Energy Loss of Electrons. Detectors for Particle Physics Part III. Intensity Attenuation. Interaction of Photons with Matter

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1 Detectors for Particle Physics Part III Interaction of electrons, photons and hadrons with matter Scintillators Photodetectors Cherenov Counters Transition radiation nergy Loss of lectrons In addition to energy loss by ionisation high energy particles also loose energy due to interaction with the Coulomb field of the nuclei: Bremsstrahlung Due to their small mass this effect is especially prominent for electrons (positrons): d dx Z 2 it is useful to introduce radiation length X x energy attenuation: = exp approx.: X 76g cm X 2 A = Z( Z + ) ln( 287 Z) xample: Cu Calorimeters - Shower development - electromagnetic - hadronic critical energy : approximately: d Brems dx = d collision dx 6MeV = Z +.24 αln carsten.niebuhr@desy.de Particle Detectors 3 carsten.niebuhr@desy.de 2 Particle Detectors 3 Interaction of Photons with Matter Intensity Attenuation σ Mb Cross section (barns/atom) kb mb Cross section (barns/atom) b b Mb kb b σ p.e. σ coherent σ incoh (a) Carbon ( Z = 6) experimental σ tot Kohlenstoff (leicht) σ p.e. σ coherent κ N σ σ incoh nuc κ e (b) Lead ( Z = 82) experimental σ tot Blei (schwer) minimum C κ N κ e Pb Three effects are important: Photoeffect: γ + atom e + atom + Z σ Ph Comptoneffect: γ + atom γ + e + atom + ln σ Compton Z Pairproduction: γ + nucl. e + + e - + nucl. σ Pair Z 2 für γ» 2m e c 2 Intensity attenuation: I( x) = I exp( µx), N with mass absorption coefficient µ A σ = [cm - ] A strongly energy dependent connection between radiation length and high energy limit for pair production: 7 σ» GeV 9 --4αr 2Z A = ln e N A X Z 3 I( x) = I exp 7 probability for pair production after x X traversing one X is 54%. σ nuc mb ev kev MeV GeV GeV Photon nergy ev kev MeV GeV GeV γ carsten.niebuhr@desy.de 3 Particle Detectors 3 carsten.niebuhr@desy.de 4 Particle Detectors 3

2 Photon Absorption Length λ Definition of mass absorption coefficient: [g cm -2 σ λ = ] with µ = ( µ ρ) A Z σ ln Ph 3.5 σ Compton Z σ Pair Z 2 Absorption length λ (g/ cm 2 ) Sn Si Fe Pb. H C N A Scintillation Detectors Phenomenon of scintillation known since long. xtensive use only after invention of photomultiplier in 944. Since then significant development of this technology. Advantage for detection of particles and photons: simplicity and robustness signal speed high density large signals good time and energy measurement Now also scintillating fibres available position resolution as well There are different mechanisms in: anorganic crystals organic substances scintillator light guide photo detector 6 ev ev kev kev kev MeV MeV MeV GeV GeV GeV Photon energy γ carsten.niebuhr@desy.de 5 Particle Detectors 3 carsten.niebuhr@desy.de 6 Particle Detectors 3 xample: Sodium-Iodide NaI insolator with bandgap of 7eV replace.% of sodium atoms with socalled activators: thallium atoms - shift of light energy into visible regime: (better for detection via photo cathode) - enhanced light yield - reduced reabsorption exciton creation by charged particles Inorganic Crystals excitons move in crystal until they reach activator energy release by photon emission (3eV λ 4nm) for this wavelength the material is transparent decay time τ 23 ns energy conduction band exciton band activator states 3eV valence band exciton electron 7eV hole electron traps Mechanism xcited vibrational modes of molecules de-excite by emission of UV light. This UV light is then transformed into visible light by so called wave length shifters that are added to the material. Mono crystals - Napthalen (C H 8 ) - Anthrazen (C H ) - p-terphenyl (C 58 H 4 ) Liquid- and plastic- scintillators consist of organic substance (polystyrol) plus scint. molecules ( %) in addition: secondary fluor compounds as wave length shifters Organic Scintillators carsten.niebuhr@desy.de 7 Particle Detectors 3 carsten.niebuhr@desy.de 8 Particle Detectors 3

