contribution scale as E-1/2 M. Livan Pavia University INFN
  154. 154. Sampling fluctuations in em and hadronic showers sampling fluctuations only minor contribution to hadronic resolution in this non compensating calorimeter em resolution dominated by sampling fluctuations M. Livan Pavia University INFN
  155. 155. Fluctuations (4) ✦ Shower leakage fluctuations ✦ These fluctuations are non-Poissonian ✦ For a given average containment, longitudinal fluctuations are larger that lateral ones ✦ Difference comes from # of particles responsible for leakage ✦ e.g. Differences between e, γ induced showers M. Livan Pavia University INFN
  156. 156. Contribution of leakage fluctuations to energy resolution ✦ Longitudinal shower fluctuations and therefore leakage are essentially driven by by fluctuations in the starting point of the shower, i.e. by the behavior of one single shower particle. ✦ Lateral shower fluctuations generated by many particles M. Livan Pavia University INFN
  157. 157. Effects back-, front, and side leakage on em energy resolution Albedo relevant for particles below 100 MeV M. Livan Pavia University INFN
  158. 158. Leakage and leakage fluctuations in electron / γ induced showers •γ-induced showers may start considerably deeper inside the absorber than electron showers. As a consequence, they are also less contained • Large event-to- event fluctuation in the starting point of γ-induced showers have no equivalent in electron showers M. Livan Pavia University INFN
  159. 159. Fluctuations (5) ✦ Instrumental effects ✦ Structural differences in sampling fraction ✦ “Channelling” effects ✦ Electronic noise, light attenuation,..... M. Livan Pavia University INFN
  160. 160. Instrumental effects: channelling in fiber calorimeters •Sampling fraction for em showers: 2% •Electrons entering the calorimeter at 0º exactly at the position of a fiber loose very little energy in the early stages of the shower development and can cause longitudinal leakage •Shower particles escaping from the back traverse a region where there is no more Pb, the fibers are bundled and the sampling fraction is almost 100% M. Livan Pavia University INFN
  161. 161. Fluctuations (6) ✦ Different effects have different energy dependence ✦ quantum, sampling fluctuations σ/E ∼ E-1/2 ✦ shower leakage σ/E ∼ E-1/4 ✦ electronic noise σ/E ∼ E-1 ✦ structural non-uniformities σ/E = constant ✦ Add in quadrature σ2tot = σ21 + σ22 + σ23 + σ24+...... M. Livan Pavia University INFN
  162. 162. The em resolution of the ATLAS em calorimeter M. Livan Pavia University INFN
  163. 163. Fluctuations in hadron showers (I) ✦ Some types of fluctuations as in em showers, plus ✦ Fluctuations in visible energy ✦ (ultimate limit of hadronic energy resolution) ✦ Fluctuations in the em shower fraction, fem ✦ Dominating effect in most hadron calorimeters (e/h≠1) ✦ Fluctuations are asymmetric in pion showers (one-way street) ✦ Differences between p, π induced showers ✦ No leading π0 in proton showers (barion # conservation) M. Livan Pavia University INFN
  164. 164. Hadron showers: fluctuations in nuclear binding energy losses ✦ Distribution of nuclear binding energy loss that may occur in spallation reaction induced by protons with a kinetic energy of 1 GeV on 238U (more of 300 different reactions contributing) ✦ Estimate of the fluctuations of nuclear binding energy loss in high-Z materials (based on the relative contributions of particles of different energies): σ/ΔEB ≈ 15%/√(ΔEB) ✦ Note the strong correlation between the distribution of the binding energy loss and the distribution of the number of neutrons produced in the spallation reactions ✦ There may be also a strong correlation between the kinetic energy carried by these neutrons and the nuclear binding energy loss M. Livan Pavia University INFN
