particle physics Experimental particle interactions in particle detectors

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1 Experimental particle physics 3. particle interactions in particle detectors lots of material borrowed from the excellent course of H.-C. Schultz-Coulon Marco Delmastro Experimental Particle Physics 1

2 How do we detect particles? In order to detect a particle, it must:! interact with the material of the detector! transfer energy in some recognizable fashion (signal) Detection of particles happens via their energy loss in the material they traverses Charged particles Photons Hadrons Neutrinos Ionization, Bremsstrahlung, Cherenkov, Photo/Compton effect, pair production Nuclear interactions Weak interactions multiple interactions single interactions multiple interactions Marco Delmastro Experimental Particle Physics 2

3 Example of particle interactions Ionization: Pair production: Compton scattering: Charged Particle Positron Electron Electron γ γ Electron Nucleus x Electron γ γ Charged Particle Photon Electron Photon Photon Atom Electron Nucleus Positron Electron Marco Delmastro Experimental Particle Physics 3

4 Energy loss by ionization: Bethe-Bloch formula For now assume: Mc 2 mec 2 Charged Particle i.e. energy loss for heavy charged particles [de/dx for electrons more difficult...] γ Interaction dominated by elastic collisions with electrons... Electron de dx = Kz 2 Z A 1 β 2 [ 1 2 ln 2m ec 2 β 2 γ 2 T max I 2 Bethe-Bloch Formula β 2 δ(βγ) 2 ] 1/β 2 ln (const β 2 γ 2 ) Marco Delmastro Experimental Particle Physics 4

5 Bethe-Bloch formula for heavy particles [see e.g. PDG 2010] de dx = Kz 2 Z A 1 β 2 [ 1 2 ln 2m ec 2 β 2 γ 2 T max I 2 β 2 δ(βγ) 2 ] [ ρ] K = 4π NA re 2 me c 2 = MeV g -1 cm 2 NA = Tmax = 2mec 2 β 2 γ 2 /(1 + 2γ me/m + (me/m) 2 ) [Max. energy transfer in single collision] z : Charge of incident particle M : Mass of incident particle Z : Charge number of medium A : Atomic mass of medium [Avogardo's number] re = e 2 /4πε0 mec 2 = 2.8 fm [Classical electron radius] me= 511 kev [Electron mass] β = v/c [Velocity] γ = (1-β 2 ) -2 [Lorentz factor] I : Mean excitation energy of medium δ : Density correction [transv. extension of electric field] Validity: density.05 < βγ < 500 M > mμ Marco Delmastro Experimental Particle Physics 5

6 Energy loss of pions in Cu Minimum ionizing particles (MIP): βγ = 3-4 de/dx falls ~ β -2 ; kinematic factor [precise dependence: ~ β -5/3 ] de/dx rises ~ ln (βγ) 2 ; relativistic rise [rel. extension of transversal E-field] Saturation at large (βγ) due to density effect (correction δ) [polarization of medium] Units: MeV g -1 cm 2 βγ = 3-4 MIP looses ~ 13 MeV/cm [density of copper: 8.94 g/cm 3 ] Marco Delmastro Experimental Particle Physics 6

7 Understanding Bethe-Bloch 1/β 2 -dependence: Remember: Slower particles Z fell electric Z force of atomic electrons dx p? = F for? dt longer = time F? v i.e. slower particles feel electric force of atomic electron for longer time... Relativistic rise for βγ > 4: High energy particle: transversal electric field increases due to Lorentz transform; Ey γey. Thus interaction cross section increases... particle at rest γ = 1 fast moving particle γ gross grows Corrections: low energy : shell corrections high energy : density corrections Marco Delmastro Experimental Particle Physics 7

8 Understanding Bethe-Bloch Density correction: Polarization effect... [density dependent] Shielding of electrical field far from particle path; effectively cuts of the long range contribution... More relevant at high γ... [Increased range of electric field; larger bmax;...] For high energies: /2! ln(~ /I)+ ln 1/2 Shell correction: Arises if particle velocity is close to orbital velocity of electrons, i.e. βc ~ ve. Assumption that electron is at rest breaks down... Capture process is possible... Density effect leads to saturation at high energy... Shell correction are in general small... Marco Delmastro Experimental Particle Physics 8

