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.
Highlights
The standard model (SM) describes elementary-particle features and their interactions, which is praiseworthy, given its relatively limited required input, consisting of specific gauge and flavor symmetries, representations, and parameters, yet aspects remain within the model whose origin and connection to other tenets is absent and that need to be addressed.among its successes, the SM predicts mass values for the W and Z bosons [1] that carry the short-range electroweak interaction, in terms of electroweak parameters, through the Higgs mechanism [2,3]
Leaving aside the more speculative nature of the spin SM extension, but complementarily to it, in this paper, we use it as a basis to derive SM connections, and the fields’ mass values in particular: SM heavy-fermion (F), vector (V), and scalar (S) fields are equivalently expressed in terms of the obtained common basis [6] for both Lorentz and electroweak d.o.f., in turn, recasting their Lagrangian components L 1⁄4 LFV þ LSV þ LSF; the identification of the scalar operator within the LSF and LSV vertices links univocally its defining parameters
We introduce the spin basis and its main features, where more information may be found in previous treatments [7,8,9,10]
Summary
The standard model (SM) describes elementary-particle features and their interactions, which is praiseworthy, given its relatively limited required input, consisting of specific gauge and flavor symmetries, representations, and parameters, yet aspects remain within the model whose origin and connection to other tenets is absent and that need to be addressed. Leaving aside the more speculative nature of the spin SM extension, but complementarily to it, in this paper, we use it as a basis to derive SM connections, and the fields’ mass values in particular: SM heavy-fermion (F), vector (V), and scalar (S) fields are equivalently expressed in terms of the obtained common basis [6] for both Lorentz and electroweak d.o.f., in turn, recasting their Lagrangian components L 1⁄4 LFV þ LSV þ LSF; the identification of the scalar operator within the LSF and LSV vertices links univocally its defining (mass) parameters Such universal electroweakly-invariant terms lead, under the Higgs mechanism, to a scalar whose lowest-energy condensate state pervades space, and generates particle masses through its vacuum expectation value v. We work in the classical framework afforded by the Lagrangian, and at tree-level, and rely on a quantum-mechanical interpretation
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