Energy loss. Calorimeters. First: EM calorimeters

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1 Calorimeters The energy of hadrons, pions, photons and electrons can be measured with calorimeters. This in contrast with muons: their momentum is measured from their track curvature (sagitta). The principle of calorimeters is based on total absorption of the energy, associated with the incoming particle(s). The particles cause a shower of many other particles, and the summed ionisation is proportional to and a good measure for the incoming energy. A straightforward calorimeter is a light-transparent crystal scintillator, large enough to contain the complete shower of secondary particles. These are indeed often applied as calorimeter for photon and electrons (called Electro-Magnetic (EM) calorimeter). For hadrons, these crystals would be impractically large and unaffordable. A hadron calorimeter is therefore often a sampling calorimeter, in the form of a stack of absorber and sample (active read-out) layers. Energy loss Electrons (or positrons) and photons Electromagnetic shower Electrons (positrons) and photons lose energy due to Bremsstrahlung and pair creation Hadrons Hadronic shower Charged and neutral hadrons undergo nuclear and subsequent electromagnetic interaction Muons No or almost no showering, mainly minimum ionising (but: high energy muons may generate Bremsstrahlung, resulting in an electromagnetic shower) Jets In particle physics calorimeters often measure the energy of a jet, a mix (hadrons, photons and electrons) of many particles coming from one point in a small cone. First: EM calorimeters Essential is the conversion of fast electrons into a photon via Bremstrahlung. The photon, in its turn, is converted into an electron-positron pair via Pair Production. For high energies, the directions of the photon, electron and positron are quite in line with the original incident electron. As a result, the incident electron is converted, after a specific length, into an electron and a positron, carrying both half the original energy, on average. The fact that not all energy of an electron is converted, in Bremstrahlung, into a photon does not change this principle: only the typical length over which the number of electrons + positrons is doubled, is increased slightly. This principle of doubling the number of participating electrons + positrons, and the consequent dilution of energy per participating electron/positron continues until the average energy of the electron/positron is such that the energy loss, over a doubling length, equals

2 the corresponding energy loss due to de/dx: the critical energy. At this level, the cascade ends quickly by classic absorption of energy. Simple EM-shower model Bremsstrahlung and pair production Each step the nr of particles in the shower doubles The energy per particle reduces with factor of two The emission angles are small so narrow shower develops When the energy falls below the critical energy Ionisation and collision become important in the energy loss Showers stops over a relatively short distance Longitudinal Transverse Electromagnetic Shower Shower maximum occurs when shower particles on average have an energy equal to the critical energy T.S.Virdee, Proc. of the 1998 European School of High-Energy Physics, CERN The Radiation Length X 0 is defined as the length over which the electron has left over 1/e of its original energy, on average. This equals 7/9 of the mean free path for pair production. Including the effect of non-100 percent Bremstrahlung conversions, X 0 corresponds about with the doubling length.

3 Radiation length Longitudinal shower development An electron has, on average, a fraction 1/e left of its original energy after traveling through X 0 The distance is usually expressed in radiation lengths A 2 Χ0 = 180 ( g cm ) 2 Z Lead Χ 0 = 0.5 cm Silicon Χ 0 = 10 cm Remember the attenuation is expressed as µx I(x) = I0e Electromagnetic showers Radiation length The distance is usually expressed in radiation lengths 2 ( g ) A Χ0 = 180 cm 2 Z Lead Χ 0 = 0.5 cm Silicon Χ 0 = 10 cm The critical energy is defined as The energy at with the energy loss due bremsstrahlung equals the energy loss due to ionisation. Assume the critical energy is 100 MeV, then a layer of 10 times the radiation length would stop a 100 GeV photon. E critical (MeV) = 800/(Z+1.2) The critical energy is a known value for a specific material.

4 Electromagnetic showers Shower development A particle with energy E 0 traverses a layer with thickness t, generating a cascade with N particles, each with energy E. t E0 N(t) = 2, E(t) = 2 t The shower maximum is defined as the position where the number of particles in the cascade is at its maximum, this is at the point where E reaches the critical energy t shower max = ln(e 0 E ln2 critical ) σ(e) σ(n E N shower max shower max ) = 1 N 1 E Electromagnetic showers With a more realistic shower model and Monte Carlo simulation techniques you find the empirical relation t = lne shower max 0 Pb: low critical energy -> shower extends over more radiation lengths T.S.Virdee, Proc. of the 1998 European School of High-Energy Physics, CERN The development of EM showers: not the vertical log scale. Hadron calorimeters A hadron looses energy due to interactions with nuclei. On average an interaction happens after the Interaction Length, which is specific for the kind of interaction, the energy of the particle and the kind of material.

