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Particle Physics 2. Prof. Glenn Patrick . Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013. Last Week - Recap. Particle Physics & Cosmology Matter Particles, Generations Spin – Fermions & Bosons Charged Leptons Antimatter Neutral Leptons - Neutrinos - PowerPoint PPT Presentation
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Particle Physics 2
Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013
Prof. Glenn Patrick
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Last Week - RecapParticle Physics & CosmologyMatter Particles, GenerationsSpin – Fermions & BosonsCharged LeptonsAntimatterNeutral Leptons - NeutrinosHadronsStrange Particles and StrangenessSymmetries, Conservation LawsQuantum Numbers, IsospinEightfold Way and Quark ModelCharm, Bottom, Top, Quark Counting
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Today’s Plan 20 November Particle Physics 2
Force CarriersFour Fundamental InteractionsQuantum Field TheoryFeynman DiagramsHigher Orders/Radiative CorrectionsAnomalous magnetic moment of muonCharged and Neutral CurrentsZ and W Vector BosonsGluonsColour Charge and Quantum Chromodynamics (QCD)Unification of Fundamental Forces, Running Coupling ConstantsHiggs Boson and Field
Copies of Lectures: http://hepwww.rl.ac.uk/gpatrick/portsmouth/courses.htm
BOOKSB.R. Martin & G. Shaw, Particle Physics, 3rd Edition, WileyDonald H. Perkins, Introduction to High Energy Physics, 4th edition, CUPCoughlan et al, The Ideas of Particle Physics, Cambridge
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I
II
III Observed in 2000
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Force Carriers
Now the smallest Particles of Matter may cohere by strongest Attractions, and
compose bigger Particles of weaker Virtue.
There are therefore Agents in Nature able to make Particles of Bodies stick together
by very strong Attractions. And it is the business of experimental Philosophy to find
them out.
ISAAC NEWTON (1680)
Last week we looked at the Matter Particles (quarks and leptons).
This week we look at the four gauge bosons that make up the Force Particles.
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The Four Forces of NatureELECTRO -MAGNETIC
WEAK GRAVITY
STRONG
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Forces in Classical PhysicsClassically, forces are described by charges and fields
Field is a physical quantity which has a value for each point in space-time.Can be a scalar or vector field.
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Quantum Field TheoryForces are transmitted by
exchange of force particles between matter particles.
4 forces with different force particles.
HeisenbergUncertainty Principle
tEEt
Mctcx Energy ΔE is “borrowed for a time Δt
Maximum distance of exchange particle
Photon has zero mass,so infinite range
If we associate M with the pion mass, we get the Yukawa potential that we saw when we talked about the “nuclear force” in Nuclear Physics 1.
particle exchange of mass1 Force of Range
Quantum Mechanics + Relativity
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Four Forces of NatureSTRONG FORCE
Strength: 1, Range: 10-15 mExchange: Gluon
ELECTROMAGNETIC FORCEStrength: 1/137, Range: Infinite
Exchange: Photon
GRAVITYStrength: 6x10-39 m,
Range: Infinite, Exchange: ?
WEAK FORCEStrength: 10-6 m, Range: 10-18 m
Exchange: W±, Z0
A FIFTH FORCE?
Modified gravity?Dark matter,
Dark energy, etc.
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1~4
2
cgS
S
1371~
4
2
ce
EM
52 10~ pFmG
362 10~ pNmG
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Fundamental InteractionsEM
e- e-
e- e-
Strongu
gluon
u
d d
Weak
Z0
e-
Weak
e e
e- e-
ddu u
du
W-
en
p
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Feynman Diagrams
positron (anti-electron)
electron
At each ‘vertex’ charge is conserved. Heisenberg
Uncertainty Principle allows energy borrowing.
Virtual ParticleDoes not have mass of a
physical particle.
Known as “off –mass shell”
(e.g. not zero for photon)
222XXX pEm
Richard Feynman Quantum Electrodynamics
(QED)
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Feynman Diagrams
External legs represent amplitudes of initial and final state particles.
Positron is drawn as electron travelling backwards in time. Internal lines (propagators) represent amplitude of
exchanged particle. Charge, baryon number and lepton number conserved at
each vertex. Quark flavour conserved for strong and EM interactions.
Vertices represent coupling strength of interacting particles.
Perturbation theory. Expand and keep the most important terms for calculations.
AnnihilationExchange
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Feynman DiagramsAssociate each vertex with the square root of the appropriate
coupling constant, i.e. . When the amplitude is squared to yield a cross-section
there will be a factor ,where n is the number of vertices (known as the “order” of the diagram).
