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##### An introduction to calorimeters for particle physics

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**An introduction to calorimeters for particle physics**Bob Brown STFC/PPD Graduate lectures 2009/10 R M Brown - RAL 1**Overview**• Introduction • 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 • General principles • Items not covered Graduate lectures 2009/10 R M Brown - RAL 2**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. • There is an absorber and a detection medium (may be one and the same) • Absorption of the incident energy is via a cascade process leading to n secondary particles, wheren EINC • 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 /E1/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 • Charged and neutral particles, and collimated jets of particles can be measured. • Hermetic calorimeters provide inferred measurements of missing (transverse) energy in collider experiments and are thus sensitive to , oetc Graduate lectures 2009/10 R M Brown - RAL 3**Absorber**The electromagnetic cascade A high energy e or gincident on an absorberinitiates a shower ofsecondary e and gvia pair productionand bremsstrahlung 1 X0 Graduate lectures 2009/10 R M Brown - RAL 4**Depth and radial extent of em showers**Longitudinal development in a given medium 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 2009/10 R M Brown - RAL 5**Average rate of Bremsstrahlung energy loss**E E(x) = Ei exp(-x/X0) dE/dx (x=0) = - Ei/X0 Ei Ei/e x X0 Graduate lectures 2009/10 R M Brown - RAL 6**EM shower development in liquid krypton**EM shower development in krypton (Z=36, A=84) GEANT simulation of a 100 GeV electron shower in the NA48 liquid Krypton calorimeter (D.Schinzel) Graduate lectures 2009/10 R M Brown - RAL 7**Hadronic cascades**High energy hadrons interact with nuclei producing secondary particles (mostly p±,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 lI 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/c. Approximately 1/3 of the pions produced are p0 which decay p0gg in ~10-16 s Thus the cascades have two distinct components: hadronic and electromagnetic Graduate lectures 2009/10 R M Brown - RAL 8**** In dense materials: X0 180 A / Z2<<lI 35 A1/3and the emcomponent develops more rapidly than the hadronic component. Thus the average longitudinal energy deposition profile is characterised by a peakclose to the first interaction, followed by an exponential fall off with scale lI eg Cu: X0 = 12.9 g.cm-2lI= 135 g.cm-2 Hadronic cascade development lI Graduate lectures 2009/10 R M Brown - RAL 9**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 fromfluctuations in the electromagnetic fraction Graduate lectures 2009/10 R M Brown - RAL 10**There are two general classes of calorimeter:**Sampling calorimeters: Layers of passive absorber (such as Pb, or Cu) alternate with activedetector 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 2009/10 R M Brown - RAL 11**Energy Resolution**The energy resolution of a calorimeter is often 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 inthe number of signal generating processes (and any further limiting process, suchas 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 arises from:- 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 For em calorimeters, energy resolution at high energy is usually dominated by c The goal of calorimeter design is to find, for a given application, the best compromise between the contributions from the three terms Graduate lectures 2009/10 R M Brown - RAL 12**IntrinsicEnergyResolutionofem 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 2009/10 R M Brown - RAL 13**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 inthe crystal, F ~ 1 (Compared with a GeLi g detector, where F ~ 0.1) Furthermore, fluctuations in the avalanche multiplication process of an APD give rise toa gain noise (‘excess noise factor’) leading to F ~ 2 for the crystal /APD combination. PbWO4 is a relatively weak scintillator. In CMS, ~ 4500 photo-electrons are released inthe APD for 1 GeV of energy deposited in the crystal. Thus the coefficient of thestochastic 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 andpile up. Thus lateral leakage contributes to the stochastic 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 2009/10 R M Brown - RAL 14**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 arenot 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 typicalhomogeneous devices, which is impractical.Typically: ssamp / E ~ 10%/ E A relevant parameter for sampling calorimeters is the sampling fraction, which bearson the noise term: Fsamp = s.dE/dx(samp) / [s.dE/dx(samp) + t.dE/dx(abs) ] (s is the thickness of the sampling