1. 880.P20 Winter 2006 Richard Kass 1 Energy Measurement (Calorimetry) Why measure energy ? I) Not always practical to measure momentum. An important contribution to momentum resolution is proportional to the momentum. Example: suppose we want to measure the momentum of a charged particle such that we can tell whether it is positively or negatively charged (to within 3  ). We demand:  p /p < 0.33 From previous notes, we found for measuring trajectory in a wire chamber (e.g. drift chamber) Use BaBar or CDF-like parameters: B=1T, L=1m, n=100,  =150  m and find p  : Thus above  250 GeV/c we can’t reliably measure the charge of the particle at the 3  level.  There are practical limits on the values of B, L, , n, etc. II) Some interesting particles do not have electrical charge. Momentum measurement using B-field only works for charged particles. What about photons,  0 ’s and  ’s (both decay to  ), K L ’s, neutrons, etc ?

2. 880.P20 Winter 2006 Richard Kass 2 Energy Measurement (Calorimetry) A calorimeter is used to measure the energy of a charged and/or neutral particle The calorimeter should absorb all of the energy of an incident particle Energy measurement by a calorimeter is a DESTRUCTIVE process. Original particle no longer exists after the measurement. Calorimeter usually located behind charged particle tracking chambers MWPCs, drift chambers, silicon trackers are non-destructive measuring devices The energy resolution of a calorimeter is determined by many factors: Actual energy deposited in calorimeter (sampling fluctuations) Leakage of energy out of the calorimeter Noise (e.g. from electronics or pickup) Ion or light collection efficiency Usually, the dominant term in the energy resolution is due to sampling fluctuations which are Poisson in nature. Thus this term in the energy resolution varies like: A is a constant A more complete description of the energy resolution is: B=contribution due to electronics (e.g. ADC resolution) C=contribution due to calibration errors and other systematic effects D=contribution due to energy leakage Since C and D are usually small energy resolution improves as E increases. This is different than momentum resolution which gets worse as momentum increases.

3. 880.P20 Winter 2006 Richard Kass 3 Calorimetry Calorimeter information can also be used to: identify particles (e.g.  ’s, e’s) measure space coordinates of particles (no B-field necessary) form a “trigger” to signal an interesting event eliminate background events (e.g. cosmic rays, beam spill) can be optimized to measure electromagnetic or hadronic energy Calorimeter usually divided into active and passive parts: Active: responsible for generation of signal (e.g. ionization, light) Passive: responsible for creating the “shower” Many choices for the “active” material in a calorimeter: inorganic crystals (CsI used by CLEO, BELLE, BABAR) organic crystals (ancthracene) {mainly used a reference for light output} plastic scintillator (ZEUS, CDF) liquid scintillator (used by miniBoone) Noble liquids (liquid argon used by D0, ATLAS) gas (similar gases as used by wire proportional chambers) glass (leaded or doped with scintillator) water (SuperK) Many choices for the “passive” material in a calorimeter: high density stuff: marble, iron, steel, lead, depleted uranium lower(er) density stuff: sand, ice, water

4. 880.P20 Winter 2006 Richard Kass 4 “Typical” Calorimeters From PDG 2004

5. 880.P20 Winter 2006 Richard Kass 5 Energy Deposition and Showering The key to calorimetry is the showering process. In a shower the original particle interacts with the passive material creating many lower energy particles. The low energy particles deposit energy (via ionization) in the active material. The amount of ionization (or light) is proportional to the amount of energy deposited in the calorimeter. Cloud chamber photo of an electromagnetic shower. A high energy electron initiates the shower. The electron radiates photons via bremsstrahlung when it goes through the first lead plate. The photons are converted to electrons and positrons by the lead and they in turn create new photons. This process continues until the photons are no longer energetic enough to undergo pair production. Lead plates

6. 880.P20 Winter 2006 Richard Kass 6 Electromagnetic Shower Recall: for  energies above 10 MeV the dominant EM process is pair production. Consider an electron with energy E>> E c. E c is the critical energy: The electron is incident on some material that is many radiation lengths (R L ) thick. Consider the following simple model of an electromagnetic shower: a) Each electron with E > E c travels 1 R L then gives up half its energy to a photon via bremsstrahlung b) Each photon with E > E c travels 1 R L then undergoes pair production with E - =E + =E  /2. c) Electrons and positrons E < E c with do not radiate energy. d) Neglect ionization energy loss for E > E c. #R L #e + +e - #  ’s 0 1 0 0-1 1 1 1-2 3 1 2-3 5 3

