Feynman Diagrams

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Feynman Vertices• Each of the three basic interactions can be described using a symbol called a Feynman vertex.• We can use the vertices in a non-mathematical way to illustrate how quarks and leptons interact with each other. • There is an electromagnetic interaction vertex, a weak interaction vertex and a strong interaction vertex.

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Forces in particle physics• Forces are explained by Emission/absorption of particles• A particle is emitted “ spontaneously”• Where does the energy to create this particle come from? (

Uncertainty video)• New law called the Heisenberg Uncertainty Principle• The particle is known as a virtual particle.

QED Video

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Uncertainty Principle

4

htE

In quantum mechanics it is possible to “borrow” an amount of energy

(from nowhere), DE for a limited amount of time Dt

A virtual W boson (mass 80 GeVc-2) is emitted in an interaction. How long does it exist for?

s

E

ht

27

199

34

101.4

106.110804

106.6

4

Data booklet

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RangeThe Range is the maximum distance travelled by a virtual particle.The formula is given in the data booklet

mc

hR

4

m

mc

hR

18

81928

9

34

101

103106.1)103(

10804

106.6

4

Find the range of a virtual W boson

Explain why a photon (em force) has infinite range (symbol = )

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Drawing Feynman Diagrams• Each vertex has an arrow going in and one going out. These

represent a lepton – lepton or quark-quark transition.• Quarks or leptons are solid straight lines• Exchange particles are either wavy (Photons, W, Z) or curly (gluons).• Time flows from left to right• Arrows from left to right represent particles moving forward in

time.• Arrows from right to left represent antiparticles moving forward in

time. (think of them as moving left to right).• Vertices are linked by a line representing an exchange particle• Charge and colour are conserved at each vertex.

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Space

time

Rotate the vertex slightly to show a real interaction

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Use of Feynman diagramsFeynman diagrams may be used to calculate probabilities for fundamental processes.

The picture represents a mathematical process called the amplitude. For the em interaction

137

1

amplitude

EM

EM

The amplitude of the diagram is the product of the interaction strength for each vertex i.e.

EMEM amplitude

Probability of taking place process = (amplitude)2

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EM vertex

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Basic em interactionsBy rotating the arms of the vertices, the following interaction possibilities are generated. Note that the time still flows from left to right and a backwards facing arrow represents an antiparticle travelling forwards in time.

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Weak VerticesWs, Z and gluons video

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Strong vertices

The gluon can be regarded as a pathway through which colour charge is exchanged between quarks and antiquarks. The quark gluon vertices could also show colour flow as quarks interact.

The left hand side represents BEFORE and the right hand side represents AFTER

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Strong interactions

Annotate to show colour and flavour

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Feynman Diagram Exampleshttp://teachers.web.cern.ch/teachers/archiv/HST2002/feynman/examples.htm

http://www.departments.bucknell.edu/physics/animations/Feynman_diagrams/

http://www2.slac.stanford.edu/vvc/theory/feynman.html

You should be able to draw Feynman diagrams for the following interactions;1. Electron scattering2. Beta decay3. Pion decay4. Electron – positron annhilation5. Pair production6. Muon decay7. Quark interactions8. Photon – photon scattering

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Learn these ones

Draw the Feynman diagram for beta (-) decay

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Strong force and gluon exchange

• Color force and strong force are essentially the same thing

• Colour force binds quarks together in hadrons by exchange of gluons

• Strong force binds colour-neutral particles together e.g. protons and neutrons in the nucleus.

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Gluons• Bosons with spin = 1 and zero mass• Gluons are themselves coloured• Gluons bind quarks together• Force between quarks increases as quarks are

separated.• Therefore isolated quarks and quarks cannot

be observed.• This is quark confinement

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Gluon colour• Quarks change colour through gluon exchange.• There are 6 coloured quarks and 2 colour neutral gluons

00 ,

,,,,,

GG

GGGGGGGBRBBGRGGRBR

Note: time should be horizontal

Click diagram for animation

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Example

1. A green s quark emits a gluon and becomes a blue quark. State the flavour of the new quark and the colours of the emitted gluon.

2. A blue u quark absorbs this gluon. What is its final colour and flavour?

3. Draw a labeled Feynman diagram for this process.

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Feynman diagram practiceUsing the basic weak interaction vertex involving a W boson and two fermions (below) draw Feynman diagrams to represent the following processes

Fermion outFermion in

W boson

K

e

e

e

e

Using quarks, draw a Feynman diagram for:

nnpp

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Websites

• www.particleadventure.com• http://teachers.web.cern.ch/teachers/archiv/

HST2002/feynman/index.html