Class #7 (Feb. 21) Reading Questions - Particle Physics, Secs. 19-23
1. With the introduction of a set of W particles one can build a diagrammatic theory of the weak interaction that is almost identical to Feynman's QED (i.e., we can define a set of weak interaction vertices and draw all Feynman diagrams for weak processes). The textbook points out that there are two types of problems that invalidate this naive approach of directly applying the QED construction to build a theory of the weak interaction. What are these two problems and what is the difference between the EM interaction and the weak interaction that gives rise to these problems.
2. What is a gauge transformation? What is the difference between a global and local gauge transformation? Noether's theorem states that every symmetry property of the Lagrangian results in a conservation law ... what is the conservation law associated with the gauge symmetry of the EM field Lagrangian?
3. Explain how the demand of local gauge invariance for the EM and weak interactions requires the existence of the photon and three W particles. Does this demand of local gauge symmetry result in a realistic theory of the EM and weak interactions?
4. What is a Goldstone boson? How is this object removed from a theory with a broken gauge symmetry? What is the difference between a Goldstone boson and a Higgs boson?
5. The GWS model of the weak interaction starts with a weak-isospin doublet (left-handed) and singlet (right-handed) and a two component Higgs field Phi (with the same structure as the weak-isospin doublet). What are the symmetries of this model and how are these symmetries related to the two additional fields: W and B. How do the three fields (Phi, W, and B) yield 12 degrees of freedom (as claimed in table 22.2)?
6. What is the weak angle theta_w? How is this angle determined? How is the weak angle related to the Cabbibo angle?
Your Question: Please give a well-formulated question that you have regarding the material covered in this reading assignment.