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

2. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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

3. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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   E INC  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:  E / 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  p /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 ,  o etc

4. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 4 The electromagnetic cascade Absorber A high energy e or  incident on a thick absorber initiates a shower of secondary e and  via pair production and bremsstrahlung 1 X 0

5. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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. X 0  180 A / Z 2 g.cm -2 For photons, the mean free path for pair production is: L pair = (9 / 7) X 0 The critical energy is defined as the energy at which energy losses by an electron through ionisation and radiation are, on average, equal:  C   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: R M = 21X 0 /  C  7A / Z g.cm -2 For an absorber of sufficient depth, 90% of the shower energy is contained within a cylinder of radius 1 R M

6. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 6 Average rate of energy loss via Bremsstrahlung E x X0X0 EiEi E i /e E(x) = E i exp(-x/X 0 ) dE/dx (x=0) = E i /X 0

7. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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)

8. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 8 Hadronic cascades High energy hadrons interact with nuclei producing secondary particles (mostly  ±,  0 ) 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 (in g.cm -2 ) by:  = (N A   / A) -1 (where N A is Avogadro’s number) In a simple geometric model, one would expect    A 2/3 and thus  A 1/3. In practice:   35 A 1/3 g.cm -2 The lateral spread of a hadronic showers arises from the transverse energy of the secondary particles which is typically ~ 350 MeV. Approximately 1/3 of the pions produced are  0 which decay  0   in ~10 -16 s Thus the cascades have two distinct components: hadronic and electromagnetic

9. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 9 Hadronic cascade development In dense materials: X 0  180 A / Z 2 <<   35 A 1/3 (eg Cu: X 0 = 12.9 g.cm -2,  = 135 g.cm -2 ) and the EM component 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 

10. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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

11. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 11 Calorimeter types 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, PbWO 4 …….), lead loaded glass. Si photodiode or PMT

12. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 12 Energy Resolution The energy resolution of a calorimeter is usually parameterised as:  E / 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 materialbefore 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

13. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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 =  N i =1 T i = (E /  C ) X 0 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:  E / E =  n / n =  (L / T) However, T is constrained by the initial energy E (see above). Thus fluctuations on n are reduced:  E / E =  (FL / T) =  (FW / E) where F is the Fano Factor

14. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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 PbWO 4, 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  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 the crystal /APD combination. PbWO 4 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: a pe =  (F / N pe ) =  (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: a leak = 1.5% (  (5x5)) and a leak =2% (  (3x3)) Thus for the  (3x3) case one expects a = a pe  a leak = 2.9% This is to be compared with the measured value: a meas = 2.8%

15. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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: n ch  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:  samp / E  1/  n ch   (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:  samp / E ~ 10%/  E A relevant parameter for sampling calorimeters is sampling fraction, which bears on the noise term: F samp = s.dE/dx(samp) / [s.dE/dx(samp) + t.dE/dx(abs) ] (s is the thickness of sampling layers)

16. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 16 Resolution of hadronic calorimeters The absorber depth required to contain hadron showers is  10  (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 a hadron shower produces a smaller signal than the EM component: e / h > 1 F  ° ~ 1/3 at low energies, increasing with energy F  ° ~ a log(E) (since the EM component ‘freezes out’) Nuclear break-up (invisible)42% Charged particle ionisation43% Neutrons with T N ~ 1 MeV 12% Photons with E  ~ 1 MeV 3% If e / h  1 :- response with energy is non-linear - fluctuations on F  ° contribute to  E /E Furthermore, since the fluctuations are non- Gaussian,  E /E scales more weakly than 1/  E Constant term: Deviations from e / h = 1 also contribute to the constant term. In addition calorimeter imperfections contribute: inter-calibration errors, response non-uniformity (both laterally and in depth), energy leakage and cracks.

17. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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 H 2, 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 238 U as the absorber: 238 U fission is exothermic, releasing neutrons that contribute to the signal - Sample energy versus depth and correct event-by-event for fluctuations on F  ° :  0 production produces large local energy deposits that can be suppressed by weighting: E* i = E i (1- c.E i ) Using one or more of these methods one can obtain an intrinsic resolution  intr / E  20%/  E

18. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 18 Compensating calorimeters Sampling fluctuations also degrade the energy resolution. As for EM calorimeters:  samp / E  d where d is the absorber thickness (empirically, the resolution does not improve for d ≾ 2 cm (Cu)) ZEUS at HERA employed an intrinsically compensated 238 U/scintillator calorimeter The ratio of 238 U thickness (3.3 mm) to scintillator thickness (2.6 mm) was tuned such that e /  = 1.00 ± 0.03 For this calorimeter:  intr / E = 26%/  Eand  samp / E = 23%/  E Giving an excellent energy resolution for hadrons:  had / E ~ 35%/  E The downside is that the 238 U thickness required for compensation (~ 1X 0 ) led to a rather modest EM energy resolution:  EM / E ~ 18%/  E

