Heavy quarks within the electroweak multiplet

Abstract

Standard-model fields and their associated electroweak Lagrangian are equivalently expressed in a shared spin basis. The scalar-vector terms are written with scalar-operator components acting on quark-doublet elements, and shown to be parametrization-invariant. Such terms, and the t- and b-quark Yukawa terms are linked by the identification of the common mass-generating Higgs operating upon the other fields, after acquiring a vacuum expectation value $v$. Thus, the customary vector masses are related to the fermions', fixing the t-quark mass $m_t$ with the relation $m^2_t+m^2_b=v^2/2$ either for maximal hierarchy, or given the b-quark mass $m_b$, implying $m_t \simeq 173.9$ GeV, for $v=246$ GeV. A sum rule is derived for all quark masses that generalizes this restriction. An interpretation follows that electroweak bosons and heavy quarks belong in a multiplet.