  165. 165. Fluctuations in hadron showers (II) ✦ Some types of fluctuations as in em showers, plus ✦ Fluctuations in visible energy ✦ (ultimate limit of hadronic energy resolution) ✦ Fluctuations in the em shower fraction, fem ✦ Dominating effect in most hadron calorimeters (e/h≠1) ✦ Fluctuations are asymmetric in pion showers (one-way street) ✦ Differences between p, π induced showers ✦ No leading π0 in proton showers (barion # conservation) M. Livan Pavia University INFN
  166. 166. Hadron showers: Fluctuations in em shower fraction (fem) ✦ Pion showers ✦ Due to the irreversibility of the production of π0s and because of the leading particle effect, there is an asymmetry between the probability that an anomalously large fraction of the energy goes into the em shower component M. Livan Pavia University INFN
  167. 167. Hadronic response function: effect of e/h ✦ Undercompensating calorimeter: showers with anomalously large fem values produce anomalously large signals ✦ Overcompensating calorimeters: such showers produce anomalously small signals ✦ Compensating calorimeters: Gaussian distribution M. Livan Pavia University INFN
  168. 168. Fluctuations in fem: differences p/π induced showers ✦ fem is smaller in proton-inducer showers than in pion- induced ones: barion number conservation prohibits the production of leading π0s and thus reduces the em component respect to pion-induced showers M. Livan Pavia University INFN
  169. 169. Fluctuations in hadron showers (III) ✦ Hadronic energy resolution of non-compensating calorimeters does not scale with E-1/2 and is often described by: σ a1 = √ ⊕ a2 E E ✦ Effects of non-compensation on σ/E is are better described by an energy dependent term: l−1 σ a1 E = √ ⊕ a2 E E E0 ✦ In practice a good approximation is: σ a1 = √ + a2 E E M. Livan Pavia University INFN
  170. 170. Hadronic resolution of non-compensating calorimeters ATLAS Fe-scintillator prototype M. Livan Pavia University INFN
  171. 171. Hadronic resolution of non-compensating calorimeters ✦ Differences between the two curves become significant only at energies 400 GeV where experimental data are not available M. Livan Pavia University INFN
  172. 172. Fluctuations in hadron showers (IV) ✦ The ultimate limit on hadronic energy resolution is determined by the correlation between ∑En and nuclear binding energy loss ✦ Better in Pb than in Uranium (14%√E vs. 21%√E) M. Livan Pavia University INFN
  173. 173. The ultimate limit on hadronic energy resolution M. Livan Pavia University INFN
  174. 174. Lessons for calorimeter design (1) ✦ Improve resolution ⇒ work on fluctuation that dominate ✦ example: 60 ton (liquid) scintillator does not make good hadron calorimeter. ✦ All fluctuations eliminated, except non-compensation: σ/E 10% at all energies! ✦ SPACAL (e/h ≈ 1.0, but other sources of fluctuation present): σ/E ≈2% at E=300 GeV M. Livan Pavia University INFN
  175. 175. Hadron calorimeters: effects of fem fluctuations on resolution M. Livan Pavia University INFN
  176. 176. Lessons for calorimeter design (II) ✦ Do not spend your money reducing fluctuations that do not dominate ✦ Practical examples: ✦ A 2 λint deep calorimeter for extraterrestrial detection of high energy cosmic hadrons is dominated by shower leakage ✦ ⇒ A high-quality crystal calorimeter is as good (bad) as a crudely sampling one ✦ A calorimeter system with a crystal em section will have a poor performance for hadron detection, no matter what you choose as hadronic section, because of the large e/h value of homogeneous devices ✦ ⇒ Don’t waste your money on the hadronic section M. Livan Pavia University INFN
  177. 177. Dominating fluctuations dominate ! M. Livan Pavia University INFN
  178. 178. Calibration of calorimeter systems ✦ Determine relationship between signal (pC, p.e.) and energy (GeV) ✦ Fundamental problem in sampling calorimeters: ✦ Different shower components are sampled differently ✦ Shower composition changes as shower develops ✦ ➞ Sampling fraction changes with shower age (also E dependent) How to intercalibrate the sections of a longitudinally segmented calorimeter? ✦ See NIM A 409 (1998), 621 and NIM A 485 (2002), 385 M. Livan Pavia University INFN
