Modified model of top quark condensation

TL;DR

This paper proposes a modified top quark condensation model where the Higgs boson is composed of all Standard Model fermions, using a non-local four-fermion interaction with a specific symmetry structure to relate the Higgs and top quark masses.

Contribution

It introduces a phenomenological model with a unified Majorana spinor framework and a specific symmetry, providing a relation between Higgs and top quark masses and addressing regularization issues.

Findings

The model establishes a one-loop relation: M_H^2 = m_t^2/2.

Symmetry breaking at larger distances generates the top quark mass.

The approach allows the use of the 1/N expansion with appropriate regularization.

Abstract

We develop the modification of the top - quark condensation scenario, in which the Higgs boson is composed of all Standard Model fermions. Within this scenario we suggest the phenomenological model with non - local four - fermion interactions in which at the distances of the order of $\sim 1/100$ GeV the theory is represented in terms of only one Majorana spinor that carries the $U(12)$ index and, in addition, belongs to the spinor representation of $O(4)$. The Standard Model fermions are the components of this spinor. The symmetry $U(12)\otimes O(4)$ is responsible for the one - loop relation between the Higgs boson mass and the top quark mass $M_H^2 = m_t^2/2$. At the distances $\gg 1/100$ GeV the mentioned symmetry is broken, and the interaction term dominates that provides the nonzero mass of the top quark. Our phenomenological model should be considered in zeta or dimensional regularization. In conventional cutoff regularization this is equivalent to the existence of the additional counter - terms that cancel all quadratic divergences. As a result the $1/N$ expansion may be applied.