layers) Graduate lectures 2009/10 R M Brown - RAL 15**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 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 /Escales 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 leakage and cracks . Graduate lectures 2009/10 R M Brown - RAL 16**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 2009/10 R M Brown - RAL 17**Compensating calorimeters**ZEUS at HERA had 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 (implying e/h = 1.00 ± 0.045) For this calorimeter the intrinsic energy resolution was: sintr / E = 26%/ E However, Sampling fluctuations also degrade the energy resolution. As for electromagnetic calorimeters calorimeters:ssamp / E twhere t is the absorber thickness For the ZEUS calorimeter: ssamp / E = 23%/ E Giving a nonetheless excellent overall 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 2009/10 R M Brown - RAL 18**Dual Readout Module (DREAM) approach**From W. Vandelli, HEP2007, Manchester Measure electromagnetic component of shower independently event-by-event Independent measurements of the scintillation and Cerenkov light yields allow an estimation of the two components, thus measuring Fp° Graduate lectures 2009/10 R M Brown - RAL 19**DREAM test results**From W. Vandelli, HEP2007, Manchester Graduate lectures 2009/10 R M Brown - RAL 20**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 • S zi = 1, S ei = 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= cEJS(zi )2 Thus: d EJ/ EJ= c S (zi )2and since S (zi )2< S zi=1 • the error on Jet energy is less than for a single particle of the same energy For example, in a calorimeter withsE / E=0.3 / E 0.05a 1 TeV jet composed of four hadrons of equal energy hasd EJ= 25 GeV, compared tod E = 50 GeV, for a single 1 TeV hadron Graduate lectures 2009/10 R M Brown - RAL 21**Particle flow calorimetry**From M. Thomson, HEP2007, Manchester Graduate lectures 2009/10 R M Brown - RAL 22**3.8T**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 for photons:≤ 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 2009/10 R M Brown - RAL 23**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 2009/10 R M Brown - RAL 24**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 2009/10 R M Brown - RAL 25**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 2009/10 R M Brown - RAL 26**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 2009/10 R M Brown - RAL 27**(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 2009/10 R M Brown - RAL 28**Particle-Flow Event Reconstruction in CMS**• The design of CMS detector is almost ideally suited to particle-flow reconstruction at LHC: • - Strong magnetic field, • - High tracking efficiency with low fake rate, • Fine granularity electromagnetic calorimeter • - Reconstruction of muons with high purity Particle-flow reconstruction improves the measurement of Missing Transverse Energy by almost a factor of 2, compared to a measurement based on calorimetry alone. Particle-flow reconstruction improves jet energy resolution dramatically below 100 GeV/c Graduate lectures 2009/10 R M Brown - RAL 29**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 2009/10 R M Brown - RAL 30**Summary**• Design optimisation is dictated by physics goals and experiment conditions • Compromises may be necessary: eg high resolution hadron calorimetry vs high resolution em calorimetry • A variety of mature technologies are available for their implementation • Calorimeters will play a crucial role in discovery physics at LHC: eg: H , ZI e+e- , SUSY (ET) • Calorimeters are key elements of almost all particle physics experiments Not covered: • Triggering with calorimeters • Particle identification • Di-jet mass resolution • ………………………… Some useful references Particle Detectors, Claus Grupen, Cambridge University Press. Calorimetry for Particle Physics, C.W. Fabian and F. Gianotti, Rev Mod Phys, 75, 1243 (2003). Graduate lectures 2009/10 R M Brown - RAL 31**Spare slides**Graduate lectures 2009/10 R M Brown - RAL 32**Coloured histograms are separate contributing backgrounds**for 1fb-1 ECAL design benchmark 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 (dq is small – q measurement relies on interaction vertex identification) Graduate lectures 2009/10 R M Brown - RAL 33**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 2009/10 R M Brown - RAL 34** = 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 2009/10 R M Brown - RAL 35**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 2009/10 R M Brown - RAL 36**(ECAL+HCAL)**For single pions with cluster-based weighting Cluster-based response compensation 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 2009/10 R M Brown - RAL 37**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 2009/10 R M Brown - RAL 38