Particle Detectors for Colliders

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

• These pages also have some notes on accelerators

http://hep.physics.utoronto.ca/~orr/wwwroot/phy2405/Lect.htm

High Energy Physics experiments?

1. Collide Particles

2. Detect Final State

3. Understand Connection of 1 + 2

Accelerators & Beams

Analysis

Detectors

andCME L

p

S

B

R.S. Orr 2009 TRIUMF Summer Institute

Layers of Detector Systems around Collision Point

Generic Detector


Generic Detector

Different Particles detected by different techniques. Tracks of Ionization – Tracking Detectors Showers of Secondary particles – Calorimeters


Generic Detector



ATLAS Detector


ATLAS Detector


Interaction of Charged Particles with Matter• All particle detectors ultimately use

interaction of electric charge with matter– Track Chambers– Calorimeters– Even Neutral particle detectors

• Ionization– Average energy loss– Landau tail

• Multiple Scattering• Cerenkov• Transition Radiation• Electron’s small mass - radiation

0n


Energy Loss to Ionization

• Heavy charged particle interacting with atomic electrons• All electrons with shell at impact parameter b• Energy loss - symmetryTp p

T T T T

dt dxp Fdt e E dt e E dx e E

dx v

• Gauss 4 ENCLOSEDE ndA Q

4

2 4

2

T

T

T

E dA ze

E bdx ze

zeE dx

b

2

2

2 4

2 2

2

2

2

T

T

e

e

zep

bv

pE

m

z eE b

m v b

• Density of electrons

eN

2 4

2

4

2

e

e

ee

dV

bd

dE b E b N

dE b E b N

z e dbdE b N d

b

x

d

v

x

m b


Physical limits of integrationmax

0 min

b

b b

2 4

2

4ln MAX

ee MIN

bdE z eN

dx m v b

• Maximum minimum b

E

• In a classical head-on collision 212 2MAX eE m v

• Relativistically 2 22 212 2 2MAX e eE m v m v

2 4

2 2

2 42

22 2

2

2

2

2 1

2

MAXe MIN

MINe e

MINe

z eE

m v b

z eb

m v m v

z eb

m v


Physical limits of integration

• Time for EM interaction b

tv

• Electrons bound in atoms• Time of interaction must be small, compared to

orbital period, else energy transfer averages to zero

• Orbital period

• Collision time

1

bt

v

1

MAX

b

v

vb

• Put in integration limits

2 32 4

2 2

4ln e

ee

m vdE z eN

dx m v ze


Ionization Loss2 32 4

2 2

4ln e

ee

m vdE z eN

dx m v ze

dE

dx

v 2 3

2 2

1ln

dE mv

dx v ze

• This works for heavy particles like α• Breaks down for PROTONM M

• Correct QED treatment gives Bethe – Bloch equation

2 222 2 2

2 22

22 ln 2e MAX

A e e

m TdE Z zN r m c

dx A I

C

Z

Maximum energy transfer in single collision

Mean excitation potential of material Density correction

Shell correction


Bethe – Bloch Equation2 22

2 2 22 2

22

2 ln 2e MAXA e e

m TdE Z zN r m c

dx A I

C

Z

22 22 0.1535A e e

cmN r m c MeV

g

2 2 22e MAX eM m T m c

• Mean excitation potential This is main parameter in B –B

Hard to calculate

measure

infer I

dE

dx

1.19

712 13

9.76 58.8 13

IeV Z

Z ZI

Z eV ZZ

• Empirically


Relativistic rise & Density Correction2 22

2 2 22 2

22

2 ln 2e MAXA e e

m TdE Z zN r m c

dx A I

C

Z

E

• Electric field polarizes material along path• Far off electrons shielded from field and contribute less

• Polarization greater in condensed materials, hence density correction

dE dE

dx dx


Particle Identification

depends on velocity

Usually measure

determines mass

dE

dx

dE

dx

p M


Particle Identification


Mass Stopping Power Mixtures of Materials

expressed as (mass)x(thickness) is relatively constant over a wide range of materials

dE

dx

Mass

Area 21

,dE dE Z

z f Id d Ax

densityRoughly constant over periodic table

ln variation

dE

dIndependent of material

2

1gm

cmCu or

2

1gm

cmFe, Al, ….

