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An introduction to calorimeters for particle physics

An introduction to calorimeters for particle physics. Bob Brown STFC/PPD. Overview. Introduction General principles Electromagnetic cascades Hadronic cascades Calorimeter types Energy resolution e/h ratio and compensation Measuring jets Energy flow calorimetry

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An introduction to calorimeters for particle physics

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  1. An introduction to calorimeters for particle physics Bob Brown STFC/PPD Graduate lectures 2007/8 R M Brown - RAL 1

  2. Overview • Introduction • General principles • Electromagnetic cascades • Hadronic cascades • Calorimeter types • Energy resolution • e/h ratio and compensation • Measuring jets • Energy flow calorimetry • DREAM approach • CMS as an illustration of practical calorimeters • EM calorimeter (ECAL) • Hadron calorimeter (HCAL) • Summary • Items not covered Graduate lectures 2007/8 R M Brown - RAL 2

  3. General principles Calorimeter: A device that measures the energy of a particle by absorbing ‘all’ the initial energy and producing a signal proportional to this energy • Absorption of the incident energy is via a cascade process leading to n secondary particles, where n EINC • Calorimeters have an absorber and a detection medium (may be one and the same) • The charged secondary particles deposit ionisation that is detected in the active elements, for example as a current pulse in Si or light pulse in scintillator. • The energy resolution is limited by statistical fluctuations on the detected signal, and therefore grows as n, hence the relative energy resolution: sE /E1/n 1/E • The depth required to contain the secondary shower grows only logarithmically In contrast, the length of a magnetic spectrometer scales as p in order to maintain sp /p constant • Calorimeters can measure charged and neutral particles, and collimated jets of particles. • Hermetic calorimeters provide inferred measurements of missing (transverse ) energy in collider experiments and are thus sensitive to , oetc Graduate lectures 2007/8 R M Brown - RAL 3

  4. Absorber The electromagnetic cascade A high energy e or g incident on a thick absorber initiates a shower of secondary e and g via pair production and bremsstrahlung 1 X0 Graduate lectures 2007/8 R M Brown - RAL 4

  5. Depth and radial extent of em showers Longitudinal development in a given material is characterised by radiation length: The distance over which, on average, an electron loses all but 1/e of its energy. X0 180A/Z2 g.cm-2 For photons, the mean free path for pair production is: Lpair = (9/7) X0 The critical energy is defined as the energy at which energy losses by an electron through ionisation and radiation are, on average, equal: eC 560/Z (MeV) The lateral spread of an EM shower arises mainly from the multiple scattering of non-radiating electrons and is characterised by the Molière radius: RM = 21X0 /eC  7A/Z g.cm-2 For an absorber of sufficient depth, 90% of the shower energy is contained within a cylinder of radius 1 RM Graduate lectures 2007/8 R M Brown - RAL 5

  6. Average rate of energy loss via Bremsstrahlung E E(x) = Ei exp(-x/X0) dE/dx (x=0) = Ei/X0 Ei Ei/e x X0 Graduate lectures 2007/8 R M Brown - RAL 6

  7. EM shower development in liquid krypton (Z=36, A=84) GEANT simulation of a 100 GeV electron shower in the NA48 liquid Krypton calorimeter (D.Schinzel) Graduate lectures 2007/8 R M Brown - RAL 7

  8. Hadronic cascades High energy hadrons interact with nuclei producing secondary particles (mostlyp±,p0) The interaction cross section depends on the nature of the incident particle, its energy and the struck nucleus. Shower development is determined by the mean free path between inelastic collisions, the nuclear interaction length, given (ing.cm-2) by: lI= (NAsI / A)-1 (where NA is Avogadro’s number) In a simple geometric model, one would expect sI  A2/3 and thus l A1/3. In practice:lI 35 A1/3g.cm-2 The lateral spread of a hadronic showers arises from the transverse energy of the secondary particles which is typically <pT>~ 350 MeV. Approximately 1/3 of the pions produced are p0 which decay p0gg in ~10-16 s Thus the cascades have two distinct components: hadronic and electromagnetic Graduate lectures 2007/8 R M Brown - RAL 8

