introduction to particle physics i · the ionisation energy loss of a singly charged particle...
TRANSCRIPT
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Introduction to Particle Physics I
Risto Orava Spring 2017
particle detection
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Lecture II particle detection
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outline • Lecture I: Introduction, the Standard Model • Lecture II: Particle detection • Lecture III: Relativistic kinematics • Lectures IV: Decay rates and cross sections • Lecture V: The Dirac equation • Lecture VI: Particle exchange • Lecture VII: Electron-positron annihilation
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outline continued... • Lecture VIII: Electron-proton elastic
scattering • Lecture IX: Deeply inelastic scattering • Lecture X: Symmetries and the quark
model
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interactions with matter 1. Charged particles ( only e- & p stable)
• ionization and excitation • bremsstrahlung • scattering in the Coulomb field of atoms • inelastic scattering
2. Neutral particles (only ν stable) • elastic&inelastic scattering
3. Electromagnetic radiation (γ) • photoelectric effect • Compton scattering • pair production
unstable particles decay after a distance of d = γvτγ = 1/√(1-v2/c2), τ = life time in rest frame
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• detection via transfer of energy by ionization or excitation of atomic electrons.
• most of the energy loss from ionization, in gases typical loss per ionization electron about 30 eV. • the ionized electrons behave as dE/E2 - most electrons have small
energies. • some electrons have enough energy for extra ionization (δ-rays or
knock-on electrons). In argon, an average of 30 primary ionizations/cm, and a total of some 100 electrons/cm are ionized.
interactions with matter
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Bethe – Bloch Formula
dEdx
≈ −4π!2c2α 2 nZmev
2 ln(2β 2γ 2mec
2
Ie)−β 2
⎡
⎣⎢
⎤
⎦⎥
the ionisation energy loss of a singly charged particle (v=βc) expressed by Hans Bethe and Felix Bloch in the 1930’s Bethe-Bloch Formula:
Ie is the ionization potential averaged over all the atomic electrons (Ie ≈ 10 Z eV) – falls as 1/β2 (β-5/3) to a minimum, then a broad minimum at βγ ≈ 4, and a slow relativistic rise with lnγ2. The relativistic rise is cancelled at high γby the ”density effect”, i.e. polarization of the medium screens more distant atoms. here dE/dx [MeVg-1cm2] depends only on β. Valid for heavy particles (m > mµ), only. Electrons & positrons require special treatment (mproj = mtgt) + Bremsstrahlung! Z/A does not differ much (H2 a special case) Note:
βγ =v / c
1− (v / c)2=pmc
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• most relativistic particles near the minimum ≈1.5 MeV/g/cm2; Al has a density of 2.7 g/cm3, a ”minimum ionizing particle” passing through 1cm of Al loses about 4 MeV of energy • the shallow rise above γ ≈ 3; the ”relativistic rise” - due to the relativistic contraction of the EM fields. • in liquids and solids, em field is effectively screened as δ(γ) ⇒ Fermi plateau. • dE/dx depends on particle velocity, used to identify particles up to E ≈ 1 GeV.
Bethe – Bloch Formula...
dE/d
x
p GeV/c
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nuclear interactions... • long lived or stable charged particles, like π±,K±,p±,n,Ko, can be
identified by their energy loss characteristics in matter:
e absorbed by 35cm of Fe π±,K±,p± absorbed by 1.7m of Fe µ± not absorbed by 1.7m of Fe
• for the long life time or stable neutral particles
γ absorbed by 35cm of Fe n,Ko absorbed by 1.7m of Fe νf’s not absorbed by 1.7m of Fe
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Delphi measurements
p (GeV/c)
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charged particle interactions • rate of energy loss with distance (dE/dx) depends on
the momentum and particle type • Bethe-Bloch formula for a given medium, and v ≈ c:
relativistic rise
~log γ
22 1/1 log)/1(/ βγγβ −=≈dxdE
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1ρdEdx
≈ −4π!2c2α 2
mev2mu
ZAln(2β
2γ 2mec2
Ie)−β 2
⎡
⎣⎢
⎤
⎦⎥
charged particle interactions - the rate of ionisation energy loss mainly depends on material density ρ
- express the number density of atoms as n = ρ/(Amu) (A = atomic mass number, mu= 1.66 ×10-27 kg = unified atomic mass unit)
- Bethe-Bloch formula now becomes.
- dE/dx (usually expressed in units MeV g-1cm2) proportional to Z/A (≈ constant); a mip has βγ ≈ 3.