9 Energy loss of (heavy) charged particles Dependence on Mass A Charge Z of target nucleus Minimum ionization: ca. 1-2 MeV/g cm -2 [H2: 4 MeV/g cm -2 ] de/dx (MeV g 1 cm 2 ) H 2 liquid He gas Fe Sn Pb Al C βγ = p/mc Muon momentum (GeV/c) Marco Delmastro Experimental Particle Physics 9

10 Identifying particles by de/dx TPC Signal [a.u.] Measured energy loss [ALICE TPC, 2009] 60 Bethe-Bloch Momentum [GeV] Remember: de/dx depends on β! Marco Delmastro Experimental Particle Physics 10

11 ALICE TPC Marco Delmastro Experimental Particle Physics 11

12 de/dx fluctuations Bethe-Bloch describes mean energy loss; measurement via energy loss ΔE in a material of thickness Δx with E = N δe n n=1 δn: number of collisions δe : energy loss in a single collision rel. probability Below excitation threshold Excitations Ionization by distant collisions Ionization by close collisions production of δ-electrons Ionization loss δe distributed statistically... so-called Energy loss 'straggling' Complicated problem... Thin absorbers: Landau distribution Standard Gauss with mean energy loss E0 + tail towards high energies due to δ-electrons energy transfer δe see also Allison & Cobb [Ann. Rev. Nucl. Part. Sci. 30 (1980) 253.] Marco Delmastro Experimental Particle Physics 12

13 Mean particle range Marco Delmastro Experimental Particle Physics 13

14 Energy loss of electrons Bethe-Bloch formula needs modification Incident and target electron have same mass me Scattering of identical, undistinguishable particles de dx el. = K Z A 1 2 apple ln m e 2 c 2 2 T 2I 2 + F ( ) [T: kinetic energy of electron] Wmax = ½T Remark: different energy loss for electrons and positrons at low energy as positrons are not identical with electrons; different treatment... Marco Delmastro Experimental Particle Physics 14

15 Bremsstrahlung and Radiation Length Bremsstrahlung arises if particles are accelerated in Coulomb field of nucleus * A JKL de dx =4 N A z 2 Z 2 A 1 e mc 2 E ln 183 Z 1 3 / E m 2 i.e. energy loss proportional to 1/m 2 main relevance for electrons or ultra-relativistic muons Consider electrons: de dx =4 N A de dx = E with X 0 = X 0 Z 2 A r2 e E ln 183 Z 1 3 E = E 0 e x/x 0 A 4 N A Z 2 r 2 e ln 183 [Radiation length in g/cm 2 ] Z 1 3 After passage of one X0 electron has lost all but (1/e) th of its energy [i.e. 63%] Marco Delmastro Experimental Particle Physics 15

16 Critical Energy Critical energy: de dx (E c) Brems = de dx (E c) Ion 200 de dx Tot = de dx Ion + de dx Brems Approximation: E Gas c E Sol/Liq c = = 710 MeV Z MeV Z de/dx X 0 (MeV) Copper X 0 = g cm 2 E c = MeV Rossi: Ionization per X 0 = electron energy Brems E Total Ionization Exact bremsstrahlung Example Copper: Ec 610/30 MeV 20 MeV Brems = ionization Electron energy (MeV) Figure 27.12: Two definitions of the critical energy. Marco Delmastro Experimental Particle Physics 16

17 Total Energy Loss of Electrons from PDG 2010 Positrons Lead (Z = 82) 0.20 Møller e e e e 1 E de (X 1 dx 0 ) Electrons Møller (e ) Ionization Bremsstrahlung (cm 2 g 1 ) e + e + Bhabha (e + ) 0.05 e Bhabha e + e Positron annihilation γ E (MeV) re 27.10: Fractional energy loss per radiation length in lead as γ Annihilation Fractional energy loss per radiation length in lead as a function of electron or positron energy Marco Delmastro Experimental Particle Physics 17

