1、Calorimetry: Energy Measurements,Prof. Robin D. Erbacher University of California, Davis,References: R. Fernow, Introduction to Experimental Particle Physics, Ch. 11D. Green, The Physics of Particle Detectors, Ch. 11, 12K. Kleinknecht, Ch. 6http:/pdg.lbl.gov/2004/reviews/pardetrpp.pdf,Measuring part
2、icles energies through Electromagnetic and Hadronic interactions,Introduction,Energy of a particle or group of particles is necessarily measured destructively. We must completely stop the particle in our detectors to measure its full energy.The energy is deposited in a localized space, so that posit
3、ion can be determined with accuracy dependent on transverse energy fluctuations and detector design.Accuracy of energy measurement comes from a:Constant term: Uniformity of the detector medium, and aStochastic term: Level of active sampling wrt total detector volumeCalorimetry can thus provide momen
4、tum of a particle redundantly to the inner tracking measurements, useful in cleaning up backgrounds.,Multipurpose Calorimeters,Calorimeter use widespread, has become almost essential.Neutral particles (s, neutrons) are only detected by this. Why?Sampling calorimeters are sometimes used as detectors.
5、Triggers for jets: as collision energies increase, particle multiplicity increases, and we get highly collimated sprays of secondary particles in a localized angular distributions.Can be made modular, and to cover large solid angles. Size scales as ln(E), but B-field tracking goes like E1/2.,Partons
6、 Particles Jets,Processes creating jets are very complicated, and consist of parton fragmentation, then both electromagnetic and hadronic showering in the detector. Reconstructing jets is, naturally, also very difficult. Jet energy scale and reconstruction is one of the largest sources of systematic
7、 error.More on Jets on Monday!,Electron and Interactions,At E 10 MeV, interactions of s and e-s in matter is dominated by e+e- pair production and Bremsstrahlung.,At lower energies, Ionization becomes important.The ratio of the energy loss for these processes is:,Critical Energy: When energy loss du
8、e to Brem and energy loss due to ionization are =.,Electromagnetic Showers,An alternating sequence of interactions leads to a cascade:Primary with E0 energy pair-produces with 54% probability in layer X0 thickOn average, each has E0/2 energyIf E0/2 Ec, they lose energy by BremNext layer X0, charged
9、particle energy decreases to E0/(2e)Brem of avg energy between E0/(2e) and E0/2 is radiatedMean # particles after layer 2X0 is 4Radiated s pair produce again,Cloud chamber photo of electromagnetic cascade between spaced lead plates.,After n generations (dx= nX0), 2n particles, avg energy E0/2n for s
10、hower. Cascade stops: e- energy critical energy Ec= E0/2n. Number of generations: n=ln(E0/Ec)/ln2. Number of particles at shower maximum: Np = 2n = E0/Ec.,EM Shower Properties,Typical properties of electromagnetic showers:# particles at shower maximum Np proportional to E0Track length (depth) of e-
11、and e+ proportional to E0Depth for maximum Xmax increases logarithmically:,Longitudinal energy deposition:,Longitudinal energy deposition for e- in lead, fit to gamma function,Transverse shower dimension: multiple scattering of low energy e-: Moliere Radius:Radial distribution in RM independent of m
12、aterial used! 99% of energy is inside a radius of 3 RM.,Energy Resolution,Energy resolution of ideal detector of infinite dimensions is limited by statistical fluctuations. Example: For Ec=11.8 MeV and detection cut-off Ek=0.5 MeV and a track length of 176 cm/GeV, best resolution Losses of Resolutio
13、n:Shower not contained in detector fluctuation of leakage energy; longitudinal losses are worse than transverse leakage.Statistical fluctuations in number of photoelectrons observed in detector. If is # photoelectrons per unit primary particle E,Sampling fluctuations if the counter is layered with i
14、nactive absorber.If active area is gas or liquid argon, low E e- move at large angles from the shower axis, Landau tail leads to “path length fluctuations”.,Electromagnetic Calorimeter Types,Homogeneous “shower counters”: Best performance from organic scintillating crystals. Example of NaI(Tl) have
15、achieved . Also use lead glass, detects Cerenkov light of electrons, limited by photoelectron statistics. Sampling calorimeters: Layers of inactive absorber (such as Pb) alternating with active detector layers, such as scintillator or liquid. Resolutions 7%/E or so. Liquid noble gases: Counters base
16、d on liquid noble gases (with lead plates, for example) can act as ionization chambers. L Ar - Pb versions obtain 10%/ E. Ionization read out by electrodes attached to plates (no PMTs!). Disadvantage: slow collection times (1 s). Variations in the 1990s: Accordion for fast readout (front/back readou
17、t) and L Kr homogeneous detector (energy&time resolution).,Electromagnetic Calorimeter Types,“lead-scintillator sandwich” calorimeterexotic crystals (BGO, PbW, .)liquid argon calorimeter E/E 18%/E,E/E 20%/E,E/E 1%/E,Energy resolutions:,Hadron Calorimeters,When a strongly interacting particle above 5
18、 GeV enters matter, both inelastic and elastic scattering between particles and nucleons occur.Secondary hadrons examples: and K mesons, p and n. Energy from primary goes to secondary, then tertiary, etc.Cascade only ceases when hadron energies small enough to stop by ionization energy loss or nucle
19、ar absorption.Hadronic Shower: spatial scale for shower development given by nuclear absorption length . Compare X0 for high-Z materials, we see that the size needed for hadron calorimeters is large compared to EM calorimeters.,Compensating Calorimeters,Improvements in energy resolution can be achie
20、ved if showers induced by electrons and hadrons of same energy produce same visible energy (detector response).Requires the losses to be “compensated” in some way.Three methods: Energy lost by nuclear reactions made up for by fission of 238U, liberating n and soft rays. Can get response close to equ
21、al: proton-rich detector em shower decreases, had shower increases due to more nuclear reactions. If have lots of H2, compensation achieved with high absorber material: in inelastic collision of hadrons w/ absorber nuclei, neutrons are produced recoil protons, larger signal. Reduce fluctuation in EM
22、 component: weight individual counter responses, and even response out across the board.,CDF Sampling Calorimeter,calorimeter is arranged in projective “towers” pointing at the interaction regionmost of the depth is for the hadronic part of the calorimeter,CMS Hadron Calorimeter,Not Covered,Shower s
23、hapes in hadron calorimeters Fluctuations in hadronic energy measurementsPosition resolution in the calorimetersShower maximum detectorsNew calorimeter designs for ILC with silicon, tracking for “particle-flow” algorithms.Next Monday, Guest Lecture: Calibrating em and hadron calorimeters, reconstruc
24、ting jets, determining the jet energy scale. (Getting from calorimetry to physics results!)Up next Prof. Conway, statistics and data analysis,Example of Gaussian Distribution,Single hit “residual” in silicon strip detector (distance from hit to known track position):,Example of Binomial Statistics,C
25、DF track trigger efficiency:,Poisson Process,Plot of observed tau lepton pair mass distribution in CDF:(Sorry, no Higgs yet)Note difference between linear and log scales!,The Higgs 2,The most famous plot in high energy physics Tells us the Higgs is close!,Complicated Confidence Interval,All the worlds knowledge about the CKM matrix,