  9. Hadronic cascade development In dense materials: X0 180A/Z2<<lI35A1/3(eg Cu: X0 = 12.9 g.cm-2, lI= 135 g.cm-2) and the EMcomponent develops more rapidly than the hadronic component. Thus the average longitudinal energy deposition profile is characterised by a peak close to the first interaction, followed by an exponential fall off with scale lI Graduate lectures 2007/8 R M Brown - RAL 9

  10. Depth profile of hadronic cascades Average energy deposition as a function of depth for pions incident on copper. Individual showers show large variations from the mean profile, arising from fluctuations in the electromagnetic fraction Graduate lectures 2007/8 R M Brown - RAL 10

  11. There are two general classes of calorimeter: Sampling calorimeters: Layers of passive absorber (such as Pb, or Cu) alternate with active detector layers such as Si, scintillator or liquid argon Homogeneous calorimeters: A single medium serves as both absorber and detector, eg: liquified Xe or Kr, dense crystal scintillators (BGO, PbWO4 …….), lead loaded glass. Si photodiode or PMT Calorimeter types Graduate lectures 2007/8 R M Brown - RAL 11

  12. Energy Resolution The energy resolution of a calorimeter is usually parameterised as: sE /E=a/E  b/E  c (where  denotes a quadratic sum) The first term, with coefficient a, is the stochastic term arising from fluctuations in the number of signal generating processes (and any further limiting process, such as photo-electron statistics in a photodetector) The second term, with coefficient b, is the noise term and includes:- noise in the readout electronics- fluctuations in ‘pile-up’ (simultaneous energy deposition by uncorrelated particles) The third term with coefficient c, is the constant term and includes:- imperfections in calorimeter construction (dimensional variations, etc.)- non-uniformities in signal collection- channel to channel inter-calibration errors - fluctuations in longitudinal energy containment- fluctuations in energy lost in dead material before or within the calorimeter The goal of calorimeter design is to find, for a given application, the best compromise between the contributions from the three terms For EM calorimeters, energy resolution at high energy is usually dominated by c Graduate lectures 2007/8 R M Brown - RAL 12

  13. Intrinsic Energy Resolution of EM calorimeters Homogeneous calorimeters: The signal amplitude is proportional to the total track length of charged particles above threshold for detection. The total track length is the sum of track lengths of all the secondary particles. Effectively, the incident electron behaves as would a single ionising particle of the same energy, losing an energy equal to the critical energy per radiation length. Thus: T = SNi=1Ti = (E/eC)X0 If W is the mean energy required to produce a ‘signal quantum’ (eg an electron-ion pair in a noble liquid or a ‘visible’ photon in a crystal), then the mean number of such ‘quanta’ produced is n = E/ W . Alternatively n = T/L where L is the average track length between the production of such quanta. The intrinsic energy resolution is given by the fluctuations on n.At first sight: sE /E = n/n = (L/T) However, T is constrained by the initial energy E (see above). Thus fluctuations on n are reduced: sE /E = (FL /T) = (FW/E) where F is the Fano Factor Graduate lectures 2007/8 R M Brown - RAL 13

  14. Resolution of crystal EM calorimeters A widely used class of homogeneous EM calorimeter employs large, dense, monocrystals of inorganic scintillator. Eg the CMS crystal calorimeter which uses PbWO4, instrumented (Barrel section) with Avalanche Photodiodes. Since scintillation emission accounts for only a small fraction of the total energy loss in the crystal, F ~ 1 (Compared with a GeLi g detector, where F ~ 0.1) Furthermore, inherent fluctuations in the avalanche multiplication process of an APD give rise to a gain noise (‘excess noise factor’) leading to F ~ 2 for thecrystal/APD combination. PbWO4 is a relatively weak scintillator. In CMS, ~ 4500 photo-electrons are released in the APD for 1 GeV of energy deposited in the crystal. Thus the coefficient of the stochastic term is expected to be: ape =  (F/Npe) =  (2/4500) = 2.1% However, so far we have assumed perfect lateral containment of showers. In practice, energy is summed over limited clusters of crystals to minimise electronic noise and pile up. Thus lateral leakage contributes to the stochasic term. The expected contributions are: aleak = 1.5% (S(5x5)) and aleak =2% (S(3x3)) Thus for the S(3x3) case one expects a = ape  aleak=2.9% This is to be compared with the measured value: ameas = 2.8% Graduate lectures 2007/8 R M Brown - RAL 14