- an example: a 10 GeV muon loses some 13 MeV cm-1 in Fe
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primary and total Ionization - fast charged particles ionize the atoms of a medium. - primary ionization often releases electrons which are energetic enough to
ionize other atoms. - total number of created electron-ion –pairs (ΔE=total energy loss,
Wi=effective average energy loss/pair):
primary ionization total ionization
ntotal =ΔEWi
=
dEdx
Δx
Wi
≈ (3− 4) ⋅nprimary
Note: The actual no. of primary electron-ion –pairs is Poisson distributed: The detection efficiency is therefore limited to: For thin layers, edet can then be significantly lower than this. For example, in Argon of d=1mm ⇒ nprimary=2.5 ⇒ εdet=0.92.
( )!
m nn eP mm
−
=
det 1 (0) 1 nP eε −= − = −
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Landau tails - real detectors have finite granularity- do not measure <dE/dx>, but the energy ΔE deposited within a layer of finite thickness δx. ΔE results from a number of collisions, i, with energy transfer, Ei, and a cross section of dσ/dE. - for thin layers (and low density materials): a few collisions, some with high energy transfer ⇒ energy loss distributions show large fluctuations towards high losses: ”Landau tails” (For thick layers and high density materials: many collisions, Central Limit Theorem ⇒Gaussian distributions)
belo
w e
xcita
tion
thre
shol
d
exci
tatio
n
ionization by close collisions, δ-electrons
energy transfer/photon exchange
rela
tive
prob
abili
ty
- how to relate F(ΔE,δx) to dσ/dE? Williams (1929), Landau (1944), Allison & Cobb (1980) etc. - Monte Carlo: (1) divide the absorber into thin layers. probability for any energy transfer within a slice is low. (2) choose energy transfer randomly according to the distribution above, (3) sum over the slices.
ioni
zatio
n by
a
dist
ant c
ollis
ion
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particle detectors
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• a historical event: one of the eight beam particles (K- at 4.2 GeV/c) entering the chamber, interacts with a proton:
K-p → Ω-K+Ko
followed by the decays
Ko → π+π-
Ω- → ΛK-
Λ → pπ- K- → π-πο
bubble chambers...
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17 Introduction to Particle Physics Lecture IX - BC picture 1 R. Orava Spring 2005
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18
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a gas ionization chamber
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spark chambers
HV pulser
plastic scintillator trigger counter
coincidence circuit
plastic scintillator trigger counter
cosmic muon
-10kV
Plate Gaps: 0.635cm Gas: 90% Ne + 10% He
a cosmic muon triggers the scintillators at top & bottom the pulser charges alternate plates to a 10kV potential difference the cosmic muon strips electrons from the He & Ne atoms, leaves a ionization trail behind the trail serves as a path of least resistance for a spark to jump across the potential difference between the plates ⇒ pattern of sparks in the 6 spark chambers traces the muon trajectory
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21
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gaseous tracking detectors – proportional tube - measures a space-point
• ionisation process yields electron-ion pairs • electrons attracted towards anode wire (r=a) • Electric field E = V0 / r log (b/a) (cathode, r=b) • as r → a , E → large : avalanche multiplication occurs due to
secondary ionisation by electrons • signal amplitude proportional to anode voltage • electron drift time * velocity = drift distance
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gaseous tracking detectors – multi-wire proportional chamber – measures space-points on many
tracks • cathode planes and a large number of anode wires • operates like a proportional tube • electron drift time * velocity = drift distance
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gaseous tracking detectors – drift chamber - measures space point(s) on many tracks
• replace cathode planes with wires • use additional ‘field shaping wires’ • longer drift distances possible • can sample position of tracks at many depths
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the MWPC
Georges Charpak began work at CERN in 1959, after working on spark chambers, invented the wire chamber 1968, for which he was awarded the physics Nobel in 1992.
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time projection chambers – time projection chamber (TPC) – measures space points in 3D
• large (2m long, 2m diameter) ionisation drift volume • central cathode plane and anode wire planes at ends • measure drift time (z-coordinate) and position of anode ‘hits’ (x-
y coordinates) • measure dE/dx energy loss from signal amplitudes
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the gas electron multiplier – gem - - new generation gas amplified detectors
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scintillation counter – ”hodoscope” 86
incident charged particle
photo cathode
focusing grid
pm base
- HT +
anode
output volts
- the scintillator covered by a non-transparent material (black tape), connected to the PM by a light guide.
light guide scintillator photomultiplier
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photomultiplier tube (PMT) 87
the dynones connected to a resistance chain in the external circuit, each one is at a succesively higher potential from cathode to anode.