10 MeV proton loses same energy in

Bragg’s Rule

1 2

1 1 2 2

1...

dE dE dE

dx dx dx

i ii

mixture

a A

A fraction by weight

No of atoms of i element molecule

ln ln

mixture i i

mixture i i

i imixture i

i

A a A

Z a Z

a ZI I

Z


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

TOTAL IONIZATION RADIATION

dE dE dE

dx dx dx

• What constitutes a heavy particle, depends on energy scale


Bethe Bloch for electrons

•Projectile deflected

•Projectile and atomic electrons have equal masses

•Also identical particles – statistics

• Equal masses 2E

MAX

TT

2

2

222

2

2

2ln 22

e

A e e FI m c

C

Z

dE Z zN r m c

dx A

identical

Electron PositronF F

non-identical


Bremsstrahlung

• Below ~100 GeV/c only important for electrons

• > 100 GeV/c becomes important for muons

• in the GeV range

22

2 2

1e

c mm

40,000

BB

E eE

e

0 /

0

0

,ov E h

RAD

dE dN h E

dx d

1

ANN

A

atoms /cc

20

RAD

dENE Z

dx

independent of function of material

1322 1

4 ln 18318er Z ZZ f

2,RAD

dEE Z

dx

can emit all energy in a fewphotons -> large fluctuations

ln ,ION

dEE Z

dx


Radiation Length

20

RAD

dENE Z

dx

2

0

dEN Z

E

assume indep of E

00

expx

E E

0ln lnE E 0

1

N

• distance over which the electron energy is reduced by1/e on average• Radiation Length

0

13

2

0

1 1834 1 lnA

e

NZ Z r f z

A Z

• for x expressed in units of 0

0

dEE

dt


Electron Energy Loss

electrons in Cu

approx valid for any material


CRITICAL ENERGY FOR VARIOUS MATERIALS

Ec (MeV)Pb 9.51Cu 24.8Fe 27.4Al 52

Water 92Air 102

RAD ION

dE dE

dx dx

good approximation (3%) except for He


High Energy Muons


Muons in Cu


Cerenkov Radiation

100

1000

10000

100 200 300 400 500 600 700

Wavelength (nm)

Cherenkov Photons / cm / sin

2

2 eV345

2

)(1

)(16

21 sin)(106.412

cmLN AA

nct

ntc

1/cos

2

1

2 22 sindN d

zdx

2 2475 sin photons/cmz 350 nm to 550 nm

measure known

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

2

2 2 2

41 2

4sin2

ee

m c pdz z r

d

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 electronsGaussian cf. experiment

more material 2

2 2

2expP d

probability of scattering through

2 RMS scattering angle


Gaussian Multiple Scattering

For detectors usually interested in RMS scattering angle – projected on a plane

most detectors measure in a plane

0

1

2RMS RMSPLANE SPACE

00 0

13.61 0.038ln

MeV x xz

cp

0

0

0

1

3

3

4 3

RMSPLANE

RMSPLANE

RMSPLANE

xy

xS

Energy Loss Distribution

• So far have discussed

• In general energy loss for a given particle

• For a mono-energetic beam

• distribution of energy losses

• Thick Absorber – Gaussian Energy Loss

• Thin Absorber – Possibility of low probability, high fractional energy transfers

MEAN

dE

dx

MEANE E


Typical Energy Loss in Thin Absorber• Scintillator• Wire Chamber Cell• Si tracker wafer

long tail

• Various Calculations• Landau – most commonly used• Vavilov - “improved” Landau

• Practical Implications

• Use of dE/dx for particle ident - Landau tails cause limitation in separation

• Position in tracking chamber

- Landau tails smear resolution

• Separation of 1 from 2 particles in an ionization/scintillator counter

- Landau tails smear ionization


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

0xI x I e

absorption coefficient


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

• Then drops because not enough energy to eject K-shell electrons

• Dependence on material

eE h Binding Energy

4 5Z


Compton Scattering

Compton Edge – Detector Calibration

2

1 2MAXT h

2e

h

m c


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

13

21 7 1834 1 ln

9 ePAIR

Z Z Nr f zZ

2Z

0

9

7PAIR Closely related to Radiation Length


Photon Absorption as Function of Energy

Pb

MeV

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Particle Detectors for Colliders