A Simplified Model of Heavy Vector Singlets for the LHC and Future Colliders

TL;DR

This paper introduces a simplified model for heavy vector singlets relevant to the LHC and future colliders, providing analytical tools, current constraints, and model matching to facilitate searches for new heavy gauge bosons.

Contribution

The work develops a simplified Lagrangian for heavy vector singlets, derives accurate mass and coupling expressions, and connects these to explicit models and existing HVT frameworks.

Findings

Current LHC constraints on heavy vectors are summarized.

Sensitivity projections for future colliders are provided.

Exact matching relations between models are established.

Abstract

We study a simplified model of two colourless heavy vector resonances in the singlet representation of $SU(2)_{L}$, with zero and unit hypercharge. We discuss mixing with the Standard Model gauge bosons due to electroweak symmetry breaking, semi-analytic formulae for production at proton colliders, requirements to obey the narrow width approximation and selected low energy constraints. We show current LHC constraints and sensitivity projections for the HL-LHC, HE-LHC, SPPC and FCC-hh on the charged and neutral heavy vectors. The utility of the simplified model Lagrangian is demonstrated by matching these results onto three explicit models: a weakly coupled abelian extension of the Standard Model gauge group, a weakly coupled non-abelian extension and a strongly coupled minimal composite Higgs model. All our results are presented in terms of physical resonance masses, using expressions which are accurate even at vector masses near the electroweak scale due to a parameter inversion we derive. We discuss the importance of this inversion and point out that its effect, and the effects of electroweak symmetry breaking, can remain important up to resonance masses of several TeV. Finally, we clarify the relation between this simplified model and the Heavy Vector Triplet (HVT) model, a simplified model for heavy $SU(2)_{L}$ triplets with zero hypercharge, and provide exact and approximate matching relations.