  15. Resolution of sampling calorimeters In sampling calorimeters, an important contribution to the stochastic term comes from sampling fluctuations. These arise from variations in the number of charged particles crossing the active layers. This number increases linearly with the incident energy and (up to some limit) with the fineness of the sampling. Thus: nch E/t (t is the thickness of each absorber layer) If each sampling is statistically independent (which is true if the absorber layers are not too thin), the sampling contribution to the stochastic term is: ssamp /E  1/nch (t/E) Thus the resolution improves as t is decreased. However, for an EM calorimeter, of order 100 samplings would be required to approach the resolution of typical homogeneous devices, which is impractical.Typically: ssamp /E ~ 10%/E A relevant parameter for sampling calorimeters is sampling fraction, which bears on the noise term: Fsamp = s.dE/dx(samp) / [s.dE/dx(samp) + t .dE/dx(abs) ] (s is the thickness of sampling layers) Graduate lectures 2007/8 R M Brown - RAL 15

  16. Resolution of hadronic calorimeters The absorber depth required to contain hadron showers is 10lI (150 cm for Cu), thus hadron calorimeters are almost all sampling calorimeters Several processes contribute to hadron energy dissipation, eg in Pb: Thus in general, the hadronic component of ahadron shower produces a smaller signal thanthe EM component: e/h > 1 Fp° ~ 1/3 at low energies, increasing with energy Fp° ~ a log(E) (since the EM component ‘freezes out’) Nuclear break-up (invisible) 42% Charged particle ionisation 43% Neutrons with TN~ 1 MeV 12% Photons with Eg~ 1 MeV 3% If e/h  1 :- response with energy is non-linear - fluctuations on Fp°contribute to sE /E Furthermore, since the fluctuations are non-Gaussian, sE /E scales more weakly than 1/E Constant term: Deviations from e/h = 1 alsocontribute to the constant term.In addition calorimeterimperfections contribute: inter-calibration errors, response non-uniformity (both laterally and in depth), energy leakageand cracks . Graduate lectures 2007/8 R M Brown - RAL 16

  17. Compensating calorimeters ‘Compensation’ ie obtaining e/h =1, can be achieved in several ways: • Increase the contribution to the signal from neutrons, relative to the contribution from charged particles: Plastic scintillators contain H2, thus are sensitive to n via n-p elastic scattering Compensation can be achieved by using scintillator as the detection medium and tuning the ratio of absorber thickness to scintillator thickness • Use 238U as the absorber: 238U fission is exothermic, releasing neutrons that contribute to the signal • Sample energy versus depth and correct event-by-event for fluctuations on Fp° : • p0 production produces large local energy deposits that can be suppressed by weighting: E*i = Ei (1- c.Ei ) • Using one or more of these methods one can obtain an intrinsic resolution • sintr /E  20%/ E Graduate lectures 2007/8 R M Brown - RAL 17

  18. Compensating calorimeters Sampling fluctuations also degrade the energy resolution. As for EM calorimeters:ssamp /E dwhere d is the absorber thickness (empirically, the resolution does not improve for d ≾ 2 cm (Cu)) ZEUS at HERA employed an intrinsically compensated 238U/scintillator calorimeter The ratio of 238U thickness (3.3 mm) to scintillator thickness (2.6 mm) was tuned such that e/p = 1.00 ± 0.03 For this calorimeter: sintr /E = 26%/E and ssamp /E = 23%/E Giving an excellent energy resolution for hadrons: shad/E ~ 35%/E The downside is that the 238U thickness required for compensation (~ 1X0) led to a rather modest EM energy resolution: sEM/E ~ 18%/E Graduate lectures 2007/8 R M Brown - RAL 18

  19. DualReadoutModule(DREAM)approach Measure electromagnetic component of shower independently event-by-event Graduate lectures 2007/8 R M Brown - RAL 19