  179. 179. Sampling fraction changes as shower develops shower dominated by mip’s shower dominated by soft γ’s Samplig fraction changes as much as 30% ! M. Livan Pavia University INFN
  180. 180. Consequences of the depth dependence of fsamp HELIOS Calorimeter M. Livan Pavia University INFN
  181. 181. Calibration of longitudinally segmented device i = calorimeter towers j = event numbers ✦ Calibration by minimizing total width: ✦ Calibration constants are energy dependent ✦ Response non-linearity is introduced ✦ Systematic mismeasurement of energy M. Livan Pavia University INFN
  182. 182. Calibrating a segmented device by minimizing total signal width GIVES WRONG RESULTS M. Livan Pavia University INFN
  183. 183. Results of miscalibration: non-linearity M. Livan Pavia University INFN
  184. 184. Results of miscalibration: mass dependence M. Livan Pavia University INFN
  185. 185. Results of miscalibration: mass dependence M. Livan Pavia University INFN
  186. 186. Calibration (hadrons) ✦ Effects are even worse for hadrons ✦ Reconstructed energy depends on starting point of shower ✦ If calorimeter is calibrated with pions, jet energies are systematically mismeasured ✦ Resolution is not only determined by the width of a signal distribution, it is also necessary that the distribution is centered around the correct value M. Livan Pavia University INFN
  187. 187. Calibration of hadron calorimeters M. Livan Pavia University INFN
  188. 188. Alternative method: each section with its own particles ✦ Problem: how about hadrons that start shower in section A? ✦ Energy systematically mismeasured depending on e/h values of sections A,B ✦ Reconstructed energy depends on starting point of shower M. Livan Pavia University INFN
  189. 189. Wrong B/A: response depends on starting point M. Livan Pavia University INFN
  190. 190. Conclusions on calibration ✦ Calibration is a very delicate issue ✦ Discussed strategies (and several others used in practice) only work for a subset of events ✦ electrons of a certain energy, pions penetrating em section, ... ✦ Negative consequences for the rest of the events ✦ Systematic mismeasurement of energy ✦ Reconstructed energy depends on starting point shower ✦ Signal non-linearity, ... ✦ Correct method: B/A =1 ✦ i.e. calibrate all calorimeter sections in the same way (electrons or if not possible muons) M. Livan Pavia University INFN
  191. 191. M. Livan The Art of Calorimetry Lecture V The state of art Towards ILC calorimetry
  192. 192. Important calorimeter features ✦ Energy resolution ✦ Position resolution (need 4-vectors for physics) ✦ Particle ID capability ✦ Signal speed M. Livan Pavia University INFN
  193. 193. The importance of energy resolution M. Livan Pavia University INFN
  194. 194. Particle ID does NOT require segmetation e/π separation using time structure of the signals M. Livan Pavia University INFN
  195. 195. The importance of signal speed M. Livan Pavia University INFN
  196. 196. Important calorimeter features ✦ Energy resolution ✦ Position resolution (need 4-vectors for physics) ✦ Signal speed ✦ Particle ID capability ✦ but also ✦ Gaussian response function (avoid bias for steeply falling distributions) ✦ Signal linearity or, at least ✦ Well known relationship between signal and energy (reliable calibration) Most hadron calorimeter fall short in this respect M. Livan Pavia University INFN
