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Last update: T_UCJF (09.04.2013)
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Last update: doc. Mgr. Milan Krtička, Ph.D. (10.06.2019)
Složení ústní zkoušky. |
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Last update: T_UCJF (19.04.2013)
[1] R.Slansky, Phys.Repts. 79 (1981) [2] P.Langacker, Phys.Repts. 72 (1981) [3] H. Georgi, Lie algebras in particle physics ISBN 0738202339 [4] S.Weinberg, Introduction to Quantum field theory ISBN 0521550025 [5] S. Coleman, Aspects of symmetry ISBN 0521267064 [6] R. Bertlmann, Anomalies in quantum field theory ISBN 0198520476 [7] M. Peskin, D. Schroeder, Introduction to Quantum field theory ISBN 0201503972 [8] G.G.Ross, Grand Unified Theories, 1984, ISBN 0805-369678 [9] R.N.Mohapatra, Unification & Supersymmetry, 1986/92, ISBN 0378-955348 [10] D.Bailin, A.Love, SUSY gauge field theories and string theory, ISBN 0750-302674 [11] R.N.Mohapatra, P.B.Pal, Massive neutrinos in Physics and Astrophysics, ISBN 9812380701 |
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Last update: doc. Mgr. Milan Krtička, Ph.D. (10.06.2019)
Požadavky ke zkoušce odpovídají sylabu předmětu v rozsahu prezentovaném na přednášce. |
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Last update: T_UCJF (19.04.2013)
⁃ 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
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