  20. DREAM test results Graduate lectures 2007/8 R M Brown - RAL 20

  21. Jet energy resolution • At colliders, hadron calorimeters serve primarily to measure jets and missing ET: • For a single particle: sE /E=a/E  c • At low energy the resolution is dominated by a, at high energy by c • Consider a jet containing N particles, each carrying an energy ei= zi EJ • Szi = 1, Sei = EJ • If the stochastic term dominates:dei = a eiand: dEJ=  S(dei )2 = Sa2ei • Thus: dEJ/ EJ=a/ EJ  the error on Jet energy is the same as for a single particle of the same energy If the constant term dominates: dEJ S(cei)2= cEJS(zi )2 Thus: dEJ/EJ= cS(zi )2and since S(zi )2< Szi=1 • the error on Jet energy is less than for a single particle of the same energy For example, in a calorimeter with sE /E=0.3/E  0.05 a 1 TeV jet composed of four hadrons of equal energy hasdEJ= 25GeV, compared todE = 50GeV, for a single 1TeV hadron Graduate lectures 2007/8 R M Brown - RAL 21

  22. Particle flow calorimetry Graduate lectures 2007/8 R M Brown - RAL 22

  23. Compact MuonSolenoid Current data suggest a light Higgs • Favoured discovery channel H gg Intrinsic width very small  Measured width, hence S/B given by experimental resolution High resolution electromagneticcalorimetry is a hallmark of CMS Target ECAL energy resolution: ≤ 0.5% above 100 GeV  120 GeV SM Higgs discovery (5s) with10fb-1(100dat1033cm-2s-1) • Length ~ 22 m • Diameter ~ 15 m • Weight ~ 14.5 kt • Objectives: • Higgs discovery • Physics beyond the Standard Model Graduate lectures 2007/8 R M Brown - RAL 23

  24. Muon Electron Hadron Photon Silicon Tracker Electromagnetic Calorimeter Superconducting Solenoid Hadron Calorimeter Iron field return yoke interleaved with Tracking Detectors Cross section through CMS Measuring particles in CMS Graduate lectures 2007/8 R M Brown - RAL 24

  25. High resolution electromagneticcalorimetry is central to the CMS design Benchmark process: H    m/m = 0.5[E1/E1 E2/E2  / tan(/2)] Where:E/E = a/E  b/E  c Aim (TDR): Barrel End cap Stochastic term: a= 2.7% 5.7% (p.e. stat, shower fluct, photo-detector, lateral leakage) Constant term: c= 0.55% 0.55% (non-uniformities, inter-calibration, longitudinal leakage) Noise: Low Lb= 155MeV 770MeV High L210MeV 915MeV (dq relies on interactionvertex measurement) Coloured histograms are separate contributing backgrounds for 1fb-1 (electronic, pile-up) Optimised analysis ECAL design objectives Graduate lectures 2007/8 R M Brown - RAL 25

  26. The Electromagnetic Calorimeter Barrel: 36 Supermodules (18 perhalf-barrel) 61200 Crystals (34 types) – total mass 67.4t Endcaps: 4 Dees (2 per Endcap) 14648 Crystals (1type) – total mass 22.9t Full Barrel ECAL installed in CMS ‘Supermodule’ The crystals are slightly tapered and point towards the collision region 22 cm Pb/Si Preshowers: 4 Dees (2/Endcap) Each crystal weighs ~ 1.5 kg Graduate lectures 2007/8 R M Brown - RAL 26

  27. Fast light emission: ~80% in 25 ns Peak emission ~425nm (visible region) Short radiation length: X0 = 0.89cm Small Molière radius: RM = 2.10cm Radiation resistant to very high doses But: • Temperature dependence ~2.2%/OC • Stabilise to  0.1OC Formation and decay of colour centresin dynamic equilibrium under irradiation • Precise light monitoring system Low light yield (1.3% NaI) • Photodetectors with gain in mag field Leadtungstateproperties Graduate lectures 2007/8 R M Brown - RAL 27

  28.  = 26.5 mm MESH ANODE Photodetectors • Barrel - Avalanche photodiodes (APD) • Two 5x5 mm2 APDs/crystal • Gain: 50 QE: ~75% • Temperature dependence: -2.4%/OC • Endcaps: - Vacuum phototriodes (VPT) • More radiation resistant than Si diodes • (with UV glass window) • - Active area ~ 280 mm2/crystal • Gain 8 -10 (B=4T) Q.E.~20% at 420nm 40mm Graduate lectures 2007/8 R M Brown - RAL 28

  29. Central impact (4x4mm2) ‘Uniform’ impact (20x20mm2)after impact-position correction 0.5% 0.5% 120 GeV 120 GeV E (GeV) E (GeV) Response for S(3x3) varies by ~3% with impact position in central crystal Correction made using information from crystals alone(works for g)Does not depend onE,, (3 x 3) around Crystal 184 (3 x 3) around Crystal 204(3 x 3) around Crystal 224 4x4 mm2 central region position ( ) Correction for impact position Graduate lectures 2007/8 R M Brown - RAL 29

  30. Series of runs at 120 GeV centred on many points within S(3x3) Results averaged to simulate the effect of random impact positions 22 mm Resolution goal of 0.5% at high energyachieved Energy resolution: random impact Graduate lectures 2007/8 R M Brown - RAL 30

  31. Hadron calorimeters in CMS Had Barrel: HB Had Endcaps: HE Had Forward: HF Had Outer: HO Hadron Barrel 16 scintillator planes ~4 mm Interleaved with Brass ~50 mm plus scintillator plane immediately after ECAL ~ 9mm plus Scintillator planes outside coil HO Coil HB HB ECAL HE HF Graduate lectures 2007/8 R M Brown - RAL 31

  32. Hadron calorimeter Light produced in the scintillators is tranported through optical fibres to photodetectors The brass absorber under construction The HCAL being inserted into the solenoid Graduate lectures 2007/8 R M Brown - RAL 32

  33. (ECAL+HCAL) raw response to pions vs energy (red line is MC simulation) Hadron calorimetry in CMS Compensated hadron calorimetry & high precision EM calorimetry are incompatible In CMS, hadron measurement combines HCAL (Brass/scint) and ECAL(PbWO4) data This effectively gives a hadron calorimeter divided in depth into two compartments Neither compartment is ‘compensating’: e/h ~ 1.6for ECAL ande/h ~ 1.4for HCAL  Hadron energy resolution is degraded and response is energy-dependent Graduate lectures 2007/8 R M Brown - RAL 33

  34. (ECAL+HCAL) For single pions with cluster-based weighting Cluster-basedresponsecompensation Use test beam data to fit for e/h(ECAL) , e/h(HCAL) and Fp° as a function of the raw total calorimeter energy (eE +eH). Then: E = (e/p)E.eE + (e/p)H.eH Where: (e/p)E,H= (e/h)E,H/[1 + ((e/h)E,H-1).Fp°)] Graduate lectures 2007/8 R M Brown - RAL 34

  35. Jet energy resolution ‘Active’ weighting cannot be used for jets, since several particles may deposit energy in the same calorimeter cell. Passive weighting is applied in the hardware: the first HCAL scintillator plane, immediately behind the ECAL, is ~2.5 x thicker than the rest. One expects: dEJ/EJ=125%/ EJ + 5% However, at LHC, the energy resolution for jets is dominated by fluctuations inherent to the jets and not instrumental effects Graduate lectures 2007/8 R M Brown - RAL 35

  36. ZI(1000 GeV) m+m- ZI(800 GeV) e+e- Calorimetry is a powerful tool at very high energy Search for heavy gauge bosons Graduate lectures 2007/8 R M Brown - RAL 36

  37. Summary • Calorimeters are key elements of almost all particle physics experiments • A variety of mature technologies are available for their implementation • Design optimisation is dictated by physics goals and experiment conditions • Compromises may be necessary: eg high resolution hadron calorimetry vs high resolution EM calorimetry • Calorimeters will play a crucial role in discovery physics at LHC: eg: H   , ZI e+e- , SUSY (ET) Not covered: • Triggering with calorimeters • Particle identification • Di-jet mass resolution • ………………………… Graduate lectures 2007/8 R M Brown - RAL 37

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