Syllabus
Electroweak interactions II
Fermi-type theory of weak interactions (brief summary). Jacob - Wick partial-wave expansion. "Unitarity bound" for four-fermion processes. Divergence index (superficial degree of divergence) of a general one-particle irreducible Feynman graph. Power-like growth of tree-level amplitudes with energy and non-renormalizability of perturbation expansion. Perturbative aspects of the weak interaction model with charged intermediate vector boson W. High-energy behaviour of partial-wave amplitudes for four-fermion processes (logarithmic violation of unitarity). Processes of production of longitudinally polarized W's - power-like growth of tree-level amplitudes at high energies. Electrodynamics of massive charged spin-1 particles. Process WW à gg in high-energy limit and interaction vertex WWg of Yang - Mills type. Process e +e - à
W + W -: arguments in favour of a non-trivial unification of weak and electromagnetic interactions. Condition of "tree unitarity". Mechanisms for compensation of divergences. Exchange of heavy lepton in t-channel. Georgi - Glashow model as an illustration: unification condition and upper bound for W mass. Exchange of neutral vector boson Z in s-channel.
Derivation of minimal electroweak standard model (SM) from the condition of tree unitarity: WWZ interaction of Yang - Mills type. Compensation of leading divergences and system of equations for vector boson ? lepton couplings. Unification condition and lower bound for W mass. Partial compensation of next-to-leading divergences and Weinberg´s formula for masses of W and Z. Sector of vector bosons. Compensation of leading divergences and direct interaction of four vector bosons. Residual divergences: need for scalar (Higgs) boson H. Derivation of H couplings to vector bosons and Yukawa interactions of leptons with H. Higgs boson self-interactions. Tree unitarity as a necessary but not sufficient condition for perturbative renormalizability: Adler - Bell - Jackiw (ABJ) triangle anomaly. Effects of ABJ anomaly in amplitudes of electroweak processes. Example of two-photon annihilation of electron-positron pair. Electroweak interactions in quark sector. Mutual compensation of quark and lepton ABJ anomalies due to VVA and AAA loops.
SM formulation in renormalizable (Rx) gauges. Equivalence theorem (ET) for longitudinal vector bosons. Illustrations for particular processes: Production of W in decay of a heavy fermion. Decay of heavy Higgs boson into a pair of W´s. Idea of ET proof - relevant Ward identities. Radiative corrections to W and Z masses, their dependence on mt (top quark mass) and mH.
Simple extensions of SM. Multiplets of Higgs fields and their influence on the mass formula for W and Z. Basic idea of effective Lagrangian in a more general formulation of electroweak theory beyond SM. Analogy with description of chiral dynamics of pions ? linear and non-linear sigma-model.
Annotation
Derivation of the standard model from the requirement of the tree unitarity. Triangle anomaly.
Renormalizable gauges. Radiative corrections.
Phenomenology of electroweak processes.