18 Energy loss for muons Stopping power [MeV cm 2 /g] Lindhard- Scharff Nuclear losses µ Anderson- Ziegler Bethe-Bloch µ + on Cu Radiative effects reach 1% [GeV/c] Muon momentum Radiative Radiative losses Without δ βγ [MeV/c] Minimum ionization Fig. 27.1: Stopping power (= E µc [TeV/c] ) forpositivemuonsincopperasa Marco Delmastro Experimental Particle Physics 18 PDG 2010

19 Cherenkov radiation Particles moving in a medium with speed larger than speed of light in that medium will loose energy by emitting electromagnetic radiation! Charged particle polarize medium generating an electrical dipole varying in time! Every point in trajectory emits a spherical EM wave, waves constructively interfere refractive index dielectric constant Marco Delmastro Experimental Particle Physics 19

20 Cherenkov radiation: radiators Parameters of Typical Radiator Medium n βthr θmax [β=1] Nph [ev -1 cm -1 ] Luft Air Isobutan Wasser Water Quartz Note: Energy loss by Cherenkov radiation very small w.r.t. ionization (< 1%). Example: [Proton with Ekin =1 GeV passing through 1 cm water ] β = p/e 0.875; cosθc = 1/nβ = θc = 30.8 d 2 N/(dE dx) = 370 sin 2 θc ev -1 cm ev -1 cm -1 ΔEloss = <E> d 2 N/(dE dx) ΔE Δx = 2.5 ev 100 ev -1 cm -1 5 ev 1 cm = 1.25 kev Visible light only! [E = 1-5 ev; λ = nm] ΔEloss < 1.25 kev Marco Delmastro Experimental Particle Physics 20

21 Identifying particles with Cherenkov radiation Marco Delmastro Experimental Particle Physics 21

22 Cherenkov radiation: momentum dependence θn = θ/θmax Nn = N/N π K p p [GeV] Cherenkov angle Number of photons grows with β and reaches asymptotic value for β = 1 [θmax = arccos (1/n); N = x 370/cm (1-1/n 2 )] Marco Delmastro Experimental Particle Physics 22

23 LHCb RICH Measurement of Cherenkov angle: Use medium with known refractive index n β Principle of: RICH (Ring Imaging Cherenkov Counter) DIRC (Detection of Internally Reflected Cherenkov Light) DISC (special DIRC; e.g. Panda) LHCb RICH Event [December 2009] LHCb RICH Marco Delmastro Experimental Particle Physics 23

24 Transition radiation Transition radiation occurs if a relativistic particle (large γ) passes the boundaries between two media with different refraction indices! Intensity of radiation is logarithmically proportional to γ Angular distribution strongly forward peaked [Interference; coherence condition] Coherent radiation is generated only over a very small formation length Volume element from which coherent radiation is emitted... Maximum energy of radiated photons limited by plasma frequency... [results from requiring V 0 ω = γωp] θ 1/γ D = γc/ωp V = π D ρ 2 max Plasma frequency [from Drude model] ρmax = γv/ω [transversal range with large polarization] Emax = γhωp [ X-Rays large γ!!] Typical values: CH2: ħωp = 20 ev; γ = 10 3 [ Air: ħωp = 0.7 ev ] D = 10 μm [d > D: absorption dominates] Marco Delmastro Experimental Particle Physics 24

25 Identifying particles with transition radiation Detection Principle: [Electron-ID] Radiator TR! 0 + TR γ-absorption + Electron de/dx Detector Signal: Radiator foils Wires de/dx δ-electron Detector should be sensitive TR to [Transition 3 ERadiation] γ 30 kev.! Gaseous detectors In gas σ photo effect Z 5 Gases with high Z are required! e.g. Xenon (Z=54) Drift time Marco Delmastro Experimental Particle Physics 25

26 ATLAS Transition Radiation Tracker Straw Tube Tracker with interspace filled with foam Barrel assembly Tracking & transition radiation End-cap assembly Marco Delmastro Experimental Particle Physics 26

27 Identifying particles with transition radiation High threshold probability ATLAS Preliminary preliminary Electron candidates Generic tracks Fit to data Mainly Pions Electron candidates Generic tracks Electrons (MC) Generic tracks (MC) Pion momentum (GeV) factor 3 10 Electrons from Conversions TRT TRT endcap Electron momentum (GeV) Marco Delmastro Experimental Particle Physics 27

