[Paper Review] Vector-fermion dark matter

Michał Iglicki|arXiv (Cornell University)|Apr 26, 2018

Dark Matter and Cosmic Phenomena27 references3 citations

TL;DR

This thesis proposes a renormalizable extension of the Standard Model with a new U(1)X gauge symmetry, introducing a vector dark matter candidate (X), two Majorana fermions (Ψ₊, Ψ₋), and an additional Higgs boson. Using a custom C++ code to solve multi-component Boltzmann equations, it demonstrates how the relic abundance of dark matter depends on parameters like masses, mixing angle sinα, and U(1)X coupling gx, revealing non-trivial effects from semi-annihilations and Higgs portal cancellation.

ABSTRACT

In this thesis a simple extension of the Standard Model has been investigated. The Standard Model gauge group has been extended by an additional $U(1)_X$ group. The model introduces a new Higgs particle as well as three particles (a gauge boson and two Majorana fermions) that can be candidates for dark matter. The thesis also contains a discussion of derivation of the Boltzmann equation, involving detailed analysis of the assumptions. The equation has been used to investigate behaviour of the dark matter density in time, with respect to values of the parameters of the model.

Motivation & Objective

• To develop a renormalizable, QFT-consistent extension of the Standard Model with a new U(1)X gauge symmetry to accommodate dark matter candidates.
• To investigate the cosmological relic abundance of dark matter in a multi-component scenario involving a vector boson, two Majorana fermions, and an additional Higgs boson.
• To derive and analyze the Boltzmann equation with full attention to underlying assumptions, often omitted in standard cosmology texts.
• To construct and validate a numerical C++ code capable of solving multi-component Boltzmann equations for dark matter, including 2- and 3-component systems.
• To explore the impact of semi-annihilation processes and Higgs portal cancellation on the final dark matter yield.

Proposed method

• Extend the Standard Model gauge group by adding a U(1)X symmetry, introducing a new gauge boson X, two Majorana fermions (Ψ₊, Ψ₋), and a new Higgs-like scalar h₂.
• Derive the Boltzmann equation from kinetic theory, carefully analyzing assumptions such as chemical equilibrium, weak coupling, and the use of the S-matrix in the early universe.
• Implement a numerical solver in C++ to integrate the coupled Boltzmann equations for the number densities of X, Ψ₊, and Ψ₋ as functions of temperature (or time).
• Compare the code’s results with micrOMEGAs for the 2-component case to validate accuracy and reliability.
• Systematically vary model parameters: mX, m₊, m₋, m₂, sinα, and gx to study their influence on the final dark matter yield.
• Analyze the role of semi-annihilation processes (e.g., Ψ₊Ψ₊ → X X, X X → Ψ₋Ψ₋) and Higgs portal cancellation (via sinα) on the relic density.

Experimental results

Research questions

• RQ1 How does the inclusion of semi-annihilation processes affect the final relic abundance of dark matter in a multi-component model?
• RQ2 To what extent does the Higgs portal cancellation (via sinα) alter the dark matter yield compared to a standard portal model?
• RQ3 How sensitive is the final dark matter density to variations in the U(1)X gauge coupling gx, especially in the regime of strong coupling?
• RQ4 What conditions lead to two stable dark matter components versus three, and how does this affect the total relic density?
• RQ5 How do the numerical solutions of the Boltzmann equations compare with established tools like micrOMEGAs in the 2-component limit?

Key findings

• The model supports up to three stable dark matter components (X, Ψ₊, Ψ₋), depending on the mass hierarchy and mixing angle sinα.
• The U(1)X coupling constant gx strongly influences the final yield: increasing gx from 0.1 to 1.0 suppresses the X-boson yield by two orders of magnitude (from ~1.1×10⁻¹⁰ to ~1.7×10⁻¹⁴) at x=100.
• Semi-annihilation processes such as Ψ₊Ψ₊ → X X and X X → Ψ₋Ψ₋ significantly alter the evolution of number densities, especially when m₊ ≈ 2mX or m₋ ≈ 2mX.
• The Higgs portal cancellation via sinα reduces the effective coupling between dark matter and the SM Higgs, leading to a suppression of SM-mediated annihilation channels, which is reflected in the yield curves.
• The C++ code successfully reproduces micrOMEGAs results for the 2-component case, validating its numerical accuracy and reliability for multi-component systems.
• The model allows for a rich phenomenology: non-standard annihilation/semi-annihilation channels and parameter-dependent stability patterns enable new avenues to probe dark matter beyond the WIMP paradigm.