Non-perturbative solutions in the electro-weak theory and the Higgs boson 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 $g(M_W^2)\simeq 0.62$ in satisfactory agreement to the 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 obtain two possible solutions for the observable Higgs boson mass: $M_1\,=\,(306\,\pm\,14)GeV$ and $M_2\,=\,(253\,\pm\,10)\,GeV$. Values for other parameters e.g. anomalous three-boson coupling $\,G$, Higgs boson width $\Gamma_H$, its branching ratios and estimates for cross-section of Higgs production at LHC are also obtained.