3 Comparison Organic vs Inorganic Scintillators Light Collection Inorganic Organic wave length shifter bars Inorganic crystals well suited for calorimetric applications (high light yield and small radiation length) Plastic scintillators fast particle registration (trigger) plexiglas lightguide total reflection in optical fibres 9 Particle Detectors 3 carsten.niebuhr@desy.de Particle Detectors 3 Conversion of Scintillation Light Photomultiplier Scintillation light must be converted into electrical signal. Requirement high sensitivity, i.e. high "quantum efficiency": Q.. = N photoelectrons / N photon γ cathode focussing dynods vacuum vessel (glass) anode Commonly used photo detectors gas based systems - e.g. RICH detectors vacuum based systems - photomultiplier solid state detectors - photodiodes etc -U D voltage divider xample: dynodes, each with gain factor N total gain M = g i = 4 6 i = g = 4 λ (nm) carsten.niebuhr@desy.de Particle Detectors 3 carsten.niebuhr@desy.de 2 Particle Detectors 3

4 Avalanche Photo Diode APD large reverse bias voltage of -2 V high internal electric field leads to avalanche formation typical gain G Combination of: photocathode - like in PMT acceleration region in vacuum - V = - 2 kv silicon detector e V 2keV 3 - Gain G = = W Si 3.6eV - Poisson statistics with n = 5 Hybrid Photo Diode HPD extremly good pulse height resolution. Single photon counting. Backscattering from silicon surface carsten.niebuhr@desy.de 3 Particle Detectors 3 carsten.niebuhr@desy.de 4 Particle Detectors 3 Cherenkov Radiation Cerenkov Angle vs β If particle velocity is larger than speed of light in medium: - asymmetric polarisation of medium - emission of Cherenkov light Opening angle of emission cone: ( c n) t cos( θ c ) = = βc t β n l light =(c/n) tl θ l part =βc t wave front finite thickness Atomic Dipoles threshold at β thr = -- (i.e. θ ) n C maximum opening angle: θ max = arccos -- (für ) n β photon yield small (λ 4-7nm): dn dx = 5sin 2 θ C [cm ] missionswinkel emission angle θ Liquids and Solids Gases BaO; AgCl Plexiglas; BaF 2 n=2..5 H 2 O Geschwindigkeit β velocity β θ Isobutan Freon Propan Äthan n=.3 Luft Geschwindigkeit velocity β carsten.niebuhr@desy.de 5 Particle Detectors 3 carsten.niebuhr@desy.de 6 Particle Detectors 3

5 Photon Yield vs β xample: Ring Imaging Cherenkov Counter RICH Photonen/cm (4-7nm) Flüssigkeiten Liquids and und Solids Feststoffe BaO; AgCl Plexiglas; BaF 2 n= H 2 O Geschwindigkeit velocity β β Photonen/m (4-7nm) Gases n=.3 Isobutan Freon Äthan Propan.295 Luft Geschwindigkeit velocity β Hermes RICH detector π particle identification θ [rad] K π K p e p [GeV] carsten.niebuhr@desy.de 7 Particle Detectors 3 carsten.niebuhr@desy.de 8 Particle Detectors 3 Transition Radiation Transition Radiation Detectors ven below the threshold for Cherenkov-radiation photons can be emitted when charged particles cross boundaries between media with different dielectric constants. dipol radiation high Z (e.g. Xe Z=54) Radiated energy per boundary: W =, i.e. only significant for highly 3 --α h ω 2π p γ γ relativistic particles (e ± ) X-ray photons are emitted in a forward cone; θ γ transition radiation only occurs very close to the track foils low Z TR hits characterised by: large amplitude occur preferentially at start of the track 3 GeV π 3 GeV e TR Application: distinguish high energetic electrons from pions discrimination possible for momenta from about GeV/c to ~ GeV/c carsten.niebuhr@desy.de 9 Particle Detectors 3 carsten.niebuhr@desy.de 2 Particle Detectors 3