1371
4
2
c
e
Lowest order Second order
Add the amplitudes from all possible diagrams to get the total amplitude, M, for a process transition probability.
For QED:
)space phase(2Rate Transition 2 M
Fermi’s Golden Rule
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Bhabha Scattering
e- e-
e+ e+
e-
e+
e-
e+
Z0
e-
e+
e-
e+
e- e-
e+ e+
Z0
Amplitude = +
++
4 Born Diagrams (Electroweak) eeee
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Radiative Corrections
Vacuum polarisation
Higher Order Quantum Loop Diagrams (QED only)
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3rd order corrections
Anomalous Magnetic Moment of the Muon
Dirac theory predicts g=2, but this is modifiedby quantum fluctuations.
00116.02
)2(21
ga
Radiation and re-absorption of virtual photons contributes an anomalous magnetic moment.
ee
+-
e-e+
e-e-
e+e+QED
µZ0
µ µ µW W
µ
WEAK
B
+ STRONG
Hundreds of diagrams!
ppm) (0.54 10116592089(exp) 11a
ppm) (0.42 10116591802)( 11thea
111080287 a ~3.6σ effectNew Physics?
Lowest order correction
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Muon g-2: Testing the Standard Model
Experimentalmeasurements of aμ
Uncertainty on aμ and physics reach as the uncertainty has
decreased.
J.P. Miller et al, Ann. Rev. Nucl. Part. Sci., 62 (Nov. 2012), 237
Beyond the Standard Model (BSM) Physics?
newweakhadQEDthe aaaaa
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Photon – EM Boson
1900 Planck Black Body Radiation explained in terms of light quanta Nobel Prize.
1905 Einstein explained thePhotoelectric Effect in terms of quanta of energy Nobel Prize.
1925 G.N. Lewis proposed the name Photon for quanta of light.
1925 Compton showed quantum (particle) nature of X-rays Nobel Prize.
hE Quantum energy of photon
h = Planck’s constant = frequency
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Charged and Neutral Currents
Z0
NX
W+
N X
-
XN XN
Neutral Current Charged Current
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Discovery of Weak Neutral Currents (1973)
21Gargamelle Bubble Chamber
electron
ee
Bremsstrahlung effects
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Z and W Story
UA1
UA2
Super Proton Synchrotron turned
into proton-antiproton collider. Stochastic cooling technique.
Carlo Rubbia (UA1) Simon van der MeerTwo Experiments:
UA1 and UA2.Rubbia came up with
idea and led UA1.
1984
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W Boson Discovery – UA1 (1982)
electron
“Missing Energy” = neutrino
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Z Boson Discovery – UA1 (1983)electron
positron
𝒁 𝟎→𝒆+¿+𝒆−¿
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Weak Charged Current and QuarksFlavour Changing Charged Currents.Quark flavour never changes except by
weak interactions that involve W± bosons.
c s
W
t b
W
u d
W
ddu u
du
W-
en
p
+ ..
decay finally understood!
In decay processes,quark always decays tolighter quark to conserve
energy.
t b c s u d
Weak charged current changes lepton and quark
flavours.Possible that flavour
changing neutral currents exist beyond (tree level)
Standard Model.
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quark
anti-quark
gluon
Gluon Discovery (1979)
JADE, TASSO, MARK-J, PLUTO
3-Jet Event
PETRA e+e- Collider, DESY, Hamburg
Third jet produced bygluon bremsstrahlung
gqqee
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Inside the Proton
There are 3 “valence” quarksinside the proton bound together
by gluons.
Quantum theory allows quarks tochange into quark-antiquark pairs
for a short time.
There is a bubbling “sea” of gluons,
quarks and antiquarks.
There is however a problem with the basic quark model…..
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Colour Charge Some particles apparently contain quarks in the
same state violates Pauli Exclusion Principle (e.g. ++ = uuu).
Quarks
Anti-quarks
Proposed that quarks carry an extra quantum numbercalled “colour”.
All physical particles are colour neutral or “white”.
baryon meson
Red Green Blue
Cyan Magenta Yellow
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Quark Speciesquarks
s
ud
u ud d
s s
antiquarks
c c c
u
d
s
u u
d d
s s
updown
c c c charmstrange
tb
t tb b
tb
ttb b
topbottom
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8 Interacting GluonsExpect 9 gluons from all combinations (3 colours x 3 anti-colours):
rb, rg, gr, gb, bg, br, rr, gg, bb
However, real gluons are a linear combinations of states.
