Gulov O. Signals of the Z' boson in modern and future experiments in the high energy physics

The object is scattering processes between elementary particles with intermediate Z' boson, lattice models of scalar fields. The aim is to select and amplify Z' signals in various experiments at modern and future colliders of elementary particles, to measure the Z' parameters by experimental data, to determine how the spontaneous breakdown of symmetry depends on the coupling constant in the models of scalar fields. Analytic and numeric methods of the quantum field theory, mathematical statistics, and Monte Carlo simulations are used. The thesis is devoted to observables for searches for a new heavy neutral vector boson (Z' boson) and amplification of its signals in scattering processes between elementary particles in modern and future experiments in the high energy physics. The experimental data collected at the Large Electron-Positron Collider, Tevatron, and the Large Hadron Collider are analyzed. Maximum likelihood estimates and confidence intervals are derived for the Z' boson couplings to leptons and quarks. In the leptonic processes signals of the particle are found at either one or two standard deviations. The efficiency of the proposed observables is estimated for the future International Linear Collider. In the scalar model with the spontaneous symmetry breakdown, a new phenomenon is discovered by Monte Carlo simulations on a lattice: the temperature phase transition of the second order changes the type while the coupling becomes weaker. The application is the data analysis at modern and future colliders of elementary particles, the grand unification theories and the models with extended symmetry groups, and the investigations of phase transitions in the quantum field theory and in the physics of condensed matter.