Download Lecture_1_Draft_3 - University of Toronto, Particle Physics and

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
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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 45
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