Heavy-quark mass relation from a standard-model boson operator representation in terms of fermions

TL;DR

This paper presents a novel fermion-based representation of the standard model, deriving quark mass relations and linking scalar, vector, and Yukawa interactions through quantum mechanical vacuum expectation values.

Contribution

It introduces a spin-extended fermion basis for the standard model, deriving heavy-quark mass relations and connecting scalar-vector and Yukawa vertices.

Findings

Reproduces vector and quark-doublet masses from quantum vacuum expectations.

Derives hierarchy relations constraining top and bottom quark masses.

Links scalar, vector, and Yukawa interactions within a fermionic framework.

Abstract

The standard-model can be equivalently represented with its fields in a spin-extended basis, departing from fermion degrees of freedom. The common Higgs operator connects the electroweak and Yukawa sectors, restricting the top and bottom quark masses[Phys. Rev. D 99, 073001, 2019]. Using second quantization, within the heavy-particle sector, electroweak vectors, the Higgs field, and symmetry operators are expanded in terms of bilinear combinations of top and bottom quark operators, considering discrete degrees of freedom and chirality. This is interpreted as either a basis choice or as a description of composite models. The vacuum expectation value is calculated quantum mechanically, which relates to the common mass-generating scalar operator and it reproduces the vector and quark-doublet masses. This also links the corresponding scalar-vector and Yukawa vertices, and restricts the t- and b-quark masses in a hierarchy relation.