EDIT - Calorimetry Calorimetry The Standard Model Particles Numerology Electromagnetic Interactions Hadronic Interactions The EM Shower The Hadronic Shower ECAL, HCAL Detector Systems – PF, DRC Calorimeter Futures
EDIT - Calorimetry Calorimetry and Heat Calor = heat (Latin) Destructive readout Total Absorption - linear A 1 TeV jet absorbed in 400 x 20 x 20 cm of water raises the T by ~ 10-12 oK.......
EDIT - Calorimetry The Standard Model Particles Why is Calorimetry crucial? Jets – u,d,s,c,b,g (g, q differ in jets - ID) EM showers – e, γ μ – mip ν – MET (backup) t-> W+b, W->l+ν, q+q Z->l+l,νν, q+q H->Z+Z,W+W,γ+γ,q+q Fast signal - trigger
EDIT - Calorimetry Numerology Size and cross section – p, nuclei For other processes Draw a Feynman diagram Count vertices, propagators and couplings Think a bit, e.g. pg. 56 – weak decays
EDIT - Calorimetry Mean Free Path Use ρz units (gm/cm2) to remove density dependence. Called x in dE/dx for historical reasons – use z here and T not E.
EDIT - Calorimetry Ionization Energy loss → scatter off atomic e (billiards). 2 vertices (α2), incoherent (Z). Time near atom (1/β2) → 1.5 MeV(gm/cm2) - “mip” Mean – but long tail. Most probable Landau is ~ ½ of the mean. (US income dist ?) backup
EDIT - Calorimetry Bremsstrahlung, Pair Production Accelerated projectile (e) in Coulomb field of nucleus. 3 vertices, Larmor – a2. Coherent, e Compton λ ~ 400 fm. Photon 1/k. Photon cannot decay in vacuum. Use nucleus. Same topology as bremsstrahlung.
EDIT - Calorimetry Critical Energy Energy where brem = ionization Projectile is accelerated. Muons do not radiate (backup) Particle id for muons backup
EDIT - Calorimetry The Electromagnetic Shower Incident e or γ interacts by bremsstrahlung or pair production Scale of each “generation” is Xo. Geometric progression.
EDIT - Calorimetry EM Shower Depth EM shower is compact ~ln(T). Below Tc shower dies off by e ionization and γ Compton and photoeffect. EM calorimetry can be compact – scale 20 cm.
EDIT - Calorimetry Low Energy e, γ Interactions Below about 100 keV, photoeffect dominates, then Compton, with pair production threshold ~ 2me~ 1MeV The photons lose by Compton scattering and then by photoelectric Absorption The e lose energy by ionization and multiple scatter
EDIT - Calorimetry Shower's End Much of the shower energy is deposited by particles with T < Tc. The minimum detectable energy depends on the transducer; Si ~ 3.6 eV, scint ~ 100 eV. The basic reactions have θ~m/T (SR) → very narrow. Transverse spread due to multiple Rutherford scatt of e on nucleus. Shower widens as depth increases. Transverse size set by Moliere radius. 95% of shower energy is contained in 2 radii
EDIT - Calorimetry Test Beam – Hanging File e in “ECAL” showers are quite uniform +-Xo Movies – from old (25 yr SSC) test beam data taken at FNAL
EDIT - Calorimetry Strong Interactions ? EM, α = 1/137 overcomes strong αs~ 0.1 due to QM coherence over nucleus → particle ID (ECAL/HCAL)
EDIT - Calorimetry Hadron Showers The shower is ransported from 1 generation to the next by charged π. Less compact than EM shower λA vs Xo. Produced πo--> γγ die off quickly since Xo<< λA Threshold to produce π is >> Tc so many fewer generations, Tπ~ 2Mπ. <n> ~ ln(T), fo = 1/3, π+ πo π- . Nucleus is disrupted (B ~ 8 MeV/nucleon). “Invisible” energy, nuclear recoils, evaporation n (slow). Highly ionizing nuclear fragments (Birks law). May be 20% of total energy with large fluctuations. Transverse size is due to basic processes, pT ~ 0.4 GeV, means RA ~ λA. Expect central EM “core” and wider charged π.
EDIT - Calorimetry Average Depth Very misleading. Not smooth at all backup
EDIT - Calorimetry All Pb Calor 90 Pb plates, 0.11 λ, 3.4 Xo. Total 9.7 λ. Charged π go ~ 9.2 plates, e go ~ 10 Xo ~ 3 plates
EDIT - Calorimetry All Pb Calor The typical “profile” is a bit misleading. Subtract the interaction point and see the fo first generation and hints 9 plates later.
EDIT - Calorimetry Depth for 95% Energy Containment (average) Leakage causes non-linearity and increased resolution Leakage “tail” induced for thin calor. Use “compartments” and overweight deep ones.