28 Interaction of photons with matter Characteristic for interactions of photons with matter: A single interaction removes photon from beam! I I - di Possible Interactions Photoelectric Effect Compton Scattering Pair Production Rayleigh Scattering (γa γa; A = atom; coherent) Thomson Scattering (γe γe; elastic scattering) Photo Nuclear Absorption (γκ pk/nk) Nuclear Resonance Scattering (γk K* γk) Delbruck Scattering (γk γk) Hadron Pair production (γk h + h K) di = µidx [ µ : absorption coe cient ] depends on E, Z, ρ Beer-Lambert law: I(x) =I 0 e µx with =1/µ =1/n [meanfreepath] Marco Delmastro Experimental Particle Physics 28

29 Interaction of photons with matter 100 from PDG 10 Absorption length λ (g/cm 2 ) H C Si Fe Sn Pb ev 100 ev 1 kev 10 kev 100 kev 1 MeV 10 MeV 100 MeV 1 GeV 10 GeV 100 GeV Photon energy Marco Delmastro Experimental Particle Physics 29

30 B)#CC&C(D,&. σ Interaction of photons with matter,0&1. κ %HD Photon σ B#1>$#% Total Cross Sections κ " B)#CC&C(D$?#%&&4.7)%CE7$#15,&-.,&-.,&/.,&/.,&.,&. σ >A(A Rayleigh scattering σ >A(A σ σ Photo effect σ B#1>$#% 4.5&6(78&4!&9&:;5 475&B7).#%&4!#9&F5 $#$ σ *A8A)A κ %HD κ " B)#CC&C(D$?#%&&4.7)%CE7$#15,&-.,&/.,&. σ >A(A σ σ B#1>$#% 4.5&6(78&4!&9&:;5 $#$ Carbon (Z = 6) Lead (Z = 82) 1 MeV 1 MeV σ *A8A)A Pair production κ %HD κ " σ B#1>$#% κ %HD κ ",0&1.,0&1.,0&(2,&/(2,&-(2,&3(2,00&3(2!"#$#%&'%()*+,0&1.,0&(2,&/(2,&-(2,&3(2,00&3(2!"#$#%&'%()*+ Pair Production Photon total cross sections as a function of Photon energytotal in carbon cross sections as a function of e Compton scattering ing the contributions of different processes: tomic photoelectric effect (electron ejection, photon Marco Delmastro Experimental Particle Physics 30

31 Pair production Air Marco Delmastro Experimental Particle Physics 31

32 Electromagnetic showers Reminder: Dominant processes at high energies... Photons : Pair production Electrons : Bremsstrahlung X0 Pair production: pair 7 4 re 2 9 Z2 ln 183 Z 1 3 Absorption coefficient: = 7 9 A N A X 0 µ = n = N A A pair [X0: radiation length] [in cm or g/cm 2 ] = 7 9 X 0 Bremsstrahlung: de dx =4 N A E = E 0 e x/x 0 Z 2 A r2 e E ln 183 Z 1 3 After passage of one X0 electron has only (1/e) th of its primary energy... [i.e. 37%] = E X 0 Marco Delmastro Experimental Particle Physics 32

33 Electromagnetic showers 200 Further basics: 100 Copper X 0 = g cm 2 E c = MeV Critical Energy [see above]: de dx (E c) Brems = de dx (E c) Ion de/dx X 0 (MeV) Rossi: Ionization per X 0 = electron energy Brems E Total Ionization Exact bremsstrahlung Approximations: E Gas c = de dx Brems 710 MeV Z de dx Ion E Sol/Liq c = Z E 800 MeV 610 MeV Z Brems = ionization Electron energy (MeV) Figure 27.12: Two definitions of the critical energy. with: de dx Brems = E X 0 & de dx Ion E c X 0 =const. Transverse size of EM shower given by radiation length via Molière radius [see also later] R M = 21 MeV E c X 0 RM : Moliere radius Ec : Critical Energy [Rossi] X0 : Radiation length Marco Delmastro Experimental Particle Physics 33

