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Transcript
Particle Detectors for Colliders Robert S. Orr University of Toronto Plan of Lectures • I’ve interpreted this title to mean: – Physical principles of detectors – How these principles are applied to representative devices • Physical principles are not particular to colliders – Realization as devices probably is, a bit • An enormous field – I can only scratch the surface – At Toronto I give this material as about 15 lectures – More comprehensive (?) notes from UofT lectures http://hep.physics.utoronto.ca/~orr/wwwroot/phy2405/Lect.htm • These pages also have some notes on accelerators High Energy Physics experiments? 1. Collide Particles Accelerators & Beams ECM and L 2. Detect Final State Detectors p 3. Understand Connection of 1 + 2 Analysis S B Generic Detector Layers of Detector Systems around Collision Point R.S. Orr 2009 TRIUMF Summer Institute Generic Detector Different Particles detected by different techniques. Tracks of Ionization – Tracking Detectors Showers of Secondary particles – Calorimeters R.S. Orr 2009 TRIUMF Summer Institute Generic Detector Different Particles detected by different techniques. Tracks of Ionization – Tracking Detectors Showers of Secondary particles – Calorimeters R.S. Orr 2009 TRIUMF Summer Institute ATLAS Detector R.S. Orr 2009 TRIUMF Summer Institute ATLAS Detector Different Particles detected by different techniques. Tracks of Ionization – Tracking Detectors Showers of Secondary particles – Calorimeters R.S. Orr 2009 TRIUMF Summer Institute Interaction of Charged Particles with Matter • All particle detectors ultimately use interaction of electric charge with matter – Track Chambers – Calorimeters – Even Neutral particle detectors n 0 • Ionization – Average energy loss – Landau tail • • • • Multiple Scattering Cerenkov Transition Radiation Electron’s small mass - radiation Energy Loss to Ionization • • • Heavy charged particle interacting with atomic electrons All electrons with shell at impact parameter b Energy loss p pT - symmetry pT Fdt e ET dt e ET • Gauss ET dA 4 ze E T 2 bdx 4 ze ET dx 2 ze b dt dx dx e ET dx v E ndA 4 Q ENCLOSED dE b E b N e dV 2 ze 2 pT bv pT E 2 • Density of electrons dE b E b N 2 bdbdx e 2me Ne 2 z 2e4 E b me v 2b 2 R.S. Orr 2009 TRIUMF Summer Institute 4 z 2 e 4 db dE b N dx e 2 me v b Physical limits of integration b 0 b max b min bMAX dE 4 z 2e4 N ln e dx mev 2 b MIN • Maximum E minimum b • In a classical head-on collision EMAX 12 me 2v 2 2 2 • Relativistically EMAX 12 me 2v 2 me v 2 EMAX 2 z 2e4 2 me v 2bMIN b 2 z 2e4 1 me v 2 2 2 me v 2 bMIN z e2 me v 2 2 MIN R.S. Orr 2009 TRIUMF Summer Institute 2 Physical limits of integration • Electrons bound in atoms • Time of interaction must be small, compared to orbital period, else energy transfer averages to zero • Orbital period • Collision time t 1 b v b v bMAX 1 v • Put in integration limits • Time for EM interaction t b v 2 me v3 dE 4 z 2e4 N e ln 2 2 dx me v ze R.S. Orr 2009 TRIUMF Summer Institute Ionization Loss 2 me v3 dE 4 z 2e4 Ne ln 2 2 dx mev ze dE dx v dE dx 1 2 mv3 ln 2 2 v ze • This works for heavy particles like α • Breaks down for M M PROTON • Correct QED treatment gives Bethe – Bloch equation Maximum energy transfer in single collision 2 2 2 2 m TMAX dE Z z e 2 N A re2 me c 2 ln dx A 2 I2 Mean excitation potential of material C 2 2 2 Z Density correction Shell correction R.S. Orr 2009 TRIUMF Summer Institute Bethe – Bloch Equation dE Z z 2 2me 2 2TMAX 2 2 2 N A re me c ln 2 dx A I2 cm2 2 N r me c 0.1535 MeV g 2 A e C 2 2 2 Z M 2 me TMAX 2mec 2 2 2 • Mean excitation potential This is main parameter in B –B Hard to calculate measure dE dx infer I • Empirically I 7 12 eV Z 13 Z Z I 9.76 58.8 Z 1.19 eV Z R.S. Orr 2009 TRIUMF Summer Institute Z 13 Relativistic rise & Density Correction dE Z z 2 2me 2 2TMAX 2 2 2 N A re me c ln dx A 2 I2 C 2 2 2 Z E • Electric field polarizes material along path • Far off electrons shielded from field and contribute less dE dE dx dx • Polarization greater in condensed materials, hence density correction R.S. Orr 2009 TRIUMF Summer Institute Particle Identification dE depends on velocity dx Usually measure p M dE dx determines mass R.S. Orr 2009 TRIUMF Summer Institute Particle Identification R.S. Orr 2009 TRIUMF Summer Institute Mass Stopping Power dE expressed as (mass)x(thickness) is dx relatively constant over a wide range of materials Mass Area dE 1 dE Z z2 f , I d dx A density dE d ln variation Roughly constant over periodic table Mixtures of Materials Bragg’s Rule 1 dE 1 dE 2 dE ... dx 1 dx1 2 dx2 fraction by weight i ai Ai Amixture No of atoms of i element molecule Amixture ai Ai Independent of material 10 MeV proton loses same energy in 1gm Cu or 1gm Fe, Al, …. cm 2 cm 2 R.S. Orr 2009 TRIUMF Summer Institute Z mixture ai Z i ln I mixture ai Z i ln I i Zi Electron Energy Loss •More complicated than heavy particles discussed so far •Small mass radiation (bremsstrahlung) dominates •Above critical energy, radiation dominates •Below critical energy, ionization dominates dE dE dE dx TOTAL dx IONIZATION dx RADIATION • What constitutes a heavy particle, depends on energy scale R.S. Orr 2009 TRIUMF Summer Institute Bethe Bloch for electrons •Projectile deflected •Projectile and atomic electrons have equal masses •Also identical particles – statistics TMAX • Equal masses dE Z z2 2 2 2 N A re me c dx A 2 F 2 2 C ln F 2 2 Z 2 I me c Electron identical TE 2 F Positron non-identical R.S. Orr 2009 TRIUMF Summer Institute Bremsstrahlung e • Below ~100 GeV/c only important for electrons e2 • > 100 GeV/c becomes important for muons 2 mc E e • E B in the GeV range B 40, 000 1 dE N dx RAD v0 Eo / h 0 d h E0 , d dE 2 NE0 Z dx RAD 2 N 1 m2 NA A independent of function of material 1 1 4Z 2 re2 ln 183Z 3 f Z 18 dE 2 E , Z can emit all energy in a few dx RAD photons -> large fluctuations dE ln E , Z dx ION R.S. Orr 2009 TRIUMF Summer Institute atoms /cc Radiation Length dE 2 NE0 Z dx RAD assume indep of E dE N Z 2 E0 ln E ln E 0 x E E0 exp 0 0 1 N • 0 distance over which the electron energy is reduced by1/e on average • Radiation Length N A 2 183 1 4Z Z 1 r ln f z 1 e Z 3 0 A • for x expressed in units of 0 dE E0 dt R.S. Orr 2009 TRIUMF Summer Institute Electron Energy Loss approx valid for any material electrons in Cu R.S. Orr 2009 TRIUMF Summer Institute CRITICAL ENERGY FOR VARIOUS MATERIALS Pb Cu Fe Al Water Air Ec (MeV) 9.51 24.8 27.4 52 92 102 dE dE dx dx RAD ION good approximation (3%) except for He R.S. Orr 2009 TRIUMF Summer Institute High Energy Muons R.S. Orr 2009 TRIUMF Summer Institute Muons in Cu R.S. Orr 2009 TRIUMF Summer Institute Cerenkov Radiation 5 cos measure 4 3 2 eV c / nt 1 ct n known 2 d dN 2 2 2 z sin 1 dx N 1 2 4.6 106 1 2 ( A) 1 1( A) L(cm) sin 2 475z 2 sin 2 photons/cm 350 nm to 550 nm R.S. Orr 2009 TRIUMF Summer Institute Multiple Coulomb Scattering • Can be a very important limitation on detector angle/momentum resolution • For Charged particles traversing a material (ignore radiation) – Inelastic collisions with electrons - ionization – elastic scattering from atomic nuclei Rutherford scattering m c p d z12 z22 re2 e d 4sin 4 2 2 vast majority of scatters – small angle • is polar angle • number of scatters > 20 • negligible energy loss • Gaussian statistical treatment is usually ok Gaussian Multiple Scattering 15.7 MeV electrons Gaussian cf. experiment more material probability of scattering through P 2 R.S. Orr 2009 TRIUMF Summer Institute 2 2 2 exp 2 d RMS scattering angle Gaussian Multiple Scattering For detectors usually interested in RMS scattering angle – projected on a plane most detectors measure in a plane RMS 0 PLANE 1 RMS SPACE 2 x 13.6MeV x 0 z 1 0.038ln cp 0 0 1 0 3 x 0 3 x 0 4 3 RMS PLANE RMS yPLANE RMS S PLANE R.S. Orr 2009 TRIUMF Summer Institute Energy Loss Distribution • So far have discussed dE dx MEAN • In general energy loss for a given particle E E MEAN • For a mono-energetic beam • distribution of energy losses • Thick Absorber – Gaussian Energy Loss • Thin Absorber – Possibility of low probability, high fractional energy transfers Typical Energy Loss in Thin Absorber • Scintillator • Wire Chamber Cell • Si tracker wafer • Practical Implications • Use of dE/dx for particle ident - Landau tails cause limitation in separation long tail • Position in tracking chamber - Landau tails smear resolution • Various Calculations • Landau – most commonly used • Vavilov - “improved” Landau • Separation of 1 from 2 particles in an ionization/scintillator counter - Landau tails smear ionization R.S. Orr 2009 TRIUMF Summer Institute Energy Loss of Photons in Matter Important for Electromagnetic Showers • Photoelectric Effect • Compton Scattering • Pair Production – completely dominant above a few MeV • For a beam of or survival probability of a single I x I 0 e x absorption coefficient R.S. Orr 2009 TRIUMF Summer Institute Photoelectric Effect Pb K absorption edge – inner, most tightly bound electrons • Atomic electron absorbs photon and is ejected • Cross section for absorption increases with decreasing energy until Ee h Binding Energy • Then drops because not enough energy to eject K-shell electrons • Dependence on material R.S. Orr 2009 TRIUMF Summer Institute Z 45 Compton Scattering Compton Edge – Detector Calibration 2 TMAX h 1 2 h me c 2 R.S. Orr 2009 TRIUMF Summer Institute Pair Production • Central to electromagnetic showers • Can only occur in field of nucleus • Rises with energy cf. Compton and PE • Same Feynman diagram as Brems Mean Free Path 1 PAIR 7 183 4Z Z 1 Nre2 ln 1 f z 3 9 Z 2 Z 9 7 PAIR 0 Closely related to Radiation Length R.S. Orr 2009 TRIUMF Summer Institute Photon Absorption as Function of Energy Pb MeV R.S. Orr 2009 TRIUMF Summer Institute