Structure of matter

  2. Atomic, nuclear and particles
  3. Structure of matter
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 Matter is vast and varied throughout the universe. Yet, zoom in enough and this complex story has a simple core - the Standard Model.

 This is good example of Occam´s razor. The simplest is most likely to be the correct solution.

Particles interact and experience forces due to the transfer of exchange particles. These interactions can be represented by diagrams.

Key Concepts

Photons and virtual photons

Photons are the exchange particles associated with the electromagnetic force. A photon is a wave packet that carries an energy that is proportional to its frequency:

\(E=hf\)

Virtual photons only exist between particles, not interacting with anything else. They exist for a short time without breaking the law of conservation of energy.

Heisenberg's uncertainty principle states that, if the photon exists for only a short time Δt, then it can have energy \(\Delta E\Delta t\geq {h\over 4 \pi}\) without violating the law of conservation of energy. The shorter the time, the higher the energy.

 

Feynman diagrams

Feynman diagrams represent particle interactions. This diagram is an example of a vertex:

Here an electron emits a photon.

Note that the arrows and lines do not represent the paths of the particles. They represent the progression through time (left > right). So we start with an electron, it emits a photon and it's still an electron.

Rules for drawing vertices:

  1. Straight lines are used for particles; wavy lines are photons.
  2. Each vertex has two straight lines and one wavy line.
  3. Time progresses from left to right or sometimes drawn with time going up.
  4. Particles point forwards in time; antiparticles have arrows pointing backwards.
  5. There is always one arrow entering and one leaving.

Once a Feynman diagram is drawn for a known interaction, the arrows can be rotated to predict other ones.

 

Two-particle interactions

Electron repulsion

To represent the interaction between two electrons we need two vertices.

Strong nuclear force

The strong nuclear force is responsible for holding together nucleons. It exists due to the exchange of pi mesons:

Weak nuclear force

The weak nuclear force is responsible for beta decay. It exists due to W bosons.

 

Fundamental forces

The strength and range of the fundamental forces varies:

  Relative strength Range (m)
Strong 1 10-15
Electromagnetic 10-2 infinite
Weak 10-6 10-18
Gravity 10-38 infinite

 

 

Essentials

Types of particle

Protons and neutrons

Protons and neutrons are affected by the strong force:

  • Both have masses about 900 MeVc-2
  • The proton has charge +e and the neutron charge 0
  • Both have spin \(1\over 2\)

Electrons

Electrons are affected by the electric force:

  • Mass \(\approx\) 0.5 MeVc-2
  • Charge -e
  • Spin \(1\over 2\)

Neutrinos

Neutrinos are affected by weak force:

  • Mass \(\approx\) 0
  • Charge 0
  • Spin \(1\over 2\)

Pions

Pions are affected by strong force:

  • Mass \(\approx\) 200 MeVc-2
  • Charge -e
  • Spin 0

Photons

Photons take part in electromagnetic interactions:

  • Mass 0
  • Charge 0
  • Spin 1

Hadrons

Hadron is a collective term for heavy particles that interact with the strong force:

  • proton
  • neutron
  • pion

Baryons are a sub-set of hadrons containing 3 constituent quarks:

  • proton
  • neutron

Mesons are a sub-set of hadrons containing 2 constituent quarks, i.e. pion.

 

Fundamental particles

Fundamental particles are not composed of a combination of any other particles.

Leptons

Lepton is a collective term for light particles that don't interact with the strong force, e.g. electron, anti-electron neutrino.

Quarks

There are 6 flavours of quark:

Flavour Symbol Relative charge
Up u +2/3
Down d -1/3
Strange s -1/3
Charm c +2/3
Bottom b -1/3
Top t +2/3

Quarks are the building blocks of the hadrons:

  • Protons are composed of uud (to give relative charge +1)
  • Neutrons are composed of udd (to give relative charge 0)

Quarks are also the building blocks of the mesons. Pions contain one quark and one antiquark, e.g. π+ is \(\mathrm{u} \bar{\mathrm{d}}\).

 

Conservation laws

Lepton number: 

  • Leptons have lepton number = 1
  • Anti-leptons have lepton number = -1

 In any interaction lepton number must be conserved.

Baryon nymber:

  • Baryons have baryon number = 1
  • Mesons and leptons have baryon number = 0

 In any interaction baryon number must be conserved.

Strangeness:

The strangeness number of hadrons is determined by the number of strange quarks

  • +1 for antistrange
  • -1 for strange

 Strangeness is not conserved in weak interactions since quarks can change flavour.

 

Quarks

Quark confinement

Every time two quarks are pulled apart two more quarks are created. For that reason there are never any single quarks.

Colours

We can use colours to represent the types of quark.

  • Quarks (e.g. up) are red, green and blue
  • Antiquarks are anti-red, anti-green and anti-blue

All particles are made of combinations of quarks that are colourless.

Gluons are colour anticolour combinations e.g. blue-antiblue

Feynman diagrams for quark interactions

The interaction between two quarks:

Beta decay:

NB: If flavour is changed, it's a weak interaction.

 

Gauge bosons

The gauge bosons responsible for the fundamental forces are as follows: 

Name Interaction
Photon Electromagnetic
W Weak
Gluon Strong

 

 

Summary

Here is a recap of The Standard Model so far.

 

Test Yourself

Use flashcards to practise your recall.

Show flashcards
 

Just for Fun

Check out this πg physics summary.

 
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