3ggbbrr
62 ggbbrr
2bbrr This combination is
colourless and symmetric.
Does not take part in the strong interaction.
Hence, we have 8 gluons. These two plus those from , , , , ,
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Counting ColoursIn Particle Physics 1, we counted quarks. Can also count colours using R.
below top energy
threshold
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Quantum Chromodynamics (QCD)
Gluons carry colour+anti-colourcharge, e.g. red-anti blue.
Colour charge always conservedso quarks can change colour when
emitting a gluon.
Since gluons (8) carry colour charge,they can interact with one another!
If a quark is pulled from a neighbour,the colour field “stretches”.
At some point, it is easier for the field to snap into two new quarks.
Quantum Chromodynamics (QCD) is the theory of the Strong Interaction in the Standard Model.
Fragmentation
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Confinement is a property of the strong force.
The strong force works by gluon exchange, but at “large” distance the self-interaction of the gluons
breaks the inverse square-law forming “flux tubes”:
Confinement
Quarks and gluons carry “colour “ quantum numbers analogous to electric charge –
but only “colourless” objects like baryons (3-quark states) and mesons (quark-antiquark states) escape confinement.
Confinement
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Quark Interactions
Only one pair of quarks interact, the rest are spectators.
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Residual Forces
How do protons bind to formthe nucleus? Protons & neutrons
are colour neutral.
Residual Strong Interactionbetween quarks in different
protons overcomes EMrepulsion.
How do molecules form ifatoms are electrically neutral?
Residual EM Force Electrons in one atom are
attracted to protons in another atom.
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Force Particles
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Bosons = Spin 1Force Particle Charge Mass Relative
Range (GeV) Strength
(m)Strong gluon (g) 0 0 1 10-15
EM photon () 0 0 1/137 infinite
Weak Z0 boson 0 91.2 10-5 10-18
W boson 1 80.4
Bosons = Spin 2Gravitygraviton 0 0 10-39 infinite
(not observed yet!)
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Particles and Forces
Charge Strong EM Weaku quark +2/3 Yes Yes Yesd quark -1/3 Yes Yes Yeselectron -1 No Yes Yese 0 No No Yesc quark +2/3 Yes Yes Yess quark -1/3 Yes Yes Yesmuon -1 No Yes Yes 0 No No Yest quark +2/3 Yes Yes Yesb quark -1/3 Yes Yes Yestau -1 No Yes Yes 0 No No Yes
Summary of how different particles feel the different forces:
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Unification of the Forces
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Grand Unification – Unite strong interaction with electroweak
interaction.
Grand Unified Theories (GUTs) predict that protons are unstable.
Final step would then be to add quantum gravity to form a Theory
of Everything (TOE).Because gravitons interact with one another field theory is non-re-normalisable. Graviton has
not been discovered!
Planck UnitsLength 1.62 x 10-35 mTime 5.39 x 10-44 sEnergy 1.22 x 1019 GeV/c2
Temp 1.42 x 1032 K
~Planck scale
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Electroweak Forceor EW symmetry breaking
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035999074.1371
4 0
2
c
e
Running Coupling Constants
Coupling constants have an energy dependence due to (higher order) virtual interactions.
These change the measured value of the coupling constant and make it depend on the energy scale at which it is measured
(logarithmic dependence).The strong and weak couplings decrease with energy whilst the EM
coupling increases.It is therefore possible that at some energy scale, all 3 forces
become equal.
EM coupling constant = fine structure constant
53
2
1003.1~
cMGFW
1~)()(2
cEgE S
S
at lowenergy
Weak
Strong40
2
105~4
c
MGNg
Gravity
41
Grand Unification
LEP, Amaldi et al, 1991
Grand-Unified Theories (GUT), favoured, (e.g. by non-zero masses) predict the 3 coupling constants (QED, Weak, QCD) to unify at GUT scale of 3x1016 GeV.
This unification does not happen in the Standard Model (+GUT), but does in Supersymmetry with a 1 TeV scale.
Starting from the measured values of αQED(mZ) and sin2W as input, one can
predict:
To be compared to the experimental value (mostly constrained by LEP):
Baryon Number violated in GUTs. Conflict with measurements? SUSY at 1 TeV + GUT
Standard Model + GUT
GUT) (Standard 002.0073.0)( ZS mGUT) (SUSY 010.0129.0)( ZS m
003.0118.0)( ZS m
(SuperK) 10)( 340 yrsep
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Missing Ingredient: Higgs SectorGenerates mass?
Gravitonnot yet found
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Why do some particles have large masses whilst others have little or no mass?