34 Electromagnetic showers Typical values for X0, Ec and RM of materials used in calorimeter X0 [cm] Ec [MeV] RM [cm] Pb Scintillator (Sz) Fe Ar (liquid) BGO Sz/Pb PB glass (SF5) Marco Delmastro Experimental Particle Physics 34

35 A simple shower model Simple shower model: [from Heitler] Only two dominant interactions: Pair production and Bremsstrahlung... γ + Nucleus Nucleus + e + + e [Photons absorbed via pair production] e + Nucleus Nucleus + e + γ s elektromagnetischen Sch K + [Energy loss of electrons via Bremsstrahlung] Shower development governed by X0... After a distance X0 electrons remain with only (1/e) th of their primary energy... Photon produces e + e -pair after 9/7X0 X0... Assume: E > Ec : no energy loss by ionization/excitation E < Ec : energy loss only via ionization/excitation Electromagnetic Shower [Monte Carlo Simulation] Use Simplification: Eγ = Ee E0/2 [Ee looses half the energy] Ee E0/2 [Energy shared by e + /e ]... with initial particle energy E0 Marco Delmastro Experimental Particle Physics 35

36 A simple shower model Simple shower model: [continued] Shower characterized by: Number of particles in shower Location of shower maximum Longitudinal shower distribution Transverse shower distribution Number of shower particles after depth t: Energy per particle after depth t: N(t) =2 t E = E 0 N(t) = E 0 2 t t =log 2 ( E 0/E) Longitudinal components; measured in radiation length... Total number of shower particles with energy E1: t = x X 0 N(E 0,E 1 )=2 t 1 =2 log 2 (E 0/E 1 ) = E 0 Number of shower particles at shower maximum: N(E 0,E c )=N max =2 t max = E 0 Shower maximum at: 0 E 0 / 2 E 0/ 4 E 0/ 8 E 0/ t [X 0 ] t max / ln( E 0/E c )... use: E c E 1 / E 0 Marco Delmastro Experimental Particle Physics 36

37 A simple shower model Simple shower model: [continued] Longitudinal shower distribution increases only logarithmically with the primary energy of the incident particle... Some numbers: Ec 10 MeV, E0 = 1 GeV tmax = ln ; Nmax = 100 E0 = 100 GeV tmax = ln ; Nmax =10000 Relevant for energy measurement (e.g. via scintillation light): Marco Delmastro Experimental Particle Physics 37

38 EM shower longitudinal development Longitudinal profile MeV Parametrization: [Longo 1975] de dt = E 0 t e t α,β:free parameters t α : at small depth number of secondaries increases... e βt : at larger depth absorption dominates... de / dt [MeV/X 0 ] MeV 1000 MeV 500 MeV Numbers for E = 2 GeV (approximate): α = 2, β = 0.5, tmax = α/β t [X 0 ] More exact [Longo 1985] de dt = E 0 ( t) [Γ: Gamma function] 1 e t ( ) t max = 1 =ln E0 E c + C e with: C e = 0.5 C e = 1.0 [γ-induced] [e-induced] Marco Delmastro Experimental Particle Physics 38

39 EM shower longitudinal development Depth [X0] Energy deposit per cm [%] Energy deposit of electrons as a function of depth in a block of copper; integrals normalized to same value [EGS4* calculation] Depth of shower maximum increases logarithmically with energy t max / ln( E 0/E c ) *EGS = Electron Gamma Shower Depth [cm] Marco Delmastro Experimental Particle Physics 39

40 EM shower transverse development Transverse shower development... Opening angle for bremsstrahlung and pair production Multiple coulomb scattering h 2 i ( m /E) 2 = 1 / 2 Small contribution as me/ec = 0.05 x/2 x Multiple scattering deflection angle in 2-dimensional plane... kx h k 2 i = 2 m = kh 2 i p h 2 i m= MeV/c p r x X 0 s plane Ψ plane y plane θ plane ure 27.9: Quantities used to describe multiple Coulomb scattering. Assuming the approximate range of electrons [β = 1] to be X0 yields lateral extension: R = θ X0... In 3-dimensions extra factor 2: p h 2 i 3d 19.2 MeV/c p r x X 0 [β = 1] R M = x=x0 X 0 21MeV E C X 0 Molière Radius; characterizes lateral shower spread... Marco Delmastro Experimental Particle Physics 40