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Detector Type
Resolution Time
Dead Time
Bubble Chamber 1ms 50ms Spark Chamber* a few ms a few ms Proportional Chamber 50ns 200ns Drift Chamber 2ns 100ns Scintillator 150ps 10ns Silicon Strip <15ns* unknown
detector characteristics
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measurements - observables
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basic observables " momentum
" time-of-flight
" energy loss
" particle identity
" invariant mass
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observables
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data analysis
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momentum " definition
" Newtonian mechanics: " special relativity
How is the momentum of a particle measured?
mvp =mvp γ=
2cv11
)/(−=γ
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momentum " arrange a constant magnetic field B into the spectrometer volume
" particles with electrical charges, velocity v, are deflected by the Lorentz force:
" Since the Lorentz force acts in perpedicular to the direction of the B field, it causes a ’centripetal’ force:
" particle momentum is now obtained as:
BvqFM!!
×=
RmvF
2
C =
qBRmvp == γ
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• curvature of a charged track: in magnetic field a charged particle moves along a helical track
• radius of the helix is given by:
• for a unit charge use: • also holds for relativistic particles
3-momentum
qBpR θsin
= Bv!! and between angle theis θ
meters.in R and Teslain GeV/c,in with 3.0/sin BpBpR θ=
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3-momentum
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example: track chamber
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track reconstruction
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track fit A 200 MeV/c track in a storage ring detector in the rφ-plane from a Monte Carlo simulation. The curve shown is a circle fitted to the data points. The data points are two accurate hits measured in a silicon vertex detector, and hits measured in two drift chambers. Two hits with a reduced accuracy are measured between the two drift chambers in a special z-chamber. The χ2 of the fit is, due to multiple scattering, rather large. The deviations of the hits from the circle are however not visible in this plot (see next page).
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L
s
Θ ρ
x
y
2 2
( / ) 0.3 ( )0.3sin
2 2 2sin 0.3
0.3(1 cos )2 8 8
T
T
T
T T
T
p qBrp GeV c B TmL LB
pp p LB
L Bsp
ρ
ρ
ρ ρ
=
=
Θ Θ= ≈ ⇒Θ ≈
Δ = Θ ≈
Θ Θ= − ≈ ≈
1 32
2
2
The sagitta s is determined by three measurements with error: ( )2
3 3( ) ( )8( ) ( ) 2 20.3
For N equidistant measurements one obtains:
( ) ( ) 720 (for N0.3 4
TmeasT
T
measT T
T
x xx x
x x pp sp s s BL
p x pp BL N
σ
σ σσ σ
σ σ
+= −
= = =
=+
10)
Example: 1 / , 1 , 1 , ( ) 200 , 10( ) 0.5% (s=3.75cm)
T
measT
T
p GeV c L m B T x m Npp
σ µ
σ
≥
= = = = =
≈
3-momentum...
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detection of electrons & photons
• at large energies, E > Ecritical, energy loss dominated by bremsstrahlung: photon emission in the electrostatic field created by the atomic nuclei
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electron bremsstrahlung
• critical energy: Ecritical ≈ 800/Z MeV • rate of the bremsstrahlung process proportional to 1/M2
• at low energies photons mainly interact through photoelectric effect (photon absorbed by an atomic electron ejected from the atom)
• at higher energies (Eγ ≈ 1 MeV) the Compton scattering process: γe- -> γe-
• above Eγ > 10 MeV, photon interactions leading to e+e- pairs dominate
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radiation length
X0 =1
4αnZ 2re2 ln(287/Z1/2
re =e2
4πε0mec2 = 2.8 × 10
−15m
• em interactions of high energy electrons & photons characterized by the radiation length:
• “classical radius” of e-
• an average distance over which the electron energy is reduced by 1/e
• approximately 7/9 of the mean free path of the e+e- pair production process
• for example: X0(Fe) = 1.76 cm, X0(Pb) = 0.56 cm
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electromagnetic showers • secondary electrons/positrons produce bremsstrahlung which results in further
pair production, leads to formation of an electromagnetic shower which grows until all the primary energy is consumed
• EM showers initiated by photons and electrons
• the shower particles approximately double after each X0 of material: <E> ≈ E/2x • shower maximum at , for Pb Ecritical ≈ 10 MeV, E = 100 GeV
shower has a maximum at xmax≈ 13 X0. xmax =
ln(E / Ecritical )ln2
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electromagnetic calorimeters
σ E
E≈3%−10%E /GeV
• em energy resolution typically:
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electromagnetic calorimeter -OPAL
individual lead glass blocks
- OPAL EM Calorimeter
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nuclear Iinteractions • hadrons entering material create a cascades by nuclear interactions • much more diverse and larger compared to the EM showers • characteristics:
Material Xo λ l/Xo
Air 300m 740m 2.5
Al 8.9cm 39.4cm 4.4
Fe 1.78cm 17.0cm 9.5
Pb 0.56cm 17.9cm 30.4 λ is the nuclear absorption length, I = Ioexp(-λ/λο)