EDIT - Calorimetry fo and Fo Simple hadronic shower model – analogue of EM shower. Each generation has fo = 1/3 Each generation has n ~ln(√E) Secondaries share energy equally EM component drops out. Charged pions transport to the next generation fo → Fo because of the transport. For P = 250 GeV, Fo ~ 0.7. Few (3) generations.
EDIT - Calorimetry fo and Fo vs. T Data shows the expected growth in the neutral fraction, from 1/3 at low energy to ~ 0.7 at 250 GeV.
EDIT - Calorimetry Hadronic Shower Composition The effective fo or Fo increases with energy. The “hadronic” is ~ charged π ionization. Nuclei disrupted. There are few generations Tπ >> Tc. Flucuations in The number in the shower limit the hadronic resolution – much worse than EM. Intrinsic.
EDIT - Calorimetry e and h in Hadronic Shower Response to EM energy (e) is not = to response to hadronic energy (h) in general due to binding energy, slow n, heavy fragments..... Typically e/h > 1. There are fluctuations in the neutrals produced in the shower event by event which worsens the energy resolution. The response is also intrinsically nonlinear because Fo depends on energy For a given calorimeter measure Te/Tπ as a function of energy to extract e/h. If e/h = 1, this is a constant and dT is minimized.
EDIT - Calorimetry Constant Term ? Compensation Approximate the dFo/Fo by first generation dfo/fo . For <n> = 9 and e-h = 0.2 there is a “constant term” in the hadronic energy resolution of ~ 3.8 %. Solve this with “compensation” - lower e or raise h. Lowering e hurts ECAL. Raising h by capturing n slows down the HCAL. Not as popular now with stress on precision ECAL (crystals have very bad e/h). Alleviate with “particle flow”? More later.
EDIT - Calorimetry ECAL Design Choices Granularity: there is information in each (Xo)3 volume. But calibration, monitoring (constant term) and cost. Timing: The EM showers are fast. Readout transducer of light (Cerenkov, scint) or charge (Si). Si ~ 8 nsec Scint ~ 15 nsec LA ~ 250 nsec Sampling: Fully active (crystals, noble liquid) homogeneous or sampling (scint, Si)? Readout: Analogue or digital? backup
EDIT - Calorimetry Sampling or Homogeneous? Basic design choice:Fully active has best energy resolution ~ 2 % but no z info and e/h is large. Sampling looses info → poorer energy resolution ~ 10% but best transverse segmentation and info on z shower development.
EDIT - Calorimetry ECAL Crystals Examples backup
EDIT - Calorimetry ECAL Sampling Fluctuations Plate thickness choice – energy resolution vs cost and channel count (z readout) Stochastic coefficient -> fluctuations in the number of shower particles sampled by the active medium. Coefficient goes ~ as square root of the sampling thickness
EDIT - Calorimetry Readout: Analogue or Digital Measure energy of the shower or the number of distinct particles in the shower. There are fluctuations in the deposited energy. Mean vs. most probable. Hard collisions, δ rays ( recall muon “mip”). Noise. Intrinsiclly better to just count the # of shower particles. But that requires extreme granularity to avoid mis-counting.
EDIT - Calorimetry ECAL Energy Resolution Existing ECALs
EDIT - Calorimetry Transducer Speeds Choice is very application specific There is a premium on fast speeds For LHC and “FCC”, not so much for ILC.
EDIT - Calorimetry Summary CMS/ATLAS ECAL Still, both managed to find the Higgs! (CDF, D0)
EDIT - Calorimetry HCAL Design Choices The spatial scale is (λA)3 but information on Fo is also important if e/h > 1. Large detectors. Granularity ~ Xo ? The total depth should be ~ 10 λA. Longitudinal sementation should be a fraction of λA The transverse segmentation should be at least a fraction of λA , perhaps ~ RM early in the shower – fo. It must be hermetic – minimal, gaps, dead material for good MET (υ). It is likely to be the support structure for ECAL and Tracking. Is the HCAL inside the B field coil ($, leakage) or outside (dead material – constant term induced)?
EDIT - Calorimetry HCAL Energy Resolution The small number of shower particles and the invisible energy limit the fractional resolution to be ~ 30 %/√T. Leakage creates a low energy tail ~ /T1/4. Noise and pileup contribute ~ 1/T. For 200 PU with a jet cone R = 0.5 there is ~ 120 GeV of PU energy. Non-uniform construction or calibration error or dead material contribute to a constant term. Non compensatin contribute an intrinsic constant term ~ 4% for e/h = 1.2.
EDIT - Calorimetry Simple 2 TeV Jet In collider detectors the goal is to measure jets, not single hadrons. Make a simple model to explore what is needed. Note that above a Pt of ~ 400 GeV, W → u + d and t → W + b jets merge into a single “fat” jet. zD(z) = a(1-z)b , dσ/dkt2 ~exp(-gkt2). Leads to <n> ~ ln(PJ) <n> = 45, <z> = 0.026 (52 GeV), z = k/PJ <zmax> = 0.24 (400 GeV), leading particle. <kt> = 0.56 GeV, fo = 1/3 Due to D(z) there are large fluctuations in n, z and the neutral energy fraction.
