Questions d'examen: partie théorique

1. Explain the concept of gauge theory. Give an interpretation in terms of connections.
2. Construct a Yang-Mills theory. In particular, what are the interaction terms for three and four gauge bosons?
3. Show that the amplitude for [math]\displaystyle{ qq\rightarrow gg }[/math] is gauge invariant.
4. What is meant by the factorisation theorem in QCD? How does it enable short-range calculations?
5. In deep inelastic scattering, define the proton structure functions and prove the Callan-Gross relation.
6. Explain what is meant by the evolution of parton distributions and by the factorisation scale. Derive one of the splitting functions.
7. Give the expression for the Glashow Lagrangian for weak interactions and explain how it is constructed.
8. Explain the Higgs mechanism of the Standard Model.
9. Explain how the fermion masses are introduced into the Standard Model and what is meant by flavour mixing.
10. What are the decay widths of the W and Z bosons in the Standard Model? What is the production cross-section of the Z boson in electron-positron collisions?