Hadronic Showers KIP Journal Club: Calorimetry and Jets 2009/10/28 A.Kaplan & A.Tadday
Hadronic Showers em + strong interaction with absorber similarities to em-showers, but much more complex different scales ( X 0 λ int ) iron: X 0 = 1.8cm λ int = 16.8cm π 0, decay electromagnetically -> em-fraction invisible energy: part of the energy is fundamentally undetectable 2
Insertion: Electromagnetic Showers Radiation length X 0 : Length a charged particle can travel before it has lost 63% of its initial energy due to Bremsstrahlung Photons: λ pair = (9/7) X 0 γ γ γ e e + γ e e + e γ e + 3
Hadronic Showers: Nuclear Interaction Length Probability to travel distance z without nuclear interaction: P(z) = exp(-z / λ int ) Nuclear interaction length λ int = A/(N A σtot) σtot ~ A 2/3 -> λ int ~ A 1/3 Interaction probability depends on size of hadrons -> λ int for pions is longer than for protons, e.g. 10 λ int for protons 7 λ int for pions -> higher punch-through probability for pions exp(-10) = 5e-5 exp(-7) = 1e-3 4
Hadronic Showers One way street 5
Electromagnetic Fraction 1/3 of produced particles are π 0 (per collision) decay: π 0 γγ one-way street approximation: <f em > = 1 - (1-1/3) n (after n generations of reactions) parameterization: <f em > = 1 - (E/E 0 ) k-1 = 1 - <m> n(k-1) - <f em > is slightly Z dependent - Energy to produce π 0 in Cu: E 0 0.7 GeV, in Pb: E 0 1.3 GeV - k 0.8 is related to the average multiplicity <m> 6
Electromagnetic Fraction Cu Pb Em-fraction is increasing with Energy (more generations) <f em > = 1 - (E/E 0 ) k-1 = 1 - <m> n(k-1) E 0 is Z dependent (smaller em-fraction in high Z materials because of ionization loss in between nuclear interactions) 7
Ionization Losses Charged hadrons lose energy by ionization of the material (average travel distance 1 λ int ) Pions travel 25% longer distance Minimum ionizing protons Shower pions often have low energy No mips! -> High energy loss 300MeV -> Z-dependence of <f em > 8
Pions or Protons? Smaller response for protons in QFCAL -> Smaller em-fraction! QFCAL (highly noncompenating! e/h 7) Proton has to conserve baryon number in interactions (i.e. baryon will be produced and carry large fraction of initial energy) -> Less energy for meson production! 9
Nuclear Sector Nuclear interaction induced by 30 GeV proton 10
Nuclear spallation reactions most likely process for incoming high energy hadrons striking nuclei, two-stage process: spallation 1. fast intranuclear cascade - quasi-free collisions with nucleons, which in turn collide with others -> cascade of fast nucleons forward directed 2.slower evaporation stage - de-excitation of struck nucleus -> evaporation of free nucleons and γ s (few MeV) (sometimes also α evaporation or even fission, e.g. in Uranium) isotropic hundreds of different reactions occur with comparable probability -> enormous diversity of processes can occur in nuclear sector 11
Spallation Nucleons huge differences depending on absorber material number of nucleons released is much bigger for lead strong asymmetry between protons and neutrons for Pb (not for Fe - factor 4 less n) reasons: different binding energy, different proton/ neutron ratios in nuclei, volumes of nuclei consequences: em-fraction, invisible energy choice of absorber important for detector performance! 12
Invisible Energy For all nucleons released, binding energy is lost for calorimetric purposes -> invisible energy Large event-to-event fluctuations -> much worse energy resolution than for em-showers (no equivalent fluctuations) Extreme case 1: π + n -> π 0 p almost all kinetic energy to π 0 (decays into γγ) proton does ionization -> no invisible energy Extreme case 2: 60% of total energy invisible 13
Neutrons can only react strongly (also weakly - but rare) almost all neutrons present in absorber structure after few ns are evaporation neutrons evaporation neutron energies follow Maxwell distribution: dn de = E exp( E/T ) correlation between total kinetic energy of neutrons and amount of invisible energy (can be used for calorimetry) 14
Neutron reactions in matter for Energies few ev - 1 MeV: elastic scattering mean free path: few cm, energy loss per collision: 50% hydrogen, 3.4% iron and 0.96% for lead -> very different from charged particles at lower energies: neutron capture - nuclear binding energy (invisible) is gained back 3-20 MeV: production of α particles inelastic scattering: very material dependent - kinetic energy excites nuclei: n -> n + γ - in Pb: insignificant below 2.6 MeV - in Fe: significant well below 1 MeV 15
Hadronic Shower Profiles 16
Longitudinal Profiles energy deposited rises roughly linear maximum depends on energy and particle nature (pion / proton) 300 GeV π- less steep decay than initial rise Example from CALICE: corrected for λ int 17
Lateral Profiles (SPACAL) Hadron showers: much greater depth & considerably broader than em-showers. Narrow core: em-shower component Halo representing non-em part of the shower lateral profiles for different longitudinal positions, em-part vanishes lateral profiles for different energy deposition processes 18
Fluctuations 270 GeV pions Profiles shown so far were average over large number of showers. Energy deposit profiles of individual showers may deviate strongly from these averages like average long travel before interaction many π 0 in 1st interaction 3 generations of π 0 production 2nd generation interaction large event-by-event fluctuations such stochastic energy deposit profiles are usual! 19
Čerenkov Calorimeters negative 80 GeV pions much narrower profile, in spite of the lower Z and density of the QCAL absorber material Only relativistic charged particles contribute: e + /e - > 700keV, charged pions > 190 MeV and protons > 1.3 GeV (for n=1.4) Velocity: v > c / n (n: diffraction index of medium e + /e - dominate -> mainly em shower core is detected -> impact: narrower 3d shower profiles calorimeter signals in general are not proportional to the amount of energy deposited in the area read out - extreme case: Čerenkov Calorimeters 20
Shower Containment one of the most important decisions in experiment design: thickness of the calorimeter (->cost!) The effects of shower leakage on data quality is determined by event-to-event fluctuations, not by the containment itself longitudinal lateral For higher energies, a thicker absorber is necessary to contain 95% of the energy. The higher the energy the narrower the cylinder needed to contain the shower -> consequence of the energy dependence of <f em > 21
Summary hadronic showers are more complicated than em ones they contain electromagnetic fraction shower development strongly fluctuates -> fluctuations determine energy resolution of hadronic energy measurements shower shapes heavily depend on absorber material -> chose your calorimeter material wisely... hadronic showers are not as well understood as em ones -> contrary predictions from simulations... 22
backup slides... 23
Molière Radius m used to describe the transverse development of em showers in an (approx.) material independent way on average, 90% of the shower energy is deposited in a cylinder with radius m around the shower axis definition: ρ m = E s X 0 c 24