Syllabus
* I. The GSW Standard Model [4,5,6,7]
⁃ A short Standard model recap
• Field contents, gauge interactions, Goldstone theorem, Higgs mechanism
• Virtues: matching to the Feynman-Gell Mann theory, unification condition & IVB masses
• Miracles: gauge anomaly cancelation, the QCD baryonic spectrum & asymptotic freedom
• Drawbacks: charge quantisation via anomalies, the flavour problem, B & L accidental, neutrino masses & leptonic mixing, strong CP problem
⁃ A closer look at the anomalies in the SM
• Gauge anomaly cancellation & gauge invariance
• The essential role of global anomalies in the SM, the neutral pion decay
• Anomalies in B & L and their non-conservation in the SM, B-L passing the necessary condition for being gauged
* II. Hints on physics beyond the SM [9,11]
• Experimental evidence for non-zero neutrino masses & mixing
• Solar neutrinos, Davis & Bahcall, KamLAND
• Atmospheric neutrinos, Super-K
• Reactor neutrinos
• Absolute neutrino mass scale from neutrinoless double beta decay, cosmology
⁃ Neutrino masses beyond SM
• d=5 Weinberg operator, Majorana neutrinos, seesaw mechanism (I+II+III), the scales
⁃ The hierarchy issue
⁃ The dark matter issue
⁃ The cosmological constant issue
* III. Precision SM observables and rare processes [7,9]
⁃ Peskin-Takeuchi parameters
⁃ Lepton flavour violation
⁃ Electric dipole moments and anomalous magnetic moment of muon
⁃ New physics due to d=6 operators - baryon number non-conservation
• Proton decay rate and the scale of the underlying physics
• neutron-antineutron oscillations
• Other leptoquark-driven rare processes
⁃ L non-conservation as a lower bound on the B-L breakdown scale, relation to proton decay
* IV. Running couplings [4,7]
⁃ The concept of a running coupling in phi^4
• Running coupling in momentum schemes, decoupling of heavy degrees of freedom
• Running coupling in other schemes, calculating the beta function from counterterms in MS
⁃ Running gauge couplings in Yang-Mills theories with fermions and scalars at one loop
• The meaning of the relevant group-theory factors
⁃ The running SM couplings and the new physics at 10^16 GeV
⁃ Identification of the minimal extra high-scale degrees of freedom so that unification is real
• The coloured triplets in the scalar sector
• The bi-fundamental extra vector bosons
* V. Intermezzo 1: Elementary intro into Lie groups, Lie algebras and their representations [1,2,3,5]
⁃ Lie groups and Lie algebras
⁃ Simple, semisimple Lie algebras, compactness
⁃ Subgroups, subalgebras
⁃ Elements of representation theory
• real x complex representations, reducible x irreducible representations
• fundamental x antifundamental representations, adjoint representation
• index, symmetry features
⁃ Examples - basic SU(N) representations, Young tableaux, SO(n) representations, spinors
⁃ Decompositions or irreps with respect to subgroups, Clebsch-Gordan coefficients
⁃ The meaning of relations like 5=(3,1)+(1,2), 10=(3bar,1)+(3,2)+(1,1) etc.
⁃ Uniqueness of SU(5) from the group theory point of view
• Cartan subalgebra, weights & roots
• Classification of simple Lie algebras, Dynkin diagrams
• SM Cartans & need to look for rank 4 or more
• Need for complex representations
• SU(5) as a single simple rank 4 option
* VI. The minimal SU(5) model [2,8,9,10]
⁃ Normalization issues & 'canonical' vs. 'physical' normalization of U(1) charges in GUTs
⁃ Quantization of the SM (hyper)charge
⁃ Structure of the minimal SU(5) model
• Higgs sector, singlets with respect to a subgroup, Higgs mechanism
⁃ Non-trivial predictions
• GUT-scale Weinberg angle
• Third family Yukawa convergence
⁃ Proton decay
• Basic decay modes
• SU(3)xU(1) and SU(3)xSU(2)xU(1) classification of the relevant d=6 operators
• d=6 proton decay in the minimal SU(5) model
Annotation
We shall pass through the pros and cons of the Standard Model of particle physics and discuss the reasons why it is widely believed the SM is not the ultimate microscopic theory of nature. Among the possible SM extensions we shall focus on the gauge models in which its SU(3)xSU(2)xU(1) gauge symmetry is extended to a larger simple or semi-simple gauge group and discuss in brief the main theoretical and phenomenological consequences of such theories.