[Paper Review] Impact of Mass Generation for Simplified Dark Matter Models

Nicole F. Bell, Yi-Fu Cai+1 more|arXiv (Cornell University)|Oct 10, 2016

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper demonstrates that the mass generation mechanism in simplified dark matter models critically determines allowed interaction types, with gauge invariance restricting vector and axial-vector couplings to the spin-1 mediator. When a single dark Higgs gives mass to all dark sector fields, non-zero axial-vector coupling is required; otherwise, only pure vector couplings are allowed, and violating these restrictions leads to unitarity violations. These two-mediator scenarios yield distinct relic density and indirect detection phenomenology not captured by single-mediator models.

ABSTRACT

In the simplified dark matter models commonly studied, the mass generation mechanism for the dark fields is not typically specified. We demonstrate that the dark matter interaction types, and hence the annihilation processes relevant for relic density and indirect detection, are strongly dictated by the mass generation mechanism chosen for the dark sector particles, and the requirement of gauge invariance. We focus on the class of models in which fermionic dark matter couples to a spin-1 vector or axial-vector mediator. However, in order to generate dark sector mass terms, it is necessary in most cases to introduce a dark Higgs field and thus a spin-0 scalar mediator will also be present. In the case that all the dark sector fields gain masses via coupling to a single dark sector Higgs field, it is mandatory that the axial-vector coupling of the spin-1 mediator to the dark matter is non-zero; the vector coupling may also be present depending on the charge assignments. For all other mass generation options, only pure vector couplings between the spin-1 mediator and the dark matter are allowed. If these coupling restrictions are not obeyed, unphysical results may be obtained such as a violation of unitarity at high energies. These two-mediator scenarios lead to important phenomenology that does not arise in single mediator models. We survey two-mediator dark matter models which contain both vector and scalar mediators, and explore their relic density and indirect detection phenomenology.

Motivation & Objective

• To investigate how different mass generation mechanisms in the dark sector affect the allowed interaction types in simplified dark matter models.
• To identify constraints on vector and axial-vector couplings to spin-1 mediators arising from gauge invariance and unitarity.
• To demonstrate that single-mediator simplified models may be physically inconsistent if they ignore the implications of mass generation mechanisms.
• To explore the phenomenological consequences—particularly in relic density and indirect detection—of two-mediator models with both vector and scalar mediators.
• To show that models with a single dark Higgs field for mass generation require non-zero axial-vector couplings, while other mechanisms restrict to pure vector couplings.

Proposed method

• Analyzes the implications of three distinct dark sector mass generation mechanisms: Stueckelberg, bare mass, and dark Higgs.
• Applies gauge invariance and unitarity constraints to derive selection rules for vector and axial-vector couplings between fermionic dark matter and a spin-1 mediator.
• Constructs two-mediator models with both a spin-1 (vector or axial-vector) and a spin-0 (scalar) mediator, arising from a common dark Higgs field.
• Derives exact s-wave annihilation cross sections for processes like χχ → Z′Z′ and χχ → sZ′, including full dependence on gauge and Yukawa couplings.
• Uses the relation between gauge and Yukawa couplings (gχ ∝ yχ) to ensure consistency with the Higgs mechanism and unitarity.
• Compares phenomenology across scenarios: (I) bare mass + pure vector, (II) dark Higgs with both couplings, (III) dark Higgs with only vector, (IV) dark Higgs with only axial-vector.

Experimental results

Research questions

• RQ1 How does the choice of mass generation mechanism in the dark sector affect the allowed interaction types between dark matter and its mediators?
• RQ2 What are the gauge invariance and unitarity constraints on vector and axial-vector couplings in models with a massive spin-1 mediator?
• RQ3 Why do single-mediator simplified models fail to capture realistic phenomenology when the mass generation mechanism is ignored?
• RQ4 What new indirect detection and relic density signals emerge in two-mediator models with both vector and scalar mediators?
• RQ5 Under what conditions is a non-zero axial-vector coupling to the spin-1 mediator required for consistency with a dark Higgs mechanism?

Key findings

• When all dark sector fields gain mass via a single dark Higgs, a non-zero axial-vector coupling of the spin-1 mediator to dark matter is mandatory for gauge invariance.
• In all other mass generation scenarios (e.g., Stueckelberg or bare mass), only pure vector couplings between the spin-1 mediator and dark matter are allowed.
• Violating these coupling restrictions leads to unitarity violation at high energies, rendering the model unphysical.
• The presence of both a vector and scalar mediator enables new s-wave annihilation channels such as χχ → Z′Z′ and χχ → sZ′, which are absent in single-mediator models.
• The s-wave cross section for χχ → Z′Z′ scales as 1/mχ² when only one coupling (Q_A or Q_V) is non-zero, but as 1/mZ′² when both are non-zero due to longitudinal Z′ contributions.
• The full cross sections for χχ → sZ′ depend non-trivially on both Q_A, Q_V, and Q_S, with explicit analytical expressions derived in the appendix for all scenarios.