CALORIMETRI ELETTROMAGNETICI

• Introduzione • Interazioni di elettroni e fotoni con la materia • Sciami elettromagnetici • Calorimetri a campionamento e omogenei • Risoluzione in energia • Risoluzione in posizione • Calorimetria di precisione • Calorimetri a cristalli • Il calorimetro di CMS a LHC M. Diemoz, E. Longo INFN and La Sapienza University - Roma 1

J/  (3.1 GeV)  (1.8 GeV)  (9.5 GeV) W (80 GeV) Z (91 GeV) t (180 GeV) H, SUSY, …… M. Diemoz, E. Longo

Modern milestones

e+e e+e  p N  e+e  +  -hadrons e+e-X   ’   X e+e    e  ,  p N p p    + W  -X X  e  ,  1974 1975 1977 1983 p p  Z X  e+e ,  +  p p  tt X  WbWb WW  e  , qql  p p  X leptons X  1983 1995 20?? Tevatron, LHC INFN and La Sapienza University - Roma 2

Particle spectroscopy in radiative decays

e+e   ’  X M. Diemoz, E. Longo INFN and La Sapienza University - Roma e+e   (3S)  X 3

Higgs Boson Search

0 0.001

50 LEP 0.01

100

Natural width (GeV)

1 10 200

Higgs Mass (GeV)

400 100 800 LHC H  H  ZZ *  4 leptons H  ZZ  4 leptons H  WW or ZZjj M. Diemoz, E. Longo INFN and La Sapienza University - Roma 4

Higgs

 

at LHC

Longitudinal view of the CMS detector (one quadrant)

M. Diemoz, E. Longo INFN and La Sapienza University - Roma 5

E e -

Calorimeters: a simple concept

electric optical

S

Convert energy to detector response

S :

M. Diemoz, E. Longo

E

of incident particle

S



E

INFN and La Sapienza University - Roma thermal acoustic 6

Calorimeters: some features

• • Detection of both charged and neutral particles Particle identification by simple topological algorithms • Detection based on stochastic processes precision increases with E • Dimensions necessary to containment  lnE compactness • Segmentation measure of position and direction • Fast high rate capability, trigger M. Diemoz, E. Longo INFN and La Sapienza University - Roma 7

Electromagnetic showers

In matter electrons and photons loose energy interacting with nuclei and atomic electrons Electrons • ionization (atomic electrons) • bremsstrahlung (nuclear) Photons • photoelectric effect (atomic electrons) • Compton scattering (atomic electrons) • pair production (nuclear) Above 1 GeV radiative processes dominate energy loss by e/  M. Diemoz, E. Longo INFN and La Sapienza University - Roma 8

Electromagnetic showers

Energy loss - electrons • ionization    Z ;   ln E/m e mean energy loss (Bethe-Bloch) M. Diemoz, E. Longo INFN and La Sapienza University - Roma 9

Electromagnetic showers

Energy loss- electrons • bremsstrahlung  energy loss  dE dx  Z 2 E m 2      1 Radiation length : thickness of material that reduces the mean energy of a beam of high energy electrons by a factor e  Z(Z+1) ; lnE/m e for E<1 GeV independent of energy above M. Diemoz, E. Longo INFN and La Sapienza University - Roma 10

Electromagnetic showers

Energy loss - electrons • Critical energy

E c :

610 MeV E c  Z + 1 .

24 (solids, liquids) Strongly material dependent, it scales as 1/Z (eg. 7 MeV for lead) M. Diemoz, E. Longo INFN and La Sapienza University - Roma 11

Electromagnetic showers

Energy loss - photons • photo-electric effect 7 2  pe  Z 5  4 m e c 2 E 

  Z

5

,E

3.5

• compton scattering  c  Z ln E E  

  Z,E

1 • pair production occours if E   pair  7 9 A N A 1 X 0 > 2m e c 2 • • •   Z(Z+1) ; lnE/m e for E<1 independent of energy above 1 GeV Probability of conversion in 1 X 0 Mean free path L pair = 9/7 X 0 (  is GeV e -7/9 disappears) M. Diemoz, E. Longo INFN and La Sapienza University - Roma 12

