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Quantum ChromoDynamics
(Nobel Prize 2004)
Chris McLauchlin
Outline
The Four Fundamental ForcesThe Strong Force
History of the Strong Force
What These People Did
Experimental Support
1
Fundamental Forces
2
Gravity Weak
Electromagnetic Strong
Fundamental Coupling
3
αg ≈ 5.9 × 10-39 αW ≈ 10-6
α≈137-1 αS ≈ 1
Development of QCD
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Proton Neutron
Proton Proton
NeutronNeutron
Quantum Field Theory
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Time
Space
Electron Exchange Neutron and Proton
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Electron ExchangeNeutron and Neutron
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Electron Exchange?Proton and Proton
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Hideki Yukawa
Massive Exchange Particle
Yukawa Potential
Nobel Prize: 1949
9
E t
Mesons
Mu-MesonAnderson and Neddermeyer 1937
Street and Stevenson
Bubble Chambers- Cosmic Rays
PionPowel 1947
Bubble chamber at high altitude
10
Murray Gell-Mann
Developed the Eightfold Way in 1961
Geometric ordering of baryons and mesons
Organization by strangeness and charge
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1
-1
0
Gell-Man and Zweig
1964
QuarksComprise Hadrons
Flavors
Pauli’s Exclusion Principle
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p uudn udd
p uudn udd
So What Bonds the Quarks?
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u u
d
Quantum ChromoDynamicsStrong Force = Colour Force
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u u
d
Quantum ChromoDynamicsStrong Force = Colour Force
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u u
d
Quantum ChromoDynamicsStrong Force = Colour Force
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u
d
u
Fundamental Forces
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Nuclear Force
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The Nobel Prize
Dr’s David J. Gross, H. David Politzer and Frank Wilczek
Asymptotic Freedom
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Asymptotic Freedom
Opposite of QED
CouplingIncreases with distance
Quark Confinement
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Asymptotic Freedom Shown by the β-Function
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(g) g3
16 2
113
C2 43
T (R)
O(g5 )
This is why these guys got a Nobel Prize
Asymptotic Freedom Shown by the β-Function
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(g) g3
16 2 1123
nf
QED Screening
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+-
+-
+-
+-
+-
+-
+-
+-
QED Screening
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QCD Anti-Screening
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QCD Anti-Screening
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QCD Anti-Screening
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2V
QCD Anti-Screening
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V g2 ekmr
r g2
r g2
r
V g2 ekmr
r 1
r
1r
2V g2 k2m2 ekmr
r(r)
g2 k2m2 ekmr
r(r)
2V
Yukawa Potential
Quark Confinement
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u u
d
Quark Confinement
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u u
d
Quark Confinement
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u u
d
u
ū
Experimental Evidence
Bjorken ScalingDeep Inelastic Scattering
Structure Functions
Supports Constituent Quark Model
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Coupling Relation
33
Standard Model
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Summary
QuarksFlavor
Color Charge
Hadrons
Pions
Asymptotic FreedomQuark Confinement
ScalingLimits to three constituents
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Thank youAny Questions?
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Quarks
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Flavor Charge (e) Spin (hbar) Mass (GeV/c2 )
up 2/3 1/2 2.4x10-3
down -1/3 1/2 4.8x10-3
charmed 2/3 1/2 1.27
strange -1/3 1/2 104x10-3
top 2/3 1/2 171.2
bottom -1/3 1/2 4.2
Experimental Evidence
Hadron Production, Muon-pair Production, e- e+ ProductionADONE accelerator
Consistent with factor of 2 implied by three coloursAs opposed to 2/3 without colours
Coupling StrengthCoupling Constant αShould decrease with an increase in Energy of bombardment
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(E) 12
(33 2n)ln E2
2
Bubble Chambers
Mixture of Ne-H
Superheating
Ionization by particles
Can find q/m
3-D tracks of Particles
39
Scaling
The cross-section of a lepton scattering off of nucleon to depend on a dimensionless quantity
Implies multiple components of nucleon
This is governed by a particle’s β-FunctionMust be negative to imply scaling
Theories using this refer to it as “Asymptotic Freedom”
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q22p
What is Alpha?
