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

4

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Proton Neutron

Proton Proton

NeutronNeutron

Quantum Field Theory

5

Time

Space

Electron Exchange Neutron and Proton

6

Electron ExchangeNeutron and Neutron

7

Electron Exchange?Proton and Proton

8

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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

11

1

-1

0

Gell-Man and Zweig

1964

QuarksComprise Hadrons

Flavors

Pauli’s Exclusion Principle

12

p uudn udd

p uudn udd

So What Bonds the Quarks?

13

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

17

Nuclear Force

18

The Nobel Prize

Dr’s David J. Gross, H. David Politzer and Frank Wilczek

Asymptotic Freedom

19

Asymptotic Freedom

Opposite of QED

CouplingIncreases with distance

Quark Confinement

20

Asymptotic Freedom Shown by the β-Function

21

(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

22

(g) g3

16 2 1123

nf

QED Screening

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+-

+-

+-

+-

+-

+-

+-

+-

QED Screening

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QCD Anti-Screening

25

QCD Anti-Screening

26

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

30

u u

d

Quark Confinement

31

u u

d

u

ū

Experimental Evidence

Bjorken ScalingDeep Inelastic Scattering

Structure Functions

Supports Constituent Quark Model

32

Coupling Relation

33

Standard Model

34

Summary

QuarksFlavor

Color Charge

Hadrons

Pions

Asymptotic FreedomQuark Confinement

ScalingLimits to three constituents

35

Thank youAny Questions?

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Quarks

37

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”

40

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 *

43

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

46

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

48

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

51

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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