The role of spurions in Higgs-less electroweak effective theories

TL;DR

This work develops a spurion-driven low-energy effective theory framework for Higgs-less electroweak symmetry breaking, built on moose models that couple Goldstone bosons, gauge fields, and chiral fermions. Covariantly constant spurions implement symmetry reduction and naturally suppress unwanted couplings, yielding a controlled expansion with generalized Weinberg sum rules at leading order. The minimal EWSB case reproduces SM-like boson and fermion couplings while allowing CKM structure and neutrino masses; non-minimal extensions introduce heavy vector resonances (W', Z') or a triplet of pseudo-Goldstone bosons, illustrating how spurions shape spectra and oblique parameters. The approach unifies dynamical EWSB scenarios with QCD-like dynamics, offers a systematic method to assess radiative corrections and flavor structures, and provides a platform for exploring electroweak observables in Higgs-less theories.

Abstract

Inspired by recent developments of moose models we reconsider low-energy effective theories of Goldstone bosons, gauge fields and chiral fermions applied to low-energy QCD and to Higgs-less electroweak symmetry breaking. Couplings and the corresponding reduction of symmetry are introduced via constraints enforced by a set of non-propagating covariantly constant spurion fields. Relics of the latter are used as small expansion parameters conjointly with the usual low-energy expansion. Certain couplings can only appear at higher orders of the spurion expansion and consequently, they become naturally suppressed independently of the idea of dimensional deconstruction. At leading order this leads to a set of generalized Weinberg sum rules and to the suppression of non-standard couplings to fermions in Higgs-less EWSB models with the minimal particle content. Within the latter, higher spurion terms allow for a fermion mass matrix with the standard CKM structure and CP violation. In addition, Majorana masses for neutrinos are possible. Examples of non-minimal models are briefly mentioned.

Figures (8)

• Figure 1: Three non-linear sigma models and two Yang-Mills theories.
• Figure 2: Introduction of spurions in the model of section \ref{['sub:disconnected']}.
• Figure 3: The 'reduced' diagram for the model depicted in Fig. \ref{['fig:intr-gauge-coupl-K=2']}, after imposing the constraints.
• Figure 4: Coupling the electroweak gauge fields to the $K = 0$ moose via spurions.
• Figure 5: Introduction of fermions in the model of section \ref{['sub:one-complex-spurion']}.