Heavy-quark mass relation from standard-model boson operator expansion in terms of fermions*

Within the standard model,  fields are expanded in a composite basis,  using   second-quantization. We consider  the heavy-particle sector conformed of electroweak vectors, the Higgs field, and the top and bottom quarks, the latter constituting a basis. Thus, such bosons  and  symmetry operators are expanded in terms of bilinear combinations of quark operators, considering discrete degrees of freedom and the chiral structure. Through the Higgs mechanism, using the mass-mode components, a common mass-generating scalar operator, acting on the vectors and quark-doublet elements, allows for a quantum estimate of the Higgs vacuum expectation value, and reproduces the particles' masses. This links the corresponding scalar-vector and Yukawa vertices, and leads to a relation connecting the t-  and b-quark masses through the vacuum expectation value.