Scalars from Gauge Fields

TL;DR

This paper introduces gauge-invariant scalar variables derived from gauge fields in an SU(2)×U(1) theory, demonstrating their potential to induce spontaneous symmetry breaking and generate particle masses without external scalars.

Contribution

It proposes a novel method of constructing scalar fields directly from gauge fields, enabling symmetry breaking and mass generation intrinsically within the gauge theory framework.

Findings

Nine massive Higgs particles identified.

Pattern of heavy-vector masses and mixing matches expectations.

Emergence of Higgs-type hypercharge and charge assignments.

Abstract

In an Euclidean SU(2) $\otimes$ U(1) gauge theory without fermions, we identify scalar-field variables, functionals of the gauge fields and coming in different representations of isospin, which (i) are of mass dimension one in $d=4$, (ii) couple to their parent gauge fields through suitable gauge-covariant derivatives, and (iii) can be endowed with a hypercharge despite their parents having none. They can be interpreted as projections of the gauge vectors onto an orthonormal basis that is defined by the fields themselves. We inquire as to whether these scalars can perform the usual tasks, normally fulfilled by external scalar fields, of spontaneous symmetry breaking and mass generation through vacuum expectation values. The gauge Lagrangian, expressed in terms of these scalars, automatically has quartic and cubic terms; no extra coupling constant for quartic scalar self-interactions is needed. VEV formation takes place in one of four scalar fields populating the classical potential-energy minimum. There are nine massive Higgs particles, a neutral triplet at a mass of $m_Z \sqrt{2}$, and three conjugate pairs of charged ones at $m_W \sqrt{2}$. Seven quasi-Goldstone scalars remain massless. This results in a qualitatively correct pattern of heavy-vector masses and mixing, with the analog of the mixing angle determined by theory. Higgs-type hypercharge and charge assignments emerge naturally.