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

TL;DR

This paper demonstrates that the electro-weak interaction can spontaneously generate anomalous gauge interactions and a $ar t t$ condensate, providing a non-perturbative explanation for the $t$-quark mass and electro-weak symmetry breaking.

Contribution

It introduces a non-perturbative approach using Bogoliubov compensation to generate effective interactions and explains the $t$-quark mass via a $ar t t$ condensate, challenging the elementary Higgs paradigm.

Findings

Calculated $t$-quark mass as 177 GeV, matching experimental data.

Showed spontaneous generation of anomalous three-boson gauge interactions.

Demonstrated the viability of a $ar t t$ condensate as the source of electro-weak symmetry breaking.

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 $m_t\,=\,177\,GeV$ 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.