6 Why do we need Calorimeters? Recall: for tracking in magnetic field we have σ( p T ) p T p T L 2 momentum (energy) measurement degrades linearly with increasing energy size of detector L only detection of charged particles In contrast (as we will see) for calorimeters: σ( ) detection of - photons - neutral hadrons for high energy detectors calorimeters are essential components σ/ elmag.. calo. hadr. calorimeter tracker [GeV] lectromagnetic Shower Development Interaction of photons and electrons above MeV dominated by pairproduction γ e + e - Bremsstrahlung e ± e ± γ which are both characterised by X. Alternating sequence leads to shower which stops if energy of particles <. Simple model for shower development initiated by photon of energy = γ : within X γ produces e + e - pair assume symmetric energy sharing e = γ /2 e + e - radiate photon after X γ = e /2 number of particles at depth t = x X : N() t = 2 t with energy t () = 2 t multiplication continues until energy falls below critical energy : 2 t MAX = from then on shower particles are only absorbed. Position of shower maximum: ln t MAX = ln ln2 carsten.niebuhr@desy.de 2 Particle Detectors 3 carsten.niebuhr@desy.de 22 Particle Detectors 3 nergy Loss of lectrons Shower Depth vs nergy In addition to energy loss by ionisation high energy particles also loose energy due to interaction with the Coulomb field of the nuclei: Bremsstrahlung Due to their small mass this effect is especially prominent for electrons (positrons): d dx Z 2 it is useful to introduce radiation length X x energy attenuation: = exp X xample: Cu approx.: 76g cm X 2 A = Z( Z + ) ln( 287 Z) critical energy : d Brems dx = d collision dx αln approximately: = 6MeV Z typical range of depth for M calorimeter carsten.niebuhr@desy.de 23 Particle Detectors 3 carsten.niebuhr@desy.de 24 Particle Detectors 3

7 xample: µ-induced Shower Shower Development Multiple scattering of the e ± causes a broadening of the shower also in the transverse direction: contribution from electrons with dominates the shower width can be characterized by the so-called 2MeV Moliere-Radius R M = X c meaning: 9(95)% of shower energy is contained in cylinder with radius R M (2R M ) around the shower axis dn t α e βt dt Shower Containment: transverse: R 95% = 2R M - xample lead glass: R M =.8X 3.6 cm R 95% 7 cm longitudinal: L 95% = t MAX +.8 Z [X ] [with t MAX = ln( ) ( ln2) ] - xample: GeV e- in lead glass ( =.8 MeV t MAX 3, L 95% 23) carsten.niebuhr@desy.de 25 Particle Detectors 3 carsten.niebuhr@desy.de 26 Particle Detectors 3 Stochastic Fluctuations Number of particles at shower maximum increases linearly with initial energy: N MAX = N( t MAX ) = Total number of particles in the shower N tot N MAX = nergy Resolution In general the energy resolution of a calorimeter can be parametrised as: σ( ) = a b c Ē -- If response of calorimeter is proportional to number of shower particles it acts as a linear device for energy measurements ven for a perfect detector there are intrinsic statistical limitations for the energy resolution: - total track length T N tot X X c - detectable track length T det = F( ξ) T with ξ = ut [above energy threshold ut ] σ( ) - for relative energy resolution σ( T det ) = = T det T det Stochastic Term stochastic fluctuations in shower development sampling fluctuations in case of sampling calorimeter photo-electron statistics Constant Term inhomogeneities dead material non-linearities leakage inter-calibration between individual cells Noise Term electronic noise radioactivity pile-up carsten.niebuhr@desy.de 27 Particle Detectors 3 carsten.niebuhr@desy.de 28 Particle Detectors 3

