Syllabus
* I. Supersymmetry - theoretical foundations [10,12]
⁃ the historical SUSY motivation
⁃ two-component spinors
⁃ dotted and undotted indices
⁃ SUSY transformations
⁃ the minimal Wess-Zumino model
⁃ the minimal SUSY algebra and its representations
⁃ the superfields and their components
* II. Supersymmetry - basic model building [10,12]
⁃ The SUSY lagrangians
⁃ The F- and D-term contributions to the scalar potential
⁃ SUSY gauge interactions
* III. Minimal supersymmetric standard model [10,12]
⁃ MSSM definition in the current basis
⁃ Basic MSSM degrees of freedom, the need for two doublets
⁃ Soft SUSY-breaking terms
⁃ Flavour structure of the MSSM
* IV. The basic MSSM phenomenology [10,12]
⁃ R-parity conservation/violation
⁃ Anomalous magnetic moments and electric dipole moments in the MSSM
⁃ the flavour and CP issues in the MSSM, lepton flavour violation
⁃ basic MSSM collider phenomenology
⁃ dark matter in the MSSM
* V. Running couplings in SUSY [4,7]
⁃ SUSY gauge running
⁃ Weak mixing angle in the SUSY GUTs
⁃ Radiative symmetry breaking in SUSY
⁃ mSUGRA ansatz
⁃ soft invariants (time permitting)
* VI. Supersymmetric GUTs [9,10]
⁃ Gauge unification failure in minimal SU(5)
• A simple extension with matter in the adjoint representation
⁃ General aspects of GUTs in SUSY
⁃ The minimal SUSY SU(5) GUT
• Structure - the extra Higgs multiplet
⁃ Proton decay in SUSY
• d=5 Higgsino mediated operators, preference of kaons in the final state
⁃ The trouble with the minimal SUSY SU(5) (proton decay, neutrino sector)
* VII. SO(10) GUTs [1,2,3,6,8,9,11]
⁃ U(1)B-L [ x SU(2)R ] as a gauge symmetry
• The neutrino mass scale origin
• Pati-Salam symmetry and lepton number as a fourth colour
⁃ SO(10) GUTs
• Spinors & tensors of SO(10)
• SO(10) in SU(5) and Pati-Salam language
• SUSYx non-SUSY setting
• Renormalizable x non-renormalizable seesaw
• Proton decay in SUSY x non-SUSY SO(10) (d=4, d=5 operators)
* VIII. Exotics (time permitting) [4,5,7]
⁃ Classical non-perturbative solutions & spontaneously broken gauge theories
• Soliton in phi^4 in 1+1 dimensions
• The Derrick's theorem and the need for gauge fields
• Nielsen-Olessen vortex in 2+1 dimensions, topological charges
• t'Hooft-Polyakov monopole in 3+1 dimensions, the Georgi-Glashow SU(2) model
⁃ Monopoles in GUTs and their classification, the first and second homotopy classes
⁃ The Callan-Rubakov proton decay catalysis in presence of monopoles
⁃ Monopoles & inflation
Annotation
In the summer semester we shall initially focus on supersymmetry as another widely popular area of the BSM physics, discuss its basic structure, model building strategies as well as its basic phenomenological aspects.
Then we shall inspect in some detail the minimal potentially realistic supersymmetric extension of the Standard
Model, the Minimal Supersymmetric Standard Model, MSSM.