The Stueckelberg Mechanism in the presence of Physical Scalar Resonances

TL;DR

This paper explores incorporating physical scalar resonances into a nonlinearly realized electroweak theory with a Stueckelberg mass mechanism, analyzing its theoretical consistency and high-energy unitarity behavior.

Contribution

It demonstrates a consistent way to include scalar resonances with Stueckelberg mass terms while maintaining key functional identities and explores the unitarity implications at high energies.

Findings

The model accommodates scalar resonances with Stueckelberg mass terms.

Tree-level unitarity violation occurs at high energies if Stueckelberg mechanism contributes to mass.

The formal properties align with LHC data constraints, respecting custodial symmetry.

Abstract

We show that it is possible to accommodate physical scalar resonances within a minimal nonlinearly realized electroweak theory in a way compatible with a natural Hopf algebra selection criterion (Weak Power Counting) and the relevant functional identities of the model (Local Functional Equation, Slavnov-Taylor identity, ghost equations, b-equations). The Beyond-the-Standard-Model (BSM) sector of the theory is studied by BRST techniques. The presence of a mass generation mechanism \`a la St\"uckelberg allows for two mass invariants in the gauge boson sector. The corresponding 't Hooft gauge-fixing is constructed by respecting all the symmetries of the theory. The model interpolates between the Higgs and a purely St\"uckelberg scenario. Despite the presence of physical scalar resonances, we show that tree-level violation of unitarity in the scattering of longitudinally polarized charged gauge bosons occurs at sufficiently high energies, if a fraction of the mass is generated by the St\"uckelberg mechanism. The formal properties of the physically favoured limit after LHC7-8 data, where BSM effects are small and custodial symmetry in the gauge boson sector is respected, are studied.