7. 880.P20 Winter 2006 Richard Kass 7 Electromagnetic Showers From this simple model we can make several “predictions”: The number of particles (N) after t radiation lengths is: N(t)=N e+ (t)+N e- (t)+N  (t)= 2 t =e tln2 Given an electron with incident energy E 0 the average energy E(t) of the particles at depth t is: E(t)=E 0 /N(t)= E 0 / 2 t The shower has the maximum number of particles when E(t)=E c : t max =ln(E o /E c )/ln2 N max = E o /E c Past the distance t max the shower dies out quickly. The shower also spreads laterally. The lateral spread is characterized by the Moliere radius, R m : R m =(21MeV)R L /E c  95% of the shower is within  2R m. To understand energy deposition in more detail we use a Monte Carlo program or build a test module and put it in a beam. Depth in radiation lengths Energy deposition/unit Radius (R m units) Intensity

8. 880.P20 Winter 2006 Richard Kass 8 Electromagnetic vs Hadronic Showers Hadronic showers are more complicated than EM showers Strong and weak interactions are involved in the hadronic shower process Energy resolution of hadronic calorimeter usually worse than EM calorimeter neutrinos leak energy out of calorimeter muons will not usually be absorbed by calorimeter (unlikely to bremsstrahlung) long lived particles (K s, K L,  ) may escape calorimeter before decaying or interacting EM shower Hadronic shower MC simulation of hadronic (proton) and EM shower (photon). Hadronic showers typically have larger lateral spread compared with EM showers.

9. 880.P20 Winter 2006 Richard Kass 9 Sampling Calorimeters Sampling calorimeters have active and passive material interleaved. A few typical examples of SC’s and their active material are given below. a)Scintillator b)Scintillator with wave shifter readout c)liquid argon with ionization chamber readout d)Gas with MWPC readout For a)-d) the passive material could be lead or iron. Material Properties R L (cm)E c (MeV) a (cm) Lead 0.56 7.417.2 Iron 1.76 20.716.8 Tungsten 0.35 8.0 9.6  a = nuclear absorption length Energy Resolution

10. 880.P20 Winter 2006 Richard Kass 10 Energy vs Momentum Resolution Guidelines for the design of a lead sampling calorimeter: Longitudinal thickness necessary to contain shower: 98% of shower contained in 2.5t max =2.5ln(E o /E c )/ln2 For E 0 =5 GeV   13.1 cm For E 0 =100 GeV   19.2 cm Lateral thickness necessary to contain EM shower: 2 Moliere Radi contains 95% of shower (approx. independent of energy) R m =(21MeV)R L /E c =1.6 cm   3.2 cm Compare above lead sampling calorimeter with drift chamber+B-field: Let  E /E = 10%/E 1/2  E /E= 4.5% @ 5 GeV  E /E= 1% @ 100 GeV For “BaBar/CDF” system (B=1T, L=1m, n=100,  =150  m) Calculate the following for momentum resolution (not including MS, angle piece)  P /p= 0.65% @5 GeV  p /p= 13% @ 100 GeV The two resolutions are equal when: For high energy particles p  E. p=18 GeV/c for our “typical” systems (A=0.1, B=1T, L=1m, n=100,  = 150  m).

11. 880.P20 Winter 2006 Richard Kass 11 Crystal Calorimeters These calorimeters have only active elements (e. g. crystals) that combine a short radiation length with large light output. Material Properties R L (cm)R m (cm) a (cm) light energy resolution (%) experiments NaI 2.59 4.541.4scintillator2.5/E 1/4 crystal ball CsI(TI) 1.85 3.836.5scintillator2.2/E 1/4 CLEO, BABAR, BELLE Lead glass 2.6 3.738.0cerenkov5/E 1/2 OPAL, VENUS  a = nuclear absorption length Crystal ball (  1000 NaI crystals) CLEO II-III CsI crystals (  8000) Drift chamber BaBar and Belle also have CsI calorimeters, but CLEO’s is the best!

12. 880.P20 Winter 2006 Richard Kass 12 Electromagnetic Calorimeter (EMC) The BaBar Calorimeter BaBar EM calorimeter uses CsI crystals 5760 crystals in barrel 820 crystals in forward region each crystal has 2 photodiodes Energy resolutionangular resolution

13. 880.P20 Winter 2006 Richard Kass 13 Particle ID with Calorimeters electron/positron: Charged particle undergoes EM shower in calorimeter, compare momentum (measured in drift chamber) with energy, require E/p  1. Not efficient when electron has same energy as a minimum ionizing particle (both have E/p  1), also background from reactions:    0 X. photon: EM shower in calorimeter not matched to charged track in drift chamber. muon: Charged track in drift chamber that does not shower in EM calorimeter or interact in hadron calorimeter. Background from pions (and kaons) that decay in flight (  ) and/or non-interacting  /K. neutrino: Compare visible energy (calorimeter) with measured momentum (drift chamber) and look for imbalance in event. Could be more than one neutrino missing! neutron or K L : Hadronic shower in calorimeter that does not match to charged track in drift chamber. Need a hadronic calorimeter.  0,  : measure invariant mass of  combinations. Problems: How do you tell the charge of track initiating the shower?? What about neutrinos?