The Stueckelberg Mechanism in the presence of Physical Scalar Resonances

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.