Electromagnetic showers

Energy loss - photons Z = 6 Z = 82 M. Diemoz, E. Longo INFN and La Sapienza University - Roma 13

Electromagnetic showers

A simple model (1) M. Diemoz, E. Longo INFN and La Sapienza University - Roma 14

Electromagnetic showers

A simple model (2) Above 1 GeV the dominant processes, bremsstrahlung for e + and e and pair production for , become energy independent Trough a succession of these energy loss mechanisms an electromagnetic cascade is propagated until the energy of charged secondaries has been degraded to the regime dominated by ionization loss (below E c ) Below E c a slow decrease in number of particles occurs as electrons are stopped and photons absorbed M. Diemoz, E. Longo INFN and La Sapienza University - Roma 15

Electromagnetic showers

A simple model (3) E 0 •In 1X 0 an e loses about 2/3 a high energy  of its has a probability E of 7/9 of pair conversion •Assume X 0 as a generation length •In each generation the number of particle increases by a factor 2 @ D x=X 0  e+ e- E=E 0 /2 @ D x=tX 0 N(t) = 2 @ t max X 0 (shower max) t E(t) = E @ 0 D / 2 t x=2X 0 e   e’ E’= E 0 /4 E(t max ) = E c E 0 / 2 t max = E c t max = ln(E 0 /E c )/ln(2) N(t max ) = 2 E 0 /E c -1 M. Diemoz, E. Longo INFN and La Sapienza University - Roma 16

Electromagnetic showers

Parametrizations

dE



t



e

 

t dt

Longo e Sestili ‘75 Parametrization of energy deposition N tot   E 0 /E c t max = 1.4 ln(E 0 /E c ) Longitudinal containment

E c



1/Z

t 95% = t max + 0.08Z + 9.6

• shower max • shower tail M. Diemoz, E. Longo INFN and La Sapienza University - Roma 17

Electromagnetic showers

Parametrizations Transverse shower profile • Multiple scattering make electrons move away from shower axis • Photons with energies in the region of minimal absorption can travel far away from shower axis Molière radius sets transverse shower size, it gives the average lateral deflection of critical energy electrons after traversing 1X 0 R M  21 MeV X 0 E C R M  X 0 E C  A ( Z Z  1 ) 75% E 0 within 1R M , 95% within 2R M , 99% within 3.5R

M M. Diemoz, E. Longo INFN and La Sapienza University - Roma 18

Electromagnetic showers

Parametrizations Central core: multiple scattering M. Diemoz, E. Longo Peripheral halo: propagation of less attenuated photons, widens with depth of the shower INFN and La Sapienza University - Roma 19

Electromagnetic showers

Energy loss detection

The energy deposited in the calorimeters is converted to active detector response

• E vis  E dep  E 0 Main conversion mechanism • Cerenkov radiation from e  • Scintillation from molecules response  total track length • Ionization of the detection medium Different energy threshold signal detectability E s for M. Diemoz, E. Longo INFN and La Sapienza University - Roma 20

Electromagnetic calorimeters

Energy resolution Intrinsic limit Detectable signal is proportional to the total track length of e+ and e in the active material, intrinsic limit on energy resolution is given by the fluctuations in fraction of initial energy that generates detectable signal N tot  E E C 0 Total track length f Detectable track length s fraction of N tot with T r Fluctuations in track length: Poisson process = f s E > E s T 0 Fix E 0 M. Diemoz, E. Longo  ( )  E 1 f s E C X 0  1 f s  E Z A INFN and La Sapienza University - Roma T 0  N tot X 0  E E C 0 X 0   ( ) r  T r 1 T r  • maximize f s • minimize Z/A 21 1 E 0

Electromagnetic calorimeters

Energy resolution Sampling calorimeters: shower is sampled by layers of active medium (low-Z) alternated with dense radiator (high Z ) material. • Limited energy resolution • Detailed shower shape information • Cost d active layers negligible in the shower development • only a fraction of the shower energy is dissipated in the active medium • energy resolution is dominated by fluctuations in energy deposited in active layers: sampling fluctuations M. Diemoz, E. Longo INFN and La Sapienza University - Roma 22

