Episode 540: Quarks and the standard model

The quark model, justified by the results of deep inelastic electron scattering, creates relative order out of the chaos of particle classification.

Quarks have three ‘colour’ charges, and the rule for stability is that combinations must be colourless.

Summary

  • Discussion: Rules for quarks (15 minutes)
  • Student activity: Making non-strange hadrons with quark triangles (15 minutes)
  • Student questions: Making strange hadrons with quark triangles (15 minutes)
  • Discussion: Gluons and the force between quarks (15 minutes)
  • Student activity: Constructing Feynman diagrams (20 minutes)
  • Discussion: Summing up (10 minutes)

Discussion: Rules for quarks
Students need to be informed of the rules for combining quarks.

Where the electromagnetic interaction is due to the property of electric charge, which can be positive or negative, quark interaction is due to a property which can have three different states. This has been called ‘colour’ charge, because the three primary colours red, green and blue add to give white, a colourless combination. These three-quark combinations are the baryons.

Anti-quarks have an anti-colour; you may wish to think of the complementary colours to the three primary colours, so anti-red is cyan, anti-green is magenta and anti-blue is yellow. Three anti-quark combinations are the anti-baryons.

By combining a quark with an anti-quark of the appropriate anti-colour, a two-quark hadron can be produced. These two-quark combinations are the mesons.

Student activity: Making non-strange hadrons with quark triangles
The quark triangle are constructed so that they can be fitted together in threes, with the 120° vertices together, with the combination red, blue and green giving a baryon. A similar arrangement with anti-red, anti-blue and anti-green gives an anti-baryon. By taking one quark and fitting an anti-quark of the appropriate anti-colour alongside it so that the two long sides coincide, a meson can be constructed.

Episode 540-1: Quark triangles (Word, 121 KB)

Episode 540-2: Quark models (Word, 36 KB)

The document contains two versions of each anti-quark: one version uses the same colours as the related quarks, but with the white and coloured regions of the triangles reversed. The second version has the same pattern of colours on the triangles as the related quarks, but the complementary colours are used instead of red, blue and green: thus anti-red is cyan, anti-blue is yellow and anti-green is magenta. You can choose whichever form you prefer!

Using only u (+2/3 e) and d quarks (- 1/3 e) and their anti-quarks, u bar and d bar, in all possible colours, students can quickly use the three-colour rule to construct four possible baryons

(n, p and the unstable D- and D++ ) together with their anti-particles. Other non-strange baryons are high energy states of these four, e.g. the D and D particles are uud and udd respectively, and can decay to the proton and neutron by emitting the extra energy as a gamma photon

Δ + ® p + g     D ® n + g

They should also be able to construct four different mesons, all pions. Two of these are, in fact, the same particle (u + u bar = d + d bar = pi zero).

Issue the strange quarks, s and s bar, at this point, with the explanation that they are heavier versions of d and d bar, and that they have strangeness of -1 and +1 respectively. This allows the construction of all the particles in the baryons decuplet and meson octet.

Student questions: Gluons and the force between quarks
These questions use the u and d quark triangles and their anti-quark triangles.

Episode 540-3: Putting quarks together (Word, 56 KB)

Further questions take a similar approach to explain the baryon decuplet and meson octet. These questions can be used to structure the student activity, or else as homework to consolidate the learning afterwards.

Episode 540-4: Strange quarks (Word, 45 KB)

Discussion: Gluons and the force between quarks
Just as pions (Yukawa’s mesons) are the particles that bind baryons, the quarks in a baryon are bound by exchanging a particle. The particles here are gluons, and we envisage the transfer as exchanging the colour of the two quarks concerned: e.g. a red quark will change into a blue quark by emitting a red-antiblue gluon, which is then absorbed by a blue quark that becomes red.

Student activity:

Constructing Feynman diagrams
If your specification requires it, the Feynman diagrams used for the weak interaction can now be extended to the strong interaction, and the ‘n’ and ‘p’ of the weak interactions replaced by‘d’ and ‘u’ quarks respectively.

Episode 540-5: Feynman diagrams with quarks (Word, 99 KB)

Discussion: Summing up
This is a conclusion to the entire particle physics sequence. It should be realised that normal matter we see around us consists of two quarks and two leptons, and their anti-particles. Larger mass versions, which are not stable, occur in two generations. The muon and strange quark have already been met, and, together with the muon neutrino and the heavier version of the u quark, the charm quark (c), form the second generation. There is only one more generation, so all matter, whether stable or not, can be described in terms of 6 quarks and 6 leptons.

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Episode 540: Quarks and the standard model (Word, 301 KB)