41
(E) 12
(33 2n)ln E2
2
Quarks are Surrounded by a Gluon Cloud
Penetration of the cloud lowers Coupling
The β Function
42
(g) g
QED vs. QCD
Positive β-Function Negative β-Function
Decays with Distance Increases with Distance
Shielding by other Fermions
No Shielding *
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Strong Theory Development
Hideki Yukawa (1935)1935
Mediated by a particle like E&M, but with mass
Richard FeynmanQED
Yang-Mills (1954)Three field particles: B+, B-, B0
QED principles applied to Strong ForceNon-Abelian Gauge Theory
Not Renormalizable/ zeroth order said massless particles
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E t 2
Strong Theory Development
Gell-Mann (1959)Quarks!
Make up Protons and Neutrons (three per each)Needed another degree of freedom
Colour introduced
Nambu (1960)Discovered Spontaneous Gauge Symmetry Breaking
Gauge Theories can have Short Distances
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Strong Theory Development
Bjorken (1968)Asymptotic Freedom
ScalingCross Section of particles related to charge and momentum
Governed by the β-function
t’ Hooft discovered this, but never said anything
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Strong Theory Development
t’ Hooft (1971)Proved Non-Abelian Gauge Theories to be renormalizable!
Weak Interaction fixed And mixed with Electromagnetic
Also got the negative, but didn’t know it was right and forgot about it
New PeopleFound it again and got Nobel Prize
47
Renormalization
Any Technique to deal with Infinities in calculated quantitiesSuch as the electron
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Non-Abelian Gauge Theory
Non-Commutative
49
a*b b*avsa*b b*a
Strong Force
Short Range
Very Strong
Decreases at close distances
50 [[http://hadron.physics.fsu.edu/~crede/forces.html]]cc
Quantum Number Conservation
Baryon Number
Lepton Number
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Bosons and Fermions
Fermion: ½ integer spinsProton, Neutron, Electron
Matter Particles
Boson: Integer spinsForce Carrying Particles
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Pictures
[[1] http://theideagirlsays.wordpress.com/2012/08/18/higgs-boson-borexino-geo-neutrino-particles-weak-nuclear-force-yukawa-gluons-neutron-decays-5g-wow-seti/electromagnetic-weak-between-quarks-nucelons-strong-interaction-diagram/
[[2]] http://hadron.physics.fsu.edu/~crede/forces.html
[[3]] http://www.dichotomistic.com/matter_infinoverse_two.html
[[4]] http://www.particleadventure.org/residualstrong.html
[[5]] http://upload.wikimedia.org/wikipedia/commons/7/7b/Yukawa.jpg
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References
http://lss.fnal.gov/archive/other/ift-p-036-93.pdf
Baggot, J. (2011) The Quantum Story. Oxford: Oxford University Press.
Griffiths, D. (2008) Introduction to Elementary Particles. WILEY-VCH Verlag GmbH & Co.
Povh, B. Rith, K., Scholz, C., & Zetsche, F. (1999). Particles and Nuclei (3rd) ed.). Heidelberg:Springer-Verlag Berlin Heidelberg.
Chapter 9 for this unknown textbook on Particle Physics on Proton Structure
http://www.itp.phys.ethz.ch/education/fs11/ppp2/PPP2_9.pdf
Wikipedia (Various)
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Wikipedia
http://en.wikipedia.org/wiki/Deep_inelastic_scattering
http://en.wikipedia.org/wiki/Beta_function_(physics)
http://en.wikipedia.org/wiki/Casimir_element
http://en.wikipedia.org/wiki/Representation_of_a_Lie_group
http://en.wikipedia.org/wiki/Yukawa_potential
http://en.wikipedia.org/wiki/Quantum_chromodynamics
http://en.wikipedia.org/wiki/Asymptotic_freedom
http://en.wikipedia.org/wiki/Gauge_theory
http://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory
http://en.wikipedia.org/wiki/Special_unitary_group
http://en.wikipedia.org/wiki/Lattice_gauge_theory
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