Sampling electromagnetic showers

Cloud chamber photograph of e.m. shower developing in lead plates (thickness from top down 1.1, 1.1, 0.13 X 0 ) exposed to cosmic radiation M. Diemoz, E. Longo INFN and La Sapienza University - Roma 23



Electromagnetic calorimeters

Energy resolution Total track length T r  f s T 0  f s N tot X abs 0  f s E E abs C X abs 0 Number of crossings of active layers at distance d

N r



T r d



E f s E C abs X

0

abs

(

d d



X

0 ) Resolution scales with sampling thickness 

E

 1

N r

 1

f s E C t abs E

M. Diemoz, E. Longo INFN and La Sapienza University - Roma  24

Electromagnetic calorimeters

Energy resolution Homogeneous calorimeters: all the energy is deposited in the active medium. Absorber  active medium • Excellent energy resolution • No information on longitudinal shower shape • Cost All e+e- over threshold produce a signal M. Diemoz, E. Longo  ( E )  E 1 f s  INFN and La Sapienza University - Roma

f s



E

0 

N part E s E

0 25

Electromagnetic calorimeters

Energy resolution Compare processes with different energy threshold Scintillating crystals E s   E gap ~ eV  10 2  10 4  / MeV  / E ~ ( 1  3 )% / E ( GeV ) Lowest possible limit Cherenkov radiators   1  E s n  10  30 ~ 0 .

7 MeV  / MeV  / E ~ ( 10  5 )% / E ( GeV ) M. Diemoz, E. Longo INFN and La Sapienza University - Roma 26

• •

Electromagnetic calorimeters

Energy resolution • Energy resolution of a calorimeter can be parametrised as a  ( ) E  a E  b E  c  means quadratic sum the

stocastic term

accounts for any kind of Poisson-like fluctuations • natural merit of homogeneous calorimeters • several contributions add to the “intrinsic one” b the

noise term

responsible for degradation of low energy resolution • mainly the energy equivalent of the electronic noise • contribution from pileup: the fluctuation of energy entering the measurement area from sources other than the primary particle c the

constant term

dominates at high energy • its relevance is strictly connected to the small value of a • it is mostly dominated by the stability of calibration • contributions from energy leakage, non uniformity of signal generation and/or collection, loss of energy in dead materials,… M. Diemoz, E. Longo INFN and La Sapienza University - Roma 27

0.1

Classic calorimeters

sampling calorimeters ALEPH Crystal Ball CLEO II 0.01

crystal calorimeters L3 UA2 0.001

0.01

M. Diemoz, E. Longo 0.1

1 10 Energy (GeV) INFN and La Sapienza University - Roma 100 1000 28

Modern calorimeters

KLOE sampling calorimeters 0.1

0.01

TAPS Belle BaBar KTeV crystal calorimeters ATLAS CMS 0.001

0.01

M. Diemoz, E. Longo 0.1

1 10 Energy (GeV) INFN and La Sapienza University - Roma 100 1000 29

Electromagnetic calorimeters

Position resolution • Reconstruction of invariant masses of particles decaying into photons, electron identification using match with track measured in tracking devices • Impact position of showers is determined using the transverse (and longitudinal) energy distribution in calorimeter cells • Method based on center of gravity (COG) calculation • works for projective geometry and particles coming from the interaction vertex • calorimeter cell size d  1R M • Typical resolutions: few mm/  E M. Diemoz, E. Longo INFN and La Sapienza University - Roma 30

Electromagnetic calorimeters

Position resolution 1 4 7 2 5 8 3 6 9 X cog  d  9  1 9 1 E E i x i i • Needs corrections to account for finite cell size effect L3

X cog (mm)

31 M. Diemoz, E. Longo INFN and La Sapienza University - Roma

Electromagnetic calorimeters

Position resolution L3 d = 0.86 R M M. Diemoz, E. Longo INFN and La Sapienza University - Roma 32