41 EM shower transverse profile Transverse profile energy deposit [arbitrary unites] Parametrization: de dr = e r /R M + e r/ min α,β:free parameters RM : Molière radius λmin: range of low energetic photons... Inner part: coulomb scattering... Electrons and positrons move away from shower axis due to multiple scattering... Outer part: low energy photons... r/rm Photons (and electrons) produced in isotropic processes (Compton scattering, photo-electric effect) move away from shower axis; predominant beyond shower maximum, particularly in high-z absorber media... r r/rm Shower gets wider at larger depth... Marco Delmastro Experimental Particle Physics 41

42 EM shower profiles energy deposit [arbitrary unites] Longitudinal and transversal shower profile for a 6 GeV electron in lead absorber... [left: linear scale; right: logarithmic scale] energy deposit [arbitrary unites] longitudinal shower depth [X0] lateral shower width [X0] longitudinal shower depth [X0] lateral shower width [X0] Marco Delmastro Experimental Particle Physics 42

43 EM showers in a nutshell Radiation length: Critical energy: [Attention: Definition of Rossi used] Shower maximum: X 0 = 180A Z 2 E c = 550 MeV Z t max =ln E E c g cm 2 { Problem: Calculate how much Pb, Fe or Cu is needed to stop a 10 GeV electron. Pb : Z = 82, A = 207, ρ = g/cm 3 Fe : Z = 26, A = 56, ρ = 7.87 g/cm 3 Cu : Z = 29, A = 63, ρ = 8.92 g/cm 3 e induced shower γ induced shower Longitudinal energy containment: Transverse Energy containment: L(95%) = t max +0.08Z +9.6 [X 0 ] R(90%) = R M R(95%) = 2R M Marco Delmastro Experimental Particle Physics 43

44 Hadronic showers Shower development: N π 0 ν 1. p + Nucleus Pions + N* +... π Secondary particles... undergo further inelastic collisions until they fall below pion production threshold Sequential decays... Mean number of secondaries: ~ ln E n μ ν π0 γγ: yields electromagnetic shower Fission fragments β-decay, γ-decay Neutron capture fission Spallation... Typical transverse momentum: pt ~ 350 MeV/c Substantial electromagnetic fraction fem ~ ln E [variations significant] Cascade energy distribution: [Example: 5 GeV proton in lead-scintillator calorimeter] Ionization energy of charged particles (p,π,μ) 1980 MeV [40%] Electromagnetic shower (π 0,η 0,e) 760 MeV [15%] Neutrons 520 MeV [10%] Photons from nuclear de-excitation 310 MeV [ 6%] Non-detectable energy (nuclear binding, neutrinos) 1430 MeV [29%] 5000 MeV [29%] Marco Delmastro Experimental Particle Physics 44

45 Hadronic showers Hadronic interaction: Cross Section: tot = el + inel For substantial energies σinel dominates: at high energies also diffractive contribution!"#$$%$&'()#*%+, pp total el 10 mb 10 elastic inel / A 2 /3 [geometrical cross section] P lab GeV/c tot = tot (pa) tot(pp) A 2 /3 Hadronic interaction length: int = which yields: 1 tot n = 35 g /cm 2 A 1 /3 [σtot slightly grows with s] A pp A 2 /3 N A N(x) =N 0 exp( x/ int ) A 1 /3 s GeV [for s GeV] Total proton-proton cross section [similar for p+n in GeV range] Interaction length characterizes both, longitudinal and transverse profile of hadronic showers... Remark: In principle one should distinguish between collision length λw ~ 1/σtot and interaction length λint ~ 1/σinel where the latter considers inelastic processes only (absorption)... Marco Delmastro Experimental Particle Physics 45

46 Hadronic vs. EM showers Comparison hadronic vs. electromagnetic shower... [Simulated air showers] GeV proton 250 GeV photon altitude above sea level [km] lateral shower width [km] lateral shower width [km] Marco Delmastro Experimental Particle Physics 46