  197. 197. High resolution hadron spectroscopy ✦ High-resolution Hadron Calorimetry (for jet spectroscopy) very relevant for Linear high-energy e+e- Colliders ✦ Uncertainties due to jet algorithms/underlying event small ✦ No constrained fits as in LEP (beamsstralhung) ✦ ⇒ Intrinsic detector properties limiting factor ✦ High-resolution Electromagnetic and high-resolution Hadronic calorimetry are mutually exclusive: ✦ Good jet energy resolution ⇒ Compensation ⇒ very small sampling fraction (∼ 3%) ⇒ poor electron, photon resolution ✦ Good electromagnetic resolution ⇒ high sampling fraction (100% Crystals, 20% LAr) ⇒ large non compensation ⇒ poor jet resolution M. Livan Pavia University INFN
  198. 198. Ultimate hadron calorimetry ✦ Why not aim for hadron calorimetry with the same level of precision as achievable in electromagnetic calorimeters ? ✦ ⇒ Need to eliminate/reduce hadron-specific fluctuations ✦ Fluctuations in electromagnetic shower content (fem) ✦ Fluctuations in “visible energy” (nuclear breackup) ✦ Achievable limit: σ/E ~ 15%/√E M. Livan Pavia University INFN
  199. 199. Fluctuations in the em shower component (fem) ✦ Why are these important ? ✦ Electromagnetic calorimeter response ≠ non-em response (e/h ≠ 1) ✦ Event-to-event fluctuations are large and non-Gaussian ✦ fem depends on shower energy and age ✦ Cause of all common problems in hadron calorimeters ✦Energy scale different from electrons, in energy-dependent way ✦ Hadronic non-linearity ✦ Non-Gaussian response fuction ✦ Poor energy resolution ✦ Calibration of the sections of a longitudinally segmented detector ✦ Solutions ✦ Compensating calorimeters (e/h = 1), e.g. Pb/plastic scintillator ✦ Measure fem event-by-event M. Livan Pavia University INFN
  200. 200. High resolution jet spectroscopy Compensating Pb/scintillator calorimetry M. Livan Pavia University INFN
  201. 201. What compensation does and does not for you ✦ Compensation does not guarantee high resolution ✦ Fluctuations in fem are eliminated, but others may be very large ✦ Example: Texas Tower effect ✦ Compensation has some drawbacks ✦ Small sampling fraction required → em resolution limited ✦ Relies on neutrons → calorimeter signals have to be integrated over large volume and time. SPACAL’s 30%/ √E needed 15 tonnes and 50 ns. Not always possible in practice M. Livan Pavia University INFN
  202. 202. Compensation in a U/gas calorimeter M. Livan Pavia University INFN
  203. 203. Compensation in gas calorimeters Hadronic response function M. Livan Pavia University INFN
  204. 204. Compensation requires large integration volume! M. Livan Pavia University INFN
  205. 205. High-resolution hadron calorimetry ✦ Non-solution ✦ There is no merit in “offline compensation” (e/π by weighting) ✦ Resolution is determined by fluctuations, not by mean values ✦ Side effect: increased signal non-linearity, response depends on starting point shower,... See NIM A487 (2002) 381 M. Livan Pavia University INFN
  206. 206. “Dummy” compensation M. Livan Pavia University INFN
  207. 207. Particle Flow Analysis (PFA) ✦ Use tracking, particle ID and calorimetry to measure 4-vectors of jets ✦ Charged particles represent tipically 65% of the jet energy ✦ However, if only charged jet components are measured: (σ/Ejet) = 25-30/% independent of jet energy ➝ Calorimetry essential ✦ The problem with this method is shower overlap. Need to deconvolute contributions from showering charged particles to avoid double counting ✦ This problem is not solvable with a finer granularity. The showers have certain transverse dimensions and exhibit large fluctuations in all dimensions ✦ Larger distance vertex-calorimeter and larger B- field would help ✦ NIM A495 (2002) 107: Method may give M. Livan Pavia University of ~ 30% improvement INFN
  208. 208. - Design goal ILC: separate W, Z ➝ qq LEP-like detector ILC design goal 60%/√E 30%/√E Mjj Mjj ✦ No kinematic constrains as in LEP (Beamstrahlung) M. Livan Pavia University INFN
  209. 209. Example of PFA at LEP: ALEPH Attempt to reconstruct hadronic event structure using particle identification and software compensation M. Livan Pavia University INFN
