Quark mass generation due to scalar fields with zero dimension

TL;DR

This paper introduces a novel model where zero-dimension scalar fields mediate fermion mass generation through gravitational coupling, eliminating the need for a fundamental Higgs and achieving distinct top and bottom quark masses.

Contribution

The model demonstrates how 36 zero-dimension scalar fields can induce fermion masses dynamically via gravitational interactions without a Higgs boson.

Findings

Fermion masses can arise dynamically without a Higgs.

The model achieves different masses for top and bottom quarks.

Vanishing Weyl anomaly and vacuum energy are linked to scalar field count.

Abstract

We propose a model of dynamical symmetry breaking, in which a new type of fundamental scalar fields of zero mass-dimension mediate the couplings of fermions to the gravitational field, represented here as a tetrad field in the same manner as Riemann-Cartan gravity. In our model, the tetrad couples to the standard model fermions non-minimally, and the very coupling coefficients are the fundamental scalar fields. There are exactly 36 scalar fields in the model, which are distinguishable by flavor indices on the fields. This is the precise number of zero dimension scalar fields that leads to a vanishing Weyl anomaly and a vanishing vacuum energy. Precisely the same number of these very same scalar fields is required for the coupling of all of the different standard model fermions to the vielbein field. At the same time their interaction with fermions gives rise to fermion mass terms, without the need to introduce a fundamental Higgs field. Within the proposed theory we construct a toy model that deals solely with the top and bottom quarks, and we demonstrate that their observable masses can appear in the action dynamically. Moreover, this mechanism allows for the top and bottom quarks to acquire distinctly different masses, as opposed to our previous, even simpler toy model that contained only the top quark.