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• a calorimeter measures energies and positions of particles through total absorption • the energy resolution of a
calorimeter is paramterized as
where: a = stochastic term b = constant (containment) c = electronic noise
Ecb
Ea
E⊕⊕=
σ
hadron showers
σ E
E≥
50%E /GeV
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combined calorimetry
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collider experiments
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top-antitop production
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Cherenkov counters • Cherenkov light caused by local polarization of the material due to the passing charged particle • a particle moving faster than light in the medium, v >> c/n, where n=refractive
index of the material, an electromagnetic shock wave is produced. • during the time between a travel from O to P, the succesive centers of polarized
material along the path radiate em waves which, add up coherently to produce a wave front - moves in an angle θ with respect to the particle direction
• light is emitted on the surface of a cone with the particle moving along the axis of
the cone – light intensity ≈1% of typical scintillation light
θ
nc /
cβPO
βθ
n1cos =
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Cherenkov media
Mirror
Detector
e-! e+!
e"e"
e"
γγγ
Cherenkov...
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detection
EM hadronic B ⊗
The Interaction Point
scintillating fiber silicon tracking calorimeters (dense)
wire chambers
abso
rber
mat
eria
l
electron
photon
jet
muon neutrino -- or any non-interacting particle -- missing transverse momentum
charged particle tracks energy muon tracks
px = py = 0, pz ≠ 0, measurements often in the x-y plane
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layout of a typical collider experiment
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layout of a typical collider experiment
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cms experiment at the LHC
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CERN accelerator complex
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luminosity – fixed target
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colliding beams
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luminosity - colliding beams
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luminosity – two equal beams 1 and 2
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luminosity - examples
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luminosity - challenges
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particle physics measurement system - physics analysis pipe-line
IP5
Detectors:
sub- detector systems
FEE: front-end
electronics
DAQ: data
acquisition system
DCS
DRS: data
reduction system
PAS:
physics analysis system
Physics
SUPPLY ON-LINE DOMAIN
RAW DATA
OFF-LINE DOMAIN OUTPUT
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trigger – interaction rates are typically too high to store every
event for analysis - 40MHz at the LHC! – collision rate has to be suppressed – a fast trigger – fast electronics and buffer memories used to pick up the
interesting events – store the full data of triggered events only
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data acquisition – use computer driven fast electronic readout – only readout triggered events – analogue drift times and signal pulse heights
are converted into digital form – digitised data stored on computer disk/tape
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event reconstruction – computer analyse digitised data offline – use detector calibration constants to convert digitised
signals from each detector element into distances, times and/or energies
– apply detector alignment information – reconstruct space points – perform pattern recognition to find tracks – perform track fit to find track momentum – compute EM and hadronic shower energies – calculate dE/dx, TOF, Cherenkov angles, etc
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event reconstruction and display
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Monte Carlo simulation • Monte Carlo technique - based on random number
generation for sampling known distributions • rely on detailed and accurate simulation of detector
response to correct for detector imperfections (inefficiencies, geometric acceptance)
• requires a validated model for the basic physics processes (production, decays, interactions)
• requires a validated description of the detector geometries and material distributions
• use simulation to determine the “resolution function” for unfolding the corrected data points
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data analysis techniques – identify particles (e,µ,τ,γ,π,K,p,…) – identify jets of hadrons – search for decay vertices of shortlived hadrons
(charm and beauty quark decays) – combine 4-momenta of particles to search for other
decays e.g. – apply kinematic cuts to reduce background i.e. reject
events with improbable values – extract physics parameters (e.g. H° mass) using
various fitting methods (e.g. least squares, maximum-likelihood, etc)
– multivariate techniques!
bbHoo →→ , γγπ
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NEXT: Lecture III: Relativistic kinematics