Electromagnetic Calorimetry

Transcription

1 Electromagnetic Calorimetry Urs Langenegger (Paul Scherrer Institute) Fall 2014 Shower profile longitudinal transverse Calorimeter types homogeneous sampling 50 GeV electron in bubble chamber (Ne:H 2 = 70%:30%)

2 Introduction Calorimetry is measurement of particle energy through absorption destructive measurement calor = warmth However: 1 GeV particle into 1 liter of water: T = E/(c V m water ) = K electromagnetic vs. hadronic showers ionisation charge excitation Cherenkov or scintillation light Physical characterization radiation length de/dx = E/X 0 mean distance over which high-energy electron loses all but 1/e of its energy critical energy E c 610 MeV/(Z ) where energy loss by ionization equals energy loss by bremsstrahlung nuclear interaction length λ i : N = N 0 e x/λ i 2

3 Simplified model for e.m. showers Cascade of electron-positron pairs and photons: E n = E 0 /2 n N n = 2 n γ Absorber e e + γ e + e γ γ Maximum m given by E c m = ln(e 0 /E c )/ ln 2 Shower maximum - logarithmic dependence on E 0! Number of particles at shower maximum N p = 2 m = E 0 /E c γ X 0 e + e γ Total path length of all e + and e (s 0 is the range of electrons with E = E c ) L 2 3 X 0 m i=1 2i s 0N p = ( 4 3 X s 0) E 0 E c Total path length - proportional to E 0 linearity! Shower multiplication bremsstrahlung/pair-creation shower dissipation 3 ionization/excitation

4 Longitudinal shower development Parametrization of shower profile with, e.g. de dt = E 0 b (bt)a 1 e bt Γ(a) with scaled variables t x/x 0 ( ) y = E 0 /E c = N p plus fitted parameters a, b Maximum at t max = (a 1)/b = ln y + C j C j = 0.5 for electron showers C j = +0.5 for photon showers For ( ): use a t max b + 1 and b 0.5 (or from fits) EGS4 simulation (with E e,γ > 1.5 MeV) Γ-function parametrization fails initially N e falls off more rapidly than E deposition 4

5 Transverse extension of e.m. shower Transverse shower extension determined by multiple scattering of low-energy electrons Molière Radius R M is the average transverse excursion of electrons with E c after one radiation length: R M = 21 MeV E c X 0 7A Z [ g/ cm2 ] Molière Radius central shower component In decent approximation R(90%) = 1.0R M R(99%) = 3.5R M beyond this radius, material compositon matters 5

6 Calorimeter types Homogeneous calorimeters scintillation light e.g. crystals Sampling calorimeters shower starts in material with high Z shower measurement in detectors: scintillator (fiber,... ) gas detectors, silicon, liquid noble gases Complementarity to spectrometers electrically neutral and charged particles improved (relative) resolution at higher energies fast detectors trigger segmented detectors position resolution, particle ID 6

7 Homogeneous calorimeters Four different versions Type Example Experiment semiconductor Si, Ge cryogenic experiments Cherenkov H 2 O, PbO Super-Kamiokande, OPAL scintillator CsI(Tl), PbWO 4 BABAR, CMS liquid noble gas Argon, Xenon ArDM, XENON More details later on calorimeters with semiconductor liquid noble gases water Cherenkov detectors Advantages and disadvantages + energy resolution + (possibly) inexpensive (H 2 O) (possibly) expensive (crystals) quite large radiation length (cf. Pb) 7

8 Crystal calorimeters Compact, fast, stable, high photon yield, precise, expensive! Examples: BABAR [ cm] CsI(Tl) crystals Experiment Material N xtal L3 (1985) BGO BABAR (1999) CsI(Tl) 6580 CMS (2008) PbWO OPAL [ (38 52) cm] lead-glass(!) blocks 8

9 Example of crystal calorimeter: CMS CMS crystal calorimeter lead tungstate PbWO 4 radiation hard Very compact: front face with l = 1.5X 0 readout with APD: lengths: 16X 0, 22X 0, 23X 0 9

10 Light path and homogeneity In crystal calorimeters: Wavelength shifter Reflector Signal Diffuse reflector Photodetector WLS bars also for readout of large scintillators 10

11 Detector geometry Projective geometry elements pointing directly onto interaction point minimal number of detector segments Advantages minimal shower size minimal noise minimal systematic uncertainties shower shape comparable everywhere in detector Disadvantage Cracks in detector inefficiency crystals in general slightly non-projective Inert material (dead material) e.g. crystal wrapping systematic bias and especially fluctuations of energy loss deterioration of resolution 11

12 Energy resolution Calorimeter energy resolution parametrization σ E = a b E E c stochastic term a statistical fluctuations (sampling) noise b electronic noise pileup - contribution of additional particles (this term is missing, often) constant term c inhomogeneities in signal (detector or readout) inter-calibration shower losses (longitudinal and transverse) (CMS) 12

13 Shower loss Longitudinal losses are worse than transverse (CHARM calorimeter) 13

14 Sampling calorimeters Sandwich made of absorber: Fe, Cu, Pb, U detectors: scintillators, gas detectors, silicon, liquid noble gases (Ar) 14

15 Sampling calorimeter geometry Possibilities for optimization position resolution electron/hadron discrimination Accordion geometry response uniformity improvement of position resolution no projective cracks or inert zones improvement of time resolution minimal inductances of signal path fast shaping shortened drift time (conventional geometry with d = 2 mm and 2 kv: τ 400 ns) ATLAS barrel em calorimeter: absorber: lead-steel plates scintillator: lar (90K) Another example SPACAL H1 backward calorimeter KLOE 15

16 Sampling calorimeter resolution Total number of shower particles (path length), initial energy E 0 S = m i=0 2 i = 2 m m+1 = 2 E 0 E c If the tracks are measured in (equidistant) detector segments (fraction t), the total active path length is S = S t = 2 E 0 E c t therefore the energy resolution is σ(e) E = S S = Ec 2E0 t 1 E0 t improvement for larger energies and smaller absorbers 16

17 Fluctuations in sampling calorimeters Resolution parametrized as σ(e)/e 1/ E const. Resolution contributions statistical fluctuations of the number of e + e pairs path length multiple scattering large angles Landau fluctuations: energy depositions in active layers 17

18 Fano factor Fano factor describes deviation (improvement) with respect to Poisson statistics F = ( measured resolution Poisson expectation For total absorption expectation of pure Poisson statistics is incorrect average energy per ionisation W number of ionisations E 0 /W energy deposition in many small steps k, but k E k = E 0 furthermore: finite number of energy loss processes energy conservation reduces possible fluctuations N Fano factor difficult to calculate scintillators F 1 silicon det. F 0.06 liquid noble gases F 0.2 ) 2 18

19 Preshower detectors Measurement with high granularity of e.m. shower start point discrimination of π 0 and γ Pb Photon π 0 γ γ Preshower Detector (Si) Calorimeter CMS Example in forward direction: 1.7 < η < Si-layers, 1.9 mm pitch lead absorber with 2 and 1 X 0 material combination of preshower-readout with crystal readout 19