Syllabus
Fundamentals of the theory of electroweak interactions
Neutron beta decay. Kinematics. Fermi theory. Weak coupling constant. Fermi and Gamow - Teller transitions in nuclei. Generalization of Fermi model. Four-fermion interaction with S, V, A, T, P terms. Non-conservation of parity and its formal description within weak intaeraction Lagrangian. Non-relativistic approximation for nucleons in b-decay. Energy spectrum of b-electrons. Fierz interference terms. Kurie plot. Degree of polarization of electrons in b-decay of unpolarized neutron or nucleus. Maximal parity violation. Angular correlation of electron and antineutrino and elimination of S, T interactions. Two-component neutrino theory. Weyl equation. Helicity of neutrino. V, A interactions. Determination of coupling constants CV, CA. Angular correlation of electron and antineutrino in the decay of free neutron. Neutron mean lifetime and the corresponding Fermi constant Gb. Angular distribution of electrons in b-decay of polarized neutron and relative sign of the CV and CA. Muon decay. Electron energy spectrum and Michel parameter. Muon lifetime and the corresponding Fermi constant Gm. Difference between Gb and Gm. Strangeness-changing weak decays of hyperons. Cabibbo angle. Existence of two neutrino types. Selection rules for semileptonic hadron decays. Feynman - Gell-Mann current-current interaction Lagrangian, currents V - A. Decays of charged pion. Weak interactions of quarks and leptons. Prediction of "diagonal" leptonic processes and its confirmation. Difficulties of the theory of direct four-fermion interaction. Rapid (power-like) growth of tree-level cross sections at high energies and uni tarity condition. Cross section of elastic (anti)neutrino - electron scattering. Non-renormalizability of perturbation expansion.
Model with charged intermediate vector boson W. Propagator and polarization vectors for massive vector boson. Behaviour of longitudinal polarization vector in high-energy limit. Four-fermion processes and production of W +W - pair. Difficulties of theories with charged massive vector bosons (weak interactions and electrodynamics). Idea of unification of weak and electromagnetic interactions. Need for additional particles and interactions. Non-abelian gauge invariance and Yang-Mills field. Goldstone model of self-interaction of complex scalar field. Spontaneous symmetry breakdown and Goldstone boson. Abelian Higgs model and mass term for the vector field. Higgs mechanism. Glashow - Weinberg - Salam standard model (SM) of electroweak interactions: Electroweak unification with gauge group SU(2) x U(1). Representations of basic fields. Rule Q = T3 + Y. Weinberg (weak mixing) angle qW</
I>. Choice of the U-gauge. Interactions of neutral vector boson Z with weak neutral currents. Higgs mechanism and Weinberg relation for mW / mZ. Interactions in various sectors of the model. Electroweak interactions of quarks. Difficulties of the model with three quark flavours u, d, s. Phenomenological unacceptability of strangeness-changing neutral currents. Introduction of "charmed" c-quark and Glashow - Iliopoulos - Maiani (GIM) mechanism. Standard model with two generations of elementary fermions. Diagonalization of quark mass matrix and Cabibbo angle. Three generations and Kobayashi - Maskawa matrix. Scattering of muon (anti)neutrino off electron. Determination of the parameter sin2qW. Decays of vector bosons W and Z. Production of W +W - pair in neutrino-antineutrino annihilation (at tree level) in SM. Cancellation of high-energy divergences descending from the individual Feynman diagrams.
Annotation
The path to the phenomenological V-A theory of the weak interactions. The idea of unification of weak and electromagnetic interactions.
Nonabelian gauge fields and the Higgs mechanism. The Glashow-Weinberg-Salam standard model of electroweak interactions.