Non-perturbative solutions in the electro-weak theory with $\bar{t}t$ condensate and the $t$-quark mass

Abstract

We apply Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate a spontaneous generation of anomalous three-boson gauge invariant effective interaction. The non-trivial solution of compensation equations uniquely defines the form-factor of the anomalous interaction and parameters of the theory including value of gauge electro-weak coupling $g(M_W^2)$ in satisfactory agreement with its experimental value. A possibility of spontaneous generation of effective four-fermion interaction of heavy quarks is also demonstrated. This interaction defines an equation for a scalar bound state of heavy quarks which serve as a substitute for the elementary scalar Higgs doublet. As a result we calculate the $t$-quark mass $m_t=177GeV$ in satisfactory agreement with the experimental value. The results strongly support idea of $\bar{t}t$ condensate as a source of the electro-weak symmetry breaking.

Comments: 16 pages, 5 figures. arXiv admin note: substantial overlap with arXiv:1103.3951