5 Hadronic showers T.S.Virdee, Proc. of the 1998 European School of High-Energy Physics, CERN In a hadron shower a part of the energy is converted, via π 0 decay into EM showers. Hadron showers Hadron interaction A hadron loses energy by nuclear reactions, the probability or cross section for this process is low but the energy loss is high. The main energy loss is caused by Protons losing energy by ionisation π 0 decaying into two photons starting EM showers Breaking up nuclei (binding energy is transferred) Neutrino production The processes are complex and a simple calculation is not possible. Monte Carlo based simulations yield emperical relation for the longitudinal and transverse shower development

6 Hadron interaction Hadron showers The longitudinal shower development is expressed in terms of the interaction length: λ A λ = σ N max abs A = ln E Hadron showers Longitudinal shower development A major part of the energy is already deposited within one interaction length Nearly all energy is deposited in about five interaction lengths. T.S.Virdee, Proc. of the 1998 European School of High-Energy Physics, CERN 99-04

7 Detector types 1. Absorber and detector in one, or homogenous Good energy resolution Limited interaction depth Examples NaI,BGO crystals Cerenkov counter with lead glass 2. Absorber and detector separated -> sampling Energy deposit not equal to measured energy Longitudinal segmentation natural Examples Tungsten, Uranium, Iron or Cupper as absorbers Scintillators, Liquids or semiconductors as detectors Continues (fully active) calorimeters and sampling calorimeters Crystal calorimeters Good energy resolution Number of tracks (tracklength) determines the light output Statistical fluctuations give uncertainty σ(e ) σ(n E N 0 shower max = 0 shower max ) 1 N No sampling fluctuations Typical values for uncertainties 1% crystal-calorimeter, 5% leadglass, low number of Cerenkov (only!)-photons 1% constant term due to calibration etc.

8 Some examples... Index of refraction PDG, Summer 2002 Material properties of crystals used for (EM) calorimeters. CMS Electromagnetic Calorimeter Lead Tungstenate PbW0 4 M.Nessi, CERN academic training 1999 New material used for the CMS EM calorimeter (CMS is one of the experiments at the LHC), becoming operational in July 2008.

9 D.Fournier, CALOR2002 Layout of the CMS EM calorimeter. In total crystals are required. Sampling calorimeters Sampling Calorimeters Absorber Incident particle Lead, Tungsten, Uranium Detector MWPC, scintillator, silicon pads, noble liquid Absorber and detector separated or passive and active layers Fluctuations in visible energy: "sampling fluctuations due to variation of the pathlength of charged particles in the detector Fluctuations in conversion of energy deposited in detector into signal

10 Detection techniques Scintillator Very popular although light collection not fully efficient Fibers, tiles, layers. Gaseous detectors Small nr. Of ionisations, large Landau fluctuation Noble liquid Argon, krypton (expensive)) of xenon (very expensive!) homogeneous response, no radiation damage Need cooling (cryogenics), charge collection slow Semiconductors (too) good but expensive Cerenkov detectors Examples PDG, Summer 2002

11 Example: LAr calorimetry in the ATLAS experiment S.Akhmadaliev et al., Nucl. Instr. and Meth. A 480 (2002) "Accordeon geometry" Thin gap -> small drift time -> fast signal D.Fournier. CALOR2002 The Pb-Liquid Argon Accordeon EM calorimeter of ATLAS. Led plates are immerged in liquid argon.

12 Tower structure, three samplings in depth Three logitudinal sampling layers! The mechanical structure of the ATLAS Accordeon EM calorimeter. A unit has a readout system split in 3 parts ATLAS hadron calorimeter: "tile calorimeter" Note the orientation of the scintillating tiles: parallel to the incoming particles! The ATLAS sampling hadron calorimeter, consisting of a stack of plastic scintillators and iron absorbers.