EDIT - Calorimetry Simple Jet - II Many soft fragments – at wide angles Core of jet carrys most of the energy with a few “leading” fragments.
EDIT - Calorimetry Cone Size – 2 TeV Jet, Radius ~ 0.5 The soft fragments do not affect the energy measurement much. High pt jets may merge, e.g. W → u + d. Enables W, top “tags”
EDIT - Calorimetry Toy Model for Jet 2 TeV jet. ECAL: ae = 0.1, be = 0.01. Jet Resolutions? HCAL: e/h = 1.2 ah = 1.0 ,bh = 0.05, or e/h = 1, ah = 0.4, bh = 0.02. Variant – PF (later) for charged π with T < 100 GeV Fractional jet resolution 1%, 5% or 4% in the 3 cases.
EDIT - Calorimetry Complete Detectors The whole is greater than the sum of the parts (see later talk). Calorimetry is a subsystem of a unitary detector at the energy frontier. Tracker is non-destructive → redundant P measurements Vertex pixels – c, b “tags” of weak decays Tracker ionization vs p → particle ID at low p Tracker has dp/p~ p Tracker figure of merit ~ BR2. Charged energy better than calorimeter for low P ~ 200 GeV → Particle Flow (PF). backup backup
EDIT - Calorimetry Muon ID and HCAL Use isolated muons in HCAL for calibration. but also of use in muon ID – recall test beam movie. Impose isolation in leptonic W, Z, H decays.
EDIT - Calorimetry Future Calorimetry Energy Frontier Only- Intensity and Cosmic frontier calorimetry is specialized. Higher mass Higher luminosity(HL-LHC) or higher energy (CLIC, FCC) More PU – use timing within a bunch crossing (4D vertices) ? Use temporal granularity to reduce PU in calorimeters using ancillary detectors (Preshower) which are faster, ~ 30 ps, and more granular. More radiation damage – e.g. liquid scint, green/orange scint/WLS. Radiation hard crystals. Radiation damage will continue to be an issue.
EDIT - Calorimetry PF Strategy If all the shower charged energy in HCAL can be assigned unambiguously to a track P...... CMS HGCAL, CALICE,...
EDIT - Calorimetry Detector Systems, PF, DRC Requires very good segmentation.... Improves jet resolution at low energies where tracking resolution is better. At high energy the jet <n> is very large and jet particles may overlap. In addition, the hadronic showers will overlap leading to the “confusion term” which spoils the PF resolution in P. This makes fine segmentation a PF mandatory. Examples – Calice, CMS/HGCAL
EDIT - Calorimetry Dual Readout Calorimetry No z information or the partition into ECAL and HCAL. Use 2 types of sampling medium with different e/h values, called c and s here and read both out. Do energy scan of e/π to determine (e/h) for c and s. The 2 energies are found on an event by event basis. Each hadron has 2 equations in 2 unknowns, To and fo.Fluctuations are removed, dfo = 0. They are the major cause of energy resolution for single hadrons if e/h is not = 1.
EDIT - Calorimetry DRC T Resolution Improve single particle resolution The DRC will give the best energy resolution for a single hadron. But no z information and showers in jets will overlap. That induces a “confusion” of Ts and Tc. In R&D the transverse granularity was not very great. Without ECAL/HCAL partition e/γ ID and cleanliness is harder.
EDIT - Calorimetry FCC Studies 100 TeV ?, 30 x 1034/(cm2sec), 1000 PU, 7x more ! Largely scaling ATLAS and CMS (HL Upgrades) More granularity ~ ( 5x)2. More z segments ~ 10 PF intrinsic to design LA, Si for signals SiPM for light transducer Calorimetry inside 4 T Solenoid ?
EDIT - Calorimetry 4-d Detectors ? Sort z of the primary vertex w.r.t. precision timing ( ~ 30 ps) detector with ~ 1 nsec bunch crossing @ LHC. For 10 cm vertex → 300 ps spread in vrtx time. CMS MTD.
EDIT - Calorimetry Summary Calorimetry is crucial for HEP detectors ECAL is compact and “simple” HCAL is large and not as well behaved Transducer speed and segmentation are important for PU. Future HEP calorimetry must confront increased PU and radiation. A modern general purpose detector is “unitary”.
EDIT - Calorimetry Neutrino Cross Section Cross section ~ G2mpEv ~ 4 x 10-38 cm2/GeV below W,Z threshold. Particle ID for v MET in calor But – IceCube ?
EDIT - Calorimetry Ionization - II Called dE/dx in literature, dT/(ρz) here