Lecture 13: Detectors • Visual Track Detectors• Electronic Ionization Devices• Cerenkov Detectors• Calorimeters• Phototubes & Scintillators• Tricks With Timing• Generic Collider Detector

Sections 4.3, 4.4, 4.5Useful Sections in Martin & Shaw:

Consider a massless qq pair linked by a rotating string with ends moving at the speed of light. At rest, the string stores energy κ per unit length and we assume no transverse oscillations on the string. This configuration has the maximum angular momentum for a given mass and all of both reside in the string - the quarks have none. Consider one little bit of string at a distance r from the middle, with the quarks located at fixed distances R. Accounting for the varying velocity as a function of radial position, calculate both the mass, M, and angular momentum, J, as a function of κ and R.

3sheet 4

R

At rest: dM/dr = κIn motion: dM/dr = κ

= (1-2)-½ = [1-(r/R)2]-½

Thus, M = 2κ [1-(r/R)2]-½ dr∫= κR

Similarly, J = 2κ vr [1-(r/R)2]-½ dr

R

∫ 0

but M = κR

In natural units v = = (r/R)

= (2κR r2 [1-(r/R)2]-½ dr∫ R

∫ 0

= κR2

thus, J = M2/(2κ)

From experimental measurements of J versus M (“Regge trajectories”) it is found that κ 0.18GeV∼ 2 when expressed in natural units. Convert this to an equivalent number of tonnes. ~15

Now consider the “colour charge” contained within a Gaussian surface centred around a quarks and cutting through a flux tube of cross sectional area A . By computing an effective “field strength” (in analogy to electromagnetism), derive an expression for the energy density of the string (i.e. κ) in terms of the colour charge and the area A .

Flux tube

Gaussian surface

In analogy with EM: •Ec = c/c

Ec A = qc/c

Ec = qc/(Ac) Assume A ~ 1 fm2

κ = energy/length = (energy density) x A = ½ c Ec2 A

= qc2/(2Ac)qc

2/(4cħc) = κA/(2ħc)

s ≈ (14.4x104 kg m/s2)(10-15m)2

2 (10-34 J s)(3x108 m/s) = 0.76

Lecture 13: Detectors • Visual Track Detectors• Electronic Ionization Devices• Cerenkov Detectors• Calorimeters• Phototubes & Scintillators• Tricks With Timing• Generic Collider Detector

Section 3.3, Section 3.4

Useful Sections in Martin & Shaw:

Wilson Cloud Chamber:

Antimatter

Anderson 1933

Evaporation-type Cloud Chamber:

Photographic Emulsions

e

Discovery of the Pion (Powell et al., 1947)

e

DONUT (Direct Observation of NU Tau) July, 2000

Donald Glazer (1952)

Bubbles form at nucleation sites in regions of higher electric fields

ionization tracks

Bubble Chamber

Donald Glazer (1952)

Bubbles form at nucleation sites in regions of higher electric fields

ionization tracks

Bubble Chamber

Steve’s Tips for Becoming a Particle Physicist

2) Start Lying

3) Sweat Freely

4) Drink Plenty of Beer

1) Be Lazy

Liquid superheated by sudden expansion

Bubbles allowed togrow over 10ms

then collapsed during compression strokehydrogen,

deuterium,propaneFreon

High beam intensitiesswamp film

Acts as bothtarget & detector

Slow repetition rate

Spatial resolution100200 m

Track digitization cumbersome

Difficult to trigger

Mechanically Complex

Electric field imposed to prevent recombination

Medium must be chemically inactive (so as not to gobble-up drifting electrons)

and have a low ionization threshold (noble gases often work pretty well)

Ionization Detectors

signal smaller than initiallyproduced pairs

signal reflects total amountof ionization

initially free electronsaccelerated and furtherionize mediumsuch that signal is amplified proportional to initial ionization

acceleration causesavalance of pairsleads to dischargewhere signal sizeis independent ofinitial ionization

continuousdischarge(insensitiveto ionization)

minimumionizingparticle

heavilyionizingparticle

E(r) = V0

r log(rout/rin)

Typical Parametersrin = 10-50 mE = 104 VAmplification = 105

Proportional Counter

Multiwire Proportional Counter (MWPC)

Typical wire spacing ~ 2mm

George Charpak

Drift Chamber

Field-shaping wires provide~constant electric field socharges drift to anode wires with~constant velocity (~50mm/s)

Timing measurement comparedwith prompt external trigger canthus yield an accurate position determination (~200m)

use of MWPC indetermination of particle momenta

Time Projection Chamber (TPC)

n p + e + ebut sometimes...n p + e + e

occurs as a single quantum event within a nucleus

''double decay"

but what if e = e ?(Majorana particle)

then the following would be possible:

n p + e + e

e + n p + e ''neutrinoless double decay"