8 Calorimeter Types xamples for Sampling Calorimeters Homogeneous calorimeters: detector = absorber good energy resolution limited spatial resolution (particularly in longitudinal direction) only used for electromagnetic calorimetry Sampling calorimeters: detectors and absorber are separated only fraction of the energy is sampled heavy absorber material: compact design energy resolution limited by sampling fluctuations good spatial resolution due to segmentation can be used for electromagnetic and hadronic calorimetry Charge sensitive Amplifier Scintillator Light Guide Absorber + HV Light Detector For sampling thickness there are additional sampling fluctuations: σ( ) d X Wavelength Scintillating Fibres Shifter Lead Matrix "spaghetti" calorimeter d Liquid (LAr, LXe, LKr) MWPC Streamer Tubes carsten.niebuhr@desy.de 29 Particle Detectors 3 carsten.niebuhr@desy.de 3 Particle Detectors 3 Comparison of various Calorimeters (lectromagnetic)./ Ε./Ε High energy hadrons also develop showers in an absorber Shower development much more complicated than in M case Components in shower hadronic electromagnetic - mainly due to π o invisible - nuclear excitation - neutrons - neutrinos Typical length scale given by nuclear interaction length λ i n λ I Hadron Calorimeters e + e - e - e + π o π - π - Heavy fragment n xcited nuclei hadronic showers are much longer and much wider than electromagnetic showers lectromagnetic Component Hadronic Component carsten.niebuhr@desy.de 3 Particle Detectors 3 carsten.niebuhr@desy.de 32 Particle Detectors 3

9 Hadronic Interactions For high energies the hadronic cross section is σ [mb] 2 constant as function of energy independent of hadron type 5 2 Material dependence of total cross section is given by: σ A σ p A 2 3 = 5 Characterize hadronic interactions by hadronic 2 A πp interaction length λ I = [cm] πd N A ρ σ A [in table: λ [g/cm 2 I = λ I ρ A 3 ] ] λ I, X (cm) 3 ~ λ I interaction lenght 2 X radiation length Z Cross section (mb) Cross section (mb) Center of mass energy (GeV) 2 pp 5 2 π + p pp σ T total elastic π + p total π + p elastic σ T Center of mass energy (GeV) Problem Compensation the fraction of the different components fluctuate significantly the signal response of electromagnetic and hadronic component are in general different i.e. e/mip h/mip for good performance one needs to compensate this effect. Two possibilities: hardware compensation - careful choice of absorber & active material and their thickness - example: ZUS calorimeter: Uranium (depleted) / scintillator [3.3/2.6 mm] software compensation - if sufficient granularity one can distinguish between electromagnetic and hadronic component and correct by software weighting - example: H calorimeter: liquid argon (LAr) with steel plates due to the large fluctuations hadronic calorimeters in general have worse resolution compared to electromagnetic calorimeters typical values: σ( ) 35 5 % carsten.niebuhr@desy.de 33 Particle Detectors 3 carsten.niebuhr@desy.de 34 Particle Detectors 3 Calorimeter xamples LHC Calorimeters under Construction xperiment Kind Absorber Active material Resolution Type ZUS em Uranium Scintillator 8% / sampling ZUS had Uranium Scintillator 35% / sampling H em Pb LAr 2% / sampling H had Steel LAr 5% / sampling H SpaCal em Pb Scintill. Fibre 7.5% / sampling NA48 em LKr LKr 3.5% / homogeneous BaBar em CsI CsI 2.3% / /4 homogeneous ATLAS em Pb (Cu) LAr % / sampling ATLAS had Iron (Cu) Scintillator 47% / sampling CMS em PbWO 4 PbWO 4 4% / homogeneous CMS had Brass Scintillator 5% / sampling CMS CAL ~75 Crystals ~75 Crystals ~2 channels ATLAS CAL carsten.niebuhr@desy.de 35 Particle Detectors 3 carsten.niebuhr@desy.de 36 Particle Detectors 3

10 Calorimeter R&D for DSY At Linear Collider expect final states with heavy bosons: W, Z, H Haveto reconstruct their hadronic decay modes multi jet events Challenge: need jet resolution of 3%/ xpect ~6% of total energy in charged particles (tracker), 2% in photons (CAL), % in neutral hadrons (HCAL) and % in neutrinos new concept of particle flow: - reconstruction of individual particles - separation of particles (charged and neutral) Detector requirements: - excellent tracking, in particular in dense jets - excellent granularity in the CAL - no material in front of CAL - good granularity in the HCAL - excellent linking between tracker CAL HCAL - excellent hermeticity carsten.niebuhr@desy.de 37 Particle Detectors 3