  210. 210. PFA at Hadron Collider ✦ No kinematic constraints as at LEP M. Livan Pavia University INFN
  211. 211. PFA @ ILC: High Density + Fine Granularity ✦ In order to reduce problems of shower overlap, ILC RD focuses on reducing the shower dimensions and decreasing the calorimeter cell size X0 = 1.8 cm, λI=17 cm X0 = 0.35 cm, λI=9.6 cm Iron Tungsten ✦ How about calibration ? M. Livan Pavia University INFN
  212. 212. PFA method: “π” jet ✦ The circles indicate the characteristic size of the showers initiated by the jet fragments, i.e. ρM for em showers and λint for the hadronic ones M. Livan Pavia University INFN
  213. 213. Improvement of energy resolution expected with PFA M. Livan Pavia University INFN
  214. 214. ILC RD example (PFA): CALICE M. Livan Pavia University INFN
  215. 215. Measuring the electromagnetic shower content ✦ Measure fem event-by-event ✦ Pioneered by WA1 around 1980 ✦ Used characteristics of energy deposit profile to disentangle em/non-em shower components ✦ Works better as energy increases ✦ Does not work for jets (collection of γs, πs showering simultaneously in the same area) M. Livan Pavia University INFN
  216. 216. WA1: determine fem event by event M. Livan Pavia University INFN
  217. 217. The DREAM principle ✦ Quartz fibers are only sensitive to em shower component ! ✦ Production of Čerenkov light ⇒ Signal dominated by electromagnetic component ✦ Non-electromagnetic component suppressed by a factor 5 ⇒ e/h=5 (CMS) ✦ Hadronic component mainly spallation protons Ek ∼ few hundred MeV ⇒non relativistic ⇒ no Čerenkov light ✦ Electron and positrons emit Čerenkov light up to a portion of MeV ✦ Use dual-readout system: ✦ Regular readout (scintillator, LAr, ...) measures visible energy ✦ Quartz fibers measure em shower component Eem ✦ Combining both results makes it possible to determine fem and the energy E of the showering hadron ✦ Eliminates dominant source of fluctuations M. Livan Pavia University INFN
  218. 218. Quartz fibers calorimetry Radial shower profiles in: SPACAL (scintillating fibers) QCAL (quartz fibers) M. Livan Pavia University INFN
  219. 219. Radial hadron shower profiles (DREAM) M. Livan Pavia University INFN
  220. 220. DREAM calorimeter ✦ DREAM: Dual REAdout Module ✦ Composition: ✦ Cu : scintillator : quartz fibers : air ✦ 69.3 : 9.4 : 12.6 : 8.7 ✦ Filling fraction (active material/absorber) = 31.7% ✦ Sampling fraction for mip in Cu/scintillator = 2.1% DREAM Collaboration: Cosenza, Iowa State, Pavia, Roma I, Texas Tech, Trieste, UCSD M. Livan Pavia University INFN
  221. 221. DREAM prototype Basic structure: 4x4 mm2 Cu rods 2.5 mm radius hole 7 fibers 3 scintillating 4 Čerenkov DREAM prototype: 5580 rods, 35910 fibers, 2 m long (10 λint) 16.2 cm effective radius (0.81 λint, 8.0 ρM) 1030 Kg X0 = 20.10 mm, ρM =20.35 mm 19 towers, 270 rods each hexagonal shape, 80 mm apex to apex Tower radius 37.10 mm (1.82 ρM) Each tower read-out by 2 PMs (1 for Q and 1 for S fibers) M. Livan Pavia University INFNtwo rings 1 central tower +
  222. 222. DREAM prototype DREAM prototype: tested at the CERN H4 beam line Data samples: π from 20 to 300 GeV “Jets” from 50 to 330 GeV “Jets” mimicked by π interaction on 10 cm polyethylene target in front of the detector M. Livan Pavia University INFN
  223. 223. Experimental setup for DREAM test beam M. Livan Pavia University INFN
  224. 224. Calibration with 40 GeV electrons ✦ Tilt 2˚ respect to the beam direction to avoid channelling effects ✦ Modest energy resolution for electrons (scintillator signal): σ 20.5% = √ + 1.5% E E M. Livan Pavia University INFN
  225. 225. 100 GeV single pions (raw signals) ✦ Signal distribution e- ✦ Asymmetric, broad, smaller signal than for e- ✦ Typical features of a non-compensating calorimeter e- M. Livan Pavia University INFN
  226. 226. Hadronic response (non-linearity) M. Livan Pavia University INFN

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