CTP Part III Topics
1. g − 2. It’s theoretical issues. What operator is being measured? How is it computed? What are the other contributions within the SM (up to the accuracy of the experimental results)?
2. Neutrinos in the SM. Massive neutrinos, theoretical issues.
3. In the standard model the W and Z get masses from the Higgs mechanism. Note that the Z mass differs from the W± mass. Suppose that there were no Higg’s boson. The W and Z bosons would get masses and longitudinal degrees of freedom from the pion(s). Explain the mechanism using Feynman diagrams or effective lagrangians (or both), and compute the masses of the W± and the Z. Why does the photon stay massless?
4. What is the experimental evidence for a cosmological constant? Give three theoretical proposals for a solution.
5. What is the Higgs mechanism and describe some of the current experimental work searching for the Higgs boson. Discuss the production and decay of the standard model Higgs at the LHC. What are the dominant production mechanisms as a function of the Higgs’ mass? What are the dominant decay mechanisms, also as a function of the Higgs’ mass? What are the signatures the experimentalists expect to observe in their apparatus?
6. Discuss the Adler-Bell-Jackiw Anomaly. Among the topics you might include are: What symmetry does it violate and how does it effect the structure of the low energy chiral effective Lagrangian in QCD? What is anomalous about it? What are its implications for the decay pi0 -> 2 gamma? What does it tell us about the number of colors in QCD? How does it combine with the requirement of renormalizability to constrain the particle content of the standard model?
7. What is CP violation in the context of the Standard Model? In the standard model CP violation is encoded in the CKM matrix. What are the experimentally observed examples of CP violation? How are the experimental observations related to the theoretical parameterization?
8. Explain to us how QCD is implemented on a lattice. Among the topics you might include are: What are the degrees of freedom? What is the action? How is gauge invariance implemented? How does one take the continuum limit? How are the properties of hadrons computed?
9. The number of colors, Nc, is one of the few possible expansion parameters in QCD. ’t Hooft introduced the concept of a large Nc expansion in a famous 1974 paper. His paper described the theory of mesons. Later Witten introduced a possible theory of baryons in the large Nc limit. Please explain the application of the large Nc expansion. This is primarily a qualitative question. Among the things you might include are ’t Hooft’s “double line” graphical method; the classification of dominant families of Feynman diagrams for some simple Green’s function, for example the vacuum energy in pure glue QCD, or the meson propagator; and finally, the relationship between Witten’s ideas about baryons at large Nc and soliton models of the proton.
10. Certain grand unified models have monopole solutions. Tell us under what conditions such solutions exist, and whether they are stable. Describe a specific example in some detail. What was the “monopole problem” and how does inflation resolve it?