Modified model of top quark condensation

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 nonlocal four-fermion interactions in which at the distances of the order of $\ensuremath{\sim}1/100\text{ }\text{ }\mathrm{GeV}$ 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 $U(12)\ensuremath{\bigotimes}O(4)$ 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 $\ensuremath{\gg}1/100\text{ }\text{ }\mathrm{GeV}$, 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 counterterms that cancel all quadratic divergences. As a result, the $1/N$ expansion may be applied.