47 Hadronic vs. EM showers Hadronic vs. electromagnetic interaction length: Some numerical values for materials typical used in hadron calorimeters X 0 A Z 2 int A 4 /3 X 0 int A 1 /3 λint [cm] X0 [cm] Szint. Scint int X 0 [λint/x0 > 30 possible; see below] LAr Typical Longitudinal size: λint Typical Transverse size: one λint [95% containment] [95% containment] [EM: X0] [EM: 2 RM; compact] Fe Pb U Hadronic calorimeter need more depth than electromagnetic calorimeter... C Marco Delmastro Experimental Particle Physics 47

48 Hadronic shower development Hadronic shower development: [estimate similar to e.m. case] Depth (in units of λint): t = x int Energy in depth t: E(t) = E thr = E hni t E & hni t max E(t max )=E thr [with Ethr 290 MeV] But: Only rough estimate as... energy sharing between shower particles fluctuates strongly... part of the energy is not detectable (neutrinos, binding energy); partial compensation possible (n-capture & fission) spatial distribution varies strongly; different range of e.g. π ± and π 0... electromagnetic fraction, i.e. fraction of energy deposited by π 0 γγ increases with energy... f em f 0 ln E /(1 GeV) Shower maximum: hni t max = E E thr t max = ln (E /E thr ) lnhni Number of particles lower by factor Ethr/Ec compared to e.m. shower... Intrinsic resolution: worse by factor Ethr/Ec Explanation: charged hadron contribute to electromagnetic fraction via π p π 0 n; the opposite happens only rarely as π 0 travel only 0.2 μm before its decay ('one-way street')... At energies below 1 GeV hadrons loose their energy via ionization only... Thus: need Monte Carlo (GEISHA, CALOR,...) to describe shower development correctly... Marco Delmastro Experimental Particle Physics 48

49 Hadronic shower longitudinal development Number of nuclei [arbitrary units] Longitudinal shower development: Strong peak near λint... followed by exponential decrease... Shower depth: t max 0.2ln(E/GeV) L 95 = t max +2.5 att Longitudinal shower profile for 300 GeV π interactions in a block of uranium measured from the induced 99 Mo radioactivity... with att (E/GeV ) 0.3 Example: 300 GeV pion... tmax = 1.85; L95 = [95% within 8λint; 99% within 11 λint] 95% on average Depth [λint] Marco Delmastro Experimental Particle Physics 49

50 Hadronic shower transverse development Transverse shower profile Typical transverse momenta of secondaries: hp t i'350mev/c... Lateral extend at shower maximum: R95% λint... Electromagnetic component leads to relatively well-defined core: R RM... Exponential decay after shower maximum... # Shower p depth Lateral profile for 300 GeV π [target material 238 U] [measured at depth 4 λint] More π 0 s and γ in core Energetic neutrons and charged pions form a wider core Thermal neutrons generate broad tail Lateral shower position [cm] Measurement from induced radioactivity: 99 Mo (fission): neutron induced... [energetic neutron component] 237 U: mainly produced via 238 U(γ,n) 237 U... [electromagnetic component] 239 Np: from 239 U decay... [thermal neutrons] Ordinate indicates decay rate of different radioactive nuclides... Marco Delmastro Experimental Particle Physics 50

51 Detectors are imperfect upstream material not instrumented region passive region active region passive region not instrumented region signal readout Detection efficiency! M = P(entering active region) Upstream material, entrance windows,! R = P(generating signal) Interaction cross sections, response, fluctuations,! D = P(signal gets registered) Acceptance Readout properties, thresholds,! Instrumented/reactive region of the phase space (e.g. pseudorapity, azimuthal angle, but also energy/momentum) dynamic range Marco Delmastro Experimental Particle Physics 51

52 Detectors are imperfect Dead Time! Delay between particle entrance in detector and signal acquisition, in which the detector is rendered inactive (detector + readout)! Dead time efficiency Response linearity Response resolution Trigger! Detector cannot acquire signals continously Marco Delmastro Experimental Particle Physics 52