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

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

21. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 21 Jet energy resolution At colliders, hadron calorimeters serve primarily to measure jets and missing E T : For a single particle:  E / 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 e i = z i E J   z i = 1,   e i = E J If the stochastic term dominates:   e i = a  e i and:   E J =    (   e i ) 2 =   a 2 e i Thus:   E J / E J = a /  E J  the error on Jet energy is the same as for a single particle of the same energy If the constant term dominates:   E J     ( ce i ) 2 = cE J    ( z i ) 2 Thus:   E J / E J = c    ( z i ) 2 and since    ( z i ) 2 <   z i = 1  the error on Jet energy is less than for a single particle of the same energy For example, in a calorimeter with  E / E = 0.3 /  E  0.05 a 1 TeV jet composed of four hadrons of equal energy has   E J = 25 GeV, compared to   E = 50 GeV, for a single 1 TeV hadron

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

23. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 23 Compact Muon Solenoid Objectives: Higgs discovery Physics beyond the Standard Model Current data suggest a light Higgs  Favoured discovery channel H   Intrinsic width very small  Measured width, hence S/B given by experimental resolution High resolution electromagnetic calorimetry is a hallmark of CMS Target ECAL energy resolution: ≤ 0.5% above 100 GeV  120 GeV SM Higgs discovery (5  ) with 10 fb -1 (100 d at 10 33 cm -2 s -1 ) Current data suggest a light Higgs  Favoured discovery channel H   Intrinsic width very small  Measured width, hence S/B given by experimental resolution High resolution electromagnetic calorimetry is a hallmark of CMS Target ECAL energy resolution: ≤ 0.5% above 100 GeV  120 GeV SM Higgs discovery (5  ) with 10 fb -1 (100 d at 10 33 cm -2 s -1 )  Length ~ 22 m  Diameter ~ 15 m  Weight ~ 14.5 kt

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

25. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 25 ECAL design objectives Coloured histograms are separate contributing backgrounds for 1fb -1 (electronic, pile-up) High resolution electromagnetic calorimetry is central to the CMS design Benchmark process: H    m / m = 0.5 [  E 1 / E 1   E 2 / E 2    / 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 L b= 155 MeV 770 MeV High L 210 MeV 915 MeV (   relies on interaction vertex measurement) Optimised analysis

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

27. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 27 Lead tungstate properties Temperature dependence ~2.2%/ O C  Stabilise to  0.1 O C Formation and decay of colour centres in dynamic equilibrium under irradiation  Precise light monitoring system Low light yield (1.3% NaI)  Photodetectors with gain in mag field But: Fast light emission: ~80% in 25 ns Peak emission ~425 nm (visible region) Short radiation length: X 0 = 0.89 cm Small Molière radius: R M = 2.10 cm Radiation resistant to very high doses

28. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 28 Photodetectors Barrel - Avalanche photodiodes (APD) Two 5x5 mm 2 APDs/crystal - Gain: 50 QE: ~75% - Temperature dependence: -2.4%/ O C 40  m Endcaps: - Vacuum phototriodes (VPT) More radiation resistant than Si diodes (with UV glass window) - Active area ~ 280 mm 2 /crystal - Gain 8 -10 (B=4T) Q.E.~20% at 420nm  = 26.5 mm MESH ANODE

29. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 29 Correction for impact position 120 GeV E (GeV) Central impact (4x4 mm 2 ) 0.5% 120 GeV ‘Uniform’ impact (20x20 mm 2 ) after impact-position correction E (GeV) 0.5% Response for  (3x3) varies by ~3% with impact position in central crystal Correction made using information from crystals alone (works for  ) Does not depend on E, ,  Response for  (3x3) varies by ~3% with impact position in central crystal Correction made using information from crystals alone (works for  ) Does not depend on E, ,  position (  ) (3 x 3) around Crystal 184 (3 x 3) around Crystal 204 (3 x 3) around Crystal 224 4x4 mm 2 central region

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

31. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 31 Hadron calorimeters in CMS Had Barrel: HB Had Endcaps: HE Had Forward: HF Had Outer: HO HB HE HF 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 Coil HB ECAL

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

33. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 33 Hadron calorimetry in CMS Compensated hadron calorimetry & high precision EM calorimetry are incompatible In CMS, hadron measurement combines HCAL (Brass/scint) and ECAL (PbWO 4 ) data This effectively gives a hadron calorimeter divided in depth into two compartments Neither compartment is ‘compensating’: e/h ~ 1.6 for ECAL and e/h ~ 1.4 for HCAL  Hadron energy resolution is degraded and response is energy-dependent (ECAL+HCAL) raw response to pions vs energy (red line is MC simulation)

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

35. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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:   E J / E J = 125% /  E J + 5% However, at LHC, the energy resolution for jets is dominated by fluctuations inherent to the jets and not instrumental effects

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

37. STFC RAL Graduate lectures 2007/8 R M Brown - RAL 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  , Z I  e + e -, SUSY (E T ) Not covered:  Triggering with calorimeters  Particle identification  Di-jet mass resolution  …………………………