The Mystery of MassThe masses of compositeparticles like protons and
neutrons are mainly given by the motion of the constituents.
However, for fundamental particles, like electrons and quarks it has long been a
mystery how they acquire their masses and why they are so
different.
We
PhotonMass < 10-18 eV
ElectronMass = 511 eV
W bosonMass = 80 x 109 eV
d
u
u
NeutrinoMass < 2 eV
Proton
44
Top Quark Heavier than Silver Atom!
Silver(A=108)
M(top) = 172 GeV ± 0.9 ± 1.3 GeV
45
Higgs MechanismStandard Model in basic form leads to massless particles.
1961- 1968: Glashow, Weinberg & Salam developed theory that unifies EM and weak forces into one electroweak force. Predicted weak neutral current.Nobel Prize: 19791964: Higgs, Kibble, Brout, Englert et al introduced the Higg’s field. Gives mass to Z and W bosons.Nobel Prize: ??1971: Veltman, t Hooft - Solved the problems of infinities through renormalisation.Nobel Prize: 1999
Peter Higgs
Higgs boson is a neutral, scalar (spin=0) particle. Coupling to particles is proportional to their mass. No prediction for Higgs mass. Vacuum should be filled with Higgs field – boson is the quantum of this field
in the same way that the photon is the quantum of the EM field.
46
Space is not EmptyThe classical vacuum just consists of empty space-time and is featureless.
In reality, it’s sea of virtual particle-antiparticle pairs from quantum fluctuations.
Vacuum is the state of minimum energy for the Universe.
WARNING: Quantum field theory gives cosmological constant (or zero point energy)
120 orders of magnitude too high!
47
Higgs Field and Higgs BosonH
H
H
HH
H HH H
HH
H
H
Higg’s Boson
Higg’s Field
48
Mexican Hat Potential
Energy lowest whenfield is not zero.
EM - Electric & Magnetic Fields(Vector)
EW - Higgs Field(Scalar)
Energy lowest whenfield is zero.
Law is basically symmetric, but equilibrium state is not. Symmetry is said to be spontaneously broken.
State in which the Higgs field is zero is not the lowest energy state.
49
Electroweak Symmetry BreakingAt high enough
temperatures, particles were (symmetrically)
massless.
As the Universe cooled, ring of stable points appeared.
W and Z got mass from the field, but the stayed
massless.
50
Higgs Hunting
GeV94 29
24- Value Preferred
e+H
e-
Z0Z*f
ff
f
IndirectFit to LEP EW Measurements
Direct Searches at LEP Collider
CL) (95% GeV 114.4Hm
CL) (95% GeV 185HmAlso, limits from Tevatron
51
Higgs Particle Discovery?
4 Jul 2012, CERNFrancois Englert & Peter Higgs
52
𝑯→𝜸𝜸 𝑪𝒉𝒂𝒏𝒏𝒆𝒍
ATLASCMS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
Higgs does not couple to zero mass photon.Possible via a top quark loop.
53
𝑯→𝒁 𝒁∗→𝟒ℓ𝑪𝒉𝒂𝒏𝒏𝒆𝒍
ATLAS CMS
Phys. Lett. B 716 (17 Sept 2012), Issue 1
ℓ𝒎𝒆𝒂𝒏𝒔𝒍𝒆𝒑𝒕𝒐𝒏
54
Higgs Particle – Properties?ATLASGeVsysstatM H )(4.0)(4.00.126
)(5.0)(4.03.125 CMSGeVsysstatM H
MASS
Phys. Lett. B 716 (17 Sept 2012), Issue 1Spin/Parity of Standard Model Higgs is expected to be J 0+
Spin 0 consistent with decay channels seen so far.Spin 1 already ruled out.
The first scalar elementary particle.
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Higgs SpinSpin is quantised and measured wrt an axis. Sz = -S, -S+1, -S+2, … +S-1, +S
However, photon is massless, so in this case Sz can only be +1 or -1
ATLAS and CMS will need to do a proper spin analysis by analysing angular distributions of decay products to get the definitive answer.
c/o Aidan Randle, ATLAS
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Beyond the Standard Model?●18 input parameters from
experiment (e.g. particle masses, coupling constants).
●Gravity not included. Hierarchy problem.
●Why 3 generations of particles?
●Are these particles fundamental?
●What is mass? (Higg’s particle)
●Missing antimatter?●Missing matter (dark matter &
dark energy)?●Neutrino masses.●Cosmological constant
predicted to be 10120 too large for vacuum.