One Application of a TPC:

Example of a radial drift chamber (''Jet Chamber")

Reconstruction of 2-jetevent in the JADEJet Chamber at DESY

Angular segment ofJADE Jet Chamber

Spark Chamber

Silicon Strip Detector

electron-hole pairs instead of electron-ion pairs

etched

3.6 eV required to form electron-hole pair thin wafers still give reasonable signals and good timing (10ns) Spatial resolution 10m

CDF Silicon Tracking Detector

CerenkovRadiation

(c/n)t

cosC = ct/(nvt) = 1/(n)

vt

d2N z2 1

dxdE ℏc 2n2= 1 ( )

# photons ∝ dE ∝ d/2

blue light

CerenkovRadiation

Threshold Cerenkov Counter:

discriminates between particles of similar momentum but different mass (provided things aren’t too relativistic!)

m1 , 1 m2 ,

= (22

)/22

2 = 1 1/2

= 1 m2/E2

(m12/E1

2 m22/E2

2)

(1 m22/E2

2)=

(m12 m2

2)

(E2 m22)

≃

= (m12 m2

2)/p2

1/(n1) = 1 1/n2 = 1

2

just belowthreshold

[(1m22/E2

2) (1m12/E1

2)]

(1m22/E2

2)=

length of radiator needed increasesas the square of the momentum!

( 1 - 1/(22n2) ) = ( 1 - 1

2/22)

helium 3.3x105 123CO2 4.3x104 34pentane 1.7x103 17.2aerogel 0.0750.025 2.74.5H2O 0.33 1.52glass 0.750.46 1.221.37

Medium n1 (thresh)

light detectorson inner surface

Muon Rings

liquidradiator

gaseousradiator

Ring Imaging CHrenkov detector

Above some ''critical" energy, bremsstrahlung and pair production dominate over ionization

EC ~ (600 MeV)/Z

t = 0 1 2 3 4

Depth in radiation lengths

Maximum development will occur when E(t) = EC :

# after t radiation lengths = 2t

Avg energy/particle: E(t) = E0/2t

Assume each electron with E > EC

undergoes bremsstrahlung aftertravelling 1 radiation length, givingup half it’s energy

Assume each photon with E > EC

undergoes pair production aftertravelling 1 radiation length, dividingit’s energy equally

Neglect ionization loss above EC

Assume only collisional loss below EC

log(E0/EC)

log(2)tmax =

Calorimeters

Nmax = E0/EC

Depth of maximum increases logarithmically with primary energy Number of particles at maximum is proportional to primary energy Total track length of particle is proportional to primary energy Fluctuations vary as ≃ 1/N ≃ 1/E0

Typically, for an electromagnetic calorimeter:E 0.05 E EGeV

≃

For hadronic calorimeter, scale set by nuclear absorption length

Scale is set by radiation length: X0 ≃ 37 gm/cm2

iron nuc = 130 gm/cm2

lead nuc = 210 gm/cm2

~ 30% of incident energy is lost by nuclear excitations and theproduction of ''invisible" particles

E 0.5 E EGeV

≃

Examples of Calorimeter Construction:

Photomultiplier Tubes (PMTs) A Typical ''Good" PMT: quantum efficiency30%collection efficiency80%signal risetime2ns

ScintillatorInorganic Usually grown with small admixture of impurity centres.

Electrons created by ionization drift through lattice,are captured by these centres and form an excited state.Light is then emitted on return to the ground state.

Most important example NaI (doped with thallium)

Pros: large light output Cons: relatively slow time response (largely due to electron migration)

Organic Excitation of molecular energy levels.Medium is transparent to produced light.

Why isn’t light self-absorbed??

interatomic spacingpo

tent

ial e

nerg

y

ground state

excited state

Pros: very fast Cons: smaller light output

NaI (Tl) 2.2 250 410 3.7CsI (Tl) 2.4 900 550 4.5BGO 0.5 300 480 7.1 (Bi4Ge3O12)

anthacene 1.0 25 450 1.25toluene 0.7 3 430 0.9polystyrene 0.3 3 350 0.9+ p-terphenyl

Scintillator Relative Decay max Density light yield time (ns) (nm) (gm/cm3)

organic {inorganic {

Some Commonly Used Scintillators:

some ways of coupling plasticscintillator to phototubes toprovide fast timing signal :

t = Lc/

= ( 1 1/2 )1/2

= 1 1/2

≃ 1 1/(22)

t ≃ Lc/2 (1/2

)

= Lc/2 ( m22/E2

2 m12/E1

2 )

≃ Lc/2 ( m22 m1

2 )/E2

Time Of Flight (TOF): An Application of Promt Timing(used to discriminate particle masses)

t = Lc (1/)

High Energy Particle Detectors in a Nutshell: