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, 4.5 Useful 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.

3 sheet 4

R

At rest: dM/dr = κ In motion: dM/dr = γκ

γ = (1-β2)-½ = [1-(r/R)2]-½

Thus, M = 2κ [1-(r/R)2]-½ dr ∫ = κRπ

Similarly, J = 2κ vr [1-(r/R)2]-½ dr

R

∫ 0

but M = κRπ

In natural units v = β = (r/R)

= (2κ/R) r2 [1-(r/R)2]-½ dr ∫ R

∫ 0

= κR2π/2

thus, J = M2/(2πκ)

From experimental measurements of J versus M (“Regge trajectories”) it is found that κ ∼ 0.18GeV2 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 = ρc/εc

Ec A = qc/εc

Ec = qc/(Aεc) Assume A ~ 1 fm2

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

= qc2/(2Aεc) qc

2/(4πεcħc) = κA/(2πħc)

αs ≈ (14.4x104 kg m/s2)(10-15m)2

2π (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 νµ

π-

µ- e-

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

νe

νµ

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 to grow over ∼ 10ms

then collapsed during compression stroke hydrogen,

deuterium, propane Freon

High beam intensities swamp film

Acts as both target & detector

Slow repetition rate

Spatial resolution ∼100-200 µm

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 initially produced pairs

signal reflects total amount of ionization

initially free electrons accelerated and further ionize medium such that signal is amplified proportional to initial ionization

acceleration causes avalance of pairs leads to discharge where signal size is independent of initial ionization

continuous discharge (insensitive to ionization)

minimum ionizing particle

heavily ionizing particle

E(r) = V0 r log(rout/rin)

Typical Parameters rin = 10-50 µm E = 104 V Amplification = 105

Proportional Counter

Multiwire Proportional Counter (MWPC)

Typical wire spacing ~ 2mm

George Charpak

Drift Chamber

Field-shaping wires provide ~constant electric field so charges drift to anode wires with ~constant velocity (~50mm/µs)

Timing measurement compared with prompt external trigger can thus yield an accurate position determination (~200µm)

use of MWPC in determination of particle momenta

Time Projection Chamber (TPC)

n → p + e- + νe but sometimes... n → p + e- + νe

⇐ occurs as a single quantum event ⇐ within a nucleus

''double β-decay"

but what if νe = νe ? (Majorana particle)

then the following would be possible:

n → p + e- + νe

νe + n → p + e- ''neutrinoless double β-decay"

One Application of a TPC:

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

Reconstruction of 2-jet event in the JADE Jet Chamber at DESY

Angular segment of JADE 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 ∼10µm

CDF Silicon Tracking Detector

Cerenkov Radiation

θ

(c/n)t

cosθC = ct/(nvt) = 1/(nβ)

vt

d2Nγ αz2 1 dxdE ℏc β2n2 = 1 - ( ) # photons ∝ dE ∝ dλ/λ2

⇒ blue light

Cerenkov Radiation

Threshold Cerenkov Counter:

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

m1 , β1 m2 , β2

= (β22 - β1

2)/β22

β2 = 1 - 1/γ2

= 1 - m2/E2

(m12/E1

2 - m22/E2

2) (1 - m2

2/E22)

=

(m12 - m2

2) (E2 - m2

2) ≃

= (m12 - m2

2)/p2

1/(nβ1) = 1 1/n2 = β1

2

just below threshold

[(1-m22/E2

2) - (1-m12/E1

2)] (1-m2

2/E22) =

length of radiator needed increases as the square of the momentum!

( 1 - 1/(β22n2) ) = ( 1 - β1

2/β22)

helium 3.3x10-5 123 CO2 4.3x10-4 34 pentane 1.7x10-3 17.2 aerogel 0.075-0.025 2.7-4.5 H2O 0.33 1.52 glass 0.75-0.46 1.22-1.37

Medium n-1 γ (thresh)

light detectors on inner surface

Muon Rings

liquid radiator

gaseous radiator

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 after travelling 1 radiation length, giving up half it’s energy

Assume each photon with E > EC undergoes pair production after travelling 1 radiation length, dividing it’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: ΔE 0.05 E √EGeV

≃

For hadronic calorimeter, scale set by nuclear absorption length

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

iron ⇒ Λnuc = 130 gm/cm2

lead ⇒ Λnuc = 210 gm/cm2

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

ΔE 0.5 E √EGeV

≃

Examples of Calorimeter Construction:

Photomultiplier Tubes (PMTs) A Typical ''Good" PMT: quantum efficiency ∼ 30% collection efficiency ∼ 80% signal risetime ∼2ns

Scintillator Inorganic 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 spacing

pote

ntia

l ene

rgy

ground state

excited state

Pros: very fast Cons: smaller light output

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

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

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

organic { inorganic {

Some Commonly Used Scintillators:

some ways of coupling plastic scintillator to phototubes to provide fast timing signal :

t = Lc/β

1/β = ( 1 - 1/γ2 )-1/2

β2 = 1 - 1/γ2

≃ 1 - 1/(2γ2)

Δt ≃ Lc/2 (1/γ22 - 1/γ1

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)

Δt = Lc (1/β1 - 1/β2)

High Energy Particle Detectors in a Nutshell: